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US MICROPOLITAN AREA ECONOMIES IN THE 1990’S By MICHAEL E. DAVIDSSON Bachelor of Arts in Economics Lewis & Clark College Portland, OR 1988 Master of Arts in Economics University of Central Oklahoma Edmund, OK 1990 Submitted to the Faculty of the Graduate College of the Oklahoma State University in partial fulfillment of the requirements for the Degree of DOCTOR OF PHILOSOPHY July, 2012 ii US MICROPOLITAN AREA ECONOMIES IN THE 1990’S Dissertation Approved: Dr. Dan Rickman Dissertation Adviser Dr. Lee Adkins Dr. Michael Applegate Dr. Michael Woods Dr. Sheryl A. Tucker Dean of the Graduate College iii TABLE OF CONTENTS Chapter Page I. INTRODUCTION ...................................................................................................1 Economic Performance of Micropolitan Counties in the 1990's .............................2 Purpose of the Study ................................................................................................3 Contribution .............................................................................................................5 II. REVIEW OF THE LITERATURE Urban & Natural Amenities .....................................................................................6 Outlier Studies .........................................................................................................9 III. METHODOLOGY The Roback Model .................................................................................................11 The GlaeserTobio Model ......................................................................................16 The Empirical Model Three Hedonic Cross Section Regressions ......................................................21 Econometric Issues ..........................................................................................25 Data Discussion and Description ...........................................................................28 Purging of the Data using the Method of the Hat Matrix ................................35 Purging of the Data using the Method of the “kClustering” ..........................36 Final Data and Variance Analysis....................................................................37 Variance Decomposition of the R2  Dominance Analysis ..............................39 Beta Coefficient Analysis ................................................................................45 IV. FINDINGS Empirical Results and Analysis Regression Results The Population Regression ..............................................................................47 The Rent Regression ........................................................................................51 The Wage regression........................................................................................53 Analysis............................................................................................................57 Dominance Analysis General Dominance – Population growth ..............................................................58 General Dominance – Rent Growth .................................................................62 General Dominance – Wage growth ................................................................65 Analysis............................................................................................................67 iv Growth Effects and Analysis The Amenity Growth Effect ............................................................................75 The Productivity Growth Effect .......................................................................77 The Housing Supply Growth Effect ................................................................79 Analysis............................................................................................................82 Unexplained Growth Effects, the Role of the Housing Supply and Unexplained Outliers Unexplained Growth Effects ............................................................................83 The Role of the Housing Supply on Economic Growth ..................................94 Unexplained Outliers .......................................................................................97 V. CONCLUSION Summary & Conclusions .......................................................................................99 REFERENCES ..........................................................................................................107 APPENDIXES APPENDIX A General Dominance Analysis for the Population Regression ........................111 APPENDIX B General Dominance Analysis for the Wage Regression ................................146 v LIST OF TABLES Tables Page I. Autocorrelation Analysis Regressions .............................................................26 II. Description of Data and Data Groups ..............................................................31 III. Variance Analysis of the Dependent Variables ...............................................38 IV. Generic Variance Decomposition – Stage I – Regression Algorithm .............42 V. Generic Variance Decomposition Stage II – Average Contribution to the R2 Calculations by Each Variable Group ........................................................43 VI. Generic Variance Decomposition Stage III– Average Contribution to the R2 – Final Calculations ....................................................................................44 VII. Results for the Population Regression .............................................................49 VIII. Results for the Rent Regression .......................................................................52 IX. Results for the Wages Regression ....................................................................55 X. General Dominance Analysis Result Population Growth Regressions ......................................................................................................59 XI. Significant Beta Coefficients – Population Regression by Variable Group ...............................................................................................................59 XII. General Dominance Analysis Result  Rent Growth Regressions ......................................................................................................63 XIII. Significant Beta Coefficients – Rent Regression by Variable Group.................................................................................................63 XIV. General Dominance Analysis Result  Wage Growth Regressions ......................................................................................................66 XV. Significant Beta Coefficients – Wage Regression by Variable Group.................................................................................................66 XVI. Group Specific Amenity Growth Effect R2 Analysis......................................76 XVII. Group Specific Productivity Growth Effect R2 Analysis ................................78 vi XVIII. Group Specific Housing Supply Growth Effect R2 Analysis ..........................80 XIX. Beta Coefficient Analysis – Net Contribution to the Housing Supply Effect .....................................................................................81 XX. Wage and Population Growth Analysis for Census Divisions 3 & 4....................................................................................82 XXI. Residual Population Growth Analysis for All the 511 Micropolitan Areas ..........................................................................................85 XXII. Residual Population Growth and Residual Housing Supply Growth Effect Analysis Broken Down by Two Groups: Above and Below the Average HSGE .............................................................86 XXIII. Residual Population Growth and Residual Housing Supply Growth Effect Analysis Broken Down by Groups Based on the Number of STD from the Average HSGE ...............................................................................87 XXIV. Directional Analysis on the Population Growth  Rent Growth Relationship ..................................................................................................88 XXV. Analysis on Micropolitan areas with Housing Supply Growth Effect that is two STD’s or More Below the Average Housing Supply Growth Effect................................................................................................90 XXVI. Analysis on Micropolitan areas with Housing Supply Growth Effect that is two STD’s or More Above the Average Housing Supply Growth Effect................................................................................................91 XXVII. Growth Analysis on Micropolitan Areas with the Rent Growth  Housing Supply Ratio Above and Below the Average Rent Growth  Housing Supply Ratio ...................................................................................95 XXVIII. Growth Analysis by Census Division on Micropolitan Areas with the Rent GrowthHousing Supply Ratio (R/HS) Above and Below the Average Rent GrowthHousing Supply Ratio .....................................................................96vii LIST OF FIGURES Figure Page 1. The Basic Roback Model ......................................................................................13 2. Changes in the Level of Amenities or Productivity in the Roback Model ...........15 3. Census Regions and Divisions of the United States .............................................23 1 CHAPTER I INTRODUCTION The 1990’s were a period of prosperity in the U.S. and a period of the longest peacetime economic expansion in U.S. history. This period also marked the beginning of the “new economy” with advances in Internet, information, telecommunications and other production technology that set the stage for a decade that was characterized by robust economic growth. Economic growth and the ensuing prosperity affected every corner of the U.S., with private nonfarm employment growth remarkably even across the nation; employment growth was 22 percent for metropolitan counties, and 21.7 percent for nonmetropolitan counties. Many studies in the economic literature noticed a significant trend in migration to nonmetropolitan counties during the decade. The potential advantages that nonmetropolitan counties have over metropolitan counties for people are higher levels of natural amenities, and less urban disamenities, such as traffic congestion and crime. Nonmetropolitan counties offer lower production costs and wages for firms and when the cost of distance is less than the savings in production costs and wages and the business operations do not require face time with consumers, then a nonmetropolitan county can be a good business location.2 This trend in nonmetropolitan county growth prompted the Census Bureau to put forth a new classification of an urban area, called micropolitan area, which is based on the concept of urban clusters. Micropolitan statistical areas were first defined by the Office of Management and Budget (OMB) in 2000 as: “having at least one urban cluster with a population of at least 10,000 but less than 50,000. Under the standards, the county (or counties) in which at least 50 percent of the population resides within urban areas of 10,000 or more population, or that it contains at least 5,000 people residing within a single urban area of 10,000 or more population, is identified as a ‘central county’ (counties)1. Additional ‘outlying counties’ are included in the CBSA if they meet specified requirements of commuting to or from the central counties. Since the definition of micropolitan areas is fairly new, there are relatively few studies in the economic literature on the growth of micropolitan areas in the 1990’s. Therefore this study will analyze the sources of growth of micropolitan areas in the 1990’s. Economic Performance of Micropolitan Counties in the 1990's There are 