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AN AUGMENTED NEOCLASSICAL GROWTH MODEL WITH HUMAN CAPITAL ACCUMULAnON AND AGRICULTURAL AND NONAGRICULTURAL TRADE OPENNESS By GUSTAVO ADOLFO BARBOZA Master of Science Oklahoma State University Stillwater, Oklahoma 1994 Submitted to the Faculty ofthe Graduate College of the Oklahoma State University in partial fulfillment of the requirements for the Degree of DOCTOR OF PIDLOSOPHY December, 1997 AN AUGMENTED NEOCLASSICAL GROWTH MODEL WITH HUMAN CAPITAL ACCUMULATION AND AGRICULTURAL AND NONAGRICULTURAL TRADE OPENNESS /' Thesis A:oviser ii ACKNOWLEDGMENTS I sincerely wish to thank my adviser Dr. Michael Dicks for all his help, patience, and advise throughout my doctoral program in Agricultural Economics at Oklahoma State University. Dr. Dicks' confidence in my work and his continuous technical and financial support made this doctoral program possible. I will always thank you for all your time and support. My very special thanks to committee members Dr. Francis Epplin, Dr. David Henneberry and Dr. Gerald Lage for all their support, suggestions, and cooperation in helping me to finish this study. I thank my parents, Carlos and Fanny Barboza, for they have always provided an example of honesty, love, commitment, and dedication. Without them I would not have been able to accomplish most of what I have now. Thank you to my parents for they have believed in me throughout these years. Thanks to my brothers and sisters, specially Fanny Maria whom I always will love. I thank my wife, Sandra, who is the inspiration of my life. Her words, time, support, and example are the greatest gift God has ever given me. She always stands by my side giving me the strength I need. Thanks Sandra for you have always believed in my goals and my work. There is no word to express all my thanks to my wife for her unconditional support throughout these years, I love you Sandra. To my daughters, Maria Sofia and Monica Maria, for they have fulfilled our marriage and have brought happiness iii and joy to our family. My special dedication of this doctoral dissertation goes to my family, Sandra, Maria Sofia and Monica Maria. I want to thank the people at the Office for International Programs at the Universidad of Costa Rica for their financial support throughout my doctoral program. Thank you to the people at the Department of Economics at the Universidad of Costa Rica for they have also provide the means for me to complete my degree. I would like to thank also the people at the Great Plains Agricultural Policy Center for helping and supporting me throughout my doctoral program. Special thanks to Nolan Quiros and Edgar Pebe, for their comments and encouragement to complete my work. To them I wish the best in their personal life and professional careers. iv TABLE OF CONTENTS CHAPTER 1 1 INlRODUCTION 1 CHAPTER II ...............••...........•.......•........••............•...•.•...•.•......•••....•....••••....•.......•.........•...............•.. 14 LITERATURE REVIEW AND CONCEPTUAL FRAMEWORK 14 Literature Review 14 Conceptual Fnunework 18 Neoclassical and Structural Growth Models 18 Endogenous and Exogenous Growth Models 22 The Solow Model. 23 Adding HumanCapital Accumulation to the Solow Model 26 Trade Openness and Technological Transfer in the Solow Model Framework 29 CHAPTER IlL 33 THEORETICAL MODEL 33 Solow Model with Human Capital Accwnulation and Trade Openness 33 Nonnegativity ofXa and Xna 36 Steadystates 37 Physical CapitaL 39 Hwnan Capital 45 Agricultural Trade Openness 51 Nonagricultural Trade Openness 56 Income Per Capita 60 CHAPTER IV 68 METIIODS AND PROCEDURES 68 Expected Results 68 Estimation Method and Misspecification Tests 74 Data 78 CHAPTER V 82 EMPIRICAL RESULTS 82 OLS Estimations and Misspecification Tests 82 Overall Sample 87 Low Income Countries 91 Middle Income Countries 96 High Income Countries 101 Latin America.................................................................................................. .. 108 African Countries 112 Asian Countries 116 POOLED Estimations 122 Overall Sample 122 Low Income Countries 127 Middle Income Countries 132 v High Income COWltries 136 Latin America COWltries 140 African COWltries 144 Asian COWllries 148 CHAPTER VI 154 CONCLUSIONS AND RECOMMENDATIONS 154 REFERENCES 158 APPENDIX 161 VI LIST OF TABLES Table 1. Alternative Views of Growth 21 2. Comparison of SteadyState Conditions under Alternative Growth Models 64 3. Conceptual Comparison of Alternative Growth Models 65 4. OLS Estimated Results of Alternative Neoclassical Growth Models (Full Sample) 84 5. Estimated Results ofthe Misspecification Tests on the OLS Assumptions for the Augmented Neoclassical Growth Model with Human Capital and Trade Openness on Agricultural and Nonagricultural Goods (Full Sample) 91 6. Low Income Countries OLS Estimated Results of Alternative Neoclassical Growth Models 93 7. Low Income Countries Estimated Results of the Misspecification Tests on the OLS Assumptions for the Augmented Neoclassical Growth Model with Human Capital and Trade Openness on Agricultural and Nonagricultural Goods 96 8. Middle Income Countries OLS Estimated Results of Alternative Neoclassical Growth Models 98 9. Middle Income Countries Estimated Results of the Misspecification Tests on the OLS Assumptions for the Augmented Neoclassical Growth Model with Human Capital and Trade Openness in Agricultural and Nonagricultural Goods 10 I 10. High Income Countries OLS Estimated Results of Alternative Neoclassical Growth Models 103 II. High Income Countries Estimated Results of the Misspecification Tests on the OLS Assumptions for the Augmented Neoclassical Growth Model with Human Capital and Trade Openness in Agricultural and Nonagricultural Goods 106 12. OLS Estimates of Alternative Growth Models by Income Group with GDP per capita as Dependent Variable 107 13. Latin America OLS Estimated Results of Alternative Neoclassical Growth Models 110 14. Latin America Estimated Results of the Misspecification Tests on the OLS Assumptions for the Augmented Neoclassical Growth Model with Human Capital and Trade Openness in Agricultural and Nonagricultural Goods 112 vii 15. Africa OLS Estimated Results of Alternative Neoclassical Growth Models 114 16. Africa Estimated Results of the Misspecification Tests on the OLS Assumptions for the Augmented Neoclassical Growth Model with Human Capital and Trade Openness in Agricultural and Nonagricultural Goods 115 17. Asia OLS Estimated Results of Alternative Neoclassical Growth Models 117 18. Asia Estimated Results of the Misspecification Tests on the OLS Assumptions for the Augmented Neoclassical Growth Model with Human Capital and Trade Openness in Agricultural and Nonagricultural Goods 120 19. OLS Estimates of Alternative Growth Models by Region with GDP per capita as Dep Variable ....... 121 20. POOLED Estimated Results of Alternative Neoclassical Growth Models (Full Sample) 124 21. Low Income Countries POOLED Estimated Results of Alternative Neoclassical Growth Models .. .128 22. Middle Income Countries POOLED Estimated Results of Alternative Neoclassical Growth Models 131 23. High Income Countries POOLED Estimated Results of Alternative Neoclassical Growth Models ... 135 24. POOLED Estimates of Alternative Growth Models by Income Group with GDP per capita as Dependent Variable 141 25. Latin America POOLED Estimated Results of Alternative Neoclassical Growth Models 142 26. African Countries POOLED Estimated Results of Alternative Neoclassical Growth Models 147 27. Asian Countries POOLED Estimated Results of Alternative Neoclassical Growth Models 150 28. POOLED Estimates of Alternative Growth Models by Region with GDP per capita as Dependent Vari~ble 153 viii LIST OF FIGURES Figure 1. Exports plus Imports to GDP Ratio by Category 7 2. Exports to GDP Ratio by Category 10 3. Imports to GDP Ratio by Category 11 ix CHAPTER I INTRODUCTION Over 200 years ago Adam Smith and David Ricardo elaborated on the role that international trade has on economic growth. Smith and Ricardo emphasized the important economic gains that trade specialization, according to comparative advantage, has on augmenting overall consumption possibilities and therefore overall social welfare. Consumption and production gains result from reallocating resources to their best alternative uses. Implicitly, Ricardo and Smith stressed the importance that free trade, based on comparative advantage has on factors' productivity. In this regard, the more a country specializes domestic production and participates in international trade the larger the gains derived from this process, but only if international trade is conducted according to a comparative advantage pattern. By specializing in the production of goods a country has the comparative advantage in producing and trading in international markets, resource productivity is maximized, economies of scale develop, unemployment is reduced, and overall production and consumption increases. 1 Perhaps one of the most important issues that relate to the process of economic policy is the determination of the sources of economic growth. Throughout history economists and policy makers have stressed the importance of setting economic instruments and goals to achieve higher levels of economic growth. This has been especially true in the last fifty years, where the emphasis of international trade and economic growth policy has focused on increasing the rate of growth of total output. Meier states "conditions were higWy favorable during the 195 Os and 1960s until the slowing down of growth in the world economy after 1973. The earlier two decades were unique for the high rate of growth in the more developed countries  a historical record period  and for the growth in world trade. The demand for imports was high and rising in the more developed countries (MDCs) and the high growth rate of the MDCs fostered trade liberalization and weakened the case for protection" (p. 408). Therefore the emphasis on commercial policy focused on the gains that trade liberalization brought about. Yet, a major concern for policy makers in developing countries stressed the fact that countries that specialized in the production and commercialization of industrial goods tended to outperform those countries that specialized and trad,ed primary products. According to Prebisch, countries that produced and exported primary commodities faced a deterioration in the terms of trade, resulting in lower rates of economic growth compared to developed countries. Prebisch argued that the centerperiphery relationship occurred such that the terms of trade deteriorated in the periphery countries which specialize or produce primary goods. Meier added that "Prebisch suggested that these (periphery) countries should expand their manufacturing industries oriented toward domestic markets. 2 The purpose was to be served by industrial protection that was said to bring additional benefits through improvements in the terms oftrade" (Meier, p. 395). Nevertheless, as mentioned before, these rapid rates of growth in international trade started to slow down after a few years in the early 1970's. Among the reasons that caused this slow down in the rate of growth of international trade are higher priced oil products and changes in commercial policy in developing countries. Developing countries promoted different approaches that emphasized the use of tariffs and nontariff barriers to trade as the main strategy to achieve higher levels of income per capita growth. Indeed, the development and promotion of an industrial sector, as the engine of growth, was seen as the main goal ofdeveloping countries. Within the context of international trade and economic growth policy import substitution was thought to be a feasible way to increase output growth. Import substitution focuses on substituting domestic production for imports of primary and manufactured goods. According to Meier, in the first stage developing countries substitute the consumption of imported primary goods with domestic production. Balassa called this stage the "easy" stage of import substitution. Meier states that "Secondstage import substitution involves the replacement of intermediate goods and producer and consumer durables by domestic production.... [G]iven the relative scarcity of physical and human capital in developing countries that complete the first stage of import substitution, developing countries are at a disadvantage in the manufacture of highly physical capitalintensive intennediate goods and skillintensive producer and consumer durables. In limiting the scope for the exploitation of economies of scale, the relatively small size of their national markets also contributes to high domestic costs. At the same time, net 3 • foreign exchange savings tend to be small because of the need for importing materials and machinery" (p. 396). Nevertheless, developing countries that promoted import substitution failed to consider the positive impact of trade expansion on economic growth, measured through the increase in factors' productivity resulting from the reallocation of resources to their best alternative use. In the framework of the twogap modell, export expansion releases the foreign exchange constraint, increasing the rate of capital formation, and enhancing the growth of factor productivity. Hence, determining the impact of factors of production on the level of economic growth is of great interest in terms of economic growth policy in developed and developing countries. This issue has been heavily addressed in the economic literature, yet few studies have focused on the decomposition of trade flows between agricultural and nonagricultural trade goods and the effect of each on factor accumulation and productivity growth. In the last twenty years an increasing proportion of the General Agreement of Tariffs and Trade (GATT), have concentrated on the transformation, reduction and elimination of trade distortions. The fonnation of trade blocks such as the North American Free Trade Agreement (NAFTA), Mercado Comun Suramericano (MERCOSUR), and others, have developed to eliminate trade distortions. These trade distortions are grouped within the categories of tariffs, quotas and nontariff barriers, that directly or indirectly affect the domestic production and consumption, and the domestic and international trade of agricultural and nonagricultural goods. To increase the importance of this trade liberalization and globalization process, agricultural trade has only recently been addressed 1 Twogap models assume that developing countries are constrained by the capacity to generate domestic savings to finance investment and by the availability of foreign exchange to obtain foreign goods and services that are complementary to those available at home (Gerald Meier). 4 in trade liberalization talks and agreements. The Uruguay Round of the GATT and the North American Free Trade Agreement establish the first steps for the mutual liberalization of primary and agricultural goods as well as services. The promotion of trade liberalization has reached even those commodities once considered too sensitive to be subject to negotiation. Economic research has studied the sources of economic growth. The most widely used economic growth model is the Solow Neoclassical Growth Model. The Solow Growth model focuses on the effect of labor growth and capital accumulation on the steadystate level of income per capita. Empirical estimations of growth for developing countries found that labor is abundant and capital is the single most important factor of production. Development economists have also studied the impact that export growth has on overall factor productivity and output growth. In most cases, empirical studies give support to the hypothesis that export promotion generates economic growth (Michaely; Balassa; Tyler; Kavoussi; Feder; Mbaku; Moran; Moschos; Ram; and Barboza). While export promotion may mean freer trade, it may also refer to the protection of any particular economic sector through the use of commercial policies such as tariff and nontariff barriers. Trade barriers find political support from the argument that developing industries need a certain protective period before they can be competitive in the international markets, i.e. it takes time before industries can develop a comparative advantage. Meier states "to the extent that the domestic production of these commodities generates external economies in the fonn of labor training, the development of enterpreneurship, and the spread of technology, there is an argument for moderate infant industry protection or promotion" (p. 395). 5 Yet, there is still a major gap when one wants to understand why countries achieve different steadystate levels of income per capita. New developments in economic theory such as the convergence hypothesis assume that countries that initially start off from lower levels of income per capita tend to grow faster than otherwise. In order to attempt to explain these observable differences in income per capita growth rates across developing and developed countries, human capital accumulation has been introduced as an important determinant (Mankiw, Romer and Weil). Technological transfer has also been considered as playing a major role in detennining the longrun level of income per capita. (Edwards; Knight, Loayza and Villanueva). The economic development literature has focused on determining the impact that trade openness has on output growth through the transfer of technology and through the learning by doing process (Edwards; and Knight, Loayza and Villanueva). Edwards; and Knight, Loayza and Villanueva assume that trade openness affects the longrun level of output growth through the transfer of technology but it does not have any effect on the steadystate level of physical and human capital accumulation and income per capita, because openness is considered only as a technological shifting factor. Trade openness is the measure that relates trade flows to output and is commonly defined as the ratio of exports to total output. The overall results of empirical studies support the hypothesis that the greater the trade openness, the greater the rate ofgrowth of output. Levine and Reneh state that this result is not surprising since similar results can be obtained by using any other trade measure such as imports or total trade. Even though previous studies agree on the importance that trade openness has on output growth and hence on income per capita level, they do not differentiate between the trade flows of primary and manufactured 6 goods, a major Issue when trying to determine the sources of economic growth In developing countries. The decomposition of trade flows between agricultural and non agricultural goods is important for at least three reasons; 1) to determine the sources of economic growth and to determine which countries are likely to be the gainers or losers of moving to a larger degree of trade openness; 2) to understand the effects of trade openness on factor productivity, and 3) to better understand the tradeoffs between international trade and economic growth in order to redirect overall economic policies. Figure 1. Exports plus Imports to GOP Ratio by Category 0.60 ,, 0.50 0.40 0.30 0.20 0.1a L.....l...J'...J..'_'...J..'_'''_'''_'''_~....l..____'__....... 1973 1975 1977 1979 1981 1983 1985 1987 1989 1991 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 Tolal Nonluel Primary Other  <> * Ratios are simple averages for a sample of 62 developing countries. Figure 1 illustrates three alternative measures of trade openness. The first measure is the ratio of total exports plus total imports to Gross Domestic Product for a sample of 7 62 developing countries2 . The second and third measures are a decomposition of the first measure by category of products. Hence, the second measure illustrates the relative importance of nonfuel primary trade as a ratio of Gross Domestic Product. Finally, the third measure indicates the importance of all other trade as a ratio of Gross Domestic Product. International trade represents approximately 50 percent of the Gross Domestic Product for the sample of 62 developing countries under study. Thus, intemational trade is an important determinant of output growth and factor productivity in developing countries. The importance of international trade peaked in 1980, when trade represented approximately 56% of Gross Domestic Product for the sample of countries. International trade declined sharply in the first half of the 1980's to a level of 46% in 1986 in terms of Gross Domestic Product. This reduction in international trade coincides with the generalized balance of payments crisis of most developing countries on the early 1980's. In general, the decline in international trade resulted from a reduction in the level of trade of nonprimary goods. The decade of 1970' s was characterized for an excess supply of financial resources in the international markets. Most of this excess supply can be attributed to the high oil prices of the early 1970' s. The easy and large availability of financial resources made it easy for developing countries to borrow large amounts of foreign exchange at lower interest rates that financed the increasing trade of nonprimary goods. Developing countries were unable to continue financing the increasing amount of nonprimary imports which can be seen by the decrease in the relative importance of 2 A complete list of the 62 developing countries is provided on Table 1 of the Appendix. 8 nonprimary trade as a proportion of Gross Domestic Product. At the same time, Figure I illustrates how the total amount of trade in nonfuel primary goods has decreased constantly during the last 20 years. This trend may be explained by two factors at least. First, developed countries have become less dependent in terms of nonfuel primary production and secondly developing countries have changed their economic growth strategy to the promotion of nonprimary good exports. Figure 1 provides a clear illustration that there has been a substantial change in the composition of international trade in developing countries. The question that remains unanswered is whether this change in the trend of international trade in developing countries has resulted in an enhancement offactors' productivity and increased real income per capita. The sources of growth in international trade are further decomposed between exports of nonfuel primary and other goods; and imports of nonfuel primary and others goods in figures 2 and 3, respectively. Figure 2 illustrates the ratios of exports as a proportion of Gross Domestic Product to provide more information on the sources of growth of international trade in developing countries. On the other hand, figure 3 illustrates imports as a proportion of Gross Domestic Product. 9  Figure 2. Exports to GOP Ratio by Category 025 ., 020 015 010 0.05 1973 1975 1977 1979 1981 1983 1985 1987 1989 1991 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 Total Nonluel Pnmary Other  <> :*Ratios are simple averages for 62 developing countries Perhaps the most relevant fact of figure 2 is that developing countries have transformed their export structure in the last twenty years, toward a more industrialized system. Other exports have increased as a proportion ofGDP throughout the period under study, but shows the sharpest increase over the last six to seven years. Furthermore, developing countries are still heavily dependent on the amount of imports of industrialized goods as illustrated in figure 3. Nonfuel primary goods, as a proportion of GDP, have remained roughly constant over the last twenty years. This result is not surprising since most developing countries tend to fulfill their own domestic demand with domestic production. The largest variability in imports, is due to the variability of other imports as shown in figure 3. After the economic crisis of the first half of the 1980s there has been a tendency to increase the amount of other imports. This seems to be the result of two complementary factors; reductions in the levels of tariffs and nontariffs barriers, and more 10  stable economies growing at higher rates compared to the first half of the 1980s. Finall even though international trade has been growing since the mid 19808, the total level of exports plus imports as a ratio of Gross Domestic Product is equal to those record levels of the late 1970s and early 1980s. Figure 3. Imports to GOP Ratio by Category 0.35 0.30 025 / 0.20 0.15 0.10 0.05 0.00 L....L..L_.l....l.L_L...LLl_.LL.....L_L._Ll_.LL.....L_LJ 1973 1975 1977 1979 1981 1983 1985 1987 1989 1991 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 TolllI Nonfuel Primary Other . <> ~ Ratios are simple averages for 62 developing countries The change in structure of international trade illustrated in Figures 1, 2, and 3 raises the question of whether international trade is important for developing countries or not. Empirical studies of the economic growth and economic development argue in favor of export promotion as a source of factor productivity and output growth. However, these studies do not determine the sources ofgrowth by category of goods. 11  This study determines the sources of economic growth by using an augmented neoclassical growth model with human capital accumulation and trade flows between agricultural and nonagricultural goods. The research question is how can the degree of trade openness in agricultural and nonagricultural markets reduce resource misallocation, increase the productivity of factors of production, and increase the rate of growth of total output in developing countries? The overall objective of this study is to determine the factors that affect the rate of growth of total output (economic growth) and reduce resource use misallocation in developing countries. The specific objectives are to: 1. Determine how trade openness (free trade) in agricultural and nonagricultural sectors affects the productivity oflabor, physical capital, and human capital; 2. determine the contribution of agricultural and nonagricultural trade flows on overall economic growth; and 3. determine to what extent free trade (trade openness) in agricultural and nonagricultural markets promote economic development in developing countries. This study is divided into six sections. The first section reviews the theoretical and empirical literature relating to economic growth. Next a conceptual framework is developed to support the development of the Augmented Solow Model with Trade Openness. The methods and procedures chapter provides the necessary infonnation about data, model estimation, statistical testing, and expected results. The results chapter provide an extensive analysis ofthe empirical results first estimated by using OLS and later reestimated by using a POOLED model. This chapter also provides alternative estimation by region and by income group to determine more precisely the sources of growth in 12  developing countries. Finally, the conclusion and recommendations chapter highlights the more important remarks of the study and provides the limitations and possible solutions in terms of future research. The overall results suggest that trade openness enhances output growth in developing countries. In addition, at initially low income per capita levels agricultural openness tends to be more important than nonagricultural openness. However, as income per capita rises this tendency reverses. No definite conclusion is found in terms of region significant effects in terms of income per capita growth. 13 CHAPTER II LITERATIJRE REVIEW AND CONCEPTUAL FRAMEWORK Literature Revjew The literature on economic development is robust with studies focusing on the relationship between factors of production and total productivity. The Solow model of economic growth has been the main tool used by economists in the last three decades to determine the relationship between factors of production and output growth. Solow presents a decomposition of factors of production between physical capital accumulation and labor force. The rest of output growth is explained by total factor productivity and is considered a residual. Two different approaches have been used to measure factor contribution to output growth, the Neoclassical Accounting Growth method (NAG) and econometric based studies. The NAG method assumes that the rate of growth of output can be decomposed as the rate of growth of inputs plus a residual that is considered total factor productivity (Chenery, Robinson and Syrquin). Assuming constant returns to scale the NAG method assumes that the sum of capital and labor shares must equal one (Solow). These factor 14 shares are obtained from the data itself, and then by using the historical growth rates of inputs, the total factor productivity is obtained as a residuae. On the other hand, econometric based studies estimate the contribution of factors of production to economic growth by using a simple neoclassical production function. Totally differentiating the production function it is possible to express the rate of growth of output as a function of the rates of growth of inputs. Estimated parameters are the output elasticities with respect to factors of production. Following the fonnulation that previous studies have used4 it is possible to express the factors' contribution to economic growth as follows: (1) where Q is the real Gross National Product, K is the capital stock, L is the labor force, and t is time. Assuming that the elasticities of output with respect to the factors of production are constant and that technical change is Hicksneutral with a constant rate, equation 1 can be rewritten in tenns of rates of growth by total differentiating with respect to time (dividing through by equation]). Then equation 2 is: (2) y=a+pk+~l 3 The neoclassical growth accounting methodology is used as a accounting method and it does not include any econometric estimating. Data is adjusted so the sum of the factor shares equals one. Econometrics application of this technique have been done allowing for the possibility of constant, decreasing, and increasing returns to scale. See Chenery et al (1986) p. 29. 4 The approach foHowed here is the same as explained in Feder (1982), De Gregorio (1992), Mbaku (1989), Kavoussi (1984), Ram (1985), Moschos (1989), Knight et al (1993), Tyler (1981), and Moran (1983). 