3,087 counties and county equivalents in the continental US and of those 662 are classified as micropolitan counties. Approximately 10.6 percent of the continental population lived in these micropolitan counties in 1990, in which 13.6 percent of the population 25 years “old and over” had Bachelor’s, Master’s or Professional degrees (compared to 20.3 percent nationwide). The population increased overall by 9.8 percent in micropolitan areas in the continental US during the decade, compared to 13.2 percent population growth nationwide. The population increased much faster in 1 http://www.census.gov/population/www/metroareas/aboutmetro.html 3 micropolitan areas located in the west and south, than in micropolitan areas located in the east and north portion of the country. The center of gravity for the micropolitan population steadily drifted from northeast to southwest in the 1990’s (Mulligan & Vias, 2006). The economic performance of micropolitan counties was good during the decade, with private nonfarm employment increasing 22 percent (same as nationwide, but slightly more than the continental US). Furthermore, the employment/population ratio increased 3.2 percent points in micropolitan counties but declined 0.4 percent nationwide, which indicates that employment growth kept better pace with population growth in micropolitan areas. The manufacturing industries were moving out of metropolitan and rural counties into micropolitan counties during the decade, with manufacturing employment increasing 2.2 percent in micropolitan areas, but declining 2.9 percent nationwide. Average wages in micropolitan areas increased 40 percent (versus 51.1 percent nationwide), but rent (includes imputed rent2) increased 54 percent (versus 46.6 percent nationwide). This could indicate that the migration to micropolitan areas was amenity oriented since migrants to micropolitan areas were willing to accept less than national average growth in real wages and higher than the national average growth in rent in order to enjoy micropolitan amenities. Purpose of the Study Micropolitan areas are neither rural nor urban but can be thought of as emerging 2 See section 5.1 for methodology 4 metropolitan areas. So far the economic literature has focused mostly on the general determinants of growth of micropolitan areas, which explains the growth of the average micropolitan area. Some micropolitan areas with average level independent variables experienced growth well above the typical micropolitan area in the 1990’s. The purpose of this study is to analyze population growth that can be explained by regression analysis and unexplained outliers of population growth of micropolitan areas nationwide. Explained growth refers to the portion of the population growth that is explained by the independent variables in the population regression. Unexplained population growth refers to the portion that is not explained by the independent variables and becomes part of the residual error of the population regression. An unexplained outlier of population growth is a micropolitan area with exceptional (or extremely poor) population growth that cannot be explained by the variables in the population regression. The analysis in this study has two parts. The first part is an econometric study of micropolitan areas nationwide to identify the determinants of population growth of micropolitan areas overall (population growth explained by the regressions). The second part of the study will focus on examining the unexplained outliers of population growth of micropolitan areas nationwide. Systematic analysis will be applied in order to identify the factors that can explain the outlier performance. It is possible that the performance of micropolitan areas with outlier growth is due to factors such as economic policies not utilized elsewhere. This understanding is important in order for local governments to have effective policies that are conducive for economic growth. 5 Contribution Economic research on micropolitan areas has not been as extensive as it has been for metropolitan areas since the definition of micropolitan areas is fairly recent. Furthermore, most of the economic literature has focused on the on the average micropolitan area. This study attempts to analyze both the explained and residual sources of economic growth of micropolitan areas. The contribution of this paper to economic literature is to increase understanding of micropolitan growth and to bridge the gap in the economic literature of the knowledge of the determinants of growth between the average micropolitan area and micropolitan areas with outlier performance. 6 CHAPTER II REVIEW OF THE LITERATURE Urban & Natural Amenities Regional growth in the United States has historically been characterized by stark differences in growth between regions (Barro and SalaiMartin, 1991; Blanchard and Katz 1992). It is important for economic developers to understand the reasons for these differences in growth in order to have policies that are conducive to economic growth. The growth in jobs and incomes in rural areas has lagged behind, partly because of a decline in economic opportunities in traditional rural industries (McGranahan and Beale, 2002). There is a significant body of literature that states that historically an important factor in interregional labor migration was asymmetric regional demand shocks and lengthy adjustments in wage differentials across regions, meaning that the migration was driven by demand shocks and economic opportunities (Blanchard and Katz 1992). Many studies therefore used local wages and employment growth as the major determinant of migration (Greenwood and Hunt, 1989). Historically, regional growth and migration were thus labor demand driven. Migration was characterized by a step migration up the urban hierarchy with people moving to a bigger city/urban area for jobs (Plane et al, 2005). 7 This means that economic growth was driven by productivity. However, amenities gradually became more important in the migration decision as incomes increasedespecially urban amenities (Graves, 1983). Bigger cities have more urban amenities than small cities and towns because urban amenities are usually scale dependent. Amenities can affect both quality of life and productivity. The household utility function includes amenities and amenities are therefore capitalized into factor prices (Roback, 1988 & 1982). Many studies have found that “scale dependent” urban amenities are a normal good (Glaeser et al, 2000 and Roback, 1988) and important in migration of high skilled and educated people because these groups consume more of “scale dependent” urban amenities. Migration is therefore more likely to reflect the utility of the educated and highly skilled, rather than the low skilled (Bound and Holzer, 2000; Bartik, 1996 & 2001). This also means that cities with plentiful urban amenities are likely to have a larger portion of their labor force skilled and educated (Adamson et al, 2004). It stands to reason that changes in the household evaluation of amenities can be a catalyst for supply sided migration. Starting in the 1970’s, empirical studies began to show an increase in migration to nonmetropolitan areas (Wardwell & Brown, 1980). Improvements in the transportation infrastructure, environmental awareness, urban disamenities (crimes, congestion, etc), and increasing affluence were some of the factors that were the catalysts for this change (Chi and Marcouiller, 2011). This indicates that natural amenities became more important in the utility function for some households (especially for higher income households) and therefore the relative utility increased in high amenity areas for those households (Graves, 1979), resulting in nonmetropolitan high amenity areas to become more attractive for migration. 8 This trend continued into the 1990’s. Almost all the migration during the end of the 1990’s was down the urban hierarchy and the most significant migration flows were from the top of urban hierarchy to the bottom of the hierarchy (Plane et al, 2005). This is consistent with supply side migration for natural amenities. Supply side natural amenity migration analysis focuses on interregional differences in amenities and other specific locationbased attributes. Numerous studies using amenity models and hedonic pricing models have found that amenities affect regional growth significantly (Chen and Rosenthal, 2008; Gabriel and Rosenthal, 2004; Clark et al, 2003; Deller et al, 2001; Gyourko and Tracy, 1991; Roback, 1982). The demand for natural amenities in the south have also possibly increased because of the invention of air conditioning and other technological advances (Mueser & Graves, 1995). One can calculate the implicit value of natural amenities, if the amenities are fully capitalized into the labor market and the housing market (Gabriel et al, 2003; Beeson and Ebberts, 1989; Roback, 1980;). Distance can also affect the household amenity evaluation. Areas high in natural amenities tend to be further away from big cities and areas further away from big cities have less urban “scale dependent” household and production amenities. Two areas with the similar amenity variables can also have a different household amenity evaluation just because they differ in distance from a big city. There is evidence that preferences for more distant natural amenities are increasing. Partridge, et al. (2010) relate household amenities to distance in a study of counties in the 1990’s in order to understand how distance of counties from cities across the urban hierarchy contributes to agglomeration and they found that 9 preferences for natural amenities in rural, remote urban, and more remote metropolitan areas were increasing. Although natural amenities are important in population growth and migration, they are not all the same; a right mix of natural amenities (open land, water, forest and various type of topography) is most conducive to migration (McGranahan, 2007). Some studies on nonmetropolitan counties/areas have found that in order to increase economic growth in rural and micropolitan areas it is more important to attract people and increase the labor force rather than attract new firms and new jobs. That is because jobs follow people more than people follow jobs (Vias, 1999; Mulligan and Vias, 2006). The possible reason for that is that more workers usually mean higher density of skills which results in better labor matching, and better labor matching reduces training costs. The question about how important natural amenities are in regional economic growth and migration is still debated. Some studies continue to find that population growth in some regions was due to rising productivity (Caselli and Coleman, 2001). Furthermore, rents are seldom included in regional migration studies (Mueser and Graves, 1995). Recently however, there is new research emerging supporting the hypothesis that rents and flexible housing supply can be more important for growth of regions than amenities or productivity (Glaeser, Gyourko, and Saks, 2006). Outlier Studies Loveridge et al. (2007) argue that in order to get a deeper understanding of economic phenomena, it is of value for economic researchers to study outliers. It is a standard practice in econometrics to accept models that explain only 20 to 30 percent of the total variance in the data and the results from these models are used to explain the determinants of growth in 10 the respective areas. Therefore, a lot of variability remains unexplained in the data and the models are therefore susceptible to omitted variable bias, especially for outliers. They say that if a place is advancing more rapidly than other places with similar sociodemographics, geographic and industry characteristics, we ought to know why. Their research supplements a study by Anderson, et al. (2007) in which they used 1990 and 2000 county data in a crosssectional study to estimate the determinants of the growth in the proportion of working poor in the counties of the states in the North Central region of the U.S. In order to explain the performance of the outliers they systematically analyze the areas using economic, geographic and qualitative data (telephone surveys and interviews). They use the data to look for a group of factors that can explain the outlier performance. They are successful to explain the difference in many outliers. For example they find Michigan’s Upper Peninsula they find that the difference between the above and underperformance outliers are mostly in attitudes and policy. The above performance outliers are poised to grow within, but the underperformance outliers are counting on external growth and quick fix options for local growth. 11 CHAPTER III METHODOLOGY The Roback Model Charles Mills Tiebout (1956) observed and popularized the notion that people vote with their feet, relating migration to utilities. Sherwin Rosen (1979) expanded on this notion and related it to amenities and wages; and a few years later Jennifer Roback (1982) extended Rosen’s analysis and came out with a comprehensive model that has been widely accepted and used in the economic literature for studies on quality of life and migration. This model, now usually called the “Roback model” shows the effect of interregional differences in amenities and productivity on wages and rents. The Roback model assumes perfect competition. The regional value and cost functions are functions of wages, rents and amenities, which is a shifter: V(w,r;,s)= kv and C(w,r;s)=kc. This means that there are interregional utility and unit cost equilibriums that have to be maintained in the long run. The Roback model also assumes that people and firms sort themselves according to their preferences for amenities and other specific locational attributes. If amenities change then they will generate compensated variations in wages and rents through12 migration that will calibrate the region back into the interregional utility and cost equilibrium. Amenities are therefore a significant factor in explaining growth of regions. In the Roback model each individual maximizes his/her utility given the income constrains: max U(w,lc;s) subject to (w+l = p*x+r*lc) and firms produce a composite good X with a production function x=f(n,lp;s) where x=composite good, lc is land used by households, p=price of the composite good, r=rental costs, lp is land used in production and s = amenity. The utility function is increasing in wages, but declining in rents. The cost function is increasing in both wages and rents. The assumptions for the model are3: 1. Workers have identical tastes and are completely mobile between regions. 2. Capital is identical, completely mobile between regions 3. Production technologies are the same between regions 4. Cities are characterized as bundles of attributes, which can affect household utility and costs of production. 5. Household utility is the same in each region 6. Unit costs of production are the same in all regions. 3 Beeson & Ebberts (1989) 13 Figure 1. The Roback Model 14 The value function (indirect utility function) for the region is V(w,r;s)=k, where k is the interregional utility equilibrium. The value function is upward sloping (Figure 1) because the function is written for a fixed utility k and therefore if wages increase, rents have to increase also to offset the increase in utility from increasing wages in order to stay on the same utility curve. If amenities increase then the utility curve shifts to the right representing that when the labor supply increases in the region, ceterus paribus, it will cause wages to decline and rents to increase. The cost function for firms is C(w,r;s)=1 in which the interregional production cost equilibrium is normalized to 1. The cost function is downward sloping (Figure 1) because if wages increase then rents have to decrease to compensate in order to stay on the same cost curve. If productivity increases in the region then it will cause the cost function to shift right because now firms in the region can afford to pay both higher wages and higher rents. Amenity and Productivity Differences Between Regions Regions that have higher amenity than the region in Figure 1 will have their utility curves to the right of V(w,r;s) because they have lower wages and higher rents and regions that have less amenity will be on the left because they have higher wages and lower rents. Likewise, the cost curves for regions that are more productive than the region in the Figure I will be on the right of C(w,r;s) because firms in those regions can afford to pay higher wages and higher rents and regions that are less productive will be on the left. 15 Figure 2. Changes in the Level of Amenities or Productivity in the Roback Model 16 Changes in the Level of Amenity and/or Productivity Say that the Region in Figure II has the value function V(W0 ,R0;S0 ). Now amenities increase in the region and the utility curve shifts to the right to V(W1 ,R1;S1 ). Now wages are less and rents are higher, but the utility is restored to the same level it was before. Likewise, say that the cost function for firms in the region is C(W0 ,R0;S0 ). Now productivity increases in the region and the curve shifts to the right to C(W1 ,R1;S1 ). Firms in the region are now paying higher wages and rents, but the per unit costs are the same. The equilibrium wages increased from W1 to W3 and rents increased from R0 to R3. The total change in each variable is the sum of the impact from the change in both amenities and productivity. The Roback model shows that amenities generate compensated variations in wages and rents through migration, largely because people sort themselves according to their preferences for amenities and other specific locationbased attributes. Amenities are therefore a significant factor in explaining population growth of regions. The Glaeser & Tobio Model Glaeser & Tobio (2008), in a study on the population growth in the sunbelt states during the second half of the 20th century, noticed enormous growth in the housing supply since 1980 in the sunbelt but a slow pace of growth in housing prices relative to the rest of the country. This prompted them to hypothesize that the differences in local land use regulations between regions could have resulted in important differences in housing supply, which could have important consequences for population and employment growth. 17 Their model is based on the Roback model, in which growth of regions can be explained by differences in amenity and productivity. In the two sector Roback model, labor markets and housing markets always adjust perfectly so that if amenities change then wages and rents change to preserve the interregional utility equilibrium. Glaeser & Tobio expand the model by adding the “housing sector” to the model which was embedded into the Roback model but not modeled especially with equations describing the behavior of housing prices. Therefore the Glaeser & Tobio model also incorporates innovations in land and land prices in regional adjustment to an amenity shock and the model shows that the overall growth of regions can be explained by three effects on growth: Amenity growth effect; Productivity growth effect; and “Housing Supply” growth effect. Regional output is produced subject to the following production function: 1 Y AN KZ (1) in which “A” is an index on regional productivity,” N” is the number of workers,” K” is traded capital and “Z” is non traded capital (infrastructure, natural capital, etc). Maximizing the production function with respect to the firm’s budget gives the following inverse labor demand function: 1/(1 ) ( 1)/(1 ) (1 )/(1 ) /(1 ) W A N Z (2) in which “W” is wages, is the share of mobile capital inputs, and is the share of labor inputs. Regional households derive utility from the consumption of a traded good “C” (numeraire) and nontraded housing “H” according to the following utility function: 1 U C H (3) 18 in which “ ” represents a utility shifter and is the budget share of housing. Maximizing the utility function with respect to the household budget constraint gives the following indirect utility function: V WPh (1 )(1 ) (4) in which W is wages and Ph is price of housing. Housing suppliers use a fixed level of land “L” and structure on the land “h” in the production of housing. Housing suppliers maximize profits according to the profit function: ( ) ( ) L Ph hL h L PL (5) in which Ph is the selling price of housing, “ h ” is the cost of the housing structure ( is the elasticity of the housing supply), and” L P ” is the price of land. Maximizing the profit function to find the indirect housing supply function (assuming that land is fixed) and setting it equal to housing demand gives the inverse housing supply function at the equilibrium: ( 1)/ (1/ ) (1/ ) NW Ph h L (6) Taking the natural logs of the labor demand function, the indirect value function and the inverse housing supply function and solving simultaneously for static equilibrium gives us the static equilibrium equations: 19 ( ) ( ) (1 )( ( ) ( 1) log( ) log ( (1 ) ( 1)) N Log A Log L N K (7) ( 1) ( ) (1 )( ( ) ( 1) log( ) log ( (1 ) ( 1)) W Log A Log L W K (8) ( 1) ( ) ( ) (1 )log( ) log ( (1 ) ( 1)) P LogA Log L Ph K (9) Glaeser and Tobio assume that the evolution in amenities, productivity and housing supply are governed by the following growth equations: 1 log t A A A t A K S A (10) 1 log t A t K S (11) 1 log t L L L t L K S L (12) in which the variable S defines status. If equations 7,8, and 9 are made into a dynamic system in which equations 10,11, and 12 describe the dynamic process, then it implies the following evolution of labor, wages and housing prices: 1 ( ) (1 ) (1 ) ( 1) log ( (1 ) ( 1)) t A L N N t N S S S K N (13) 1 ( 1) (1 ) (1 ) ( 1) log ( (1 ) ( 1)) t A L W W t W S S S K W (14) 1 ( 1) ( 1) ( 1)(1 ) log ( (1 ) ( 1)) t A L Ph Ph t Ph S S S K Ph (15) 20 Where “ N K ”, “ W K ”, and “ Ph K ” are regional specific constants, the terms in the bracket are regional specific coefficients (that can be estimated by regressions) and “ N ”," W ”, and " Ph "are error terms. If we define the estimated regression coefficients on the S (status) variables as: ( ) (1 ) (1 ) ( 1) ( (1 ) ( 1)) A L N b (16) ( 1) (1 ) (1 ) ( 1) ( (1 ) ( 1)) A L W b (17) ( 1) ( 1) ( 1)(1 ) ( (1 ) ( 1)) A L Ph b (18) then we can solve the system and define the Amenity, the Productivity and the “Housing Supply” effects A , and L in terms of the regression coefficients ( N b , W b , and Ph b ) . A(1)bN(1)bW (19) Ph W b b (20) 1 Ph L N W b b b (21) N b , W b , and Ph b are regression coefficients which represent the Productivity, Amenity and “Housing Supply” effect that is explained by the population, wages and rent regressions. Since this study sets out to also analyze the residual effects (unexplained by the regressions)  the unexplained Productivity, Amenity, and “Housing Supply” effects 21 ” U A “,” U “and " U L ” are estimated with the following equations for the residuals: U (1 ) (1 ) A N W e e (22) U Ph W e e (23) 1 U Ph L N W e e e (24) In summary the theoretical model is used to identify the incentive behind the explained and unexplained growth of micropolitan areas. The regression estimates ( b ’s) are used to calculate the explained growth estimates ( ˆy ’s) for each micropolitan area. The ( ˆy ’s) are then decomposed into explained Amenity, Productivity and “Housing Supply” growth effects. The error terms are used like the ( ˆy ’s) in the model to explain the residual Amenity, Productivity and “Housing Supply effects. The Empirical Model Three Hedonic Cross Sectional Regressions In accordance with the economic literature (Glaeser & Tobio, 2008; Rickman & Rickman, 2011), three hedonic cross sectional regressions are run in order to obtain the regional specific estimates for the Amenity growth effect, Productivity growth