15 where y is the rate of growth ofoutput, k is the rate of growth of capital stock, I is the rate of growth of the labor force, and fJ and 8 are the elasticities of output with respect to capital and labor, respectively. Measuring the rate of growth of the capital stock may not be possible for most developing and developed countries due to a lack of data. As an alternative Mbaku; Kavoussi; Tyler; De Gregorio; and Moschos have approximated the rate of growth of the capital stock by using the investment rate, under the assumption that this corresponds to the growth rate of capital5 . A more appropriate approximation of the model can be obtained by further approximating the rate of growth of the capital stock by the investmentoutput ratio as done by Ram; Feder; and Mbaku: (3) where 8Q/8K is the partial derivative of output with respect to the capital stock, KlQ is the capital stockoutput ratio, and dKIK is the rate of growth of the capital stock. Then, replacing dK by 1, where 1 is the level ofinvestment, results in, (4) I y=a+2+81 Q where A. is the marginal physical output of capital. More recent studies such as Michaely; Balassa; Ram; Moschos; Tyler; Kavoussi; Feder; Mbaku; Moschos have argued that economic growth may also depend on the rate ofgrowth of total exports, assuming that exports can be considered a factor of production 5 Implicitly this approach assmnes that the capitaloutput ratio is constant not only through time but also across countries. However, this approximation is not considered appropriate since the investment rate is the second derivative of the capital stock and only expresses the rate of chan.ge of the change in the capital stock. 16  that enhances the productivity of capital and labor by releasing the foreign exchange constraint, taking advantages of economies of scale, and reducing resource use misallocation by reallocating resources based on their comparative advantage. Michaely and Balassa used a Spearman rank correlation method and found that there is a positive relationship between export growth and economic growth. To incorporate the rate of growth of exports as an explanatory variable of output growth, a new variable is included in equation 4. The resulting equation is (5) where x is the rate ofgrowth of exports and the rate of technological change is assumed to be a linear function of the growth rate of exports expressed as '1/. Ram states that if the model specification is reasonable, '1/ should indicate the direction and magnitude of the impact of export expansion on economic growth. Empirical estimations of equation 5 for developing countries reveal that capital accumulation is the most important factor of production, Jabor force is considered to be abundant6 , and exports have a positive and statistically significant effect on the output growth. In the case of developing countries, export promotion is an appropriate tool to promote rapid economic growth. Feder states that the social marginal productivity is higher in the export sector than in the nonexport sector. Studies by Kavoussi; Tyler; and Balassa, focus on the importance that export promotion, both of primary and manufactured goods, have on output growth. Kavoussi; and Tyler argue that the promotion of exports can be decomposed between primary goods 17  and manufactured goods. Furthennore, at initial or low levels of economic development the promotion of both primary and manufactured goods increase economic growth. Beyond a threshold income level export promotion of primary goods does not contribute much more to economic growth, whereas the promotion of manufactured goods increases the rate ofgrowth ofincome per capita. (Balassa; Tyler; and Kavoussi). Conceptual Framework Neoclassical and Structural Growth Models In the second half of the current century, economic development discussions have been focused on analyzing alternative approaches that attempt to determine the sources of economic growth. The discussions have attempted to discover why there are different levels of income per capita between developed and developing countries and explain why similar countries achieve different levels of income per capita in the long run. The anatysis used to lay the ground work for the discussions use models that study the difference between open and closed economy models, developed and developing countries, growth and equity, export promotion and import substitution. In this sense there has been a substantial use of alternative techniques and/or procedures to accurately estimate those sources of growth. In tum, development economists are concerned with finding explanations that define how developing countries may increase income per capita and at the same time assure macroeconomic stability. The most common techniques used by economists to evaluate the process of economic development are multisector models such as the inputoutput model, project 6 Labor force is abundant in terms of marginal productivity. Marginal productivity is either close to zero 18  evaluation, linear and nonlinear programming models, and computable general equilibrium models. Among the major concerns of policy makers and economic development specialists are the tradeoffs among economic growth, income distribution (equity), balance of payments stability, exchange rate parity, inflation, unemployment, capital accumulation, and population growth In some particular cases the debate seems to become even more complicated when alternative economic variables can be defined and/or used either as policy tools (instruments) or macroeconomic goals (target)7. Numerous perspectives exist on how to address the problem of underdevelopment and how to determine the sources of growth to elaborate alternative policy scenarios to stimulate a sustainable process of economic growth in developing countries. However, despite the emphasis on alternative estimation tools and alternative economic approaches, a vast majority of economic research related to economic growth has been circumscribed to the analysis of either neoclassical growth models or structural growth models. Within the framework of neoclassical growth models the main source of economic growth comes about through physical capital accumulation. In the context of the single neoclassical growth model, the steadystate income per capita is achieved when the rate of growth of physical capital is equal to output growth. The conclusions derived from the neoclassical framework were very useful in explaining why developing countries achieve lower levels of income per capita compared to developed countries. In this regard, empirical evidence shows that physical capital is scarce in developing countries, and labor or equal to zero. 7 Some example of economic variable that may be defined either as policy tools or macroeconomic goals are the exchange rate, the inflation rate, government spending, and so on. 19  has a very low marginal productivity in developing countries8 . Criticisms of neoclassical growth models emphasize the fact that within the context of the neoclassical models the remaining or the unexplained variability of output growth is a residual. Meier states that "the residual was initially thought of as a coefficient of technical advance, but it was quickly recognized to be a composite of the effects of many different sources." As mentioned in the previous chapter some of these sources of output growth came about through the improvement in the quality of labor, exploitation of economies of scale, reallocation of resources to best alternative uses, and economic gains derived from the international trade process. Complementary to the analysis of neoclassical growth models, the structural approach to economic growth assumes that economic growth is the result of a transformation of the production structure that takes advantage of technological changes. In the structural approach, technological change is not assumed exogenous, rather it is endogenized as a function of other factors of production. Structural economists consider as neoclassical economists do, that physical capital accumulation is an important factor to achieve economic growth. However, structural economists stress the importance that the technological component of the production function has through the process of learning by doing and technology transfer. In the structural approach it is also possible for an economy not to be at equilibrium, meaning that factors of production are not necessarily paid their corresponding marginal productivity. The outoff equilibrium condition allows economies to reallocate resources and generate economies of scale, thus increasing 8 According to Meier, labor is abundant in developing countries because its productivity does not add to overall output growth. In the extreme case, labor is said to be abundant when marginal product is equal to zero. 20  factors' productivity, per capita output, and the rate of growth of income per capita. Hence, the emphasis is on the possibility for resource reallocation, and technology transfer. To overcome the apparent limitations of neoclassical growth models, the structural approach assumes that there is a possibility for labor and capital to shift from activity to activity given the disequilibrium nature of the economy. Indeed, resource reallocation becomes a major issue in the framework of the structural models. This resource reallocation is even more important in the case of developing countries where there is a larger possibility for such a process to occur, as Meier points out. The following table taken from Meier, presents and summarizes the main difference between the neoclassical and structural models of economic growth. Table 1. Alternative Views of Growtb Neoclassical Approach Anu"!ptions Factor returns equal marginal productivity in all lUeS No economies ofscale Perfect foresight and continuos equilibrium in all markels Empirical Implications Relatively high elasticities of substitution in demand and trade Limited need for sector desegregation Sources of Growth Capital accumulation Increase in labor quantity and quality Incre.a.se in intermediate inputs Total factor productivity growth within sectors Structural Approach Income related changes in internal denwld CorwInined exumal marlcet.l and 1&gII in adjustment Transformation of productive structure producing disequilibria in factor marlcets Low price elasticities and lags in adjustment Segmented factor marlcets Lags in adopting new technology Neoclassical 50urces plus: Reallocation of resources to higher productivity aec\on Economies ofscale and learning by doing Reduction of internal and external bot1.lenecks Source: Meier, Gerald Leading Issues In Economic Development ,Fifth Edition, Oxford Univenity Press, J989, p. 98. 21  I Endogenous and Exogenous Growth Models The economic discussion on how to detennine the sources of growth and why countries achieve different levels of income per capita has recently moved to explain the differences between exogenous and endogenous growth models. The underlying assumptions of exogenous growth models are that the rate of population growth, capital accumulation, and technological change are given exogenously, i.e. they are determined outside the framework of neoclassical models. Renelt argued that endogenous growth models are characterized by removing the fixed factor constraint of neoclassical growth models by allowing constant returns to reproducible factors or by endogenizing technological change. In the same regard, Mankiw, Romer and Weil state that "Endogenousgrowth models are characterized by the assumption of non decreasing returns to the set of reproducible factors of production. Among the implications of this assumption are that countries that save more grow faster indefinitely and that countries need not converge in income per capita, even if they have the same preferences and technology" (p. 421). The same authors add that implications of endogenous growth models compared to neoclassical growth models are that in the fonner there is no steadystate level of income per capita and differences in income per capita across countries can persist indefinitely even if countries have different saving and population growth rates. This dissertation uses the neoclassical growth model framework but allows for technological change to occur through the degree of trade openness herein assumed to be a factor of production. Technological change is explicitly modeled as a function of trade openness in primary and nonprimary goods. The advantage of using the neoclassical 22  framework is that it allows for a detennination of how trade openness affects physical capital accumulation, human capital accumulation, and income per capita growth. The neoclassical framework also accounts for the possibility that countries with different rates of saving and initial income per capita levels achieve different levels of income per capita in the long run. The framework also maintains the assumptions of constant returns to scale to all factors common to neoclassical growth models, while considering the possible gains derived from the international trade process of specialization and transfer of technology. To better understand the implications of introducing trade openness as a factor of production within the context of the Solow neoclassical growth model, this dissertation provides a complete derivation of the steadystate levels of physical capital, human capital and trade openness. The outline of the matemathical derivation is presented in steps by first deriving the Solow model, then the Augmented Solow model with Human Capital, and finally the Augmented Solow model with Human Capital and Trade Openness. The Solow Model As mentioned before, the Solow model of economic growth uses a standard neoclassical production function with decreasing returns to capital and constant returns to scale for all inputs. The fundamental assumptions of the Solow model are that the rates of saving, population growth and technological progress are exogenous. Assuming a CobbDouglas production function with two inputs, capital and labor, the model is expressed as follows; (6) Y(I) = K (t r(A (t )L (t )}Q 23 0< a< 1 where Y is output, K is physical capital, L is labor and A is the level of technology. In addition, L and A are assumed to grow exogenously at rates nand g (7) (8) L(t) =L(O)e n , The Solow model also assumes that a constant fraction of output, s, is invested in physical capital. Defining k as the stock of capital per effective unit of labor, k = KJAL, and y as the level of output per effective unit of labor, y = fIAL, the evolution of k is governed by (9) (10) . k(t) =sy(t)  (n + g + 8)k(t) . k(t) = sk(tr  (n + g+8)k(t) . where 0 < 0 < I, is the rate of depreciation and k is the derivative of k with respect to time. It implies that k converges to a steadystate value k* defined by: (11) [ ( ) ] I/(Ia) k* = sf n+ g+o The steadystate capitallabor ratio (k*) is related positively to the rate of savings and negatively to the rate of population growth. Therefore, substituting (11) into (6) and taking logarithms the steadystate level ofincome per capita is given by (12) In[Y((t))] =InA(O) +gt +~ln(s)~ln(n+ g+8) Lt Ia Ia 24 Furthennore, the model assumes that In A(O) =a + &, where a is a constant and e is a countryspecific shock. Thus, log income per capita at a given time time 0 for simplicity is (13) In(Y) =a+~ln(s)~ln(n+g+6)+e L Ia Ia Knight, Loayza and Villanueva argue that "the SolowSwan growth model predicts that in the steadystate equilibrium the level of income per capita will be determined by the prevailing technology, as embodied in the production function, and by the rates of saving, population growth, and technical progress, all three of which are assumed exogenous. Since these rates differ across countries, the SolowSwan model yields testable predictions about how differing saving rates and population growth rates, for example, might affect different countries' steadystate levels of income per capita. Other things being equal, countries that have higher savings rates tend to have higher levels of income per capita, and countries with higher population growth rates tend to have lower levels of income per capita" (p. 513). More recently, research has focused on detennining whether the Solow model supports the hypotheses of conditional and unconditional convergence of income per capita across countries (Mankiw, Romer, and Weil; Knight, Loayza and Villanueva; and Edwards). The convergence hypothesis states that those countries that initially have a lower level ofincome per capita tend to grow faster than the ones that initially have higher levels of income per capita. The difference between conditional and unconditional convergence is that conditional convergence assumes that income per capita across 25 countries converges after controlling for the factors of production. Empirically, the explanatory variables of the rate of growth of income per capita are the rate of growth of the lahor force, the rate of growth of the capital stock, and the initial level of income per capita. Expansions of this model have considered inflation rate, government's share of total output, a financial variable and a freedom variable as important determinants of income per capita growth. Unconditional convergence means that the only explanatory variable of the rate of growth of income per capita is the initial level of income per capita. For the convergence hypothesis to hold the expected sign of the estimated parameter is negative for the initial level of income per capita. This means that countries that start off from lower income per capita levels tend to grow faster than those that initially have higher levels of income per capita. The Solow model predicts that countries having different saving and population growth rates tend to converge to different income per capita levels. Adding HumanCapital Accumulation to the Solow Model The new convergence approach focuses also on the inclusion of human capital accumulation as an explanatory variable of output growth. Mankiw, Romer and Weil emphasize that the accumulation of human as well as physical capital is important for economic growth, especially for those countries in which labor is not considered abundant. Mankiw, Romer and Weil argue that "to understand the relationship between savings, population growth, and income, one must go beyond the textbook Solow model" (p. 408). They argue that including human capital can potentially alter either the theoretical modeling or the empirical analysis of economic growth. At the theoretical level, 26 I properly accounting for human capital may change one's view of the nature of the growth process. Mankiw, Romer and Weil noted that, "for any given rate of human capital accumulation, higher saving or lower population growth leads to a higher level of income and thus a higher level of human capital; hence, accumulation of physical capita] and population growth have greater impacts on income when accumulation of human capital is taken into account. Further, humancapital accumulation may be correlated with saving rates and population growth rates; this would imply that omitting humancapital accumulation would bias the estimated coefficients on saving and population growth" (p. 408). The Augmented Solow model of economic growth presented by Mankiw, Romer and Weil uses the same standard specification as the model developed in equation 6. (14) Y(t) =K(tf H(tt (A(t)L(t)ra  p where a> 0, P> °and 0 < a+P < 1. In addition, H is the stock of human capital and h = H/AL, is a unit of human capital per effective unit of labor. All other variables are defined as before. Letting Sic be the fraction of income invested in physical capital and Sh the fraction invested in human capital. The evolution of the economy around k and h is now determined by (15) (16) . k(t) = Sky(t)  (n + g +o)k(t) . 17(t) =Shy(t)  (n +g + o)l1(t) 27 Mankiw, Romer and Wei! assume that a + f3 < 1, which implies that there are decreasing returns to all capital. (If a + {3 = 1 , then there are constant returns to scale in the reproducible factors. In this case, there is no steadystate for this model). In addition, 0 < 8 < 1, is the rate of depreciation and it is assumed, for simplicity, to be equal for physical and human capital. The steadystate levels of the stock of physical and human capital per effective unit oflabor are determined by (17) (18) ( lfJ fJ J1/(1afJ) k* = Sk s" n+g+8 ( a Ia JI/(lafJ) h* = Sk Sh n+g+8 Substituting (17) and (18) into (14) and taking the natural log yields the steadystate level of income per capita (19) In[Y((f))]=lnA(O)+gt+ a In(s.,)+ f3 In(sh) a+f3 In(n+g+8) Lt la{3 laf3 laf3 Like the textbook Solow model, the augmented model predicts coefficients that are functions of the factor shares. In addition, the steadystate level of income per capita also depends on the rate of human capital accumulation. Mankiw, Romer and Weil argue that the empirical estimation ofthe augmented Solow model yields better results because it shows that by adding human capital the accumulation of physical capital has a larger impact on income per capita than the textbook Solow model. A higher saving rate leads to 28 higher income per capita at the steadystate. In addition, population growth has a larger negative impact on income per capita compared to the initial Solow model. Trade Openness and Technological Transfer in the Solow Model Framework Other considerations on economic growth theory focus on the importance that international trade has on overall output growth through the transfer of technology. Two different approaches are presented, one by Knight, Loayza and Villanueva and the other by Edwards. In the first instance, Edwards argues that a country's trade policy can affect the speed at which technological improvements take place. He uses a set of new indicators on trade intervention and trade distortions to empirically investigate the role of commercial policy in explaining crosscountry growth differentials. Edwards assumes that a country's ability to appropriate technological innovations depends on the degree of openness of the economy. More open should be interpreted as referring to a less distorted or more market oriented foreign trade sector. The overall finding is that there is very strong evidence supporting the hypothesis that, with other things given, more open countries will tend to grow faster. Countries with a greater degree of openness will not only exhibit a higher level of income than countries with trade distortions but they will also have a higher long run steady state rate of growth. Edwards continues, saying that "the model implies that the out of steadystate rate of growth of aggregate output in a small country will depend positively on capital accumulation, positively on labor force growth, positively on the knowledge (or technological) gap between the country in question and the advanced nations, and 29  negatively on the degree of trade distortions. Additionally, trade policy will also affect longrun growth, with more open countries growing faster than otherwise identical countries" (p. 37). In addition, Edwards states that "The coefficient of the openness indicators provides strong support to the hypothesis that countries with a more open trade regime have, with other things given, tended to grow faster" (p. 42). On the other hand, Knight, Loayza and Villanueva propose an extension of the Augmented Solow Model developed by Mankiw, Romer, and Weil. The new model includes trade policy and the stock of public infrastructure as factors that affect labor augmenting technological change. Knight, Loayza and WeiI state "policies that foster more openness in a country's international trade regime help to stimulate laboraugmenting technological change in two ways. First, the importexport sector serves as a vehicle for technology transfer through the importation of technologically advanced capital goods, as elucidated by Barhan and Lewis (1970), Chen (1979) and Khang (1987), and as a channel for intersectoral external economies through the development of efficient and internationally competitive management, the training of skilled workers, and the spillover consequences of scale expansion (Keesing (1967) and Feder (1983)). Second, rising exports help to relieve the foreign exchange constraint  that is, a country's ability to import technologically superior capital goods is augmented directly by rising exports receipts and indirectly by the higher flows of foreign credits and direct investment caused by the country's increased ability to service debt and equity held by foreigners" (p. 515). 30  The main difference between the Knight, Loayza and Villanueva model and the Mankiw, Romer and Weil model is the specification of the technological factor A. The factor, A, is redefined in the KLV model as (20) where g is the exogenous rate of technological progress, F is the degree of openness of the domestic economy to foreign trade (with elasticity Sf), and P is the level of government fixed investment in the economy (with elasticity Sp). Knight, Loayza and Villanueva state "this modification is particularly relevant to the empirical study of economic growth in developing countries, where technological improvement tends to be absorbed domestically through imports of capital goods and where the productive sector's efficiency may depend heavily on the level of fixed investment undertaken by the government" (p. 516). Hence, given that the degree of trade openness (F) and the stock of government fixed investment (P) are included in equation 20 as part of a technological shifhng factor, the determination of the steadystate level of physical and human capital per effective unit of labor remains invariable compared to the estimates of the steadystate levels in Mankiw, Romer and WeiI model. Nevertheless, Knight, Loayza and Villanueva conclude that overall. econonuc efficiency is influenced significantly and positively by the extent of openness to international trade and by the level of government fixed investment in the domestic economy. In their words "when openness and the level of public infrastructure are taken into account, physical investment becomes quantitatively more important in the 31  growth process, implying that a better quality of investment is encouraged by a more liberal international trade regime and by more government fixed investment" (p. 536). An important finding in Knight, Loayza and Villanueva is that there are two channels through which the negative impact on growth of a restrictive trade system (proxied by the weighted average of tariffs on intermediate and capital goods) may be transmitted, through the rate of investment and through the effect on production efficiency. A high tariff structure discourages imports of capital goods and leads to less technology transfer, and thus to less technological improvement. Outwardoriented development strategies have a positive impact on economic growth. Edwards; and Knight, Loayza and Villanueva argue in favor of a positive effect that trade openness has on the productivity of physical and human capital, and also in total output growth. They argue that this positive effect comes about through the transfer of technology and the learning by doing process. Yet, at the theoretical level both approaches fail to address how trade openness affects human and physical capital productivity and therefore capital accumulation because the approaches consider trade openness as a technological shifting factor as opposed to a production factor. This effect is shown in equations 17 and 18 since k * and h· are assumed to be the steadystate levels of physical and human capital per effective unit of labor. Hence, the impact of technology changes as mentioned in Edwards; and Knight, Loayza and Villanueva is not explicitly incorporated in the steadystate levels of k and h, nor is the impact explicitly accounted for on the estimated parameters and coefficients. 32 CHAPTERm THEORETICAL MODEL Solow Model with Human Capital Accumulation and Trade Openness To detennine in a direct and precise manner how trade openness affects factor productivity, human and physical capital accumulation, and per capita output growth, this dissertation proposes an alternative Neoclassical approach that incorporates human capital and trade openness. The main difference of the approach this study follows is that the model incorporates the degree of trade openness promotion as a factor of production and not as a component of the technological shifting factor A as in previous studies. This is a key assumption in deriving the steadystate conditions in order to be able to measure the effects of trade openness on economic growth. In this regard, the model incorporates trade openness as a factor of production assuming that; i) it promotes the reallocation of resources according to comparative advantage, ii) allows for greater capacity utilization, iii) pennits the exploitation of economies of scale, iv) generates technological improvements in response to competition abroad and, v) in labor surplus countries contributes to increased employment and labor productivity. To account for the differences in its impact on sectoral production between agricultural and nonagricultural 33  goods, the model further demonstrates the importance of trade openness by category of goods through its decomposition between agricultural and nonagricultural. The decomposition of trade openness between agricultural and nonagricultural goods is relevant to the process of economic growth and economic development because differences may be determined in terms of factor productivity, resources allocation, and economies of scale between two different sectors with different structural and heterogeneous characteristics. Traditionally, it has been argued that agriculture provided surplus labor to the development of the industrial sector. Kavoussi; Tyler; and Balassa argue that the contribution of primary and manufactured export goods to output growth and capital productivity depends on the initial level of income per capita and on the composition of exports. Renelt argues that those results can be obtained using any trade openness measure, however trade openness as measured in this study includes the gains derived from international trade not only through export promotion but also by allowing greater competition through importing capital and primary goods. Technology transfer and development of economies of scale are the result of overall openness to trade and not only the outcome of a process of export promotion. Trade openness optimizes resource allocation by promoting those production activities that face international competition. Thus, this study assumes that trade openness is better understood when incorporating the investment process associated to the promotion of both exports and imports of agricultural and nonagricultural goods9 . 9 The concern of developing countries on whether they should promote exports and restrict imports is an issue that relates usually to structural balance of payments problems and/or domestic production policies oriented to protect domestic producers. However, the truthness of this argument does not relate or attempt to explain the gains a country receives by participating on international trade. 34 The Augmented Neoclassical Growth Model developed herein adheres to the Mankiw, Romer and Wei] specification of human capital from the previous chapter and includes two more factors of production, agricultural and nonagricultural trade openness promotion, A simple production function can be expressed as follows. Let (21) Y =j(K,H,Xa,Xna,L) where Yis total output, K is physical capital, H is human capital, Xa is a trade openness promotion measure in the agricultural sector, Xna is a trade openness promotion measure in the nonagricultural sector, and L is the labor force. Assuming a CobbDouglas production function with decreasing returns to scale to all reproducible factors, the Augmented Neoclassical Solow model is expressed as fonows. Let, (22) where a > 0, 13 > 0, B> 0 and 7! > 0; and 0 < a+13+ B+ 7! < 1. In addition, the model assumes that K > 0, H> 0, Xa > 0, Xna > 0 and L > O. Special cases of the model arise when any of the variables assumes a value equal to zero. These cases are particularly interesting when either Xa = 0 and/or Xna = 0. 10 As stated, A is the technological factor, and A and L follow the same specification as before (23) (24) L(t) =L(O)e'" A(t) =A(O)e EI therefore the number of effective units of labor grows at n+g like in the Solow model. The model also defines k = KlAL, h = HIAL, xa = XalAL, xna = XnalAL, andy = YIAL, as 10 A complete explanation of the theoretical implications are provided later in this chapter. 35 the physical capital, human capital, agricultural trade openness, nonagricultural trade openness and total output per effective unit oflabor, respectively. Nonnegativity ofXa and Xna Before proceeding with the actual derivation of the steadystate levels of income per capita, physical capital, human capital, agricultural trade openness, and nonagricultural trade openness, some discussion of the assumed nonnegative nature of Xa and Xna is warranted. By definition the model assumes that Xa > 0 and Xna > o. This assumption implies that countries take part in the international trade process either as exporters/importers of agricultural goods or/and exporters/importers of nonagricultural goods. However, it is possible to consider the hypothetical case where a country does not participate in international trade either because of selfsufficiency reasons)l or any other macroeconoITllc reason. Let us assume first that a country does not have any commercial relationship with any other country in agricultural goods, i.e. Xa is equal to zero. IfXa = 0 then the country is defined as been selfsufficient in agricultural goods and therefore there are no trade gains or technological improvements derived from Xa. Under this case the term Xa must be eliminated from the specification of the Augmented Solow model of equation 22. In this regard agricultural trade openness does not have any impact on the steadystate levels of physical capital, human capital, and income per capita. The second condition refers to the nonnegativity of Xna. This condition refers to the assumption that a country may be defined as being selfsufficient in the production and consumption of nonagricultural 11 Selfsufficiency does not mean that a country has comparative advantage in the production of a specific good, nor does it mean that a country can not benefit from the trade promotion process. 36  goods ifXna = O. As in the case of selfsufficiency in agricultural goods, selfsufficiency in nonagricultural goods means to eliminate the Xna term from the specification of equation 22. The implications in terms of steadystate level determinations are the same as before. Even though it is less likely for these theoretical scenarios to occur in the real world, it is convenient to keep them in mind to have a better understanding of the associated gains in productivity and consumption that international trade brings about. Having explored these possible theoretical scenarios, this study proceeds to derive the steadystate levels of income per capita, physical capital accumulation, human capital accumulation, agricultural trade openness, and nonagricultural trade openness for the Augmented Solow Model. The results of the newly developed steadystate conditions will then be used to specify the differences among growth models and to develop the growth equation for empirical estimations. Steadystates Before proceeding with the derivations of the steadystate conditions, it is convenient to remember some considerations about the Solow and MRW growth models. First, the Solow Growth Model assumes that the rate of savings of any economy is equal to the rate of investment in physical capital, where physical capital is expressed in terms of effective units oflabor. Therefore, the Solow model only derives one steadystate level for the physical capital. In the same context and following the Solow model specification mentioned above, Mankiw, Romer and Weil argue that savings can be used not only in the formation of physical capital but also in the formation of human capital. Thus, MRW assume that the overall savings level can be decomposed between Sk and Sh, where Sk is the 37  fraction of income invested in physical capital, and Sh is the fraction of income invested in human capital. Therefore, in MRW there are now two steadystate conditions, one for physical capital and the other for human capital accumulation. Using the Solow neoclassical framework and the correspondent MRW extension to it, this study further assumes that a fraction of Gross Domestic Product, Sxa, is invested in the promotion of agricultural trade, and that a fraction of Gross Domestic Product SXlIQ is invested in the promotion of nonagricultural tradel2 . The model further assumes, that the rate of depreciation for physical capital accumulation, human capital accumulation, agricultural trade openness, and nonagricultural trade openness is equal to 5, where a < 5 < 113 . Therefore, by combining the rate of depreciation 5, and the rate of savings invested in each factor of production (Si, where i = k, h, xa, and xna), it is possible to define the correspondent rates of net investment for each factor as follows~ (25) (26) (27) (28) afa a=s=Y5Xa afna a=s Y5Xna X/IQ where net investment is defined as the gross investment rate (siY where i=k, h, xa, and xna), minus the rate of depreciation of the correspondent i lil factor in time 1. Recalling the 12 Investment in the promotion of agricultural and nonagriculturaJ trade is associated with the development of economies of scale, capacity of response to foreign competition, development of comparative advantage, and promotion of technological transfer. 38 definitions of k, h, xa and xna (effective units of factors of production) it is possible to rearrange terms as to determine the total differentials ofK, H, Xa and Xna with respect to (wrt) tI.me, I..e., iK,i,f! &,'"aa nd &'"na. ThIe partl.aI de"nvatlves 0 f K, H, Xa, and Xna a a a a wrt time will then be equated to equations 25, 26, 27, and 28 respectively to determine the correspondent steadystate conditions for each factor of production. The results and procedures of the mathematical derivation are shown from equations 29 through 40. Physical Capital Let us first start with the derivation of the steadystate level for the physical capital. Thus, the first step to determine the physical capital steadystate level is to rearrange k = KlAL as K = kAL and then take the total differential of K wrt time which results in, OK ac ilL 8A = AL+kA+kL a a a a (29) iK ac  = AL+nkAL+gkAL a a where, the rate of change of the capital stock wrt time iK is equal to the sum of three a components. The first tenn at the righthandside of equation 29 refers to the change of the capital stock per effective unit of labor wrt time multiplied by the number of effective 13 This assumption simplifies the mathematical derivation of the steadystate levels of K, H, Xa, and Xna. 39  units of labor (AL). The second tenn is the change in the capital stock due to changes in the rate of growth of the labor force; and the third term indicates the change in the capital stock due to changes in the rate oftechnology growth. To solve for the steadystate level, equate equations 25 and 29 which are equivalent specifications of the change in the level of physical capital wrt time. Thus, it is possible to substitute 29 into 25, and solve for the rate of change of the level of physical capital per effective unit oflabor wrt time as follows; ac AL =sl:Y  oK  nkAL  gkAL if ac s.lI 5K nkAL gkAL = if AL AL AL AL aa =SkY  k(g+n +0) however, to solve for the steadystate level of physical capital, it is required to use the definition of output per effective unit of labor y =k ahPxa(JxnaJr and substitute it into the previous equation resulting in (30) where the net change in the level of physical capital accumulation per effective unit of labor wrt time is equal to the proportion of income invested in physical capital Changes in the assumption do not affect the overall results of this study. 40 accumulation per effective unit of labor minus the change in the level of physical capital accumulation associated with the rates of change of technology and labor force, and the depreciation rate. To solve for k from equation 30 it is further assumed that at the steadystate level k h xa xna . . the condition 30a holds. Where, (30a) refers to  = = =, and identifies the sit: Sh SXQ sr"" producer maximizing behavior that allows any economy to assign scarce resources to their best alternative uses until the last unit of savings per effective unit of labor has been allocated equally among alternative investment opportunities. This condition implicidy assumes that at the steadystate level the marginal productivity of the last dollar invested in the ith factor is equal to the marginal productivity of the last dollar invested in the l' factor, under the condition that i :I' j. Therefore, using condition 30a, it is possible to mathematically identify the following equalities that are then used to solve for the steadystate level of physical capital • k in equation 30. Thus, the model identifies that if at the steadystate level the marginal productivity of the last dollar invested in factors iUl and /' is equal, then it is possible to raise any pair of all these resulting equalities to the same power without altering the implications of this condition. This mathematical procedure then allows the model to substitute and solve for k. This is then shown as fonows; i) ii) (~J 8 =(xa) (J and Sk SXQ 41 iii) solving t, ii, and iii in tenns of II, xae, and xna" respectively gives the following results, i*) ii *) iii*) k {/ {/ xa{/= sJ(:Q/ ,and Sk Results from i*, ii*, and iii* are then substituted into equation 30, and then solved at the steadystate for k, where ac =o. The remaining of the mathematicaL derivation is an it algebraic procedure as shown below; S IP{/"k a+fJ+8+fr S fJ S 8 S "= k(g + n + 0) k h J:Q XM lfJ8tr P 8 If Sk Sh SJ:Q Sma n+g+o 42 • lafJ{/1f =k (31 ) • . (s IP8tr S PS 8 S If) lap8tr k= k h.ul XIIQ n+g+8 where k is the steadystate level of physical capital accumulation. Some considerations are important to address. The first and foremost important element to point out is that the result in equation 31 differs from those previous derivations of the steadystate level of physical capital accumulation in the Solow model of equation 11 and in the Augmented Solow model of equation 17. In the basic neoclassical Solow model the steadystate level of physical capital accumulation is positively related to the savings rate and negatively related to the rate of population growth. In the Mankiw, Romer and Weil augmented model of equation 17, the steadystate level of physical capital accumulation is determined as in the Solow model. However, equation 17 predicts a larger steadystate level of physical capital, because it incorporates the positive effect human capital accumulation has on physical capital. Not surprisingly the same results are found in equation 31. However, the Augmented Solow model with Human Capital Accumulation and Trade Openness predicts that the steadystate level of physical capital per effective unit of labor also depends positively on the income proportions invested in agricultural and nonagricultural trade openness promotion. If the model specification is correct then physical capital accumulation is positively affected by investment in trade openness because it helps to reallocate resources in a more efficient way, allowing for greater capacity utilization, exploitation of economies of scale, 43  and generating technological improvements in response to competition abroad and, in labor surplus countries contributes to increased employment, as mentioned before. A second difference between the model developed in this study and previous determinations of growth models relates to the study by Knight, Loayza and Villanueva. Following MRW approach, Knight, Loayza and Villanueva define that the degree of trade openness affects the steadystate level of physical capital accumulation and output growth only through exogenous changes in the level of technological transfer. Knight, Loayza and Villanueva assume that trade openness is an indirect determinant of output growth which only has effects on it through exogenous changes in the level of technology. Thus) trade openness does not have any direct effect on the steadystate level of physical capital accumulation. On the other hand, theoretical results from equation 31 indicate that endogenous technological change through the degree of trade openness has a positive and direct effect on the steadystate level of physical capital accumulation. This particular difference is a major shortcoming of previous theoretical growth models that will be discussed in more detail when detennining both the direct and indirect effects of trade openness on overall per capita output growth. Finally an empirical question that remains unanswered is whether the steadystate level of physical capital accumulation is larger in the augmented Solow model with trade openness than in the model estimated by Mankiw, Romer and Weil. The answer to this particular question depends directly on the relative magnitudes of Sxa, Sma, () and 1r) other things being equal. 44 Human Capital The second steadystate condition to derive corresponds to human capital accumulation. As for the physical capital, this section follows the same steps as before. It is relevant to notice that even though some of the material herein presented may be repetitive with respect to the previous section, it is still necessary to understand the derivation process for the steadystate level of human capital. Thus, using the definition of human capital per effective unit of labor h=H/AL, let us rearrange it as H=hAL, and then take the total differential wrt time. This in tum yietds, iR a, iL oA ::::0 AL+hA+hLif a if if (32) iR a, ::::0 AL+nhAL+ghAL if a where, the rate of change of the human capital stock wrt time iR is equal to the sum of a three components. The first term at the righthandside of equation 32 refers to the change of the human capital stock per effective unit of labor wrt time multiplied by the number of effective units of labor (AL). The second term is the change in the human capital stock due to changes in the rate of growth of the labor force; and the third term indicates the change in the human capital stock due to changes in the rate oftechnology growth. To solve for the steadystate level we proceed to equate equations 32 and 26 which are equivalent specifications of the change in the level of human capital wrt time. 45 Thus, it is possible to substitute 32 into 26, and solve for the rate of change of the level of human capital per effective unit of labor wrt time as follows', a, AL =ShY  5H  nhAL  ghAL it a, = ShY _ 8H _ nhAL _ ghAL it AL AL AL AL however, to solve for human capital, it is required to use the definition of output per effective unit of labor y =k a hfJ xa9 rna IC and substitute it into the previous equation resulting in (33) where the net change in the level of human capital accumulation per effective unit of labor wrt time is equal to the proportion of income invested in human capital accumulation per effective unit of labor minus the change in the level of human capital accumulation associated with the rates of change of technology and labor force, and the depreciation rate. 46  To solve for h from equation 33 the model makes use of the condition 30a, as before. Where, (30a) refers to k = h = xa = xna ,and'Ide'nftlies the producer Sh SUJ S..,,,,, maximizing behavior that allows any economy to assign scarce resources to their best alternative uses until the last unit of savings per effective unit of labor has been allocated equally among alternative jib. investment opportunities. Hence, using condition 30a, it is possible to identify the following equalities which are then used to solve for the steadystate level of physical capital h in equation 33. The model also assumes that at the steadystate level the marginal productivity of the last dollar invested in factors jib. and]I.h is equal, which in turn allows to manipulate the equalities as follows. This is then shown as; i) ii) iii) solving i, ii, and iii in terms ofka , xae, and xna" respectively gives i*) ii *) 47 iii"') h"s 1r xna" = rna If sit Results from i*, ii"', and iii'" are then substituted into equation 33, and then solved at the t11 steadystate for h, where =O. The remaining of the mathematical derivation is an a algebraic procedure as shown below; la8" a 8 " Sit Sic SXQ SXrtQ n+g+8 .1ap8tr =h (34) . (s la8If S as 8S IfJlap8'1f h= It It XQ rna n+g+8 where h represents the steadystate level of human capital accumulation. The result in equation 34 differs from that derived in Mankiw, Romer and Weil in equation 18. Mankiw, Romer and Weil predict that the steadystate level of human capital relates positively to the rate of savings invested in physical and human capital and relates negatively to the rate of population growth. Equation 34 presents similar results as those 48 implied by equation 18, however, the augmented Solow model with human capital accumulation and trade openness predicts that the steadystate level of human capital per effective unit of labor is also affected by the degree of openness both in agricultural and nonagricultural goods. The degree of trade openness provides for the exploitation of economies of scale that technology transfer and leamingbydoing processes have on the formation of human capital. Trade openness increases the process of technology transfer and leamingbydoing, increasing overall labor productivity. In turn, reallocation of labor among economic sectors increases overall marginal productivity that will not occur in economies that do not trade. Furthermore, industries and sectors which take part in the process of international trade usually have labor skill requirements higher than those industries dedicated to the production of goods for the domestic market. International trade competition results therefore in enhancement of labor quality, easing the process of technology transfer and physical capital accumulation. Hence, human capital accumulation is positively affected by the degree of openness because it reallocates resources in a more efficient way, allows for greater capacity utilization, enables the exploitation of economies of scale, and generates technological improvements in response to competition abroad and, in labor surplus countries contributes to increased employment. At the empirical level, whether the estimated magnitude of the steadystate level of human capital accumulation is larger than the one estimated by Mankiw, Romer and Weil is an empiri.cal question that depends on the absolute magnitudes of Sm, Sxna, Band 7r, other things equal. A second difference between the model developed in this study and previous determinations of growth models relates to the study by Knight, Loayza and Villanueva. 49 Following .MRW approach, Knight, Loayza and Villanueva define that the degree of trade openness affects the steadystate level of human capital accumulation and output growth only through exogenous changes in the level of technological transfer. Knight, Loayza and Villanueva assume that trade openness is an indirect determinant of output growth which only has effects on it through exogenous changes in the level of technology. Thus, trade openness does not have any direct effect on the steadystate level of human capital accumulation. On the other hand, theoretical results from equation 34 indicate that endogenous technological change through the promotion of trade openness has a positive and direct effect on the steadystate level of human capital accumulation. Perhaps, the two most relevant considerations drawn out of these steadystate conditions are; trade openness results in higher labor quality, and thus resources shift from domestic uncompetitive activities to trade related highly competitive production processes. This result derives directly from the producer maximizing behavior assumption that indicates that at the steadystate level (marginal condition) the marginal productivity of the last unit of savings has to be equal among alternative investment opportunities. This particular difference is a major shortcoming of previous theoretical growth models that will be discussed in more detail when determining both the direct and indirect effects of trade openness on overall per capita output growth. In this regard, the difference between the closed and open economy models is that in the closed economy model the economy is not maximizing either production nor social welfare. This is because the closed economy does not exploit the benefits associated with maximizing resource use allocation directly derived from the process of international trade. On the other hand, the open economy model differentiates between those 50 economies that trade accordingly to their comparative advantage and those that are not involved in international trade. Agricultural Trade Openness The Augmented Growth Model with Trade Openness proposes the derivation of two new steadystate conditions. The first condition refers to the degree of trade openness promotion in agriculture, whereas the second condition refers to the degree of trade openness promotion in the nonagriculture sectors. The model first determines the steadystate level for the agricultural trade openness promotion as follows. Using the same specification as before, let xa=Xa/AL and Xa=xaAL. Taking the derivative of Xa with respect to time. a¥a aa iL oA = AL+xaA+xaLit it it it (35) a¥a = aa AL+nxaAL+ gxaAL it it . . iWa where, the rate of change of agricultural of trade openness promotIOn wrt tIme a IS equal to the sum of three components. The first term at the righthandside of equation 35 refers to the change in agricultural trade openness promotion per effective unit of labor wrt time multiplied by the number of effective units onabor (AL). The second term is the change in agricultural trade openness promotion due to changes in the rate of growth of 51 the labor force; and the third term indicates the change in agricultural trade openness promotion due to changes in the rate oftechnology growth. To solve for the steadystate level we proceed to equate equations 27 and 35 which are equivalent specifications of the change in agricultural trade openness promotion wrt time. Thus, it is possible to substitute 27 into 35, and solve for the rate of change in agricultural trade openness promotion per effective unit of labor wrt time as follows; & S.raY  e5Xa =AL . +nxa4.L + gxaAL it &a ALit =s YbXa nxaALgxaAL JCD ilxa sJCDY bXa nxaAL = a AL AL AL gxaAL AL &a  =S.rayxa(g+n+e5) it however, to solve for the steadystate level of agricultural trade openness promotion, it is required to use the definition of output per effective unit of labor y =kahPxaoxna" and substitute it into the previous equation resulting in (36) where the net change in agricultural trade openness promotion per effective unit of labor wrt time is equal to the proportion of income invested in agricultural trade openness 52 promotion per effective unit of labor minus the change in the level of agricultural trade openness promotion associated with the rates of change of technology and labor force, and the depreciation rate. To solve for xa from equation 36 it is further assumed that at the steadystate level the condition 30a holds. As before, the model assumes that at the steadystate level the marginal productivity of the last dollar invested in the itr. factor is equal to the marginal productivity of the last dollar invested in thell factor, under the condition that i :I; j . Therefore, using condition 30a, it is possible to identify the following equalities which are then used to solve for the steadystate level of agricultural trade openness promotion in equation 36. This is then shown as follows; i) ii) iii) (:.Y =(~)' and solving i, ii, and iii for kD., hP, and xna'l respectively gives i*) ii *) iii "') p P fJ _ xa Sh d h  p ,an SJCQ xa"s " xna" = :rna Sh " 53 Results from i·, ii·, and iii· are then substituted into equation 36, and then solved at the iJxG steadystate for xa, where =0 . The results is then it ' IapI< a+p+B+tr a P I< ( >:) Sxa xa SI< Sh S;ma =xa g+n+u IapI< a p I< Sxa SI< Sh SXI'IQ n+g+8 • IapBI< =xa (37) where • (s lap" S as fJ S "J lafJBI< xa = xa "h;ma n+g+8 xa is the steadystate level of agricultural trade openness per effective unit of labor. The model predicts that xa depends positively on the rate of savings invested in physical and human capital, and on the proportion of income invested on agricultural and nonagricultural trade; and negatively on the rate of population growth. According to equation 37, physical and human capital positively affects agriculture by allocating to the production and trade of agricultural goods, only those resources that are productive in such activity. The relative size of agricultural trade openness compared to nonagricultural trade openness depends finally on the levels of Sxa, Sma, Sh, and Sic. Nevertheless, for a country with a large agricultural base x·a is expected to be larger than otherwise. In most 54 cases as countries move their production structure from agricultural to nonagricultural industries, a reversal in the relative sizes of the steadystate levels might be expected, becoming nonagriculture more important than before. In this regard, countries that start off having a comparative advantage in the production and therefore, trade of agricultural goods may reflect larger relative sizes of agricultural trade as ratio of the specific sectoral production. At the empirical level countries which have a comparative advantage in the production and trade of agricultural goods would, other things given, reflect a positive sign related to income per capita. It is convenient to remember that the positive effect of trade openness prom060n comes about because the model assumes that countries' production and trade behavior follow a pattern directly associated with their comparative advantage. On the other hand, if a country becomes involved in international trade not accordingly to its inherent or current comparative advantage, then there wou~d be a resource use misallocation that contradicts the basic assumption of producer maximizing behavior. This in turn would be reflected in general loss of social welfare, which would be reflected as well, in a negative sign of empirical estimates for agricultural and nonagricultural trade openness promotion. Furthennore, this resource use misallocation would reduce the marginal productivity of all factors of production, driving countries away their longrun steadystate level of income per capita. 