effect and the “Housing Supply” growth effect: population growth regression; rent growth regression and wage growth regression. This paper uses the following vectors for each cross sectional regression using 1990 data to explain the growth of micropolitan areas in the 19902000 22 period: / Vector Vector Vector Vector Vector of of of of of Census Amenity Demographic Education Fiscal Policy District Variables Variables Variables Variabl Variables Growth Vector Vector of of Economic Urbanization es Variables Variables (25) The same variables were used for each regression except for the control variables (see Table II for complete data description). In the wage regression, the beginning rent is excluded; however, the beginning wages and population density are included. In the population regression, the beginning rent and beginning wages are excluded and the population density is included. In the rent regression, the beginning wages and population density are excluded, but beginning rent is included. The explained effects on the dependent variables not accounted for in the first six groups are accounted for by the Census division group, which measures the fixed effect that is attributed to the Census divisions. A map of the Census divisions can be seen in Figure III 23 Figure 3 24 Figure III Cont. 25 Econometric Issues Heteroskedasticity is often a problem in cross sectional data. Cross sectional data involves economic units of different sizes and it is likely that areas with larger economic units such as large firms or households have larger variation in the data because they have more members. This means that the variance (σ2) in the variancecovariance matrix is not constant due to structural/spatial instability. If micropolitan areas close to larger metropolitan areas tend to have larger population, it could result in a larger variation in their economic units and the overall data. This research study uses Ordinary Least Squares (OLS) model regressions and the consequences of spatial heteroskedasticity on the OLS estimates are incorrect standard errors and the variancecovariance matrix for the estimators is incorrect. The estimators are still unbiased but are not the best linear unbiased estimators (BLUE). In order to correct this problem, all the regressions in this study are ran using the White’s adjusted variance in the variancecovariance matrix which has been widely accepted and used in economic literature. Serial correlation can also be a problem in cross sectional data; although, unusual and typically not worrisome (Schmidt, 2005 P.225). If a data set includes both metropolitan and nonmetropolitan county data then a situation can occur where unexplained population (wage or rent) growth in metropolitan counties can cause unexplained population (wage or rent) growth in adjacent nonmetropolitan counties. Therefore, cov(eiej)≠0 indicating spatial dependence and autocorrelation, which means that the estimators are not BLUE. However, the data in this study includes only micropolitan areas that are fairly well scattered across the nation and are not adjacent to each other. 26 In order to analyze the extent of the problem with autocorrelation, the error terms for all the micropolitan areas in this study were regressed on the Census divisions for all three regressions (population growth, rent growth and wage growth) in order to determine if the Census divisions were able to explain the distribution of the error terms. The results show that there is no significant spatial dependency in the error terms (see Table I). Table I PopulationGroup Regression Dependent Variable: ehat Residual Number of Observations Read 511 Analysis of Variance F Value Pr > F <.0001 Parameter Estimates Variable DF Parameter Estimate Standard Error t Value Pr > t Intercept 1 3.60E13 0.88368 0 1 Division 1 5.62E14 0.16465 0 1 27 Table I Continued RentGroup Regression With Dependent Variable: ehat Residual Number of Observations Read 511 Analysis of Variance F Value Pr > F <.0001 Parameter Estimates Variable DF Parameter Estimate Standard Error t Value Pr > t Intercept 1 5.97E13 1.20417 0 1 Division 1 8.45E14 0.22437 0 1 WagesGroup Regression The REG Procedure Model: white Dependent Variable: ehat Residual Number of Observations Read 511 Analysis of Variance F Value Pr > F <.0001 Parameter Estimates Variable DF Parameter Estimate Standard Error t Value Pr > t Intercept 1 3.82E13 1.02181 0 1 Division 1 6.68E14 0.19039 0 1 28 Data Discussion and Description A decision was made to focus on the micropolitan areas that are located in the 48 contiguous continental states using the definition that was set out by the Office of Management and Budget in December of 2003. Going by that classification and after adjustments, the study started out with 554 micropolitan areas that encompass 662 counties in the lower 48 states. The study used 1990 and 2000 Census data for micropolitan areas (as defined by the Office of Management and Budget as of June 6, 2003  PHCT29). Due to the paucity of data collected for micropolitan areas, the study uses county level data that is aggregated into the Census micropolitan area definitions. The median gross rent is a weighted average of the median gross monthly rent for rental housing (complete count) and imputed rent for owner occupied housing (complete count), with the shares of renter and owner occupied houses as the weights. The median gross rent for rental housing is defined as contract rent plus the estimated average monthly cost of utilities (utilities are included, because they are sometimes included in the rental payment and therefore the median contract rent would be a biased estimator on median rent). The median imputed rent for owner occupied housing is calculated by converting the median value of owner occupied housing (complete count) using a discount rate of 7.85% (Peiser & Smith, 1985; Blomquist et al., 1988; Gabriel et al., 2003). The median gross rent does not control for differences in housing quality between regions. Average wages were calculated by dividing private nonfarm payroll by the private nonfarm employment. 29 Dividing the independent variables into groups enables broader analysis of the causational importance and better understanding of the growth effects. The data were therefore divided into seven groups (see Table II): 1. Amenity variable group (includes only natural amenities); 2. Demographics variable group; 3. Education variable group; 4. Fiscal and Other Policy variable group; 5. Economic variable group; 6. Urbanization variable group; 7. Census Division variable group. The Amenity variable group includes only natural amenities. The Amenity variable group includes: January and July temperatures; humidity; water area; and typography. The Demographic variable group includes: births per 1000 population; percent of married households; percent of African, Hispanic and Asian Americans; and percent of people in the 2549, 5064 and 65 plus age groups. The Educational variable group includes: percent of people with high school and “Bachelor’s, Master’s or Professional” degrees and the presence of a landgrant university to assess the education and accumulated knowledge in the area. 30 The Fiscal and Other Policy variable group includes: county and state property and sales taxes; county and state government spending on highway and safety; county spending on education; state spending on health and hospitals; state personal and corporation income taxes; and finally, right to work laws. All the state tax and spending variables are divided by the respective state personal income and all the county tax and spending variables are divided by the respective county personal income in order to access the effective burden of the policies to assure comparability between the different micropolitan areas. The Economic variable group includes: percent jobs in farming; agservice, forestry & fishing {from now on called agservices&ff}; mining; construction; manufacturing; services; government and the unemployment rate to control for the business cycle. Median gross rent is added in the rent regression and the average wage in the wage regression to control for beginning rents and wages in these regressions. The Urbanization variable group includes: the distance to nearest metropolitan area; and the incremental distance to the next metropolitan area with a population of 250 thousands, 500 thousands, and 1.5 million; and population density was included in the population and wage regressions to isolate the impact from industrial structure because industrial structure and population density can be correlated (Mueser & Graves, 1995). The Census division variable group includes Census divisions 29. 31 Table II. Description of Data and Data Groups Amenity Variables Obs Mean Std Dev Minimum Maximum Data Source Humidity 511 57.10 13.69 18 79 USDA Land Surface Form Typography codes: 511 8.49 6.67 1 21 USDA Mean January Temperature 511 33.08 11.69 3.1 63.4 USDA Mean July Temperature 511 75.79 5.38 55.9 86.7 USDA Water Sq. Miles 511 3.87 8.95 0.01 66.13 USA Counties Program: US Census Demographic Variables Obs Mean Std Dev Minimum Maximum Data Source Births per 1,000 population 1990 511 14.88 2.40 9.1 26.4 USA Counties Program: US Census Percent African American 1990 511 8.71 13.87 0 64.6 USA Counties Program: US Census Percent Asian American 1990 511 0.52 0.48 0.04 3.57 USA Counties Program: US Census Percent Hispanic American 1990 511 4.31 10.94 0.2 84.4 USA Counties Program: US Census Percent of Married Households 1990 511 59.39 4.68 42.5 73.3 USA Counties Program: US Census Percent of Population in over 65 or Older 1990 511 14.51 2.88 5.1347 31.3137 USA Counties Program: US Census Percent of Population in the 2549 Age Group 1990 511 34.51 2.35 26.1 46.7 USA Counties Program: US Census Percent of Population in the 5064 Age Group 1990 511 13.66 1.57 7.8099 20.9226 USA Counties Program: US Census 32 Education Variables Obs Mean Std Dev Minimum Maximum Data Source Educational attainment  persons 25 years and over  Bachelor’s, Master’s, or Professional degree 1990 511 13.27 4.50 5.5 36.3 USA Counties Program: US Census Educational attainment  persons 25 years and over  percent high school graduate or higher 1990 511 69.75 8.68 42.9 89.1 USA Counties Program: US Census Pretense of a Land Grant University 511 0.03 0.17 0 1 Association of Public and Land Grant Universities Fiscal and Other Policy Variables Obs Mean Std Dev Minimum Maximum Data Source Local Per Capita Sales Tax Revenues 1992 511 0.00 0.00 0 0.023533 USA Counties Program: US Census Local Per Capita Spending on Health Care 1992 511 0.01 0.00 0.00435 0.015885 Economic Census 1992 Local Per Capita Spending on Highway Infrastructure 1992 511 0.01 0.00 0.000622 0.024515 Economic Census 1992 Local Per Capita Spending on Public Education 1992 511 0.05 0.01 0.02926 0.13888 Economic Census 1992 Local Per Capita Spending on Public Safety 1992 511 0.01 0.00 0.000804 0.021972 Economic Census 1992 Local Per Captia Property Tax Revenues 1992 511 0.03 0.01 0.00371 0.09937 USA Counties Program: US Census Right to Work State 511   0 1 Dr Rickman State Per Capita Spending on Highway Infrastructure 1992 511 0.01 0.00 0.007904 0.039311 Economic Census 1992 State Per Capita Spending on Public Safety 1992 511 0.01 0.00 0.007207 0.021361 Economic Census 1992 33 State Per Captia Corporate Income Tax Revenues 1992 511 0.00 0.00 0 0.0097879 Economic Census 1992 State Per Captia Income Tax Revenues 1992 511 0.02 0.01 0 0.039943 Economic Census 1992 State Per Captia Property Tax Revenues 1992 511 0.03 0.01 0.010091 0.060725 Economic Census 1992 State Per Captia Sales Tax Revenues 1992 511 0.02 0.01 0 0.051105 Economic Census 1992 Economic Variables Obs Mean Std Dev Minimum Maximum Data Source Average Wages 1990 511 16.88 2.38 10.4361 29.0493 USA Counties Program: US Census Employment in AgService: Percent of Total Jobs 511 1.20 1.11 0 12.6 USA Counties Program: US Census Employment in Farming: Percent of Total Jobs 511 6.26 3.64 0.4 20.8 USA Counties Program: US Census Jobs in Construction: Percent of Total Private Non Farm Jobs 511 4.77 1.78 0 14.9 USA Counties Program: US Census Jobs in Government: Percent of Total Employment 511 16.87 7.46 6.9 60.8 USA Counties Program: US Census Jobs in Manufacturing: Percent of Total Private Non Farm Jobs 511 18.35 10.25 1.3 47.6 USA Counties Program: US Census Jobs in Manufacturing: Percent of Total Private Non Farm Jobs 511 21.08 5.33 0 37.2 USA Counties Program: US Census Jobs in Mining: Percent of Total Private Non Farm Jobs 511 1.54 3.35 0 25.2 USA Counties Program: US Census Mean Gross Rent 1990 511 325.60 86.99 176.915 906.013 USA Counties Program: US 34 Census The Unemployment Rate 511 7.07 2.39 1.9 15.7 USA Counties Program: US Census Urbanization Variables Obs Mean Std Dev Minimum Maximum Data Source Distance to Next Metropolitan area 511 78.42 45.92 17.011 334.945 Partridge et al, 2010 Incremental Distance to the Next Metropolitan Area with a Population of 1.5 million or less 511 98.86 117.95 0 532.302 Partridge et al, 2010 Incremental Distance to the Next Metropolitan Area with a Population of 500,000 or less 511 34.42 55.11 0 362.772 Partridge et al, 2010 Incremental Distance to the Next Metropolitan Area with a Population of 250,000 or less 511 47.16 79.87 0 601.043 Partridge et al, 2010 Population Density 1990 511 62.38 41.68 1.787 265.301 USA Counties Program: US Census Census Division Variables Obs Mean Std Dev Minimum Maximum Data Source Census Divisions 29 511   0 1 US Census 35 A micropolitan area can be an outlier of growth because of two reasons: 1. Micropolitan areas with average level independent variables experiencing growth well above/below the typical micropolitan area. 2. Micropolitan areas with outlier independent variables The scope of this study includes the first reason, but not the second. Therefore the data were also purged of micropolitan areas with extreme outliers in the independent variables in order to be able to focus on outliers of micropolitan growth with average level independent variables. Purging of the Outliers using the Method of the Hat Matrix Analysis on the raw data revealed a significant variation in the data for the independent variables. A decision was made to purge the areas with disproportionate values of the independent variables, using the method of the Hat Matrix, in order to be able to focus on micropolitan areas that had outlier growth in the dependent variables, but more average level independent variables. The regression estimator b is based on both the X variables and the Y variable 1 ( ) T T b x x x y (26) and the hat matrix is defined as h = 1 ( ) T T x x x (27) bh*y (28) Therefore, the X variables in the hat matrix multiplied with dependent variable yield the 36 regression estimate. On way to purge the disproportionate X variables is based on leverage analysis on the Hat Diagonal Matrix (Belsley, Kuh, and Welsch, 1980). This method measures the influence of each observation on the regression estimates. The proposed cutoff for the influence statistic is: 2* p n (29) where “p” is number of parameters and “n” is the number of observations. Purging of the Outliers using the Method of kMeans Clustering The method of “kmeans” clustering was also used to identify outliers of micropolitan growth in the independent variables. The “kmeans” clustering method allocates all the data points in a set into k clusters in a way that minimizes the Euclidean distance between the average in the cluster (cluster center) and each point in the cluster4. This is an evolutionary algorithm which initially selects the k cluster means randomly from the data points and then it selects the closest points from the data to the kcluster means based on the Euclidean distance and then the cluster mean is recomputed. These steps are repeated until all the data points are allocated to clusters and reallocation of data between clusters is not going make any significant difference. The Fastclus procedure in SAS was used to do “five centroid” cluster analysis and micropolitan areas with extreme above and below growth performance in the dependent variables were identified for each dependent variable. Most of the outliers identified corresponded to outliers that were identified by the “Hat matrix” method. 4 http://support.sas.com/documentation/cdl/en/statugcluster/61777/PDF/default/statugcluster.pdf 37 Final Data and Variance Analysis The study started out with 554 micropolitan areas. After analyzing the data, there were four observations with data problems that were removed. The “Hat Matrix” method resulted in the purging of 40 observations and an additional three areas of observations were purged due to being extreme outliers in the cluster analysis. Therefore, data from 511 micropolitan areas were used for the study. This purging of disproportionate “X” variables resulted in a reduction of total variance of 25.2 percent in the population growth regression, 9.1 percent in the rent growth regression, and 20.3 percent in the wages growth regression. The data still show significant variation in the dependent variables as shown in Table III: population growth ranged from negative 17.1 percent to 73.6 percent during the period; negative 2.8 percent to 133.7 percent for rent (mean gross rent); and negative 2.9 percent to 97.9 percent for wages. 38 Table III. Variance Analysis of the Dependent Variables Dependent Variables N Min Max Mean STD Pop Growth 511 17.1% 73.6% 9.3% 11.2% Rent Growth 511 2.8% 133.7% 54.6% 19.2% Wages Growth 511 2.9% 97.9% 40.7% 11.1% 39 Variance Decomposition of the R2  Dominance Analysis It is of value to know the usefulness of the different variable groups for the dependent values and to find out which group is most important, the second most important, etc. Analyzing bivariate correlations between the dependent variables and the independent variables is not going to suffice because the bivariate correlation ignores other variables in the regression. In order to assess the contribution of the different variable groups to the explained behavior in the dependent variable it is possible to use some type of variance decomposition method to find out how big a portion of the total explained variation in the population, rent and the wage regressions is explained by the different variable groups. One way to do that is with dominance analysis based on the explained variance. The ideal method should meet three criteria: importance of a predictor should be defined in terms of a variance reduction error; the method should allow for direct comparison, rather than inferred measures; and importance of a predictor should reflect the direct effect (when considered by itself), total effect (conditional on all other variables) and the partial effect (conditional on a subset of predictors). Dominance analysis satisfies all these requirements and the results are transitive relationships and are not affected by any elimination of a subset of predictors from the model (Budescu, 1993). However, complete dominance cannot always be established between every pair of predictors. Complete dominance cannot be established if an additional contribution of a predictor to the R2 is greater than other predictors for some but not all of the subset models (X1 might dominate X2 independently, but X2 might contribute more when you add it to X1 40 than if you add X1 to X2). In that case, one can use “conditional dominance” or “general dominance.” Conditional dominance analysis focus on dominance between the different groups of the subset models and general dominance is based on the averaging of these conditional values. General dominance is therefore found by adding and averaging the conditional values and then the additional average contribution can be compared and it can be ordered. A predictor will generally dominate another predictor when it has a higher averaged additional contribution to the R2 and therefore accounts for a bigger portion of average explained variation of the dependent variable (Azen and Budescu, 2003). Complete dominance and conditional dominance analysis are outside the scope of this study and therefore general dominance analysis was undertaken to analyze the contribution of the different variable groups to explained variance in the data. With seven variable groups there are (271) = 127 possible different statistical combinations possible for the variable group regressions {combination (7,0)….combination (7, 6)}, which are the base regressions that have to be run to compare to. Furthermore, there are 63 additional regressions that have to be run for each group to find out the additional contributions to R2 when the respective variable group is added to the base regressions or a total 441 additional contribution regressions. Therefore, a total of 1450 regressions were run for all three models (population, wages and rent) for the general dominance analysis. Tables IV, V, & VI show the regression algorithm used for the variance decomposition to determine the order of general dominance for the variable groups in the population regression. Table IV shows a generic example of the calculations necessary to determine contributions for the X1 group (the Amenity variable group) for each line in the possible 64 variable group combinations (tables with complete results for all groups in all 41 regressions are listed in Appendix A). The variables in Table IV refer to: X1 = the Amenity variable group; X2 = the Demographics variable group; X3 = the Education variable group; X4 = the Fiscal and Other Policy variable group; X5 = the Economic variable group; the X6 = Urbanization variable group; and the X7 = Census division variable group (see Table II for description of the data). Table V shows how the average contribution was found for each of the seven combination subgroups (k=0..k=6) which then are also summed up and averaged. The average contribution to the R2 by the X1 group is {(0.120+ 0.097+ 0.074+ 0.056+ 0.044+ 0.035+ 0.027)/7}= 0.065. Similar regressions and calculations were run to get the contribution of each of the groups. Table VI shows how the average contribution to the R2 by each variable group is then summed up and equals 0.514 in the table. The relative contribution/general dominance for each variable group is then found by dividing the average R2 of each sub group into the total sum of R2 for all groups (Budescu, 1993). We can see that the X1 variable group has an average contribution to the explained variation in the population regression of 0.065 points, accounting for 12.6 percent of explained variation in the population data. The results from the dominance analysis will be analyised in detail the next section. Finally, this study used the adjusted R2 for the general dominance analysis rather than R2. That is because the adjusted R2 is preferable for decomposition when you have many variables and different number of variables in some groups between the models that are being compared. The adjusted R2 is a better estimate of the population R2, and that is what the R2 should be estimating (Wooldridge, 2005 p. 207). 