55 Nonagricultural Trade Openness Finally, the steadystate level for the nonagricultural trade openness is determined as follows. Given xna=Xna/AL, let Xna=rnaAL, and take the derivative of Xna with respect to time. 8Xna ana tL 8A = AL+xnaA+xnaLif a if a (38) OXna Oma = AL+ nxnaAL + grnaAL a a where, the rate of change of nonagricultural oftrade openness promotion wrt time iWna a is equal to the sum of three components. The first term at the righthandside of equation 38 refers to the change in nonagricultural trade openness promotion per effective unit of labor wrt time multiplied by the number of effective units of labor (AL). The second term is the change in nonagricultural trade openness promotion due to changes in the rate of growth of the labor force; and the third term indicates the change in nonagricultural trade openness promotion due to changes in the rate of technology growth. To solve for the steadystate level we proceed to equate equations 28 and 38 which are equivalent specifications of the change in nonagricultural trade openness promotion wrt time. Thus, it is possible to substitute 28 into 38, and solve for the rate of change in nonagricultural trade openness promotion per effective unit of labor wrt time as follows; 56 iJxna SrnaY  liXna =AL+ nxnaAL + gxnaAL a iJxna ALa =S Y  8Xna  nxnaAL  gxnaAL .l7IQ ana srnaY liXna nxnaAL = a AL AL AL gxnaAL AL iJxna =snoaY  xna(g + n +0) a however, to solve for the steadystate level of nonagricultural trade openness promotion, it is required to use the definition of output per effective unit of labor y =k a hPxa8 xna 1< and substitute it into the previous equation resulting in (39) where the net change in nonagricultural trade openness promotion per effective unit of labor wrt time is equal to the proportion of income invested in nonagricultural trade openness promotion per effective unit of labor minus the change in the level of nonagricultural trade openness promotion associated with the rates of change of technology and labor force, and the depreciation rate. 57 To solve for xna from equation 39 this study makes use of condition 30a. Therefore, usmg condition 30a, it is possible to mathematically identify the following equalities which are then used to solve for the steadystate level of nonagricultural trade openness promotion in equation 39. This is then shown as follows; i) ii) iii) (:.J' =(::J'and ( xa)9 =(xna) (J , sro sma solving i, ii, and iii for ka , hP, and xae respectively gives the following results. i*) ii*) iii*) f3 f3 f3 _ rna sit d h f3 ,an s:J:lI(J Results from i*, ii *, and iii* are then substituted into equation 39, and then solved at the 8xna I . h steadystate for xna, wherea = O. The resu ts IS ten, 58 Jaf30 a~/3+(J~1< a /3 6 ( ) sDlQ rna Sir s~ Sxa =rna g+n+8 • laf301< =rna (40) n+g+8 ( • S laf36 S a S f3S 0) lafJ 61< rna = J:1IQ Ie h ;t;a n+g+8 . where rna is the steadystate level of nonagricultural trade openness per effective unit of . labor. The model predicts that xna depends positively on the rates of saving invested in physical and human capital, and on the proportion of income spent on agricultural and nonagricultural trade; and negatively on the rate of population growth. According to equation 40, physical and human capital positively affects nonagriculture by allocating to the production and trade of nonagricultural goods, only those resources that are productive in such activity. For a country with a large nonagricultural base x ~ a is expected to be larger than otherwise. Countries that have comparative advantage in the production of nonagricultural goods may reflect larger relative sizes of nonagricultural trade as ratio to the specific sectoral production. At the empirical level countries which have comparative advantage in the production and trade of nonagricultural goods would, other things given, reflect a positive sign related to income per capita. In general, how much a country participates on international trade depends positively on how much the country invests on physical capital, human capital, trade openness in agriculture and trade openness in nonagriculture promotion. The more a country dedicates resources to the 59 enhancement of physical capital accumulation and to increase the level of labor education (training), the more competitive this economy becomes. Income Per Capita The procedure to determine the effects that K, H, Xa, and Xna have on income per capita, and to find the steadystate level of income per capita, is to substitute equations 3 1, 34, 37, and 40 into the initial production function, equation 22. To empirically estimate the resulting production function, this study proceeds to transform the original Cobb Douglas type of production function into a linear function, by taking the natural logarithm. This transformation allows the use of econometric techniques to empirical estimate the coefficient. It is important to mention that empirical estimations of the model can only be performed if the coefficients of the model are expressed in linear form. Therefore, the equation to be estimated is a fJ Y ( _ =A lfJBrrS {J S B5 rrJ Ia{JBrr (5 la8rrS a5 BS rrJ la{J8rr 5Ie h xa xna 11 Ie xa X71Q L n+g+8 n+g+8 8 1r ( s lafJtr S a5fl s trJ lafJ81r (5 Ia{JBS as {J5OJ IaflBIr xa lehxna xna lehxa n+g+8 n+g+8 In(Yt) =lnA(O) +gt + a 1~(s/.D8"s/s,",8S:maK)1 a+ f3;8;1r In(n+g+8) Lt 1 a  f3  ()  1r 1\  a    1r 60 + n In(SDII:J lap8Sk a SirfJ S 8) lafJ8n = The final result is: (41 ) (n) a+p+8+n a )n  =lnA(O)+gt In(n+g+8)+ Ins Lt lafJ8n lap8n k fJ 8 n + Insh + Ins + Ins lafJ8n lafJ8n = lap8n xna Equation 41 predicts that the longrun steadystate level of income per capita depends positively on the degree of trade openness promotion in agricultural (Sxa) and nonagricultural (Sxna). It also predicts, as expected, that population growth (n)14 affects negatively the longrun steadystate level of income per capita and that physical capital (Sk) accumulation and human capital (Sh) accumulation positively affect the longrun steadystate level of income per capita growth. In addition, the longrun steadystate income per capita coefficients in equation 41 are a function ofthe factor share parameters a, 13, 8, and Jr. The malO difference with the approaches followed by Edwards; and Knight, Loayza and Villanueva is that trade openness affects both the steady state of physical and human capital accumulation and the steadystate level of income per capita. If the 61 specification of the model is correct, the introduction of openness in agricultural and nonagricultural markets as factors of production, on the grounds mentioned throughout the dissertation, has changed the traditional view that exports and imports affect physical capital, human capital, and output growth only through the exogenous transfer of technology. The new specification of the Solow model predicts difference in magnitude on the empirical estimates as it will be mentioned in the next section. The model predicts that the estimated coefficients of physical and human capital are affected by the introduction of trade openness. Considering trade openness as a component of the technological factor (A) implies that estimated coefficients remained unchanged when comparing the closed and open economy growth models. This assumption implies that there is no difference in the steadystate levels of physical and human capital accumulation between the closed and open economy models. A result that seems unplausible. Indeed, one would expect that trade openness would affect the productive and steadystate levels of both physical and human capital. Whether the final steadystate levels of physical and human capital accumulation are larger or sroaner after trade compared to the before trade situation is an empirical question that depends on the relative magnitudes of the production coefficients. Nevertheless, one expects that trade openness results in a positive effect on overall income per capita through the reatlocation of resources, economies of scale, and transfer oftechnology of the trading process. 14 The model assumes that the rate of change of technology transfer g and the rate of depreciation 15 remain constant. 62 Summary Tables 2 and 3 provide a comparative analysis of the alternative growth models discussed in Chapter III. These tables clearly state the differences among models. Table 2 illustrates the differences in terms of mathematical derivations for the steadystate levels of the correspondent factors of production. Table 3 provides the conceptual analysis that relates to the derivations outlined in table 2, below. The main differences and their correspondent implications are explained as follow. The summary presented on tables 2 and 3 indicate that by endogenizing technological change as a function of the degree of trade openness, one can explain the effect that trade openness has on output growth, factor accumulation and overall factor productivity in the context of the Solow model. The BarbozaDicks proposed model specification also allows the determination of both the direct and indirect effects that trade openness promotion has on the longrun rate of growth of income per capita and on the correspondent steadystate level. 63 Table 2. Comparison of SteadyState Conditions under Alternative Growth Model! Solow • Mankiw et al • Edwards; and Proposed BarbozaDicks C Knight et aI b Physical Capital Human Capital Agric. Openness Nonagric. Openness 1 [s/(n+g+~]la ( 1{3 13 )IIPaf31 SI: ~ n+g+8 ( a la )1/(1aP) 51: ~ n+g+8 ( 113 13 )l/(laPl S. Sir n+g+8 ( a Ia )1I(1aP) 51: s" n+g+8 I ( .s:..IafHrSstas:~Ir)1afJfMc n+g+8 • Closed economy growth models b Open economy growth model with trade openness as a component of technological change factor A C Open economy growth model with endogenous technological change through trade openness 64 Table 3. Conceptual Comparison of Alternative Growth Models Solow Mankiw et aJ Edwards; aDd Knight et al Proposed BarbozaDicks Functional Form Input.! Technolocy Factor A JnpUls Per CapiJa JnCDm~ Capital and Labor. Labor grows exogenously at rate n. Exogenously given with growth rate g. Residual componenl Positive on savings rate, negative on labor growth (n) and negative on exogenous technological change. Positive on physical capital, negative on labor, and positive on exogenous technology change. Physical capital, human capital and labor. Labor grows exogenously at rate n. Exogenously given with growth rate g. Residual componenl Positive on investment in physical and human capital, negative on labor force growth, and negative 011 exogenous technological change. Positive on physical and human capital, negative on labof, and positive on exogenous technology change. 65 Physical capital, human capitA.I and labor. Labor grows exogenously at rate n. Exogenously given with growth rate g, and depends positive on trade openness and government infrastructure. Positive on investment in physical and huJlW1 capital. negative on labor force growth, and negative on exogenous technological change. POISitive on physical capital, human capital, and trade openness; negative on labor, and positive on exogenous technology change. Open economies grow fasteT toward given steadystate. Physical capital, human capital, trade openness in agricu Iture and nonagrlculture. Labor grows exogenously at rate n. Partially endogenized as linear function oftrade openneu in agriculture and nonagriculture goods. Remaining portion grows at rate g. Positive on investment in physical and human capital, negati ve on labor force growth, and negative on eKogenoWi technological change. Positive on the degree oftrade openness in agriculture and nonagriculture goods. In addition. rteadyst.a.te levels of physical and human capital accumulation depend upon the degree oftrade openness. Positive on physical capital, human capital, agriculture and nonagricullure trade openness; negative on labor, and positive on exogenous technology change. Open economies tend to grow faster toward steadystate, and open economies achieve different studystales as trade openness factors vary. Lower savings rate required to achieve same growth level compared to the closed economy scmano. The indirect impact is reflected in the effect that trade openness has on the steadystate levels of physical and human accumulation (as indicated in table 2), and hence on the parameter coefficients for the physical and human capital accumulation. On the other hand, the direct impact of trade openness on the longrun level of income per capita is indicated by the parameter coefficients of the degree of trade openness for agriculture and nonagriculture trade activities; where open economies tend to grow faster than closed economies other things given1s. In addition, as technology change is endogenized through the promotion of trade openness, open economies are able to achieve different longrun steadystate level of income per capita as trade openness factor vary. This particular feature of endogenous technological change differentiates the Proposed BarbozaDicks model from the closed economy Solow model the MRW model and the KLV open economy growth model with exogenous technological change. To stress the importance of the last paragraph's theoretical implications Tables 2 and 3 outline three relevant differences between the closed and open economy specification of the Neoclassical Growth Models. In this regard, the first difference is that the longrun steadystate level of income per capita is always larger in the open economy model. Thus, allowing open economies to achieve larger steadystate levels of income per capita and greater longrun rates of growth of income per capita toward a given steadystate level. This result is particularly interesting because it suggests that a lower level of capital accumulation (human and physical) is needed in the open economy compared to the closed economy to achieve the same level oflongrun per capita output. 15 Other things given refer to the same level of domestic savings, same rate of depreciation, and same level of technological transfer. 66 The second implication is that in the open economy model lower levels of domestic saving are associated with larger levels of per capita output growth. This is possible, because the productivity of physical and human capital is enhanced as a result of the process of technology transfer associated with the promotion of international trade openness according to a comparative advantage behavior. Thirdly, as trade factors vary, endogenized technological change allows economies to achieve different steadystate levels of income per capita and physical and human capital. This particular implication of the expanded model is not possible in the closed economy model with exogenous technological change. Therefore, this study argues that by endogeni:zing technological change through the degree of trade openness promotion, the model provides evidence to close the gap to allow for endogenous changes in steadystate levels of income per capita which is not possible in the closed economy Solow model. 67 CHAPTER IV METBODSANDPROCEDURES Expected Results This study estimates equation 41, by using a crosssection timeseries model. The model detennines the effects of human and physical capital accumulation and agricultural and nonagricultural trade openness on income per capita. Easterly et al. point out that combining timeseries with crosssection data is necessary because the growth perfonnance of LDCs shows substantial variation over time. Moreover, it is possible to capture any countryspecific effects. Second, it allows us to expand the sample size. Further, to appropriately estimate the model in equation 41, the model assumes In A(0) =a + E, where a is a constant and E is a countryspecific shock. In addition t is assumed to be equal to zero. In terms ofthe empirical estimation, this redefines the model of equation 41 as (42) I Xa Xna InGNPPC =ao +aJ InL +a2 In +a3 InSchoo/ +a4 In +asln+ 6' Q Q Q 68 where ao IS a constant and aI, a2, a3, a4, a~ are the parameters to be estimated. The dependent variable in equation 43 In( ~) is approximated by the natural logarithm of the per capita Gross Domestic Product and it is defined as InGNPPC. Per capita income is defined as the Gross Domestic Product in constant 1987 US $ divided by total population. This allows to have a relative comparable unit of measure for income per capita across all countriesl6 . To approximate the natural logarithm of the rate of population growth, In(n) in equation 43, (assuming that g+8 are constant) this study uses the natural logarithm of the labor force, InL. Labor force is defined as the "economically active" proportion of total population that is classified from 14 to 65 years of age. The natural logarithm of the savings invested in physical capital, In(st), is approximated by natural logarithm of the ratio of gross domestic investment to total output, In( ~) .Investment corresponds to total gross investment l ? and output is defined as the Gross Domestic Product. Gross investment and Gross Domestic Product are defined in domestic currency for each country and then a ratio is calculated to make data across countries comparable. The natural logarithm of the savings invested in human capital, In(sh), is approximated by the secondary enrollment ratio, InSchool. The secondary enrollment ratio is defined as the 16 The author recognizes that per capita income as defined in this study presents significant problems to correctly compared to actual purchasing power of individuals across nations. However, per capita income is the only available cross section time series data useful to conduct this study. Some of the major problems while comparing per capita income across countries are that "informal" sectors and other relevant economic activities in developing countries are not recorded in the traditional definition of Gross Domestic Product. In addition, differences in real exchange rates are not considered when transfonning data from domestic currency to constant US $. 69 ratio of gross enrollment of all ages at secondary level as a percentage of children in the country's secondary school age group, including pupils enrolled in vocational or teachertraining secondary schools. The natural logarithm of the income proportion spent on agricultural trade openness, In(S",a) , is approximated by the natural logarithm of the ratio ofnonfuel primary exports and imports to total output, In( ~) . According to the World Bank Database (Stars) the classification corresponding to nonfuel primary exports plus imports include commodities in SITC revision 1, Section 0, I, 2, 4, and Division 68 (food and live animals, beverages and tabacco, inedible crude materials, oils, fats, waxes and nonferrous metals). Finally, the natural logarithm of the income proportion spent on nonagricultural trade openness, In(sxna ), is approximated by the natural logarithm of the ratio of all other exports and imports18 to total output, In( X~Q) . All other exports plus imports include fuel and manufactured goods. The fuel category includes SITC revision ] Section 3 which incorporates mineral fuels and lubricants and related materials. While manufactured goods cover SITe revision 1, Sections 5 through 9 (chemicals and related products, basic manufactures, machinery and transportation equipment, other manufactured articles and goods not elsewhere classified, excluding Division 68). The QJ coefficient in equation 42 corresponds to a + fJ + () + Jr in equation 41, Ia fJ()Jr and it represents the effect of population growth on per capita output. As the Solow 17 Gross Domestic Investment is defined as the sum of gross domestic fixed investment and the change in capital stocks. 18 AU other exports and imports are calculated as total exports plus imports minus exports plus imports of nonfuel primary goods. 70 model predicts per capita output growth depends negatively on the rate of growth of population. The magnitude of 01 is expected to be larger in absolute tenns than the one estimated by Mankiw, Romer and Weil, because it incorporates the effects that trade openness on agriculture and nonagriculture has on population growth. In practical tenns, the numerator is larger and the denominator is smaller than the one presented by Mankiw, Romer and Weil in equation 19. The second coefficient 02 corresponds to a lapOlr in equation 41 and it represents the effect that physical capital has on overall output growth. This coefficient is expected to be positive in sign. This dissertation supports the idea that by including trade openness as a factor of production, the estimated impact of physical capital on output growth should be larger than the one reported in previous studies. At the practical level the numerator a remains invariant compared to previous estimations of the Solow model, however, the denominator incorporates the factor coefficients for trade openness in agriculture (8) and nonagriculture (n), resulting in a smaller value for the denominator and therefore a larger overall coefficient. The hypothesis to be tested is whether empirically this coefficient is larger once trade is included. Feder argues that factor productivity on the export sector is higher than productivity in the nonexport sector. If this is true then trade has a positive effect on physical capital productivity and therefore it should be reflected in the coefficient 02 as the model of equation 41 suggests. Empirical studies that determine the impact of export on per capita output growth report that there is a positive and statistically significant relationship between export growth and per capita output growth (Michaely; Balassa; Tyler; Kavoussi; Feder; Mbaku; 71 Moran~ Moschos; Ram~ and Barboza). In addition, these studies support the hypothesis that export growth enhances factor productivity, which is reflected in large values for estimated coefficients on physical and human capital as suggested in equation 41. This study provides an alternative theoretical approach to the exogenous neoclassical theory of economic growth with a feasible explanation why these empirical estimates may have larger values once export growth (or any trade measure as Renelt and Levine argue) is included as an explanatory variable of per capita output growth. One important result of this model is that even though the estimated parameters for the physical and human capital may be larger than the ones reported by Mankiw, Romer and Weil, there is still a possibility that the absolute value of the steadystate level of physical and human capital accumulation may be smaller if certain conditions on Su, S""", () and 7r are met. Edwards; and Knight, Loayza and Villanueva considers trade openness as a component of the technological factor (A) that only has affect on longrun output growth. This means that in the models of equations 19 and 20, empirical estimates of the coefficients for physical and human capital are not affected by the inclusion of trade openness, i.e. the factorinput elasticities remain invariant when comparing the closed and open economy models. On the other hand, the model developed in this study shows that trade openness has a positive affect on the magnitude of the parameters for physical and human capital, and a negative effect on the labor force growth parameter estimate. These theoretical implications are for the most part in accordance with the empirical evidence found in Michaely~ Balassa; Tyler; Kavoussi; Feder; Mbaku; Moran; Moschos; Ram; and Barboza. 72 The third coefficient a3 corresponds to fJ In equation 41 and it lafJBtr represents the effect that human capital has on overall output growth. Likewise, the coefficient for human capital is expected to be positive in sign. This study supports the idea that by including trade openness as a factor of production, the estimated impact of human capital on output growth is larger than the one reported in previous studies. The variation in the magnitude ofthe coefficient comes because of the reduction in the value of the denominator, where the value of the factor share of a labor augmented unit of technology, (la~()...1'C), is now smaller than in previous studies, (lafJ), resulting in a larger a3 coefficient. The hypothesis to be tested is whether empirically this coefficient is indeed larger once trade is included. The coefficient a4 is equal to B in equation 41 and it measures the lafJOtr effect that agricultural trade openness has on per capita output growth. According to Balassa~ Kavoussi~ Levine and Renelt; and Tyler, this coefficient should be positive. Furthermore, a4 should be larger, positive and statistically significant for low income developing countries whereas it should be either small or not statistically significant for middle and high income developing countries. The overall expected sign for a4 is positive. Finally, the coefficient a~ is defined as IapOtr in equation 41 and it measures the contribution of nonagricultural trade openness on output growth. For middle to high income developing countries a~ should be statistically significant and positively related to per capita output growth. The magnitude ofa~ is expected to be larger than the one for a4. Technology transfer and economies of scale tend to be larger on the nonagricultural sector compared to the agricultural sector (Balassa; Tyler~ and Kavoussi). 73 One interesting outcome of the model developed in equation 41 is that once trade openness is considered a factor of production and not a component of the technological factor (A), the steadystate levels of physical and human capital may be lower than in the closed economy model of equation 19. Further, the longrun steadystate level of income per capita growth is larger when trade openness is included than otherwise. The theoretical development of the Augmented Solow Model with Trade Openness in equation 41 suggests that a lower level of capital accumulation is needed to achieve the same level of longrun per capita output growth once trade openness is considered as a factor of production. Hence, an economy that is involved in international trade achieves a larger steadystate level of income per capita growth than an economy that does not trade, other things being equal. Countries that trade develop economies of scale, reduce unemployment, grow faster, and achieve higher levels of income per capita than countries under the same conditions that do not trade. Estimation Method and Misspecification Tests The model of equation 42 is initially estimated by ordinary least squares (OLS). Traditionally, economic research in the area of economic growth uses the OLS technique. OLS is thought to provide the necessary tools to empirically estimate this linear model. In this particular regard, McGuirk, Driscoll and Alwang suggest tests to determine the presence of misspecification errors for each of the classical OLS assumptions, I.e. normality, functional form, static and dynamic homoskedasticity, no autocorrelation, and parameter stability. Since, this study incorporates crosscountry data and it is estimated as a crosssection timeseries study by using four years average annual data only the 74 misspecification tests for normality, functional fonn, and static and dynamic homoskedasticity are performed. Four year averages of real Gross Domestic Product, the investmentoutput ratio, the labor force, education level, trade openness in agriculture, and trade openness in nonagriculture, are used as base data. McGuirk, Driscoll and Alwang recommend that tests on the classical OLS assumptions should be performed as much as one can, i.e. one should conduct as many misspecification tests as possible to improve confidence and power of statistical testing of economic hypothesis. In the case of this study, as mentioned before, the tests that will be performed are those for the normality, functional form, static and dynamic homoskedasticity. The no autocorrelation, and parameter stability assumption19 tests are not conducted. In general, misspecification tests are rarely seen in applied economic theory, especially when estimating the relationship between factors of production and overall economic growth. Whereas some crosssection studies test for the possibility of static heteroskedasticity, most do not conduct misspecification tests on the other relevant assumptions. If the appropriate misspecification tests are omitted then there is a large possibility that the empirical results are biased, inconsistent, and inefficient, which in tum results in a loss of power in the statistical tests. This study provides the results of the misspecification tests on the use of OLS for testing Neoclassical Growth Models in tables 5,7,9, 11, 14, 16, and 18. The analysis of the results of the tests are in the next chapter. According to McGuirk, Driscoll and Alwang to test the normality assumption, three different tests are applied, the kurtosis test, the skewness test, and the omnibus test. For the functional form the KolmogorovGabor polynomial (KG2), and the Regression 75 Specification Error Test 2 (RESET2), tests are applied. For static and dynamic homoskedasticity the RESET2 and White's heteroskedasticity test are used. Based on the results of Tables 5,7,9, 11, 14, 16, and 18, an alternative estimation method is used. At first instance, this study proceeds to use the POOLED estimation technique as described by Kmenta (1986 Section 12.2 pp. 616625) and implemented by the econometric software SHAZAM. The POOLED technique consists of a Generalized Least Square estimation that accounts for the existence of heteroskedasticity and autocorrelation across countries and time. The procedure as described in Kmenta (1986) is detailed as follows. The general assumptions about timeseries studies is that the error may present an autoregressive process but they need not to be heteroskedastic. On the other hand, a crosssection study assumes that error may be heteroskedastic but not necessarily autoregressive. When both processes are combined it is reasonable to assume that both heteroskedasticity and autocorrelation are present. Therefore, this study combines both assumptions to construct a crosssectionally heteroskedastic and timewise autoregressive model. The model specification indicates that: (43) where eI, indicates the presence of heteroskedasticity for each specific cross section. Furthermore equation 44 indicates that there is crosssectional independence. Finally equation 45 illustrates that there is an autoregressive process. 19 McGuirk et aI., present a complete description of all available misspecification test for Ordinary Least Squares, besides the ones that are performed in this study. 76 (44) (45) find consistent estimates for the variance covariance matrix, the ordinary least squares method is initially used to obtain consistent estimates of the ei,. These error terms are in turn used to estimate the Pi elements of the transfonned variance covariance matrix. To assure convergence the estimates of the Pi elements are confined to have a value within the range of {1,1} for any given sample size20 Thus, the initial observations are transformed by using the correlation estimates. The following specification is copied from Kmenta (1986, p. 619). The transformed variables are denoted by the superscript C·) as follows: (46) ~ =AX~ I + P2 X~, 2 +.. '+Pk X;, ~ + /I" " ". I. ." r" where y;,=~1_~,2 YI/ for t = 1, and Y,= Yir~' Y,,rl for t = 2,3, . ,T. In addition, the correspondent transformed explanatory variables are defined in the same manner as the dependent variable. The transfonnation of the vector of explanatory variables X in equation 46 is expressed as follows. 77 X/.k =JI ~,2 X il.k for t = 1, and X/.k =Xi/,k  ~j X,.H,t for t = 2, 3, ... , T Where k = 1,2, '" ,K, and i = 1,2, ... , N. As described in Kmenta, "The purpose of this transfonnation is to estimate el, from observations that are, at least asymptotically, nonautoregressive since estimated variances based on autoregressive disturbance are, in general, biased." (p. 620). Therefore, this procedure allows to obtain consistent estimators of P, and eli, and therefore consistent estimators of the variance covariance matrix. This finally allows to achieve maximum likelihood estimates. For the purpose of the empirical estimations of this study, it is assumed that the parameter P presents the same value for all crosssectional units21 . In other words, Pi = Pi =P for all i ,j = 1, 2, ... , N.22 Data Averages consisting of four years are used instead of annual data to avoid the problem of year specific characteristics and also as a tool to increase the size of the number of observati.ons compared to a pure crosssection study. Four year averages are used because it is assumed that within four years most policy effects or economic shocks will be absorbed by the economy. Further, by using four year averages it is possible to reduce large variation on annual data that are commonly presented in developing countries. For instance, it is not rare that income per capita suffers large variations from 20 Kmenta indicates that when the sample size is to small there is a possibility for Pi to have an estimated absolute value larger than 1. 21 Initial computations to calculate a convergence value for p for each crosssectional unit indicated that there were too few observations to successfully complete the convergence procedure. The alternative estimation required assuming the same value of p for an crosssectional units. 22 For a complete derivation of the estimation procedure for the POOLED technique see Kmenta (1986). 78 year to year In countries with an unstable political system. Also trade openness can fluctuate largely due to the imposition of tariff and nontariff barriers to solve temporarily balance of payments disequilibriums. This study assumes that by using four year averages most of this variation will be eliminated. If a crosssection timeseries study is conducted without using annual averages then dummy variables should be included if one wants to account for year specific events in each country. Yet, explaining yearspecific events requires detailed information that is rarely available in most developing countries. To detennine the contribution that each factor of production has on overall per capita output growth and how they affect productivity of others factors, five different regressions are perfonned. Estimation 1 includes the average annual investmentoutput ratio, and the annual average labor force as explanatory variables of income per capita. Estimation 2 includes the average annual investmentoutput ratio, the secondary enrollment rate, and the average annual labor force as explanatory variables of the average annual per capita GDP. To account for the presence of international trade, estimation 3 includes the average annual degree of trade openness as explanatory variable of per capita GDP, in addition to those included in estimation 2. Estimation 4 decomposes the degree of trad
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Title  Augmented Neoclassical Growth Model with Human Capital Accumulation and Agricultural and Nonagricultural Trade Openness 
Date  19971201 
Author  Barboza, Gustavo Adolfo 
Document Type  
Full Text Type  Open Access 
Note  Thesis 
Rights  © Oklahoma Agricultural and Mechanical Board of Regents 
Transcript  AN AUGMENTED NEOCLASSICAL GROWTH MODEL WITH HUMAN CAPITAL ACCUMULAnON AND AGRICULTURAL AND NONAGRICULTURAL TRADE OPENNESS By GUSTAVO ADOLFO BARBOZA Master of Science Oklahoma State University Stillwater, Oklahoma 1994 Submitted to the Faculty ofthe Graduate College of the Oklahoma State University in partial fulfillment of the requirements for the Degree of DOCTOR OF PIDLOSOPHY December, 1997 AN AUGMENTED NEOCLASSICAL GROWTH MODEL WITH HUMAN CAPITAL ACCUMULATION AND AGRICULTURAL AND NONAGRICULTURAL TRADE OPENNESS /' Thesis A:oviser ii ACKNOWLEDGMENTS I sincerely wish to thank my adviser Dr. Michael Dicks for all his help, patience, and advise throughout my doctoral program in Agricultural Economics at Oklahoma State University. Dr. Dicks' confidence in my work and his continuous technical and financial support made this doctoral program possible. I will always thank you for all your time and support. My very special thanks to committee members Dr. Francis Epplin, Dr. David Henneberry and Dr. Gerald Lage for all their support, suggestions, and cooperation in helping me to finish this study. I thank my parents, Carlos and Fanny Barboza, for they have always provided an example of honesty, love, commitment, and dedication. Without them I would not have been able to accomplish most of what I have now. Thank you to my parents for they have believed in me throughout these years. Thanks to my brothers and sisters, specially Fanny Maria whom I always will love. I thank my wife, Sandra, who is the inspiration of my life. Her words, time, support, and example are the greatest gift God has ever given me. She always stands by my side giving me the strength I need. Thanks Sandra for you have always believed in my goals and my work. There is no word to express all my thanks to my wife for her unconditional support throughout these years, I love you Sandra. To my daughters, Maria Sofia and Monica Maria, for they have fulfilled our marriage and have brought happiness iii and joy to our family. My special dedication of this doctoral dissertation goes to my family, Sandra, Maria Sofia and Monica Maria. I want to thank the people at the Office for International Programs at the Universidad of Costa Rica for their financial support throughout my doctoral program. Thank you to the people at the Department of Economics at the Universidad of Costa Rica for they have also provide the means for me to complete my degree. I would like to thank also the people at the Great Plains Agricultural Policy Center for helping and supporting me throughout my doctoral program. Special thanks to Nolan Quiros and Edgar Pebe, for their comments and encouragement to complete my work. To them I wish the best in their personal life and professional careers. iv TABLE OF CONTENTS CHAPTER 1 1 INlRODUCTION 1 CHAPTER II ...............••...........•.......•........••............•...•.•...•.•......•••....•....••••....•.......•.........•...............•.. 14 LITERATURE REVIEW AND CONCEPTUAL FRAMEWORK 14 Literature Review 14 Conceptual Fnunework 18 Neoclassical and Structural Growth Models 18 Endogenous and Exogenous Growth Models 22 The Solow Model. 23 Adding HumanCapital Accumulation to the Solow Model 26 Trade Openness and Technological Transfer in the Solow Model Framework 29 CHAPTER IlL 33 THEORETICAL MODEL 33 Solow Model with Human Capital Accwnulation and Trade Openness 33 Nonnegativity ofXa and Xna 36 Steadystates 37 Physical CapitaL 39 Hwnan Capital 45 Agricultural Trade Openness 51 Nonagricultural Trade Openness 56 Income Per Capita 60 CHAPTER IV 68 METIIODS AND PROCEDURES 68 Expected Results 68 Estimation Method and Misspecification Tests 74 Data 78 CHAPTER V 82 EMPIRICAL RESULTS 82 OLS Estimations and Misspecification Tests 82 Overall Sample 87 Low Income Countries 91 Middle Income Countries 96 High Income Countries 101 Latin America.................................................................................................. .. 108 African Countries 112 Asian Countries 116 POOLED Estimations 122 Overall Sample 122 Low Income Countries 127 Middle Income Countries 132 v High Income COWltries 136 Latin America COWltries 140 African COWltries 144 Asian COWllries 148 CHAPTER VI 154 CONCLUSIONS AND RECOMMENDATIONS 154 REFERENCES 158 APPENDIX 161 VI LIST OF TABLES Table 1. Alternative Views of Growth 21 2. Comparison of SteadyState Conditions under Alternative Growth Models 64 3. Conceptual Comparison of Alternative Growth Models 65 4. OLS Estimated Results of Alternative Neoclassical Growth Models (Full Sample) 84 5. Estimated Results ofthe Misspecification Tests on the OLS Assumptions for the Augmented Neoclassical Growth Model with Human Capital and Trade Openness on Agricultural and Nonagricultural Goods (Full Sample) 91 6. Low Income Countries OLS Estimated Results of Alternative Neoclassical Growth Models 93 7. Low Income Countries Estimated Results of the Misspecification Tests on the OLS Assumptions for the Augmented Neoclassical Growth Model with Human Capital and Trade Openness on Agricultural and Nonagricultural Goods 96 8. Middle Income Countries OLS Estimated Results of Alternative Neoclassical Growth Models 98 9. Middle Income Countries Estimated Results of the Misspecification Tests on the OLS Assumptions for the Augmented Neoclassical Growth Model with Human Capital and Trade Openness in Agricultural and Nonagricultural Goods 10 I 10. High Income Countries OLS Estimated Results of Alternative Neoclassical Growth Models 103 II. High Income Countries Estimated Results of the Misspecification Tests on the OLS Assumptions for the Augmented Neoclassical Growth Model with Human Capital and Trade Openness in Agricultural and Nonagricultural Goods 106 12. OLS Estimates of Alternative Growth Models by Income Group with GDP per capita as Dependent Variable 107 13. Latin America OLS Estimated Results of Alternative Neoclassical Growth Models 110 14. Latin America Estimated Results of the Misspecification Tests on the OLS Assumptions for the Augmented Neoclassical Growth Model with Human Capital and Trade Openness in Agricultural and Nonagricultural Goods 112 vii 15. Africa OLS Estimated Results of Alternative Neoclassical Growth Models 114 16. Africa Estimated Results of the Misspecification Tests on the OLS Assumptions for the Augmented Neoclassical Growth Model with Human Capital and Trade Openness in Agricultural and Nonagricultural Goods 115 17. Asia OLS Estimated Results of Alternative Neoclassical Growth Models 117 18. Asia Estimated Results of the Misspecification Tests on the OLS Assumptions for the Augmented Neoclassical Growth Model with Human Capital and Trade Openness in Agricultural and Nonagricultural Goods 120 19. OLS Estimates of Alternative Growth Models by Region with GDP per capita as Dep Variable ....... 121 20. POOLED Estimated Results of Alternative Neoclassical Growth Models (Full Sample) 124 21. Low Income Countries POOLED Estimated Results of Alternative Neoclassical Growth Models .. .128 22. Middle Income Countries POOLED Estimated Results of Alternative Neoclassical Growth Models 131 23. High Income Countries POOLED Estimated Results of Alternative Neoclassical Growth Models ... 135 24. POOLED Estimates of Alternative Growth Models by Income Group with GDP per capita as Dependent Variable 141 25. Latin America POOLED Estimated Results of Alternative Neoclassical Growth Models 142 26. African Countries POOLED Estimated Results of Alternative Neoclassical Growth Models 147 27. Asian Countries POOLED Estimated Results of Alternative Neoclassical Growth Models 150 28. POOLED Estimates of Alternative Growth Models by Region with GDP per capita as Dependent Vari~ble 153 viii LIST OF FIGURES Figure 1. Exports plus Imports to GDP Ratio by Category 7 2. Exports to GDP Ratio by Category 10 3. Imports to GDP Ratio by Category 11 ix CHAPTER I INTRODUCTION Over 200 years ago Adam Smith and David Ricardo elaborated on the role that international trade has on economic growth. Smith and Ricardo emphasized the important economic gains that trade specialization, according to comparative advantage, has on augmenting overall consumption possibilities and therefore overall social welfare. Consumption and production gains result from reallocating resources to their best alternative uses. Implicitly, Ricardo and Smith stressed the importance that free trade, based on comparative advantage has on factors' productivity. In this regard, the more a country specializes domestic production and participates in international trade the larger the gains derived from this process, but only if international trade is conducted according to a comparative advantage pattern. By specializing in the production of goods a country has the comparative advantage in producing and trading in international markets, resource productivity is maximized, economies of scale develop, unemployment is reduced, and overall production and consumption increases. 1 Perhaps one of the most important issues that relate to the process of economic policy is the determination of the sources of economic growth. Throughout history economists and policy makers have stressed the importance of setting economic instruments and goals to achieve higher levels of economic growth. This has been especially true in the last fifty years, where the emphasis of international trade and economic growth policy has focused on increasing the rate of growth of total output. Meier states "conditions were higWy favorable during the 195 Os and 1960s until the slowing down of growth in the world economy after 1973. The earlier two decades were unique for the high rate of growth in the more developed countries  a historical record period  and for the growth in world trade. The demand for imports was high and rising in the more developed countries (MDCs) and the high growth rate of the MDCs fostered trade liberalization and weakened the case for protection" (p. 408). Therefore the emphasis on commercial policy focused on the gains that trade liberalization brought about. Yet, a major concern for policy makers in developing countries stressed the fact that countries that specialized in the production and commercialization of industrial goods tended to outperform those countries that specialized and trad,ed primary products. According to Prebisch, countries that produced and exported primary commodities faced a deterioration in the terms of trade, resulting in lower rates of economic growth compared to developed countries. Prebisch argued that the centerperiphery relationship occurred such that the terms of trade deteriorated in the periphery countries which specialize or produce primary goods. Meier added that "Prebisch suggested that these (periphery) countries should expand their manufacturing industries oriented toward domestic markets. 2 The purpose was to be served by industrial protection that was said to bring additional benefits through improvements in the terms oftrade" (Meier, p. 395). Nevertheless, as mentioned before, these rapid rates of growth in international trade started to slow down after a few years in the early 1970's. Among the reasons that caused this slow down in the rate of growth of international trade are higher priced oil products and changes in commercial policy in developing countries. Developing countries promoted different approaches that emphasized the use of tariffs and nontariff barriers to trade as the main strategy to achieve higher levels of income per capita growth. Indeed, the development and promotion of an industrial sector, as the engine of growth, was seen as the main goal ofdeveloping countries. Within the context of international trade and economic growth policy import substitution was thought to be a feasible way to increase output growth. Import substitution focuses on substituting domestic production for imports of primary and manufactured goods. According to Meier, in the first stage developing countries substitute the consumption of imported primary goods with domestic production. Balassa called this stage the "easy" stage of import substitution. Meier states that "Secondstage import substitution involves the replacement of intermediate goods and producer and consumer durables by domestic production.... [G]iven the relative scarcity of physical and human capital in developing countries that complete the first stage of import substitution, developing countries are at a disadvantage in the manufacture of highly physical capitalintensive intennediate goods and skillintensive producer and consumer durables. In limiting the scope for the exploitation of economies of scale, the relatively small size of their national markets also contributes to high domestic costs. At the same time, net 3 • foreign exchange savings tend to be small because of the need for importing materials and machinery" (p. 396). Nevertheless, developing countries that promoted import substitution failed to consider the positive impact of trade expansion on economic growth, measured through the increase in factors' productivity resulting from the reallocation of resources to their best alternative use. In the framework of the twogap modell, export expansion releases the foreign exchange constraint, increasing the rate of capital formation, and enhancing the growth of factor productivity. Hence, determining the impact of factors of production on the level of economic growth is of great interest in terms of economic growth policy in developed and developing countries. This issue has been heavily addressed in the economic literature, yet few studies have focused on the decomposition of trade flows between agricultural and nonagricultural trade goods and the effect of each on factor accumulation and productivity growth. In the last twenty years an increasing proportion of the General Agreement of Tariffs and Trade (GATT), have concentrated on the transformation, reduction and elimination of trade distortions. The fonnation of trade blocks such as the North American Free Trade Agreement (NAFTA), Mercado Comun Suramericano (MERCOSUR), and others, have developed to eliminate trade distortions. These trade distortions are grouped within the categories of tariffs, quotas and nontariff barriers, that directly or indirectly affect the domestic production and consumption, and the domestic and international trade of agricultural and nonagricultural goods. To increase the importance of this trade liberalization and globalization process, agricultural trade has only recently been addressed 1 Twogap models assume that developing countries are constrained by the capacity to generate domestic savings to finance investment and by the availability of foreign exchange to obtain foreign goods and services that are complementary to those available at home (Gerald Meier). 4 in trade liberalization talks and agreements. The Uruguay Round of the GATT and the North American Free Trade Agreement establish the first steps for the mutual liberalization of primary and agricultural goods as well as services. The promotion of trade liberalization has reached even those commodities once considered too sensitive to be subject to negotiation. Economic research has studied the sources of economic growth. The most widely used economic growth model is the Solow Neoclassical Growth Model. The Solow Growth model focuses on the effect of labor growth and capital accumulation on the steadystate level of income per capita. Empirical estimations of growth for developing countries found that labor is abundant and capital is the single most important factor of production. Development economists have also studied the impact that export growth has on overall factor productivity and output growth. In most cases, empirical studies give support to the hypothesis that export promotion generates economic growth (Michaely; Balassa; Tyler; Kavoussi; Feder; Mbaku; Moran; Moschos; Ram; and Barboza). While export promotion may mean freer trade, it may also refer to the protection of any particular economic sector through the use of commercial policies such as tariff and nontariff barriers. Trade barriers find political support from the argument that developing industries need a certain protective period before they can be competitive in the international markets, i.e. it takes time before industries can develop a comparative advantage. Meier states "to the extent that the domestic production of these commodities generates external economies in the fonn of labor training, the development of enterpreneurship, and the spread of technology, there is an argument for moderate infant industry protection or promotion" (p. 395). 5 Yet, there is still a major gap when one wants to understand why countries achieve different steadystate levels of income per capita. New developments in economic theory such as the convergence hypothesis assume that countries that initially start off from lower levels of income per capita tend to grow faster than otherwise. In order to attempt to explain these observable differences in income per capita growth rates across developing and developed countries, human capital accumulation has been introduced as an important determinant (Mankiw, Romer and Weil). Technological transfer has also been considered as playing a major role in detennining the longrun level of income per capita. (Edwards; Knight, Loayza and Villanueva). The economic development literature has focused on determining the impact that trade openness has on output growth through the transfer of technology and through the learning by doing process (Edwards; and Knight, Loayza and Villanueva). Edwards; and Knight, Loayza and Villanueva assume that trade openness affects the longrun level of output growth through the transfer of technology but it does not have any effect on the steadystate level of physical and human capital accumulation and income per capita, because openness is considered only as a technological shifting factor. Trade openness is the measure that relates trade flows to output and is commonly defined as the ratio of exports to total output. The overall results of empirical studies support the hypothesis that the greater the trade openness, the greater the rate ofgrowth of output. Levine and Reneh state that this result is not surprising since similar results can be obtained by using any other trade measure such as imports or total trade. Even though previous studies agree on the importance that trade openness has on output growth and hence on income per capita level, they do not differentiate between the trade flows of primary and manufactured 6 goods, a major Issue when trying to determine the sources of economic growth In developing countries. The decomposition of trade flows between agricultural and non agricultural goods is important for at least three reasons; 1) to determine the sources of economic growth and to determine which countries are likely to be the gainers or losers of moving to a larger degree of trade openness; 2) to understand the effects of trade openness on factor productivity, and 3) to better understand the tradeoffs between international trade and economic growth in order to redirect overall economic policies. Figure 1. Exports plus Imports to GOP Ratio by Category 0.60 ,, 0.50 0.40 0.30 0.20 0.1a L.....l...J'...J..'_'...J..'_'''_'''_'''_~....l..____'__....... 1973 1975 1977 1979 1981 1983 1985 1987 1989 1991 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 Tolal Nonluel Primary Other  <> * Ratios are simple averages for a sample of 62 developing countries. Figure 1 illustrates three alternative measures of trade openness. The first measure is the ratio of total exports plus total imports to Gross Domestic Product for a sample of 7 62 developing countries2 . The second and third measures are a decomposition of the first measure by category of products. Hence, the second measure illustrates the relative importance of nonfuel primary trade as a ratio of Gross Domestic Product. Finally, the third measure indicates the importance of all other trade as a ratio of Gross Domestic Product. International trade represents approximately 50 percent of the Gross Domestic Product for the sample of 62 developing countries under study. Thus, intemational trade is an important determinant of output growth and factor productivity in developing countries. The importance of international trade peaked in 1980, when trade represented approximately 56% of Gross Domestic Product for the sample of countries. International trade declined sharply in the first half of the 1980's to a level of 46% in 1986 in terms of Gross Domestic Product. This reduction in international trade coincides with the generalized balance of payments crisis of most developing countries on the early 1980's. In general, the decline in international trade resulted from a reduction in the level of trade of nonprimary goods. The decade of 1970' s was characterized for an excess supply of financial resources in the international markets. Most of this excess supply can be attributed to the high oil prices of the early 1970' s. The easy and large availability of financial resources made it easy for developing countries to borrow large amounts of foreign exchange at lower interest rates that financed the increasing trade of nonprimary goods. Developing countries were unable to continue financing the increasing amount of nonprimary imports which can be seen by the decrease in the relative importance of 2 A complete list of the 62 developing countries is provided on Table 1 of the Appendix. 8 nonprimary trade as a proportion of Gross Domestic Product. At the same time, Figure I illustrates how the total amount of trade in nonfuel primary goods has decreased constantly during the last 20 years. This trend may be explained by two factors at least. First, developed countries have become less dependent in terms of nonfuel primary production and secondly developing countries have changed their economic growth strategy to the promotion of nonprimary good exports. Figure 1 provides a clear illustration that there has been a substantial change in the composition of international trade in developing countries. The question that remains unanswered is whether this change in the trend of international trade in developing countries has resulted in an enhancement offactors' productivity and increased real income per capita. The sources of growth in international trade are further decomposed between exports of nonfuel primary and other goods; and imports of nonfuel primary and others goods in figures 2 and 3, respectively. Figure 2 illustrates the ratios of exports as a proportion of Gross Domestic Product to provide more information on the sources of growth of international trade in developing countries. On the other hand, figure 3 illustrates imports as a proportion of Gross Domestic Product. 9  Figure 2. Exports to GOP Ratio by Category 025 ., 020 015 010 0.05 1973 1975 1977 1979 1981 1983 1985 1987 1989 1991 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 Total Nonluel Pnmary Other  <> :*Ratios are simple averages for 62 developing countries Perhaps the most relevant fact of figure 2 is that developing countries have transformed their export structure in the last twenty years, toward a more industrialized system. Other exports have increased as a proportion ofGDP throughout the period under study, but shows the sharpest increase over the last six to seven years. Furthermore, developing countries are still heavily dependent on the amount of imports of industrialized goods as illustrated in figure 3. Nonfuel primary goods, as a proportion of GDP, have remained roughly constant over the last twenty years. This result is not surprising since most developing countries tend to fulfill their own domestic demand with domestic production. The largest variability in imports, is due to the variability of other imports as shown in figure 3. After the economic crisis of the first half of the 1980s there has been a tendency to increase the amount of other imports. This seems to be the result of two complementary factors; reductions in the levels of tariffs and nontariffs barriers, and more 10  stable economies growing at higher rates compared to the first half of the 1980s. Finall even though international trade has been growing since the mid 19808, the total level of exports plus imports as a ratio of Gross Domestic Product is equal to those record levels of the late 1970s and early 1980s. Figure 3. Imports to GOP Ratio by Category 0.35 0.30 025 / 0.20 0.15 0.10 0.05 0.00 L....L..L_.l....l.L_L...LLl_.LL.....L_L._Ll_.LL.....L_LJ 1973 1975 1977 1979 1981 1983 1985 1987 1989 1991 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 TolllI Nonfuel Primary Other . <> ~ Ratios are simple averages for 62 developing countries The change in structure of international trade illustrated in Figures 1, 2, and 3 raises the question of whether international trade is important for developing countries or not. Empirical studies of the economic growth and economic development argue in favor of export promotion as a source of factor productivity and output growth. However, these studies do not determine the sources ofgrowth by category of goods. 11  This study determines the sources of economic growth by using an augmented neoclassical growth model with human capital accumulation and trade flows between agricultural and nonagricultural goods. The research question is how can the degree of trade openness in agricultural and nonagricultural markets reduce resource misallocation, increase the productivity of factors of production, and increase the rate of growth of total output in developing countries? The overall objective of this study is to determine the factors that affect the rate of growth of total output (economic growth) and reduce resource use misallocation in developing countries. The specific objectives are to: 1. Determine how trade openness (free trade) in agricultural and nonagricultural sectors affects the productivity oflabor, physical capital, and human capital; 2. determine the contribution of agricultural and nonagricultural trade flows on overall economic growth; and 3. determine to what extent free trade (trade openness) in agricultural and nonagricultural markets promote economic development in developing countries. This study is divided into six sections. The first section reviews the theoretical and empirical literature relating to economic growth. Next a conceptual framework is developed to support the development of the Augmented Solow Model with Trade Openness. The methods and procedures chapter provides the necessary infonnation about data, model estimation, statistical testing, and expected results. The results chapter provide an extensive analysis ofthe empirical results first estimated by using OLS and later reestimated by using a POOLED model. This chapter also provides alternative estimation by region and by income group to determine more precisely the sources of growth in 12  developing countries. Finally, the conclusion and recommendations chapter highlights the more important remarks of the study and provides the limitations and possible solutions in terms of future research. The overall results suggest that trade openness enhances output growth in developing countries. In addition, at initially low income per capita levels agricultural openness tends to be more important than nonagricultural openness. However, as income per capita rises this tendency reverses. No definite conclusion is found in terms of region significant effects in terms of income per capita growth. 13 CHAPTER II LITERATIJRE REVIEW AND CONCEPTUAL FRAMEWORK Literature Revjew The literature on economic development is robust with studies focusing on the relationship between factors of production and total productivity. The Solow model of economic growth has been the main tool used by economists in the last three decades to determine the relationship between factors of production and output growth. Solow presents a decomposition of factors of production between physical capital accumulation and labor force. The rest of output growth is explained by total factor productivity and is considered a residual. Two different approaches have been used to measure factor contribution to output growth, the Neoclassical Accounting Growth method (NAG) and econometric based studies. The NAG method assumes that the rate of growth of output can be decomposed as the rate of growth of inputs plus a residual that is considered total factor productivity (Chenery, Robinson and Syrquin). Assuming constant returns to scale the NAG method assumes that the sum of capital and labor shares must equal one (Solow). These factor 14 shares are obtained from the data itself, and then by using the historical growth rates of inputs, the total factor productivity is obtained as a residuae. On the other hand, econometric based studies estimate the contribution of factors of production to economic growth by using a simple neoclassical production function. Totally differentiating the production function it is possible to express the rate of growth of output as a function of the rates of growth of inputs. Estimated parameters are the output elasticities with respect to factors of production. Following the fonnulation that previous studies have used4 it is possible to express the factors' contribution to economic growth as follows: (1) where Q is the real Gross National Product, K is the capital stock, L is the labor force, and t is time. Assuming that the elasticities of output with respect to the factors of production are constant and that technical change is Hicksneutral with a constant rate, equation 1 can be rewritten in tenns of rates of growth by total differentiating with respect to time (dividing through by equation]). Then equation 2 is: (2) y=a+pk+~l 3 The neoclassical growth accounting methodology is used as a accounting method and it does not include any econometric estimating. Data is adjusted so the sum of the factor shares equals one. Econometrics application of this technique have been done allowing for the possibility of constant, decreasing, and increasing returns to scale. See Chenery et al (1986) p. 29. 4 The approach foHowed here is the same as explained in Feder (1982), De Gregorio (1992), Mbaku (1989), Kavoussi (1984), Ram (1985), Moschos (1989), Knight et al (1993), Tyler (1981), and Moran (1983). 