42 Table IV. Generic Variance Decomposition Stage I – Regression Algorithm Generic Example Regressions and Calculations to Find the Average Contribution to the R2 by the X1 Group X1 X2  X2 X1 X3  X3 X1 X4  X4 X1 X5  X5 X1 X6  X6 X1 X7  X7 X1 X2 X3  X2 X3 X1 X2 X4  X2 X4 X1 X2 X5  X2 X5 X1 X2 X6  X2 X6 X1 X2 X7  X2 X7 X1 X3 X4  X3 X4 X1 X3 X5  X3 X5 X1 X3 X6  X3 X6 X1 X3 X7  X3 X7 X1 X4 X5  X4 X5 X1 X4 X6  X4 X6 X1 X4 X7  X4 X7 X1 X5 X6  X5 X6 X1 X5 X7  X5 X7 X1 X6 X7  X6 X7 X1 X2 X3 X4  X2 X3 X4 X1 X2 X3 X5  X2 X3 X5 X1 X2 X3 X6  X2 X3 X6 X1 X2 X3 X7  X2 X3 X7 X1 X2 X4 X5  X2 X4 X5 X1 X2 X4 X6  X2 X4 X6 X1 X2 X4 X7  X2 X4 X7 X1 X2 X5 X6  X2 X5 X6 X1 X2 X5 X7  X2 X5 X7 X1 X2 X6 X7  X2 X6 X7 X1 X3 X4 X5  X3 X4 X5 X1 X3 X4 X6  X3 X4 X6 X1 X3 X4 X7  X3 X4 X7 X1 X3 X5 X6  X3 X5 X6 X1 X3 X5 X7  X3 X5 X7 X1 X3 X6 X7  X3 X6 X7 X1 X4 X5 X6  X4 X5 X6 X1 X4 X5 X7  X4 X5 X7 X1 X4 X6 X7  X4 X6 X7 X1 X5 X6 X7  X5 X6 X7 X1 X2 X3 X4 X5  X2 X3 X4 X5 X1 X2 X3 X4 X6  X2 X3 X4 X6 X1 X2 X3 X4 X7  X2 X3 X4 X7 X1 X2 X3 X5 X6  X2 X3 X5 X6 X1 X2 X3 X5 X7  X2 X3 X5 X7 X1 X2 X3 X6 X7  X2 X3 X6 X7 X1 X2 X4 X5 X6  X2 X4 X5 X6 X1 X2 X4 X5 X7  X2 X4 X5 X7 X1 X2 X4 X6 X7  X2 X4 X6 X7 X1 X2 X5 X6 X7  X2 X5 X6 X7 X1 X3 X4 X5 X6  X3 X4 X5 X6 X1 X3 X4 X5 X7  X3 X4 X5 X7 X1 X3 X4 X6 X7  X3 X4 X6 X7 X1 X3 X5 X6 X7  X3 X5 X6 X7 X1 X4 X5 X6 X7  X4 X5 X6 X7 X1 X2 X3 X4 X5 X6  X2 X3 X4 X5 X6 X1 X2 X3 X4 X5 X7  X2 X3 X4 X5 X7 X1 X2 X3 X4 X6 X7  X2 X3 X4 X6 X7 X1 X2 X3 X5 X6 X7  X2 X3 X5 X6 X7 X1 X2 X4 X5 X6 X7  X2 X4 X5 X6 X7 X1 X3 X4 X5 X6 X7  X3 X4 X5 X6 X7 X1 X2 X3 X4 X5 X6 X7  X2 X3 X4 X5 X6 X7 X1 Total of 64 Lines 43 Table V. Generic Variance Decomposition Stage II – Average Contribution to the R2 Calculations by Each Variable Group Additional Number Base Adj. Contribution Contribution Combination Regr Regr R2 Regression Adj R2 Economic K=0 1 0 X1 0.120 0.120 K=1 X2 0.100 X2 X1 0.192 0.092 : : : : : K=1 Avg. (sum/6) 6 0.097 K=2 X2 X3 0.212 X2 X3 X1 0.295 0.084 : : : : : K=2 Avg. (sum/15) 15 0.074 K=3 X2 X3 X4 0.342 X2 X3 X4 X1 0.36 0.36 : : : : : K=3 Avg. (sum/20) 20 0.056 K=4 X2 X3 X4 X5 0.394 X2 X3 X4 X5 X1 0.435 0.435 : : : : : K=4 Avg. (sum/15) 15 0.044 K=5 X2 X3 X4 X5 X6 0.407 X2 X3 X4 X5 X6 X1 0.443 0.443 : : : : : K=5 Avg. (sum/6) 6 0.035 K=6 1 X2 X3 X4 X5 X6 X7 0.483 X2 X3 X4 X5 X6 X7 X1 0.51 0.027 Total/Overall Avg 64 (0.120+0.097+0.074+0.056+0.044+0.035+0.027)/7 0.065 44 Table VI Generic Variance Decomposition Stage III Avg. Contribution Simple Average R2 Percent X1 0.065 12.6% X2 0.086 16.8% X3 0.035 6.7% X4 0.087 17.0% X5 0.114 22.2% X6 0.022 4.3% X7 0.105 20.4% Sum 0.514 100% 45 Beta Coefficient Analysis Dominance analysis on the variable groups only tells us the relative importance of the respective variable groups. It is also of value to access the size and statistical significance of the coefficients to compare their relative importance within the respective variable groups. Achen (1982) states that “ j ” measures the potential influence of the variable and is independent of the sample; “ X “(where j X is the mean of the jth variable) measures the level importance and is dependent on the sample; and j j y (the Beta coefficient) measures the dispersion/relative importance because it is adjusted for the scale of the data. The regular OLS/GLS regression coefficients are sensitive to scale of the data and the standardized “Beta” coefficients were therefore used to analyze the relative importance of the different coefficients within each variable group. The impact is measured in terms of standard units rather than the original units of the independent and dependent variables. By doing that, all the variables are in the same equivalent standard deviation units and it brings out their relative importance (Achen, 1982). All the Beta coefficients from the 64 possible combinations for each variable in each group were added up and averaged to get the average standardized impact from each variable within the groups (The calculation of all the average Beta coefficients are listed in Appendix B). There are mostly two types of problems that have been discussed with the Beta coefficients (from now on they are sometimes referred to as BC) in the economic literature. 46 Firstly, some variables do not change a whole lot over time, while others do5. That is not a major obstacle here because this study uses crosssectional data. Secondly, some economic literature suggests that if there are positive and negative coefficients that are averaged, then there can be problems with the average impact and perhaps the directional effect (Azen and Budescu, 2009 p.304). Analyses were undertaken to find out the extent of alternate signs in all three models and to evaluate if there was a problem with averaging due to alternating positive/negative coefficients. The problem was found to be trivial because the alternating positive/negative coefficients were mostly in groups with little relative importance in the respective models and overall alternating signs only happened about 12.2 percent of the time. 5 Beta coefficients have been criticized because some variables are not possible to change while others are easy to change (Larry D. Schroeder, David L. Sjoquist, Paula E. Stephan. Understanding regression analysis, Sage Publications, 1986, ISBN 0803927584, p.3132. 47 CHAPTER IV FINDINGS Regression Results This chapter reviews the findings and analyses the viability of the regression results. The findings are also analysed in detail in the context of general dominance analysis and the GlaeserTobio model. The Population Regression The population growth regression included 50 variables and had an R2 of 55.8 percent. A total of 23 variables were significant at the 5 percent level and an additional 3 at the 10 percent level (see Table VII). The following variables induced population growth in micropolitan areas during the period: January temperatures, percent Bachelor’s degrees, birth rates, percent of 5064 age group, percent married households, per capita county highway spending, per capita spending on public education and Census divisions 36 & 8, (East North Central, West North Central, South Atlantic, East South Central and Mountain divisions) which are all significant at the 5 percent level. Typography (1=flat plains, the48 higher number the more hills and mountains), percent of farm jobs and Census division 7 (West South Central division) are significant at the 10 percent level). The fiscal variables should be interpreted cautiously. Taxes and government spending should be considered together because everything else being equal then taxes can be expected to have a negative impact on the attractiveness of an area wheras government spending is expected to have an positive impact. All the fiscal variables in the model should also be interpreted relative to the fiscal variables that are not in the model. Positive coefficients of the fiscal variables in the population regression in the context of the GlaeserTobio model framework contribute to local amenities, only if it also has the impact to increase rents and reduce wages (causing a decline in real wages). These variables decreased population growth: July temperatures, humidity, distance to next metropolitan area regardless of size, incremental distance to the next metropolitan area with a population of 250,000 or less, percent of agservice jobs, mining and manufacturing jobs, percent of Hispanics, county spending on safety, state spending on hospitals and the state income tax burden. 49 TABLE VII Results for Population Regression Dependent Variable: GrPop9000 Number of Observations Read 511 Analysis of Variance F Value Pr > F <.0001 Parameter Estimates Variable DF Parameter Estimate Standard Error t Value Pr > t Intercept 1 36.47122 25.51977 1.43 0.1536 TempJan 1 0.5659 0.11155 5.07 <.0001 TempJuly 1 0.64762 0.19694 3.29 0.0011 Humidity 1 0.20592 0.08001 2.57 0.0104 Water 1 0.06641 0.04978 1.33 0.1829 Typography 1 0.16507 0.08574 1.93 0.0548 Dist to next Metro 1 0.02659 0.01065 2.5 0.0129 incmetgt250k 1 0.01723 0.00645 2.67 0.0078 incmetgt500k 1 0.00336 0.00769 0.44 0.6623 incmetgt1500k 1 0.00123 0.00471 0.26 0.7939 D2 1 5.04378 3.79443 1.33 0.1844 D3 1 9.93344 3.50554 2.83 0.0048 D4 1 10.57837 3.83796 2.76 0.0061 D5 1 18.05848 3.94865 4.57 <.0001 D6 1 10.92284 4.12424 2.65 0.0084 D7 1 7.95805 4.29385 1.85 0.0645 D8 1 14.78795 5.3179 2.78 0.0056 D9 1 1.9461 5.67182 0.34 0.7317 PopDens90 1 0.00095755 0.01442 0.07 0.9471 LandGrantU 1 0.54496 2.234 0.24 0.8074 PcFarmJobs90 1 0.3111 0.17017 1.83 0.0682 PcAgServ&ffJobs90 1 1.2743 0.44447 2.87 0.0043 PcMinJobs90 1 0.95969 0.16074 5.97 <.0001 PcConstJobs90 1 0.39792 0.2578 1.54 0.1234 PcMfgJobs90 1 0.19688 0.07875 2.5 0.0128 PcServsJobs90 1 0.11551 0.10111 1.14 0.2538 PcGovJobs90 1 0.1347 0.09807 1.37 0.1703 PcBA90 1 0.88382 0.19945 4.43 <.0001 PrcntHsch 1 0.03016 0.11761 0.26 0.7977 PcUnempl90 1 0.28651 0.27988 1.02 0.3065 Births90 1 0.72105 0.24772 2.91 0.0038 PcPopBlack90 1 0.01306 0.0658 0.2 0.8428 PcPopHisp90 1 0.13504 0.0566 2.39 0.0174 PcPopAsian90 1 0.40852 1.10754 0.37 0.7124 PcAge2549 1 0.24725 0.26248 0.94 0.3467 PcAge5064 1 1.20285 0.50468 2.38 0.0176 PcAge65plus 1 0.23504 0.29608 0.79 0.4277 PCMrdHH90 1 0.72772 0.16284 4.47 <.0001 50 cty92property 1 48.96037 53.11723 0.92 0.3571 cty92sales 1 196.10321 133.7142 1.47 0.1432 cty92highway 1 558.957 150.79019 3.71 0.0002 cty92safety 1 520.9902 227.21944 2.29 0.0223 cty92education 1 92.60638 45.06497 2.05 0.0404 stl92property 1 1.08845 96.87452 0.01 0.991 stl92sales 1 46.00734 86.19853 0.53 0.5938 stl92inctax 1 218.52629 67.00757 3.26 0.0012 stl92corptax 1 9.13939 292.02945 0.03 0.975 stl92hosp 1 604.83367 307.36527 1.97 0.0497 stl92highway 1 93.30443 143.22857 0.65 0.5151 stl92pblsfty 1 438.0431 324.02459 1.35 0.1771 Right to Work 1 0.06422 1.58681 0.04 0.9677 51 The Rent Regression The rent growth regression included 50 variables (see Table VIII) and had R2 of 71.77 percent. A total of 29 of the variables were significant at the 5 percent level and an additional 3 were significant at the 10 percent level. Thereof, 19 were also significant in the population regression. Interestingly, 18 of those had the same sign in both regressions. The significant variables common to both regressions with a positive sign were: Census divisions 38 (Census division 7 was significant at the 10 % level in the population regression), percent Bachelor’s degrees, percent of 5064 age group, percent married households, per capita county spending on highways and public education. The significant variables common to both regressions with a negative sign were: July temperatures, distance to next metropolitan area regardless of size, incremental distance to the next metropolitan area with a population of 250,000 or less, percent of mining jobs, percent of agservice jobs and manufacturing jobs (at 10 percent significance), and percent Hispanics. The only variable significant in both regressions with opposite sign to the population regression was the birth rate, which had a negative sign in the rent regression. The following variables with positive sign were significant in the rent regression, but not the population regression: water area, Census division 2 and 9 (the Middle Atlantic and Pacific Census divisons), county sales tax, and the right to work. 52 TABLE VIII Results for Rent Regression Dependent Variable: GrRent9000 Number of Observations Read 511 Analysis of Variance F Value Pr > F <.0001 Variable DF Parameter Estimate Standard Error t Value Pr > t Intercept 1 126.47013 34.58933 3.66 0.0003 TempJan 1 0.12653 0.1517 0.83 0.4047 TempJuly 1 1.20862 0.27016 4.47 <.0001 Humidity 1 0.14783 0.10979 1.35 0.1788 Water 1 0.33217 0.06614 5.02 <.0001 Typography 1 0.15657 0.11703 1.34 0.1816 Dist to next Metro 1 0.08026 0.01428 5.62 <.0001 incmetgt250k 1 0.0606 0.00882 6.87 <.0001 incmetgt500k 1 0.03601 0.01044 3.45 0.0006 incmetgt1500k 1 0.00394 0.00658 0.6 0.5498 D2 1 23.74669 5.65662 4.2 <.0001 D3 1 51.50236 5.38473 9.56 <.0001 D4 1 42.94197 5.73542 7.49 <.0001 D5 1 40.96864 5.84281 7.01 <.0001 D6 1 38.67004 6.08033 6.36 <.0001 D7 1 32.39297 6.3042 5.14 <.0001 D8 1 62.27736 7.61715 8.18 <.0001 D9 1 67.32323 7.9478 8.47 <.0001 MGR90 1 0.0923 0.01279 7.22 <.0001 LandGrantU 1 0.05374 3.04394 0.02 0.9859 PcFarmJobs90 1 0.30076 0.22947 1.31 0.1906 PcAgServJobs90 1 1.14988 0.60717 1.89 0.0589 PcMinJobs90 1 1.16698 0.22352 5.22 <.0001 PcConstJobs90 1 0.27303 0.3534 0.77 0.4402 PcMfgJobs90 1 0.19112 0.11024 1.73 0.0836 PcAgServ&ffJobs90 1 0.07885 0.13827 0.57 0.5688 PcGovJobs90 1 0.30236 0.13486 2.24 0.0254 PcBA90 1 1.10344 0.28983 3.81 0.0002 PrcntHsch 1 0.13439 0.1598 0.84 0.4008 PcUnempl90 1 0.88648 0.3922 2.26 0.0243 Births90 1 0.86789 0.33957 2.56 