15 where y is the rate of growth ofoutput, k is the rate of growth of capital stock, I is the rate of growth of the labor force, and fJ and 8 are the elasticities of output with respect to capital and labor, respectively. Measuring the rate of growth of the capital stock may not be possible for most developing and developed countries due to a lack of data. As an alternative Mbaku; Kavoussi; Tyler; De Gregorio; and Moschos have approximated the rate of growth of the capital stock by using the investment rate, under the assumption that this corresponds to the growth rate of capital5 . A more appropriate approximation of the model can be obtained by further approximating the rate of growth of the capital stock by the investmentoutput ratio as done by Ram; Feder; and Mbaku: (3) where 8Q/8K is the partial derivative of output with respect to the capital stock, KlQ is the capital stockoutput ratio, and dKIK is the rate of growth of the capital stock. Then, replacing dK by 1, where 1 is the level ofinvestment, results in, (4) I y=a+2+81 Q where A. is the marginal physical output of capital. More recent studies such as Michaely; Balassa; Ram; Moschos; Tyler; Kavoussi; Feder; Mbaku; Moschos have argued that economic growth may also depend on the rate ofgrowth of total exports, assuming that exports can be considered a factor of production 5 Implicitly this approach assmnes that the capitaloutput ratio is constant not only through time but also across countries. However, this approximation is not considered appropriate since the investment rate is the second derivative of the capital stock and only expresses the rate of chan.ge of the change in the capital stock. 16  that enhances the productivity of capital and labor by releasing the foreign exchange constraint, taking advantages of economies of scale, and reducing resource use misallocation by reallocating resources based on their comparative advantage. Michaely and Balassa used a Spearman rank correlation method and found that there is a positive relationship between export growth and economic growth. To incorporate the rate of growth of exports as an explanatory variable of output growth, a new variable is included in equation 4. The resulting equation is (5) where x is the rate ofgrowth of exports and the rate of technological change is assumed to be a linear function of the growth rate of exports expressed as '1/. Ram states that if the model specification is reasonable, '1/ should indicate the direction and magnitude of the impact of export expansion on economic growth. Empirical estimations of equation 5 for developing countries reveal that capital accumulation is the most important factor of production, Jabor force is considered to be abundant6 , and exports have a positive and statistically significant effect on the output growth. In the case of developing countries, export promotion is an appropriate tool to promote rapid economic growth. Feder states that the social marginal productivity is higher in the export sector than in the nonexport sector. Studies by Kavoussi; Tyler; and Balassa, focus on the importance that export promotion, both of primary and manufactured goods, have on output growth. Kavoussi; and Tyler argue that the promotion of exports can be decomposed between primary goods 17  and manufactured goods. Furthennore, at initial or low levels of economic development the promotion of both primary and manufactured goods increase economic growth. Beyond a threshold income level export promotion of primary goods does not contribute much more to economic growth, whereas the promotion of manufactured goods increases the rate ofgrowth ofincome per capita. (Balassa; Tyler; and Kavoussi). Conceptual Framework Neoclassical and Structural Growth Models In the second half of the current century, economic development discussions have been focused on analyzing alternative approaches that attempt to determine the sources of economic growth. The discussions have attempted to discover why there are different levels of income per capita between developed and developing countries and explain why similar countries achieve different levels of income per capita in the long run. The anatysis used to lay the ground work for the discussions use models that study the difference between open and closed economy models, developed and developing countries, growth and equity, export promotion and import substitution. In this sense there has been a substantial use of alternative techniques and/or procedures to accurately estimate those sources of growth. In tum, development economists are concerned with finding explanations that define how developing countries may increase income per capita and at the same time assure macroeconomic stability. The most common techniques used by economists to evaluate the process of economic development are multisector models such as the inputoutput model, project 6 Labor force is abundant in terms of marginal productivity. Marginal productivity is either close to zero 18  evaluation, linear and nonlinear programming models, and computable general equilibrium models. Among the major concerns of policy makers and economic development specialists are the tradeoffs among economic growth, income distribution (equity), balance of payments stability, exchange rate parity, inflation, unemployment, capital accumulation, and population growth In some particular cases the debate seems to become even more complicated when alternative economic variables can be defined and/or used either as policy tools (instruments) or macroeconomic goals (target)7. Numerous perspectives exist on how to address the problem of underdevelopment and how to determine the sources of growth to elaborate alternative policy scenarios to stimulate a sustainable process of economic growth in developing countries. However, despite the emphasis on alternative estimation tools and alternative economic approaches, a vast majority of economic research related to economic growth has been circumscribed to the analysis of either neoclassical growth models or structural growth models. Within the framework of neoclassical growth models the main source of economic growth comes about through physical capital accumulation. In the context of the single neoclassical growth model, the steadystate income per capita is achieved when the rate of growth of physical capital is equal to output growth. The conclusions derived from the neoclassical framework were very useful in explaining why developing countries achieve lower levels of income per capita compared to developed countries. In this regard, empirical evidence shows that physical capital is scarce in developing countries, and labor or equal to zero. 7 Some example of economic variable that may be defined either as policy tools or macroeconomic goals are the exchange rate, the inflation rate, government spending, and so on. 19  has a very low marginal productivity in developing countries8 . Criticisms of neoclassical growth models emphasize the fact that within the context of the neoclassical models the remaining or the unexplained variability of output growth is a residual. Meier states that "the residual was initially thought of as a coefficient of technical advance, but it was quickly recognized to be a composite of the effects of many different sources." As mentioned in the previous chapter some of these sources of output growth came about through the improvement in the quality of labor, exploitation of economies of scale, reallocation of resources to best alternative uses, and economic gains derived from the international trade process. Complementary to the analysis of neoclassical growth models, the structural approach to economic growth assumes that economic growth is the result of a transformation of the production structure that takes advantage of technological changes. In the structural approach, technological change is not assumed exogenous, rather it is endogenized as a function of other factors of production. Structural economists consider as neoclassical economists do, that physical capital accumulation is an important factor to achieve economic growth. However, structural economists stress the importance that the technological component of the production function has through the process of learning by doing and technology transfer. In the structural approach it is also possible for an economy not to be at equilibrium, meaning that factors of production are not necessarily paid their corresponding marginal productivity. The outoff equilibrium condition allows economies to reallocate resources and generate economies of scale, thus increasing 8 According to Meier, labor is abundant in developing countries because its productivity does not add to overall output growth. In the extreme case, labor is said to be abundant when marginal product is equal to zero. 20  factors' productivity, per capita output, and the rate of growth of income per capita. Hence, the emphasis is on the possibility for resource reallocation, and technology transfer. To overcome the apparent limitations of neoclassical growth models, the structural approach assumes that there is a possibility for labor and capital to shift from activity to activity given the disequilibrium nature of the economy. Indeed, resource reallocation becomes a major issue in the framework of the structural models. This resource reallocation is even more important in the case of developing countries where there is a larger possibility for such a process to occur, as Meier points out. The following table taken from Meier, presents and summarizes the main difference between the neoclassical and structural models of economic growth. Table 1. Alternative Views of Growtb Neoclassical Approach Anu"!ptions Factor returns equal marginal productivity in all lUeS No economies ofscale Perfect foresight and continuos equilibrium in all markels Empirical Implications Relatively high elasticities of substitution in demand and trade Limited need for sector desegregation Sources of Growth Capital accumulation Increase in labor quantity and quality Incre.a.se in intermediate inputs Total factor productivity growth within sectors Structural Approach Income related changes in internal denwld CorwInined exumal marlcet.l and 1&gII in adjustment Transformation of productive structure producing disequilibria in factor marlcets Low price elasticities and lags in adjustment Segmented factor marlcets Lags in adopting new technology Neoclassical 50urces plus: Reallocation of resources to higher productivity aec\on Economies ofscale and learning by doing Reduction of internal and external bot1.lenecks Source: Meier, Gerald Leading Issues In Economic Development ,Fifth Edition, Oxford Univenity Press, J989, p. 98. 21  I Endogenous and Exogenous Growth Models The economic discussion on how to detennine the sources of growth and why countries achieve different levels of income per capita has recently moved to explain the differences between exogenous and endogenous growth models. The underlying assumptions of exogenous growth models are that the rate of population growth, capital accumulation, and technological change are given exogenously, i.e. they are determined outside the framework of neoclassical models. Renelt argued that endogenous growth models are characterized by removing the fixed factor constraint of neoclassical growth models by allowing constant returns to reproducible factors or by endogenizing technological change. In the same regard, Mankiw, Romer and Weil state that "Endogenousgrowth models are characterized by the assumption of non decreasing returns to the set of reproducible factors of production. Among the implications of this assumption are that countries that save more grow faster indefinitely and that countries need not converge in income per capita, even if they have the same preferences and technology" (p. 421). The same authors add that implications of endogenous growth models compared to neoclassical growth models are that in the fonner there is no steadystate level of income per capita and differences in income per capita across countries can persist indefinitely even if countries have different saving and population growth rates. This dissertation uses the neoclassical growth model framework but allows for technological change to occur through the degree of trade openness herein assumed to be a factor of production. Technological change is explicitly modeled as a function of trade openness in primary and nonprimary goods. The advantage of using the neoclassical 22  framework is that it allows for a detennination of how trade openness affects physical capital accumulation, human capital accumulation, and income per capita growth. The neoclassical framework also accounts for the possibility that countries with different rates of saving and initial income per capita levels achieve different levels of income per capita in the long run. The framework also maintains the assumptions of constant returns to scale to all factors common to neoclassical growth models, while considering the possible gains derived from the international trade process of specialization and transfer of technology. To better understand the implications of introducing trade openness as a factor of production within the context of the Solow neoclassical growth model, this dissertation provides a complete derivation of the steadystate levels of physical capital, human capital and trade openness. The outline of the matemathical derivation is presented in steps by first deriving the Solow model, then the Augmented Solow model with Human Capital, and finally the Augmented Solow model with Human Capital and Trade Openness. The Solow Model As mentioned before, the Solow model of economic growth uses a standard neoclassical production function with decreasing returns to capital and constant returns to scale for all inputs. The fundamental assumptions of the Solow model are that the rates of saving, population growth and technological progress are exogenous. Assuming a CobbDouglas production function with two inputs, capital and labor, the model is expressed as follows; (6) Y(I) = K (t r(A (t )L (t )}Q 23 0< a< 1 where Y is output, K is physical capital, L is labor and A is the level of technology. In addition, L and A are assumed to grow exogenously at rates nand g (7) (8) L(t) =L(O)e n , The Solow model also assumes that a constant fraction of output, s, is invested in physical capital. Defining k as the stock of capital per effective unit of labor, k = KJAL, and y as the level of output per effective unit of labor, y = fIAL, the evolution of k is governed by (9) (10) . k(t) =sy(t)  (n + g + 8)k(t) . k(t) = sk(tr  (n + g+8)k(t) . where 0 < 0 < I, is the rate of depreciation and k is the derivative of k with respect to time. It implies that k converges to a steadystate value k* defined by: (11) [ ( ) ] I/(Ia) k* = sf n+ g+o The steadystate capitallabor ratio (k*) is related positively to the rate of savings and negatively to the rate of population growth. Therefore, substituting (11) into (6) and taking logarithms the steadystate level ofincome per capita is given by (12) In[Y((t))] =InA(O) +gt +~ln(s)~ln(n+ g+8) Lt Ia Ia 24 Furthennore, the model assumes that In A(O) =a + &, where a is a constant and e is a countryspecific shock. Thus, log income per capita at a given time time 0 for simplicity is (13) In(Y) =a+~ln(s)~ln(n+g+6)+e L Ia Ia Knight, Loayza and Villanueva argue that "the SolowSwan growth model predicts that in the steadystate equilibrium the level of income per capita will be determined by the prevailing technology, as embodied in the production function, and by the rates of saving, population growth, and technical progress, all three of which are assumed exogenous. Since these rates differ across countries, the SolowSwan model yields testable predictions about how differing saving rates and population growth rates, for example, might affect different countries' steadystate levels of income per capita. Other things being equal, countries that have higher savings rates tend to have higher levels of income per capita, and countries with higher population growth rates tend to have lower levels of income per capita" (p. 513). More recently, research has focused on detennining whether the Solow model supports the hypotheses of conditional and unconditional convergence of income per capita across countries (Mankiw, Romer, and Weil; Knight, Loayza and Villanueva; and Edwards). The convergence hypothesis states that those countries that initially have a lower level ofincome per capita tend to grow faster than the ones that initially have higher levels of income per capita. The difference between conditional and unconditional convergence is that conditional convergence assumes that income per capita across 25 countries converges after controlling for the factors of production. Empirically, the explanatory variables of the rate of growth of income per capita are the rate of growth of the lahor force, the rate of growth of the capital stock, and the initial level of income per capita. Expansions of this model have considered inflation rate, government's share of total output, a financial variable and a freedom variable as important determinants of income per capita growth. Unconditional convergence means that the only explanatory variable of the rate of growth of income per capita is the initial level of income per capita. For the convergence hypothesis to hold the expected sign of the estimated parameter is negative for the initial level of income per capita. This means that countries that start off from lower income per capita levels tend to grow faster than those that initially have higher levels of income per capita. The Solow model predicts that countries having different saving and population growth rates tend to converge to different income per capita levels. Adding HumanCapital Accumulation to the Solow Model The new convergence approach focuses also on the inclusion of human capital accumulation as an explanatory variable of output growth. Mankiw, Romer and Weil emphasize that the accumulation of human as well as physical capital is important for economic growth, especially for those countries in which labor is not considered abundant. Mankiw, Romer and Weil argue that "to understand the relationship between savings, population growth, and income, one must go beyond the textbook Solow model" (p. 408). They argue that including human capital can potentially alter either the theoretical modeling or the empirical analysis of economic growth. At the theoretical level, 26 I properly accounting for human capital may change one's view of the nature of the growth process. Mankiw, Romer and Weil noted that, "for any given rate of human capital accumulation, higher saving or lower population growth leads to a higher level of income and thus a higher level of human capital; hence, accumulation of physical capita] and population growth have greater impacts on income when accumulation of human capital is taken into account. Further, humancapital accumulation may be correlated with saving rates and population growth rates; this would imply that omitting humancapital accumulation would bias the estimated coefficients on saving and population growth" (p. 408). The Augmented Solow model of economic growth presented by Mankiw, Romer and Weil uses the same standard specification as the model developed in equation 6. (14) Y(t) =K(tf H(tt (A(t)L(t)ra  p where a> 0, P> °and 0 < a+P < 1. In addition, H is the stock of human capital and h = H/AL, is a unit of human capital per effective unit of labor. All other variables are defined as before. Letting Sic be the fraction of income invested in physical capital and Sh the fraction invested in human capital. The evolution of the economy around k and h is now determined by (15) (16) . k(t) = Sky(t)  (n + g +o)k(t) . 17(t) =Shy(t)  (n +g + o)l1(t) 27 Mankiw, Romer and Wei! assume that a + f3 < 1, which implies that there are decreasing returns to all capital. (If a + {3 = 1 , then there are constant returns to scale in the reproducible factors. In this case, there is no steadystate for this model). In addition, 0 < 8 < 1, is the rate of depreciation and it is assumed, for simplicity, to be equal for physical and human capital. The steadystate levels of the stock of physical and human capital per effective unit oflabor are determined by (17) (18) ( lfJ fJ J1/(1afJ) k* = Sk s" n+g+8 ( a Ia JI/(lafJ) h* = Sk Sh n+g+8 Substituting (17) and (18) into (14) and taking the natural log yields the steadystate level of income per capita (19) In[Y((f))]=lnA(O)+gt+ a In(s.,)+ f3 In(sh) a+f3 In(n+g+8) Lt la{3 laf3 laf3 Like the textbook Solow model, the augmented model predicts coefficients that are functions of the factor shares. In addition, the steadystate level of income per capita also depends on the rate of human capital accumulation. Mankiw, Romer and Weil argue that the empirical estimation ofthe augmented Solow model yields better results because it shows that by adding human capital the accumulation of physical capital has a larger impact on income per capita than the textbook Solow model. A higher saving rate leads to 28 higher income per capita at the steadystate. In addition, population growth has a larger negative impact on income per capita compared to the initial Solow model. Trade Openness and Technological Transfer in the Solow Model Framework Other considerations on economic growth theory focus on the importance that international trade has on overall output growth through the transfer of technology. Two different approaches are presented, one by Knight, Loayza and Villanueva and the other by Edwards. In the first instance, Edwards argues that a country's trade policy can affect the speed at which technological improvements take place. He uses a set of new indicators on trade intervention and trade distortions to empirically investigate the role of commercial policy in explaining crosscountry growth differentials. Edwards assumes that a country's ability to appropriate technological innovations depends on the degree of openness of the economy. More open should be interpreted as referring to a less distorted or more market oriented foreign trade sector. The overall finding is that there is very strong evidence supporting the hypothesis that, with other things given, more open countries will tend to grow faster. Countries with a greater degree of openness will not only exhibit a higher level of income than countries with trade distortions but they will also have a higher long run steady state rate of growth. Edwards continues, saying that "the model implies that the out of steadystate rate of growth of aggregate output in a small country will depend positively on capital accumulation, positively on labor force growth, positively on the knowledge (or technological) gap between the country in question and the advanced nations, and 29  negatively on the degree of trade distortions. Additionally, trade policy will also affect longrun growth, with more open countries growing faster than otherwise identical countries" (p. 37). In addition, Edwards states that "The coefficient of the openness indicators provides strong support to the hypothesis that countries with a more open trade regime have, with other things given, tended to grow faster" (p. 42). On the other hand, Knight, Loayza and Villanueva propose an extension of the Augmented Solow Model developed by Mankiw, Romer, and Weil. The new model includes trade policy and the stock of public infrastructure as factors that affect labor augmenting technological change. Knight, Loayza and WeiI state "policies that foster more openness in a country's international trade regime help to stimulate laboraugmenting technological change in two ways. First, the importexport sector serves as a vehicle for technology transfer through the importation of technologically advanced capital goods, as elucidated by Barhan and Lewis (1970), Chen (1979) and Khang (1987), and as a channel for intersectoral external economies through the development of efficient and internationally competitive management, the training of skilled workers, and the spillover consequences of scale expansion (Keesing (1967) and Feder (1983)). Second, rising exports help to relieve the foreign exchange constraint  that is, a country's ability to import technologically superior capital goods is augmented directly by rising exports receipts and indirectly by the higher flows of foreign credits and direct investment caused by the country's increased ability to service debt and equity held by foreigners" (p. 515). 30  The main difference between the Knight, Loayza and Villanueva model and the Mankiw, Romer and Weil model is the specification of the technological factor A. The factor, A, is redefined in the KLV model as (20) where g is the exogenous rate of technological progress, F is the degree of openness of the domestic economy to foreign trade (with elasticity Sf), and P is the level of government fixed investment in the economy (with elasticity Sp). Knight, Loayza and Villanueva state "this modification is particularly relevant to the empirical study of economic growth in developing countries, where technological improvement tends to be absorbed domestically through imports of capital goods and where the productive sector's efficiency may depend heavily on the level of fixed investment undertaken by the government" (p. 516). Hence, given that the degree of trade openness (F) and the stock of government fixed investment (P) are included in equation 20 as part of a technological shifhng factor, the determination of the steadystate level of physical and human capital per effective unit of labor remains invariable compared to the estimates of the steadystate levels in Mankiw, Romer and WeiI model. Nevertheless, Knight, Loayza and Villanueva conclude that overall. econonuc efficiency is influenced significantly and positively by the extent of openness to international trade and by the level of government fixed investment in the domestic economy. In their words "when openness and the level of public infrastructure are taken into account, physical investment becomes quantitatively more important in the 31  growth process, implying that a better quality of investment is encouraged by a more liberal international trade regime and by more government fixed investment" (p. 536). An important finding in Knight, Loayza and Villanueva is that there are two channels through which the negative impact on growth of a restrictive trade system (proxied by the weighted average of tariffs on intermediate and capital goods) may be transmitted, through the rate of investment and through the effect on production efficiency. A high tariff structure discourages imports of capital goods and leads to less technology transfer, and thus to less technological improvement. Outwardoriented development strategies have a positive impact on economic growth. Edwards; and Knight, Loayza and Villanueva argue in favor of a positive effect that trade openness has on the productivity of physical and human capital, and also in total output growth. They argue that this positive effect comes about through the transfer of technology and the learning by doing process. Yet, at the theoretical level both approaches fail to address how trade openness affects human and physical capital productivity and therefore capital accumulation because the approaches consider trade openness as a technological shifting factor as opposed to a production factor. This effect is shown in equations 17 and 18 since k * and h· are assumed to be the steadystate levels of physical and human capital per effective unit of labor. Hence, the impact of technology changes as mentioned in Edwards; and Knight, Loayza and Villanueva is not explicitly incorporated in the steadystate levels of k and h, nor is the impact explicitly accounted for on the estimated parameters and coefficients. 32 CHAPTERm THEORETICAL MODEL Solow Model with Human Capital Accumulation and Trade Openness To detennine in a direct and precise manner how trade openness affects factor productivity, human and physical capital accumulation, and per capita output growth, this dissertation proposes an alternative Neoclassical approach that incorporates human capital and trade openness. The main difference of the approach this study follows is that the model incorporates the degree of trade openness promotion as a factor of production and not as a component of the technological shifting factor A as in previous studies. This is a key assumption in deriving the steadystate conditions in order to be able to measure the effects of trade openness on economic growth. In this regard, the model incorporates trade openness as a factor of production assuming that; i) it promotes the reallocation of resources according to comparative advantage, ii) allows for greater capacity utilization, iii) pennits the exploitation of economies of scale, iv) generates technological improvements in response to competition abroad and, v) in labor surplus countries contributes to increased employment and labor productivity. To account for the differences in its impact on sectoral production between agricultural and nonagricultural 33  goods, the model further demonstrates the importance of trade openness by category of goods through its decomposition between agricultural and nonagricultural. The decomposition of trade openness between agricultural and nonagricultural goods is relevant to the process of economic growth and economic development because differences may be determined in terms of factor productivity, resources allocation, and economies of scale between two different sectors with different structural and heterogeneous characteristics. Traditionally, it has been argued that agriculture provided surplus labor to the development of the industrial sector. Kavoussi; Tyler; and Balassa argue that the contribution of primary and manufactured export goods to output growth and capital productivity depends on the initial level of income per capita and on the composition of exports. Renelt argues that those results can be obtained using any trade openness measure, however trade openness as measured in this study includes the gains derived from international trade not only through export promotion but also by allowing greater competition through importing capital and primary goods. Technology transfer and development of economies of scale are the result of overall openness to trade and not only the outcome of a process of export promotion. Trade openness optimizes resource allocation by promoting those production activities that face international competition. Thus, this study assumes that trade openness is better understood when incorporating the investment process associated to the promotion of both exports and imports of agricultural and nonagricultural goods9 . 9 The concern of developing countries on whether they should promote exports and restrict imports is an issue that relates usually to structural balance of payments problems and/or domestic production policies oriented to protect domestic producers. However, the truthness of this argument does not relate or attempt to explain the gains a country receives by participating on international trade. 34 The Augmented Neoclassical Growth Model developed herein adheres to the Mankiw, Romer and Wei] specification of human capital from the previous chapter and includes two more factors of production, agricultural and nonagricultural trade openness promotion, A simple production function can be expressed as follows. Let (21) Y =j(K,H,Xa,Xna,L) where Yis total output, K is physical capital, H is human capital, Xa is a trade openness promotion measure in the agricultural sector, Xna is a trade openness promotion measure in the nonagricultural sector, and L is the labor force. Assuming a CobbDouglas production function with decreasing returns to scale to all reproducible factors, the Augmented Neoclassical Solow model is expressed as fonows. Let, (22) where a > 0, 13 > 0, B> 0 and 7! > 0; and 0 < a+13+ B+ 7! < 1. In addition, the model assumes that K > 0, H> 0, Xa > 0, Xna > 0 and L > O. Special cases of the model arise when any of the variables assumes a value equal to zero. These cases are particularly interesting when either Xa = 0 and/or Xna = 0. 10 As stated, A is the technological factor, and A and L follow the same specification as before (23) (24) L(t) =L(O)e'" A(t) =A(O)e EI therefore the number of effective units of labor grows at n+g like in the Solow model. The model also defines k = KlAL, h = HIAL, xa = XalAL, xna = XnalAL, andy = YIAL, as 10 A complete explanation of the theoretical implications are provided later in this chapter. 35 the physical capital, human capital, agricultural trade openness, nonagricultural trade openness and total output per effective unit oflabor, respectively. Nonnegativity ofXa and Xna Before proceeding with the actual derivation of the steadystate levels of income per capita, physical capital, human capital, agricultural trade openness, and nonagricultural trade openness, some discussion of the assumed nonnegative nature of Xa and Xna is warranted. By definition the model assumes that Xa > 0 and Xna > o. This assumption implies that countries take part in the international trade process either as exporters/importers of agricultural goods or/and exporters/importers of nonagricultural goods. However, it is possible to consider the hypothetical case where a country does not participate in international trade either because of selfsufficiency reasons)l or any other macroeconoITllc reason. Let us assume first that a country does not have any commercial relationship with any other country in agricultural goods, i.e. Xa is equal to zero. IfXa = 0 then the country is defined as been selfsufficient in agricultural goods and therefore there are no trade gains or technological improvements derived from Xa. Under this case the term Xa must be eliminated from the specification of the Augmented Solow model of equation 22. In this regard agricultural trade openness does not have any impact on the steadystate levels of physical capital, human capital, and income per capita. The second condition refers to the nonnegativity of Xna. This condition refers to the assumption that a country may be defined as being selfsufficient in the production and consumption of nonagricultural 11 Selfsufficiency does not mean that a country has comparative advantage in the production of a specific good, nor does it mean that a country can not benefit from the trade promotion process. 36  goods ifXna = O. As in the case of selfsufficiency in agricultural goods, selfsufficiency in nonagricultural goods means to eliminate the Xna term from the specification of equation 22. The implications in terms of steadystate level determinations are the same as before. Even though it is less likely for these theoretical scenarios to occur in the real world, it is convenient to keep them in mind to have a better understanding of the associated gains in productivity and consumption that international trade brings about. Having explored these possible theoretical scenarios, this study proceeds to derive the steadystate levels of income per capita, physical capital accumulation, human capital accumulation, agricultural trade openness, and nonagricultural trade openness for the Augmented Solow Model. The results of the newly developed steadystate conditions will then be used to specify the differences among growth models and to develop the growth equation for empirical estimations. Steadystates Before proceeding with the derivations of the steadystate conditions, it is convenient to remember some considerations about the Solow and MRW growth models. First, the Solow Growth Model assumes that the rate of savings of any economy is equal to the rate of investment in physical capital, where physical capital is expressed in terms of effective units oflabor. Therefore, the Solow model only derives one steadystate level for the physical capital. In the same context and following the Solow model specification mentioned above, Mankiw, Romer and Weil argue that savings can be used not only in the formation of physical capital but also in the formation of human capital. Thus, MRW assume that the overall savings level can be decomposed between Sk and Sh, where Sk is the 37  fraction of income invested in physical capital, and Sh is the fraction of income invested in human capital. Therefore, in MRW there are now two steadystate conditions, one for physical capital and the other for human capital accumulation. Using the Solow neoclassical framework and the correspondent MRW extension to it, this study further assumes that a fraction of Gross Domestic Product, Sxa, is invested in the promotion of agricultural trade, and that a fraction of Gross Domestic Product SXlIQ is invested in the promotion of nonagricultural tradel2 . The model further assumes, that the rate of depreciation for physical capital accumulation, human capital accumulation, agricultural trade openness, and nonagricultural trade openness is equal to 5, where a < 5 < 113 . Therefore, by combining the rate of depreciation 5, and the rate of savings invested in each factor of production (Si, where i = k, h, xa, and xna), it is possible to define the correspondent rates of net investment for each factor as follows~ (25) (26) (27) (28) afa a=s=Y5Xa afna a=s Y5Xna X/IQ where net investment is defined as the gross investment rate (siY where i=k, h, xa, and xna), minus the rate of depreciation of the correspondent i lil factor in time 1. Recalling the 12 Investment in the promotion of agricultural and nonagriculturaJ trade is associated with the development of economies of scale, capacity of response to foreign competition, development of comparative advantage, and promotion of technological transfer. 38 definitions of k, h, xa and xna (effective units of factors of production) it is possible to rearrange terms as to determine the total differentials ofK, H, Xa and Xna with respect to (wrt) tI.me, I..e., iK,i,f! &,'"aa nd &'"na. ThIe partl.aI de"nvatlves 0 f K, H, Xa, and Xna a a a a wrt time will then be equated to equations 25, 26, 27, and 28 respectively to determine the correspondent steadystate conditions for each factor of production. The results and procedures of the mathematical derivation are shown from equations 29 through 40. Physical Capital Let us first start with the derivation of the steadystate level for the physical capital. Thus, the first step to determine the physical capital steadystate level is to rearrange k = KlAL as K = kAL and then take the total differential of K wrt time which results in, OK ac ilL 8A = AL+kA+kL a a a a (29) iK ac  = AL+nkAL+gkAL a a where, the rate of change of the capital stock wrt time iK is equal to the sum of three a components. The first tenn at the righthandside of equation 29 refers to the change of the capital stock per effective unit of labor wrt time multiplied by the number of effective 13 This assumption simplifies the mathematical derivation of the steadystate levels of K, H, Xa, and Xna. 39  units of labor (AL). The second tenn is the change in the capital stock due to changes in the rate of growth of the labor force; and the third term indicates the change in the capital stock due to changes in the rate oftechnology growth. To solve for the steadystate level, equate equations 25 and 29 which are equivalent specifications of the change in the level of physical capital wrt time. Thus, it is possible to substitute 29 into 25, and solve for the rate of change of the level of physical capital per effective unit oflabor wrt time as follows; ac AL =sl:Y  oK  nkAL  gkAL if ac s.lI 5K nkAL gkAL = if AL AL AL AL aa =SkY  k(g+n +0) however, to solve for the steadystate level of physical capital, it is required to use the definition of output per effective unit of labor y =k ahPxa(JxnaJr and substitute it into the previous equation resulting in (30) where the net change in the level of physical capital accumulation per effective unit of labor wrt time is equal to the proportion of income invested in physical capital Changes in the assumption do not affect the overall results of this study. 40 accumulation per effective unit of labor minus the change in the level of physical capital accumulation associated with the rates of change of technology and labor force, and the depreciation rate. To solve for k from equation 30 it is further assumed that at the steadystate level k h xa xna . . the condition 30a holds. Where, (30a) refers to  = = =, and identifies the sit: Sh SXQ sr"" producer maximizing behavior that allows any economy to assign scarce resources to their best alternative uses until the last unit of savings per effective unit of labor has been allocated equally among alternative investment opportunities. This condition implicidy assumes that at the steadystate level the marginal productivity of the last dollar invested in the ith factor is equal to the marginal productivity of the last dollar invested in the l' factor, under the condition that i :I' j. Therefore, using condition 30a, it is possible to mathematically identify the following equalities that are then used to solve for the steadystate level of physical capital • k in equation 30. Thus, the model identifies that if at the steadystate level the marginal productivity of the last dollar invested in factors iUl and /' is equal, then it is possible to raise any pair of all these resulting equalities to the same power without altering the implications of this condition. This mathematical procedure then allows the model to substitute and solve for k. This is then shown as fonows; i) ii) (~J 8 =(xa) (J and Sk SXQ 41 iii) solving t, ii, and iii in tenns of II, xae, and xna" respectively gives the following results, i*) ii *) iii*) k {/ {/ xa{/= sJ(:Q/ ,and Sk Results from i*, ii*, and iii* are then substituted into equation 30, and then solved at the steadystate for k, where ac =o. The remaining of the mathematicaL derivation is an it algebraic procedure as shown below; S IP{/"k a+fJ+8+fr S fJ S 8 S "= k(g + n + 0) k h J:Q XM lfJ8tr P 8 If Sk Sh SJ:Q Sma n+g+o 42 • lafJ{/1f =k (31 ) • . (s IP8tr S PS 8 S If) lap8tr k= k h.ul XIIQ n+g+8 where k is the steadystate level of physical capital accumulation. Some considerations are important to address. The first and foremost important element to point out is that the result in equation 31 differs from those previous derivations of the steadystate level of physical capital accumulation in the Solow model of equation 11 and in the Augmented Solow model of equation 17. In the basic neoclassical Solow model the steadystate level of physical capital accumulation is positively related to the savings rate and negatively related to the rate of population growth. In the Mankiw, Romer and Weil augmented model of equation 17, the steadystate level of physical capital accumulation is determined as in the Solow model. However, equation 17 predicts a larger steadystate level of physical capital, because it incorporates the positive effect human capital accumulation has on physical capital. Not surprisingly the same results are found in equation 31. However, the Augmented Solow model with Human Capital Accumulation and Trade Openness predicts that the steadystate level of physical capital per effective unit of labor also depends positively on the income proportions invested in agricultural and nonagricultural trade openness promotion. If the model specification is correct then physical capital accumulation is positively affected by investment in trade openness because it helps to reallocate resources in a more efficient way, allowing for greater capacity utilization, exploitation of economies of scale, 43  and generating technological improvements in response to competition abroad and, in labor surplus countries contributes to increased employment, as mentioned before. A second difference between the model developed in this study and previous determinations of growth models relates to the study by Knight, Loayza and Villanueva. Following MRW approach, Knight, Loayza and Villanueva define that the degree of trade openness affects the steadystate level of physical capital accumulation and output growth only through exogenous changes in the level of technological transfer. Knight, Loayza and Villanueva assume that trade openness is an indirect determinant of output growth which only has effects on it through exogenous changes in the level of technology. Thus) trade openness does not have any direct effect on the steadystate level of physical capital accumulation. On the other hand, theoretical results from equation 31 indicate that endogenous technological change through the degree of trade openness has a positive and direct effect on the steadystate level of physical capital accumulation. This particular difference is a major shortcoming of previous theoretical growth models that will be discussed in more detail when detennining both the direct and indirect effects of trade openness on overall per capita output growth. Finally an empirical question that remains unanswered is whether the steadystate level of physical capital accumulation is larger in the augmented Solow model with trade openness than in the model estimated by Mankiw, Romer and Weil. The answer to this particular question depends directly on the relative magnitudes of Sxa, Sma, () and 1r) other things being equal. 44 Human Capital The second steadystate condition to derive corresponds to human capital accumulation. As for the physical capital, this section follows the same steps as before. It is relevant to notice that even though some of the material herein presented may be repetitive with respect to the previous section, it is still necessary to understand the derivation process for the steadystate level of human capital. Thus, using the definition of human capital per effective unit of labor h=H/AL, let us rearrange it as H=hAL, and then take the total differential wrt time. This in tum yietds, iR a, iL oA ::::0 AL+hA+hLif a if if (32) iR a, ::::0 AL+nhAL+ghAL if a where, the rate of change of the human capital stock wrt time iR is equal to the sum of a three components. The first term at the righthandside of equation 32 refers to the change of the human capital stock per effective unit of labor wrt time multiplied by the number of effective units of labor (AL). The second term is the change in the human capital stock due to changes in the rate of growth of the labor force; and the third term indicates the change in the human capital stock due to changes in the rate oftechnology growth. To solve for the steadystate level we proceed to equate equations 32 and 26 which are equivalent specifications of the change in the level of human capital wrt time. 45 Thus, it is possible to substitute 32 into 26, and solve for the rate of change of the level of human capital per effective unit of labor wrt time as follows', a, AL =ShY  5H  nhAL  ghAL it a, = ShY _ 8H _ nhAL _ ghAL it AL AL AL AL however, to solve for human capital, it is required to use the definition of output per effective unit of labor y =k a hfJ xa9 rna IC and substitute it into the previous equation resulting in (33) where the net change in the level of human capital accumulation per effective unit of labor wrt time is equal to the proportion of income invested in human capital accumulation per effective unit of labor minus the change in the level of human capital accumulation associated with the rates of change of technology and labor force, and the depreciation rate. 46  To solve for h from equation 33 the model makes use of the condition 30a, as before. Where, (30a) refers to k = h = xa = xna ,and'Ide'nftlies the producer Sh SUJ S..,,,,, maximizing behavior that allows any economy to assign scarce resources to their best alternative uses until the last unit of savings per effective unit of labor has been allocated equally among alternative jib. investment opportunities. Hence, using condition 30a, it is possible to identify the following equalities which are then used to solve for the steadystate level of physical capital h in equation 33. The model also assumes that at the steadystate level the marginal productivity of the last dollar invested in factors jib. and]I.h is equal, which in turn allows to manipulate the equalities as follows. This is then shown as; i) ii) iii) solving i, ii, and iii in terms ofka , xae, and xna" respectively gives i*) ii *) 47 iii"') h"s 1r xna" = rna If sit Results from i*, ii"', and iii'" are then substituted into equation 33, and then solved at the t11 steadystate for h, where =O. The remaining of the mathematical derivation is an a algebraic procedure as shown below; la8" a 8 " Sit Sic SXQ SXrtQ n+g+8 .1ap8tr =h (34) . (s la8If S as 8S IfJlap8'1f h= It It XQ rna n+g+8 where h represents the steadystate level of human capital accumulation. The result in equation 34 differs from that derived in Mankiw, Romer and Weil in equation 18. Mankiw, Romer and Weil predict that the steadystate level of human capital relates positively to the rate of savings invested in physical and human capital and relates negatively to the rate of population growth. Equation 34 presents similar results as those 48 implied by equation 18, however, the augmented Solow model with human capital accumulation and trade openness predicts that the steadystate level of human capital per effective unit of labor is also affected by the degree of openness both in agricultural and nonagricultural goods. The degree of trade openness provides for the exploitation of economies of scale that technology transfer and leamingbydoing processes have on the formation of human capital. Trade openness increases the process of technology transfer and leamingbydoing, increasing overall labor productivity. In turn, reallocation of labor among economic sectors increases overall marginal productivity that will not occur in economies that do not trade. Furthermore, industries and sectors which take part in the process of international trade usually have labor skill requirements higher than those industries dedicated to the production of goods for the domestic market. International trade competition results therefore in enhancement of labor quality, easing the process of technology transfer and physical capital accumulation. Hence, human capital accumulation is positively affected by the degree of openness because it reallocates resources in a more efficient way, allows for greater capacity utilization, enables the exploitation of economies of scale, and generates technological improvements in response to competition abroad and, in labor surplus countries contributes to increased employment. At the empirical level, whether the estimated magnitude of the steadystate level of human capital accumulation is larger than the one estimated by Mankiw, Romer and Weil is an empiri.cal question that depends on the absolute magnitudes of Sm, Sxna, Band 7r, other things equal. A second difference between the model developed in this study and previous determinations of growth models relates to the study by Knight, Loayza and Villanueva. 49 Following .MRW approach, Knight, Loayza and Villanueva define that the degree of trade openness affects the steadystate level of human capital accumulation and output growth only through exogenous changes in the level of technological transfer. Knight, Loayza and Villanueva assume that trade openness is an indirect determinant of output growth which only has effects on it through exogenous changes in the level of technology. Thus, trade openness does not have any direct effect on the steadystate level of human capital accumulation. On the other hand, theoretical results from equation 34 indicate that endogenous technological change through the promotion of trade openness has a positive and direct effect on the steadystate level of human capital accumulation. Perhaps, the two most relevant considerations drawn out of these steadystate conditions are; trade openness results in higher labor quality, and thus resources shift from domestic uncompetitive activities to trade related highly competitive production processes. This result derives directly from the producer maximizing behavior assumption that indicates that at the steadystate level (marginal condition) the marginal productivity of the last unit of savings has to be equal among alternative investment opportunities. This particular difference is a major shortcoming of previous theoretical growth models that will be discussed in more detail when determining both the direct and indirect effects of trade openness on overall per capita output growth. In this regard, the difference between the closed and open economy models is that in the closed economy model the economy is not maximizing either production nor social welfare. This is because the closed economy does not exploit the benefits associated with maximizing resource use allocation directly derived from the process of international trade. On the other hand, the open economy model differentiates between those 50 economies that trade accordingly to their comparative advantage and those that are not involved in international trade. Agricultural Trade Openness The Augmented Growth Model with Trade Openness proposes the derivation of two new steadystate conditions. The first condition refers to the degree of trade openness promotion in agriculture, whereas the second condition refers to the degree of trade openness promotion in the nonagriculture sectors. The model first determines the steadystate level for the agricultural trade openness promotion as follows. Using the same specification as before, let xa=Xa/AL and Xa=xaAL. Taking the derivative of Xa with respect to time. a¥a aa iL oA = AL+xaA+xaLit it it it (35) a¥a = aa AL+nxaAL+ gxaAL it it . . iWa where, the rate of change of agricultural of trade openness promotIOn wrt tIme a IS equal to the sum of three components. The first term at the righthandside of equation 35 refers to the change in agricultural trade openness promotion per effective unit of labor wrt time multiplied by the number of effective units onabor (AL). The second term is the change in agricultural trade openness promotion due to changes in the rate of growth of 51 the labor force; and the third term indicates the change in agricultural trade openness promotion due to changes in the rate oftechnology growth. To solve for the steadystate level we proceed to equate equations 27 and 35 which are equivalent specifications of the change in agricultural trade openness promotion wrt time. Thus, it is possible to substitute 27 into 35, and solve for the rate of change in agricultural trade openness promotion per effective unit of labor wrt time as follows; & S.raY  e5Xa =AL . +nxa4.L + gxaAL it &a ALit =s YbXa nxaALgxaAL JCD ilxa sJCDY bXa nxaAL = a AL AL AL gxaAL AL &a  =S.rayxa(g+n+e5) it however, to solve for the steadystate level of agricultural trade openness promotion, it is required to use the definition of output per effective unit of labor y =kahPxaoxna" and substitute it into the previous equation resulting in (36) where the net change in agricultural trade openness promotion per effective unit of labor wrt time is equal to the proportion of income invested in agricultural trade openness 52 promotion per effective unit of labor minus the change in the level of agricultural trade openness promotion associated with the rates of change of technology and labor force, and the depreciation rate. To solve for xa from equation 36 it is further assumed that at the steadystate level the condition 30a holds. As before, the model assumes that at the steadystate level the marginal productivity of the last dollar invested in the itr. factor is equal to the marginal productivity of the last dollar invested in thell factor, under the condition that i :I; j . Therefore, using condition 30a, it is possible to identify the following equalities which are then used to solve for the steadystate level of agricultural trade openness promotion in equation 36. This is then shown as follows; i) ii) iii) (:.Y =(~)' and solving i, ii, and iii for kD., hP, and xna'l respectively gives i*) ii *) iii "') p P fJ _ xa Sh d h  p ,an SJCQ xa"s " xna" = :rna Sh " 53 Results from i·, ii·, and iii· are then substituted into equation 36, and then solved at the iJxG steadystate for xa, where =0 . The results is then it ' IapI< a+p+B+tr a P I< ( >:) Sxa xa SI< Sh S;ma =xa g+n+u IapI< a p I< Sxa SI< Sh SXI'IQ n+g+8 • IapBI< =xa (37) where • (s lap" S as fJ S "J lafJBI< xa = xa "h;ma n+g+8 xa is the steadystate level of agricultural trade openness per effective unit of labor. The model predicts that xa depends positively on the rate of savings invested in physical and human capital, and on the proportion of income invested on agricultural and nonagricultural trade; and negatively on the rate of population growth. According to equation 37, physical and human capital positively affects agriculture by allocating to the production and trade of agricultural goods, only those resources that are productive in such activity. The relative size of agricultural trade openness compared to nonagricultural trade openness depends finally on the levels of Sxa, Sma, Sh, and Sic. Nevertheless, for a country with a large agricultural base x·a is expected to be larger than otherwise. In most 54 cases as countries move their production structure from agricultural to nonagricultural industries, a reversal in the relative sizes of the steadystate levels might be expected, becoming nonagriculture more important than before. In this regard, countries that start off having a comparative advantage in the production and therefore, trade of agricultural goods may reflect larger relative sizes of agricultural trade as ratio of the specific sectoral production. At the empirical level countries which have a comparative advantage in the production and trade of agricultural goods would, other things given, reflect a positive sign related to income per capita. It is convenient to remember that the positive effect of trade openness prom060n comes about because the model assumes that countries' production and trade behavior follow a pattern directly associated with their comparative advantage. On the other hand, if a country becomes involved in international trade not accordingly to its inherent or current comparative advantage, then there wou~d be a resource use misallocation that contradicts the basic assumption of producer maximizing behavior. This in turn would be reflected in general loss of social welfare, which would be reflected as well, in a negative sign of empirical estimates for agricultural and nonagricultural trade openness promotion. Furthennore, this resource use misallocation would reduce the marginal productivity of all factors of production, driving countries away their longrun steadystate level of income per capita. 