0.0109 PcPopBlack90 1 0.14546 0.09353 1.56 0.1206 PcPopHisp90 1 0.16669 0.07706 2.16 0.031 PcPopAsian90 1 3.59393 1.50481 2.39 0.0173 PcAge2549 1 0.5035 0.36879 1.37 0.1728 PcAge5064 1 1.81365 0.69043 2.63 0.0089 PcAge65plus 1 1.21424 0.40455 3 0.0028 53 PCMrdHH90 1 0.55723 0.23489 2.37 0.0181 cty92property 1 84.39263 73.3082 1.15 0.2502 cty92sales 1 394.74195 182.38784 2.16 0.031 cty92highway 1 455.18353 203.01268 2.24 0.0254 cty92safety 1 157.88553 308.85868 0.51 0.6095 cty92education 1 135.94803 61.35159 2.22 0.0272 stl92property 1 26.56184 135.47593 0.2 0.8446 stl92sales 1 204.71917 117.45434 1.74 0.082 stl92inctax 1 134.7349 91.23756 1.48 0.1404 stl92corptax 1 175.14744 405.41684 0.43 0.6659 stl92hosp 1 89.08006 415.72019 0.21 0.8304 stl92highway 1 95.77941 195.23795 0.49 0.624 stl92pblsfty 1 1337.89128 458.40038 2.92 0.0037 Right to Work 1 4.94588 2.16231 2.29 0.0226 The following variables with negative sign were significant in the rent regression, but not the population regression: incremental distance to the next metropolitan area with a population of 500,000 or less, average rent, percent of government jobs, percent of unemployment, percent of Asian population, percent of people over 65, spending on public safety, and state sales tax (at 10 percent significance). The Wage Regression The wage growth regression included 51 variables (see Table IX) and had R2 of 39.23 percent. A total of 12 variables were significant at the 5 percent level and an additional 5 variables were significant at the 10 percent level. Six of those variables were also significant in the population and the rent regressions. Percent of Bachelor's degree and Census division 8 (Mountain division) has a positive coefficient in all three regressions and incremental distance to the next metropolitan area with a population of 250,000 or less and percent agservices&ff jobs had negative coefficent in all three regressions. 54 July temperatures and percent of manufacturing jobs (at 10 % significance for both) had positive coefficient in the wage regressions, but negative in the other regressions. This makes sense because wages are overall lower in the south and manfacturing firms with standardized product seek out places with low wages to reduce unit costs. At the same time, very high July temperatures makes it more difficult to enjoy local natural amenities and reduce migration and rent. January temperatures was significant in the wage regression and the population regression. It had a negative sign in the wage regression, but a positive sign in the population regression. Four coefficients were significant in the wage regression and the rent regression. Water area and Census division 9 (the Pacific division) had positive coefficients in both regressions and percent unemployment and incremental distance to the next metropolitan area with 500,000 or less (10% significance) had negative coefficients. Six variables were significant only in the wage regression. Incremental distance to the next metropolitan area with 1.5 million or less, average wages and state highway spending (10 percent significance) had negative impact on wages. However, percent of construction jobs, percent of black population and percent of 2549 age group (at 10 percent significance) had a positive impact on wages. 55 TABLE IX WageRegression Dependent Variable: Grwage9000 Number of Observations Read 511 Analysis of Variance F Value Pr > F <.0001 Variable DF Parameter Estimate Standard Error t Value Pr > t Intercept 1 22.3544 29.58206 0.76 0.4502 TempJan 1 0.47141 0.12939 3.64 0.0003 TempJuly 1 0.43192 0.22799 1.89 0.0588 Humidity 1 0.07688 0.09262 0.83 0.407 Water 1 0.12748 0.05767 2.21 0.0276 Typography 1 0.02333 0.09949 0.23 0.8147 Dist to next Metro 1 0.01688 0.01233 1.37 0.1716 incmetgt250k 1 0.01811 0.00748 2.42 0.0159 incmetgt500k 1 0.01568 0.0089 1.76 0.0787 incmetgt1500k 1 0.01153 0.00546 2.11 0.0351 D2 1 0.55476 4.39495 0.13 0.8996 D3 1 4.74925 4.0582 1.17 0.2425 D4 1 2.34333 4.44419 0.53 0.5983 D5 1 1.02669 4.57362 0.22 0.8225 D6 1 3.79214 4.78308 0.79 0.4283 D7 1 5.52136 4.97295 1.11 0.2675 D8 1 16.24993 6.15748 2.64 0.0086 D9 1 13.44462 6.5658 2.05 0.0412 AvgWage90 1 2.86843 0.26085 11 <.0001 PopDens90 1 0.01009 0.0167 0.6 0.5463 LandGrantU 1 0.2277 2.58838 0.09 0.9299 PcFarmJobs90 1 0.16661 0.19785 0.84 0.4002 PcAgServ&ffJobs90 1 1.03119 0.51572 2 0.0461 PcMinJobs90 1 0.06999 0.19257 0.36 0.7164 PcConstJobs90 1 0.85484 0.30091 2.84 0.0047 PcMfgJobs90 1 0.1832 0.09455 1.94 0.0533 PcServsJobs90 1 0.09622 0.11709 0.82 0.4116 PcGovJobs90 1 0.13944 0.11455 1.22 0.2241 PcBA90 1 0.47593 0.23112 2.06 0.04 PrcntHsch 1 0.11461 0.13979 0.82 0.4127 PcUnempl90 1 0.68748 0.32809 2.1 0.0367 Births90 1 0.03462 0.28678 0.12 0.904 PcPopBlack90 1 0.1736 0.07644 2.27 0.0236 PcPopHisp90 1 0.03317 0.0656 0.51 0.6133 PcPopAsian90 1 1.29629 1.28328 1.01 0.313 PcAge2549 1 0.57519 0.30498 1.89 0.0599 PcAge5064 1 0.78115 0.58451 1.34 0.1821 PcAge65plus 1 0.28774 0.3428 0.84 0.4017 PCMrdHH90 1 0.22655 0.19092 1.19 0.236 56 cty92property 1 23.55257 61.519 0.38 0.702 cty92sales 1 69.01308 155.05052 0.45 0.6565 cty92highway 1 33.81344 174.90351 0.19 0.8468 cty92safety 1 36.95562 265.18802 0.14 0.8892 cty92education 1 76.33809 52.32938 1.46 0.1453 stl92property 1 60.63414 112.72005 0.54 0.5909 stl92sales 1 7.69884 100.15981 0.08 0.9388 stl92inctax 1 28.91794 77.56926 0.37 0.7095 stl92corptax 1 169.91916 338.04747 0.5 0.6155 stl92hosp 1 47.75289 355.83419 0.13 0.8933 stl92highway 1 289.30196 166.14442 1.74 0.0823 stl92pblsfty 1 109.43551 375.12284 0.29 0.7706 Right to Work 1 2.54241 1.85205 1.37 0.1705 57 Analysis Almost 56 percent of the total variance in the population data is explained by the regression, 72 percent in the rent regression and 39 perecent in the wage regression. The fact that the explained variation in the rent regression is almost two times that of the wage regression is not unusual. That is because rent regressions explain one way impacts from both population migration and firm migration on rents. Rent increases in both cases. Wage regressions usually have a lower R2 because they explain two way (offsetting) impacts from firm migration and population migration on wages. When companies move to an area it results in higher wages due to increased labor demand, ceterus paribus. Higher wages then induce people to move to the area and the labor supply increases in the area resulting in lower wages, ceteris paribus. To a certain degree these opposite effects cancel each other out resulting in a lower R2. All of the variables in all the three regressions had plausible or expected signs. The fact that 19 of the significant coefficients in the population regression were also significant in the rent regression with only one having different signs (local birth rates increased population growth, but decreased rents) is good because higher/lower population growth, ceterus paribus, usually results in higher/lower rent. General Dominance Analysis General dominance for the different variable groups in the regressions is established in the next three sections and followed by identificiation and analysis of the factors that induced migration and economic growth to micropolitan areas. 58 General Dominance – Population Growth The average contribution to the explained population growth by the different variable groups is shown in Table X. The Economic variable group had the highest contribution to the explained variation in the population regression with an average contribution of 11.4 percent points to the average adjusted R2, accounting for 22.2 percent of explained variation in the population data. As mentioned in the section about data discussion and description, then the Beta coefficients from the 64 possible combinations for each variable in each group for all three regressions were added up and averaged to get the average standardized impact from each variable within each group in order indicate the relative importance of the respective variable within the group (see Appendix B). The relative size of the average standardized Beta coefficients show that concentration of employment in the mining industry (BC = 0.299), and the manufacturing industry (BC = 0.201) are significant detriment in migration in micropolitan areas (see Table XI). Farming had a positive impact but was only significant at 10 percent level (BC= 0.056) and agservices&ff (BC = 0.08) reduced migration .59 TABLE X. General Dominance  Population Growth Regressions Combinations Amenity Demographics Education Fiscal Economic Urbanization Census Division K=0 0.120 0.100 0.012 0.165 0.139 0.035 0.159 K=1 0.097 0.104 0.040 0.157 0.146 0.030 0.138 K=2 0.074 0.099 0.045 0.096 0.138 0.027 0.116 K=3 0.056 0.091 0.045 0.068 0.122 0.023 0.097 K=4 0.044 0.082 0.041 0.050 0.104 0.018 0.083 K=5 0.035 0.071 0.034 0.040 0.085 0.013 0.073 K=6 0.027 0.057 0.025 0.035 0.064 0.008 0.067 Simple Avg. 0.065 0.086 0.035 0.087 0.114 0.022 0.105 Percent of Explained Variation 12.6% 16.8% 6.7% 17.0% 22.2% 4.3% 20.4% TABLE XI. Significant Beta Coefficients Population Regression Amenity Demographics Education TempJan 0.482 PCMrdHH90 0.266 PcBA90 0.257 CCTypogC 0.113 PcAge5064 0.205 Humidity 0.196 Births90 0.151 TempJuly 0.236 PcPopHisp90 0.113 Fiscal Economic Urbanization cty92highway 0.130 PcFarmJobs90 0.056 CDist 0.131 cty92education 0.053 PcAgServJobs90 0.083 incmetgt250k 0.143 cty92safety 0.141 PcMfgJobs90 0.201 stl92inctax 0.143 PcMinJobs90 0.299 stl92hosp 0.211 Census Division D5 0.464 D8 0.340 D6 0.293 D7 0.210 D4 0.194 D3 0.170 60 The Census division variable group accounts for 20.4 percent of the average explained variation; contributing 10.5 percent points to the average adjusted R2. Although, there is no variation in the fixed effect, a higher Beta coefficient shows higher importance within the group. The South Atlantic Census (D5) division (BC = 0.464) seems to have (by far) the most region specific characteristics that are conducive to inmigration and explained by the regression, followed by: the Mountain (D8) division (BC = 0.34); the East South Central (D6) division (BC = 0.293); the West South Central (D7) division (BC = 0.210 at 10 percent significance); the West North Central (D4) division (BC = 0.194); and the East North Central (D3) division (BC = 0.17). It is interesting that the Middle Atlantic division which includes high population density cities such as New York and Philadelphia did not have a significant impact on population growth of micropolitan areas. Perhaps there are spillover effects from these megacities on their own region that people who move to micropolitan areas do not like. The Fiscal and Other Policy variable group explains 17.0 percent of variation in population growth that is explained by the regression adding 8.7 percentage points to the average adjusted R2. As explained in section 4.1, all the spending and tax variables are divided by the local personal income to estimate the effective burden from these policies in order to be able to compare between micropolitan areas in the same state and different states. The county spending on highway infrastructure (BC = 0.13) was the most conducive for inmigration, followed by county spending on education (BC = 0.053). All the other significant state and local tax variables reduced the attractiveness of 61 micropolitan areas: county spending on safety (BC = 0.141); state income tax (BC = 0.143) and the state spending on health and hospitals (BC = 0.21) The Demographics variable group contributes about 16.8 percent to the explained variation in data with average adjusted R2 being 8.6 percent. The percentage of married households (BC = 0.266) is the most significant factor that is conducive to population growth/migration to micropolitan areas in the demographic group, followed by the percent of people in the 5064 age group (BC = 0.204); and the birth rate (BC = 0.151). The least conducive local demographic characteristics for migration