55 Nonagricultural Trade Openness Finally, the steadystate level for the nonagricultural trade openness is determined as follows. Given xna=Xna/AL, let Xna=rnaAL, and take the derivative of Xna with respect to time. 8Xna ana tL 8A = AL+xnaA+xnaLif a if a (38) OXna Oma = AL+ nxnaAL + grnaAL a a where, the rate of change of nonagricultural oftrade openness promotion wrt time iWna a is equal to the sum of three components. The first term at the righthandside of equation 38 refers to the change in nonagricultural trade openness promotion per effective unit of labor wrt time multiplied by the number of effective units of labor (AL). The second term is the change in nonagricultural trade openness promotion due to changes in the rate of growth of the labor force; and the third term indicates the change in nonagricultural trade openness promotion due to changes in the rate of technology growth. To solve for the steadystate level we proceed to equate equations 28 and 38 which are equivalent specifications of the change in nonagricultural trade openness promotion wrt time. Thus, it is possible to substitute 28 into 38, and solve for the rate of change in nonagricultural trade openness promotion per effective unit of labor wrt time as follows; 56 iJxna SrnaY  liXna =AL+ nxnaAL + gxnaAL a iJxna ALa =S Y  8Xna  nxnaAL  gxnaAL .l7IQ ana srnaY liXna nxnaAL = a AL AL AL gxnaAL AL iJxna =snoaY  xna(g + n +0) a however, to solve for the steadystate level of nonagricultural trade openness promotion, it is required to use the definition of output per effective unit of labor y =k a hPxa8 xna 1< and substitute it into the previous equation resulting in (39) where the net change in nonagricultural trade openness promotion per effective unit of labor wrt time is equal to the proportion of income invested in nonagricultural trade openness promotion per effective unit of labor minus the change in the level of nonagricultural trade openness promotion associated with the rates of change of technology and labor force, and the depreciation rate. 57 To solve for xna from equation 39 this study makes use of condition 30a. Therefore, usmg condition 30a, it is possible to mathematically identify the following equalities which are then used to solve for the steadystate level of nonagricultural trade openness promotion in equation 39. This is then shown as follows; i) ii) iii) (:.J' =(::J'and ( xa)9 =(xna) (J , sro sma solving i, ii, and iii for ka , hP, and xae respectively gives the following results. i*) ii*) iii*) f3 f3 f3 _ rna sit d h f3 ,an s:J:lI(J Results from i*, ii *, and iii* are then substituted into equation 39, and then solved at the 8xna I . h steadystate for xna, wherea = O. The resu ts IS ten, 58 Jaf30 a~/3+(J~1< a /3 6 ( ) sDlQ rna Sir s~ Sxa =rna g+n+8 • laf301< =rna (40) n+g+8 ( • S laf36 S a S f3S 0) lafJ 61< rna = J:1IQ Ie h ;t;a n+g+8 . where rna is the steadystate level of nonagricultural trade openness per effective unit of . labor. The model predicts that xna depends positively on the rates of saving invested in physical and human capital, and on the proportion of income spent on agricultural and nonagricultural trade; and negatively on the rate of population growth. According to equation 40, physical and human capital positively affects nonagriculture by allocating to the production and trade of nonagricultural goods, only those resources that are productive in such activity. For a country with a large nonagricultural base x ~ a is expected to be larger than otherwise. Countries that have comparative advantage in the production of nonagricultural goods may reflect larger relative sizes of nonagricultural trade as ratio to the specific sectoral production. At the empirical level countries which have comparative advantage in the production and trade of nonagricultural goods would, other things given, reflect a positive sign related to income per capita. In general, how much a country participates on international trade depends positively on how much the country invests on physical capital, human capital, trade openness in agriculture and trade openness in nonagriculture promotion. The more a country dedicates resources to the 59 enhancement of physical capital accumulation and to increase the level of labor education (training), the more competitive this economy becomes. Income Per Capita The procedure to determine the effects that K, H, Xa, and Xna have on income per capita, and to find the steadystate level of income per capita, is to substitute equations 3 1, 34, 37, and 40 into the initial production function, equation 22. To empirically estimate the resulting production function, this study proceeds to transform the original Cobb Douglas type of production function into a linear function, by taking the natural logarithm. This transformation allows the use of econometric techniques to empirical estimate the coefficient. It is important to mention that empirical estimations of the model can only be performed if the coefficients of the model are expressed in linear form. Therefore, the equation to be estimated is a fJ Y ( _ =A lfJBrrS {J S B5 rrJ Ia{JBrr (5 la8rrS a5 BS rrJ la{J8rr 5Ie h xa xna 11 Ie xa X71Q L n+g+8 n+g+8 8 1r ( s lafJtr S a5fl s trJ lafJ81r (5 Ia{JBS as {J5OJ IaflBIr xa lehxna xna lehxa n+g+8 n+g+8 In(Yt) =lnA(O) +gt + a 1~(s/.D8"s/s,",8S:maK)1 a+ f3;8;1r In(n+g+8) Lt 1 a  f3  ()  1r 1\  a    1r 60 + n In(SDII:J lap8Sk a SirfJ S 8) lafJ8n = The final result is: (41 ) (n) a+p+8+n a )n  =lnA(O)+gt In(n+g+8)+ Ins Lt lafJ8n lap8n k fJ 8 n + Insh + Ins + Ins lafJ8n lafJ8n = lap8n xna Equation 41 predicts that the longrun steadystate level of income per capita depends positively on the degree of trade openness promotion in agricultural (Sxa) and nonagricultural (Sxna). It also predicts, as expected, that population growth (n)14 affects negatively the longrun steadystate level of income per capita and that physical capital (Sk) accumulation and human capital (Sh) accumulation positively affect the longrun steadystate level of income per capita growth. In addition, the longrun steadystate income per capita coefficients in equation 41 are a function ofthe factor share parameters a, 13, 8, and Jr. The malO difference with the approaches followed by Edwards; and Knight, Loayza and Villanueva is that trade openness affects both the steady state of physical and human capital accumulation and the steadystate level of income per capita. If the 61 specification of the model is correct, the introduction of openness in agricultural and nonagricultural markets as factors of production, on the grounds mentioned throughout the dissertation, has changed the traditional view that exports and imports affect physical capital, human capital, and output growth only through the exogenous transfer of technology. The new specification of the Solow model predicts difference in magnitude on the empirical estimates as it will be mentioned in the next section. The model predicts that the estimated coefficients of physical and human capital are affected by the introduction of trade openness. Considering trade openness as a component of the technological factor (A) implies that estimated coefficients remained unchanged when comparing the closed and open economy growth models. This assumption implies that there is no difference in the steadystate levels of physical and human capital accumulation between the closed and open economy models. A result that seems unplausible. Indeed, one would expect that trade openness would affect the productive and steadystate levels of both physical and human capital. Whether the final steadystate levels of physical and human capital accumulation are larger or sroaner after trade compared to the before trade situation is an empirical question that depends on the relative magnitudes of the production coefficients. Nevertheless, one expects that trade openness results in a positive effect on overall income per capita through the reatlocation of resources, economies of scale, and transfer oftechnology of the trading process. 14 The model assumes that the rate of change of technology transfer g and the rate of depreciation 15 remain constant. 62 Summary Tables 2 and 3 provide a comparative analysis of the alternative growth models discussed in Chapter III. These tables clearly state the differences among models. Table 2 illustrates the differences in terms of mathematical derivations for the steadystate levels of the correspondent factors of production. Table 3 provides the conceptual analysis that relates to the derivations outlined in table 2, below. The main differences and their correspondent implications are explained as follow. The summary presented on tables 2 and 3 indicate that by endogenizing technological change as a function of the degree of trade openness, one can explain the effect that trade openness has on output growth, factor accumulation and overall factor productivity in the context of the Solow model. The BarbozaDicks proposed model specification also allows the determination of both the direct and indirect effects that trade openness promotion has on the longrun rate of growth of income per capita and on the correspondent steadystate level. 63 Table 2. Comparison of SteadyState Conditions under Alternative Growth Model! Solow • Mankiw et al • Edwards; and Proposed BarbozaDicks C Knight et aI b Physical Capital Human Capital Agric. Openness Nonagric. Openness 1 [s/(n+g+~]la ( 1{3 13 )IIPaf31 SI: ~ n+g+8 ( a la )1/(1aP) 51: ~ n+g+8 ( 113 13 )l/(laPl S. Sir n+g+8 ( a Ia )1I(1aP) 51: s" n+g+8 I ( .s:..IafHrSstas:~Ir)1afJfMc n+g+8 • Closed economy growth models b Open economy growth model with trade openness as a component of technological change factor A C Open economy growth model with endogenous technological change through trade openness 64 Table 3. Conceptual Comparison of Alternative Growth Models Solow Mankiw et aJ Edwards; aDd Knight et al Proposed BarbozaDicks Functional Form Input.! Technolocy Factor A JnpUls Per CapiJa JnCDm~ Capital and Labor. Labor grows exogenously at rate n. Exogenously given with growth rate g. Residual componenl Positive on savings rate, negative on labor growth (n) and negative on exogenous technological change. Positive on physical capital, negative on labor, and positive on exogenous technology change. Physical capital, human capital and labor. Labor grows exogenously at rate n. Exogenously given with growth rate g. Residual componenl Positive on investment in physical and human capital, negative on labor force growth, and negative 011 exogenous technological change. Positive on physical and human capital, negative on labof, and positive on exogenous technology change. 65 Physical capital, human capitA.I and labor. Labor grows exogenously at rate n. Exogenously given with growth rate g, and depends positive on trade openness and government infrastructure. Positive on investment in physical and huJlW1 capital. negative on labor force growth, and negative on exogenous technological change. POISitive on physical capital, human capital, and trade openness; negative on labor, and positive on exogenous technology change. Open economies grow fasteT toward given steadystate. Physical capital, human capital, trade openness in agricu Iture and nonagrlculture. Labor grows exogenously at rate n. Partially endogenized as linear function oftrade openneu in agriculture and nonagriculture goods. Remaining portion grows at rate g. Positive on investment in physical and human capital, negati ve on labor force growth, and negative on eKogenoWi technological change. Positive on the degree oftrade openness in agriculture and nonagriculture goods. In addition. rteadyst.a.te levels of physical and human capital accumulation depend upon the degree oftrade openness. Positive on physical capital, human capital, agriculture and nonagricullure trade openness; negative on labor, and positive on exogenous technology change. Open economies tend to grow faster toward steadystate, and open economies achieve different studystales as trade openness factors vary. Lower savings rate required to achieve same growth level compared to the closed economy scmano. The indirect impact is reflected in the effect that trade openness has on the steadystate levels of physical and human accumulation (as indicated in table 2), and hence on the parameter coefficients for the physical and human capital accumulation. On the other hand, the direct impact of trade openness on the longrun level of income per capita is indicated by the parameter coefficients of the degree of trade openness for agriculture and nonagriculture trade activities; where open economies tend to grow faster than closed economies other things given1s. In addition, as technology change is endogenized through the promotion of trade openness, open economies are able to achieve different longrun steadystate level of income per capita as trade openness factor vary. This particular feature of endogenous technological change differentiates the Proposed BarbozaDicks model from the closed economy Solow model the MRW model and the KLV open economy growth model with exogenous technological change. To stress the importance of the last paragraph's theoretical implications Tables 2 and 3 outline three relevant differences between the closed and open economy specification of the Neoclassical Growth Models. In this regard, the first difference is that the longrun steadystate level of income per capita is always larger in the open economy model. Thus, allowing open economies to achieve larger steadystate levels of income per capita and greater longrun rates of growth of income per capita toward a given steadystate level. This result is particularly interesting because it suggests that a lower level of capital accumulation (human and physical) is needed in the open economy compared to the closed economy to achieve the same level oflongrun per capita output. 15 Other things given refer to the same level of domestic savings, same rate of depreciation, and same level of technological transfer. 66 The second implication is that in the open economy model lower levels of domestic saving are associated with larger levels of per capita output growth. This is possible, because the productivity of physical and human capital is enhanced as a result of the process of technology transfer associated with the promotion of international trade openness according to a comparative advantage behavior. Thirdly, as trade factors vary, endogenized technological change allows economies to achieve different steadystate levels of income per capita and physical and human capital. This particular implication of the expanded model is not possible in the closed economy model with exogenous technological change. Therefore, this study argues that by endogeni:zing technological change through the degree of trade openness promotion, the model provides evidence to close the gap to allow for endogenous changes in steadystate levels of income per capita which is not possible in the closed economy Solow model. 67 CHAPTER IV METBODSANDPROCEDURES Expected Results This study estimates equation 41, by using a crosssection timeseries model. The model detennines the effects of human and physical capital accumulation and agricultural and nonagricultural trade openness on income per capita. Easterly et al. point out that combining timeseries with crosssection data is necessary because the growth perfonnance of LDCs shows substantial variation over time. Moreover, it is possible to capture any countryspecific effects. Second, it allows us to expand the sample size. Further, to appropriately estimate the model in equation 41, the model assumes In A(0) =a + E, where a is a constant and E is a countryspecific shock. In addition t is assumed to be equal to zero. In terms ofthe empirical estimation, this redefines the model of equation 41 as (42) I Xa Xna InGNPPC =ao +aJ InL +a2 In +a3 InSchoo/ +a4 In +asln+ 6' Q Q Q 68 where ao IS a constant and aI, a2, a3, a4, a~ are the parameters to be estimated. The dependent variable in equation 43 In( ~) is approximated by the natural logarithm of the per capita Gross Domestic Product and it is defined as InGNPPC. Per capita income is defined as the Gross Domestic Product in constant 1987 US $ divided by total population. This allows to have a relative comparable unit of measure for income per capita across all countriesl6 . To approximate the natural logarithm of the rate of population growth, In(n) in equation 43, (assuming that g+8 are constant) this study uses the natural logarithm of the labor force, InL. Labor force is defined as the "economically active" proportion of total population that is classified from 14 to 65 years of age. The natural logarithm of the savings invested in physical capital, In(st), is approximated by natural logarithm of the ratio of gross domestic investment to total output, In( ~) .Investment corresponds to total gross investment l ? and output is defined as the Gross Domestic Product. Gross investment and Gross Domestic Product are defined in domestic currency for each country and then a ratio is calculated to make data across countries comparable. The natural logarithm of the savings invested in human capital, In(sh), is approximated by the secondary enrollment ratio, InSchool. The secondary enrollment ratio is defined as the 16 The author recognizes that per capita income as defined in this study presents significant problems to correctly compared to actual purchasing power of individuals across nations. However, per capita income is the only available cross section time series data useful to conduct this study. Some of the major problems while comparing per capita income across countries are that "informal" sectors and other relevant economic activities in developing countries are not recorded in the traditional definition of Gross Domestic Product. In addition, differences in real exchange rates are not considered when transfonning data from domestic currency to constant US $. 69 ratio of gross enrollment of all ages at secondary level as a percentage of children in the country's secondary school age group, including pupils enrolled in vocational or teachertraining secondary schools. The natural logarithm of the income proportion spent on agricultural trade openness, In(S",a) , is approximated by the natural logarithm of the ratio ofnonfuel primary exports and imports to total output, In( ~) . According to the World Bank Database (Stars) the classification corresponding to nonfuel primary exports plus imports include commodities in SITC revision 1, Section 0, I, 2, 4, and Division 68 (food and live animals, beverages and tabacco, inedible crude materials, oils, fats, waxes and nonferrous metals). Finally, the natural logarithm of the income proportion spent on nonagricultural trade openness, In(sxna ), is approximated by the natural logarithm of the ratio of all other exports and imports18 to total output, In( X~Q) . All other exports plus imports include fuel and manufactured goods. The fuel category includes SITC revision ] Section 3 which incorporates mineral fuels and lubricants and related materials. While manufactured goods cover SITe revision 1, Sections 5 through 9 (chemicals and related products, basic manufactures, machinery and transportation equipment, other manufactured articles and goods not elsewhere classified, excluding Division 68). The QJ coefficient in equation 42 corresponds to a + fJ + () + Jr in equation 41, Ia fJ()Jr and it represents the effect of population growth on per capita output. As the Solow 17 Gross Domestic Investment is defined as the sum of gross domestic fixed investment and the change in capital stocks. 18 AU other exports and imports are calculated as total exports plus imports minus exports plus imports of nonfuel primary goods. 70 model predicts per capita output growth depends negatively on the rate of growth of population. The magnitude of 01 is expected to be larger in absolute tenns than the one estimated by Mankiw, Romer and Weil, because it incorporates the effects that trade openness on agriculture and nonagriculture has on population growth. In practical tenns, the numerator is larger and the denominator is smaller than the one presented by Mankiw, Romer and Weil in equation 19. The second coefficient 02 corresponds to a lapOlr in equation 41 and it represents the effect that physical capital has on overall output growth. This coefficient is expected to be positive in sign. This dissertation supports the idea that by including trade openness as a factor of production, the estimated impact of physical capital on output growth should be larger than the one reported in previous studies. At the practical level the numerator a remains invariant compared to previous estimations of the Solow model, however, the denominator incorporates the factor coefficients for trade openness in agriculture (8) and nonagriculture (n), resulting in a smaller value for the denominator and therefore a larger overall coefficient. The hypothesis to be tested is whether empirically this coefficient is larger once trade is included. Feder argues that factor productivity on the export sector is higher than productivity in the nonexport sector. If this is true then trade has a positive effect on physical capital productivity and therefore it should be reflected in the coefficient 02 as the model of equation 41 suggests. Empirical studies that determine the impact of export on per capita output growth report that there is a positive and statistically significant relationship between export growth and per capita output growth (Michaely; Balassa; Tyler; Kavoussi; Feder; Mbaku; 71 Moran~ Moschos; Ram~ and Barboza). In addition, these studies support the hypothesis that export growth enhances factor productivity, which is reflected in large values for estimated coefficients on physical and human capital as suggested in equation 41. This study provides an alternative theoretical approach to the exogenous neoclassical theory of economic growth with a feasible explanation why these empirical estimates may have larger values once export growth (or any trade measure as Renelt and Levine argue) is included as an explanatory variable of per capita output growth. One important result of this model is that even though the estimated parameters for the physical and human capital may be larger than the ones reported by Mankiw, Romer and Weil, there is still a possibility that the absolute value of the steadystate level of physical and human capital accumulation may be smaller if certain conditions on Su, S""", () and 7r are met. Edwards; and Knight, Loayza and Villanueva considers trade openness as a component of the technological factor (A) that only has affect on longrun output growth. This means that in the models of equations 19 and 20, empirical estimates of the coefficients for physical and human capital are not affected by the inclusion of trade openness, i.e. the factorinput elasticities remain invariant when comparing the closed and open economy models. On the other hand, the model developed in this study shows that trade openness has a positive affect on the magnitude of the parameters for physical and human capital, and a negative effect on the labor force growth parameter estimate. These theoretical implications are for the most part in accordance with the empirical evidence found in Michaely~ Balassa; Tyler; Kavoussi; Feder; Mbaku; Moran; Moschos; Ram; and Barboza. 72 The third coefficient a3 corresponds to fJ In equation 41 and it lafJBtr represents the effect that human capital has on overall output growth. Likewise, the coefficient for human capital is expected to be positive in sign. This study supports the idea that by including trade openness as a factor of production, the estimated impact of human capital on output growth is larger than the one reported in previous studies. The variation in the magnitude ofthe coefficient comes because of the reduction in the value of the denominator, where the value of the factor share of a labor augmented unit of technology, (la~()...1'C), is now smaller than in previous studies, (lafJ), resulting in a larger a3 coefficient. The hypothesis to be tested is whether empirically this coefficient is indeed larger once trade is included. The coefficient a4 is equal to B in equation 41 and it measures the lafJOtr effect that agricultural trade openness has on per capita output growth. According to Balassa~ Kavoussi~ Levine and Renelt; and Tyler, this coefficient should be positive. Furthermore, a4 should be larger, positive and statistically significant for low income developing countries whereas it should be either small or not statistically significant for middle and high income developing countries. The overall expected sign for a4 is positive. Finally, the coefficient a~ is defined as IapOtr in equation 41 and it measures the contribution of nonagricultural trade openness on output growth. For middle to high income developing countries a~ should be statistically significant and positively related to per capita output growth. The magnitude ofa~ is expected to be larger than the one for a4. Technology transfer and economies of scale tend to be larger on the nonagricultural sector compared to the agricultural sector (Balassa; Tyler~ and Kavoussi). 73 One interesting outcome of the model developed in equation 41 is that once trade openness is considered a factor of production and not a component of the technological factor (A), the steadystate levels of physical and human capital may be lower than in the closed economy model of equation 19. Further, the longrun steadystate level of income per capita growth is larger when trade openness is included than otherwise. The theoretical development of the Augmented Solow Model with Trade Openness in equation 41 suggests that a lower level of capital accumulation is needed to achieve the same level of longrun per capita output growth once trade openness is considered as a factor of production. Hence, an economy that is involved in international trade achieves a larger steadystate level of income per capita growth than an economy that does not trade, other things being equal. Countries that trade develop economies of scale, reduce unemployment, grow faster, and achieve higher levels of income per capita than countries under the same conditions that do not trade. Estimation Method and Misspecification Tests The model of equation 42 is initially estimated by ordinary least squares (OLS). Traditionally, economic research in the area of economic growth uses the OLS technique. OLS is thought to provide the necessary tools to empirically estimate this linear model. In this particular regard, McGuirk, Driscoll and Alwang suggest tests to determine the presence of misspecification errors for each of the classical OLS assumptions, I.e. normality, functional form, static and dynamic homoskedasticity, no autocorrelation, and parameter stability. Since, this study incorporates crosscountry data and it is estimated as a crosssection timeseries study by using four years average annual data only the 74 misspecification tests for normality, functional fonn, and static and dynamic homoskedasticity are performed. Four year averages of real Gross Domestic Product, the investmentoutput ratio, the labor force, education level, trade openness in agriculture, and trade openness in nonagriculture, are used as base data. McGuirk, Driscoll and Alwang recommend that tests on the classical OLS assumptions should be performed as much as one can, i.e. one should conduct as many misspecification tests as possible to improve confidence and power of statistical testing of economic hypothesis. In the case of this study, as mentioned before, the tests that will be performed are those for the normality, functional form, static and dynamic homoskedasticity. The no autocorrelation, and parameter stability assumption19 tests are not conducted. In general, misspecification tests are rarely seen in applied economic theory, especially when estimating the relationship between factors of production and overall economic growth. Whereas some crosssection studies test for the possibility of static heteroskedasticity, most do not conduct misspecification tests on the other relevant assumptions. If the appropriate misspecification tests are omitted then there is a large possibility that the empirical results are biased, inconsistent, and inefficient, which in tum results in a loss of power in the statistical tests. This study provides the results of the misspecification tests on the use of OLS for testing Neoclassical Growth Models in tables 5,7,9, 11, 14, 16, and 18. The analysis of the results of the tests are in the next chapter. According to McGuirk, Driscoll and Alwang to test the normality assumption, three different tests are applied, the kurtosis test, the skewness test, and the omnibus test. For the functional form the KolmogorovGabor polynomial (KG2), and the Regression 75 Specification Error Test 2 (RESET2), tests are applied. For static and dynamic homoskedasticity the RESET2 and White's heteroskedasticity test are used. Based on the results of Tables 5,7,9, 11, 14, 16, and 18, an alternative estimation method is used. At first instance, this study proceeds to use the POOLED estimation technique as described by Kmenta (1986 Section 12.2 pp. 616625) and implemented by the econometric software SHAZAM. The POOLED technique consists of a Generalized Least Square estimation that accounts for the existence of heteroskedasticity and autocorrelation across countries and time. The procedure as described in Kmenta (1986) is detailed as follows. The general assumptions about timeseries studies is that the error may present an autoregressive process but they need not to be heteroskedastic. On the other hand, a crosssection study assumes that error may be heteroskedastic but not necessarily autoregressive. When both processes are combined it is reasonable to assume that both heteroskedasticity and autocorrelation are present. Therefore, this study combines both assumptions to construct a crosssectionally heteroskedastic and timewise autoregressive model. The model specification indicates that: (43) where eI, indicates the presence of heteroskedasticity for each specific cross section. Furthermore equation 44 indicates that there is crosssectional independence. Finally equation 45 illustrates that there is an autoregressive process. 19 McGuirk et aI., present a complete description of all available misspecification test for Ordinary Least Squares, besides the ones that are performed in this study. 76 (44) (45) find consistent estimates for the variance covariance matrix, the ordinary least squares method is initially used to obtain consistent estimates of the ei,. These error terms are in turn used to estimate the Pi elements of the transfonned variance covariance matrix. To assure convergence the estimates of the Pi elements are confined to have a value within the range of {1,1} for any given sample size20 Thus, the initial observations are transformed by using the correlation estimates. The following specification is copied from Kmenta (1986, p. 619). The transformed variables are denoted by the superscript C·) as follows: (46) ~ =AX~ I + P2 X~, 2 +.. '+Pk X;, ~ + /I" " ". I. ." r" where y;,=~1_~,2 YI/ for t = 1, and Y,= Yir~' Y,,rl for t = 2,3, . ,T. In addition, the correspondent transformed explanatory variables are defined in the same manner as the dependent variable. The transfonnation of the vector of explanatory variables X in equation 46 is expressed as follows. 77 X/.k =JI ~,2 X il.k for t = 1, and X/.k =Xi/,k  ~j X,.H,t for t = 2, 3, ... , T Where k = 1,2, '" ,K, and i = 1,2, ... , N. As described in Kmenta, "The purpose of this transfonnation is to estimate el, from observations that are, at least asymptotically, nonautoregressive since estimated variances based on autoregressive disturbance are, in general, biased." (p. 620). Therefore, this procedure allows to obtain consistent estimators of P, and eli, and therefore consistent estimators of the variance covariance matrix. This finally allows to achieve maximum likelihood estimates. For the purpose of the empirical estimations of this study, it is assumed that the parameter P presents the same value for all crosssectional units21 . In other words, Pi = Pi =P for all i ,j = 1, 2, ... , N.22 Data Averages consisting of four years are used instead of annual data to avoid the problem of year specific characteristics and also as a tool to increase the size of the number of observati.ons compared to a pure crosssection study. Four year averages are used because it is assumed that within four years most policy effects or economic shocks will be absorbed by the economy. Further, by using four year averages it is possible to reduce large variation on annual data that are commonly presented in developing countries. For instance, it is not rare that income per capita suffers large variations from 20 Kmenta indicates that when the sample size is to small there is a possibility for Pi to have an estimated absolute value larger than 1. 21 Initial computations to calculate a convergence value for p for each crosssectional unit indicated that there were too few observations to successfully complete the convergence procedure. The alternative estimation required assuming the same value of p for an crosssectional units. 22 For a complete derivation of the estimation procedure for the POOLED technique see Kmenta (1986). 78 year to year In countries with an unstable political system. Also trade openness can fluctuate largely due to the imposition of tariff and nontariff barriers to solve temporarily balance of payments disequilibriums. This study assumes that by using four year averages most of this variation will be eliminated. If a crosssection timeseries study is conducted without using annual averages then dummy variables should be included if one wants to account for year specific events in each country. Yet, explaining yearspecific events requires detailed information that is rarely available in most developing countries. To detennine the contribution that each factor of production has on overall per capita output growth and how they affect productivity of others factors, five different regressions are perfonned. Estimation 1 includes the average annual investmentoutput ratio, and the annual average labor force as explanatory variables of income per capita. Estimation 2 includes the average annual investmentoutput ratio, the secondary enrollment rate, and the average annual labor force as explanatory variables of the average annual per capita GDP. To account for the presence of international trade, estimation 3 includes the average annual degree of trade openness as explanatory variable of per capita GDP, in addition to those included in estimation 2. Estimation 4 decomposes the degree of trad 



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