is the percent of Hispanic population (BC = .011). The Amenity variable group contributed 6.5 percentage points to the average adjusted R2 and the group explained 12.6 percent of the explained variation in population growth. Mild January temperatures stand out as being the natural amenity that is conducive to migration to micropolitan areas (BC = 0.482) followed by topography (BC = 0.113 at 10 percent significance). High July temperatures reduce inmigration significantly (BC = 0.236) as well high humidity (BC = 0.196). The Education variable group accounted for 6.7 percent of all explained variation in the data, adding 3.5 percent to the average adjusted R2. The percent of the population with Bachelor’s degree or higher (BC = 0.257) seems to be the only variable within the group of real importance in making the micropolitan area more attractive for migration. Finally, the Urbanization group explained only 4.3 percent of total explained variation, contributing 2.2 percentage points to the average adjusted R2. Interestingly, all the coefficents showed that being further away from a metropolitan area reduced the 62 attractiveness of the micropolitan area for migration. Incremental distance to a metropolitan area with 250,000 people (BC = 0.143) reduced attractiveness of microplitan areas more than any other distance variable, followed by the distance to the next metropolitan area (BC = 0.131). The other distance variables were not significant. It is especially noteworthy that the population density variable was not significant. General Dominance – Rent Growth The general dominance analysis on the rental regressions shows that the most important factor contributing to the explained behaviour in the rental data is the Census division group, which accounts for 40.8 percent of the explained variation of the rental data and adds 28.0 percentage points to the average adjusted R2 (see Table XII). All the Census divisions have relatively large Beta coefficents, indicating that the fixed effects are very important in explaining growth in rent for all regions (see Table XIII). It is difficult to say why the Census divisons fixed effect are so significant, but the analysis of the explained and residual (unexplained) growth effects later will help us understand that. Not surprisingly the Economic variable group ranks number two in explanatory importance, contributing 16.5 percent to the overall average explained variation, adding 11.3 percentage points to the average adjusted R2. All the significant variables in the group had a negative impact on rent growth. The most significant variables within the group are the median gross contract rent in 1990 (BC = 0.373) followed by the percent of jobs in mining (BC = 0.262); the percent of jobs in government (BC = 0.165); the unemployment rate (BC = 0.1); percent agservice jobs (BC = 0.067 at 10 percent 63 Table XIII Significant Beta Coefficients  Rent Regression Amenity Demographics Education Water 0.102 PcAge5064 0.161 PcBA90 0.004 TempJuly 0.365 PCMrdHH90 0.059 PcPopAsian90 0.071 Births90 0.141 PcPopHisp90 0.177 PcAge65plus 0.283 Fiscal Economic Urbanization cty92highway 0.133 PcMfgJobs90 0.066 incmetgt500k 0.025 RTW 0.132 PcAgServJobs90 0.067 CDist 0.127 cty92education 0.034 PcUnempl90 0.100 incmetgt250k 0.189 cty92sales 0.024 PcGovJobs90 0.165 stl92sales 0.064 PcMinJobs90 0.262 stl92pblsfty 0.111 MGR90 0.373 Census Division D3 1.202 D4 0.981 D5 0.885 D8 0.884 D9 0.837 D6 0.836 D7 0.742 D2 0.380 Table XII. General Dominance  Rent Growth Regressions Combinations Amenity Demographics Education Fiscal Economic Urbanization Census Division K=0 0.104 0.130 0.076 0.153 0.164 0.024 0.405 K=1 0.107 0.100 0.039 0.122 0.151 0.020 0.365 K=2 0.105 0.079 0.021 0.099 0.136 0.027 0.327 K=3 0.095 0.064 0.011 0.077 0.116 0.036 0.285 K=4 0.079 0.050 0.007 0.056 0.096 0.044 0.240 K=5 0.060 0.039 0.007 0.035 0.075 0.049 0.193 K=6 0.040 0.027 0.009 0.017 0.054 0.049 0.146 Simple Avg. 0.085 0.070 0.024 0.080 0.113 0.035 0.280 Percent of Explained Variation 12.3% 10.2% 3.5% 11.6% 16.5% 5.2% 40.8% 64 significance); and the percent of jobs in manufacturing (BC = 0.066 at 10 percent significance). The Amenity variable group accounted for 12.3 percent of the variation in the rent data, with the average adjusted R2 equal to 8.5 percent (which is close to the impact it had on population growth). The water area variable (BC = 0.102) is the most important variable in the group that explains increases in rent and the July temperatures (BC = 0.365) was the most important explaining lack of growth in rent. The other amenity variables do not seem to have much impact. The Fiscal and Other Policy variable group contributed 11.6 percentage points to the explained variation, adding 8.0 percentage points to the avarage adjusted R2. County spending on highway infrstructure (BC = 0.133) was the most important variable contributing to growth in rent, followed by right to work (BC = 0.132); county spending on education (BC = 0.034), and county sales taxes (0.024). State spending on public safety seems to reduce rent (BC = 0.11) as well as state sales taxes (BC =  0.064 at 10 percent significance). The Demographics variable group accounted for 10.2 percent of explained variation in the data, contributing 7.0 percentage points to the average adjusted R2. Percent of people over 65 (BC = 0.283) had the largest impact to reduce rent, followed by the percent of Hispanics (BC = 0.177), the birth rate (BC = 0.14) and the percent of the Asian population (BC 0.071). Two variables increased rent. The “percent of people in the 5064 age group” variable (BC = 0.161), which had a relatively large impact on rent growth and the percent of married households (BC = 0.059). 65 The Urbanization and the Education variable groups did not seem very important in explaining the variation in the rent data, contributing 5.2 and 3.5 percentage points to the explained variation in rent growth and adding average adjusted R2 of 3.5 percent and 2.4 respectively. All of the variables, except incremental distance to a metropolitan area with 1.5 million or less, were significant with negative coefficients in the Urbanization group, but only the percent of the population with Bachelor’s degree or higher was significant in the Education group and it had the impact of increasing rent. General Dominance – Wage Growth Factors that affect productivity, such as industry structure, affect wage increases significantly. There is, therefore, no surprise that the Economic Group is ranked on top in explaining wage growth in micropolitan areas (see Table XIV). However, what is a surprise is that the Economic Group accounts for 77.4 percent of all explainied variation in the wage data, contributing 25.1 percent to the R2 (far more than any other group). The most important variables in the group conducive to increase in producivity and wages (see Table VX) are the percent of jobs in manufacturing (BC = 0.201 pvalue = 5.3 percent) and construction (BC = 0.16). Average wages in 1990 (BC = 0.579) had the largest negative impact on wage growth followed by the unemployment rate (0.152) and the percent of jobs in agservices&ff (BC = 0.106). 66 Table XIV General Dominance  Wages Growth Regressions Combinations Amenity Demographics Education Fiscal Economic Urbanization Census Division K=0 0.019 0.009 0.013 0.007 0.256 0.002 0.011 K=1 0.025 0.003 0.015 0.012 0.262 0.001 0.015 K=2 0.028 0.004 0.015 0.014 0.263 0.005 0.018 K=3 0.030 0.009 0.014 0.014 0.259 0.008 0.019 K=4 0.030 0.013 0.011 0.011 0.251 0.010 0.018 K=5 0.028 0.014 0.007 0.006 0.240 0.011 0.015 K=6 0.025 0.014 0.002 0.002 0.229 0.012 0.011 Simple Avg. 0.026 0.006 0.011 0.009 0.251 0.006 0.015 Percent of Explained Variation 8.1% 1.9% 3.3% 2.7% 77.4% 1.9% 4.7% Table XV Significant Beta Coefficients  Wage regression Amenity Demographics Education TempJuly 0.178 PcPopBlack90 0.119 PcBA90 0.194 Water 0.099 PcAge2549 0.080 TempJan 0.399 Fiscal Economic Urbanization stl92highway 0.117 PcMfgJobs90 0.201 incmetgt500k 0.074 PcConstJobs90 0.160 incmetgt1500k 0.093 PcAgServJobs90 0.106 incmetgt250k 0.096 PcUnempl90 0.152 AvgWage90 0.579 Census Division D8 0.218 D9 0.101 67 Analysis in the earlier section on the “Economic Performance of Micropolitan Counties in the 1990's” indicated that the Manufacturing industries were moving out of metropolitan areas and rural areas to micropolitan areas. It is likely that the type of manufacturing that is moving into micropolitan areas is mature with a standardized product and therefore not affected much by urbanization economies. The Manufacturing industry is therefore likely moving out of metropolitan areas to areas with low wages (Vias, 1999) and it might be moving out of rural areas due to cost of distance. The second most important group is the Amenity group which contributes 8.1 percentage points to average explained variation and adds 2.6 percent to the average adjusted R2. It is interesting that “the percent water area” variable (BC = 0.100) has the largest significant positive impact on wage growth (perhaps because of access to navigable water transportation systems which is a firm amenity). July temperatures (BC = 0.178) also increased wages at the 10 percent significance level. High January temperatures (BC = 0.399) reduced the growth in wages. Other groups have negligible contribution to the average explained variation in the data. Analysis These results indicate that the migration to micropolitan areas was related to amenities. That is not a surprise because other studies have found natural amenities important in nonmetropolitan migration in the 1990s (Rappaport 2003 , Deller et al 2001, McGranahan 2007). The Economics Group is very important explaining the growth of population and rent (most important explaining population growth and the second most important 68 explaining rent growth). If the migration was demand sided and driven by job opportunities then relatively high percent of employment in manufacturing would be expected to affect inmigration and rent in a positive way because high levels of manufacturing employment may serve as an indicator of economic health (Gunderson et al, 2008). Relatively high wages also induce demand sided migration (Blanchard and Katz, 1992). However, all the significant employment variables in both regressions reduced migration and rent, except for farming employment in the population regression. Both manufacturing and mining have strong negative impact on migration and rent, which is consistent with amenity oriented migration. Both of these industries are often associated with pollution and environmental degradation and have a negative public perception  one that brings to mind pollution, low wages, assemblyline work and layoffs6. The average population growth was furthermore 10.8 percent in the 317 micropolitan areas that had less than average wage of all the 511 micropolitan areas in the study in 1990, well above the 7.2 percent growth of the 194 micropolitan areas that had higher than the average wage. Furthermore, these 317 locations have higher average amenity scale7 which is consistent with the GlaeserTobio model which clearly shows that locations high in amenities have lower wages than areas with low level of amenities in order to maintain the regional utility equilibrium. 6 See negative perception of manufacturing work at http://wtnnews.com/articles/2464 7 See USDA Natural Amenity Index at http://www.ers.usda.gov/Browse/view.aspx?subject=NaturalResourcesEnvironment 69 The percent of farm jobs had a positive coefficient in the population growth regression. Numerous studies have determined that farming is an amenity and some of these studies estimated the amenity value of farmland by calculating the implicit value of amenities associated with farming or with contingent studies (Bergstrom and Ready, 2009). The percent of agservices&ff jobs variable had a negative coefficient. If farming is generally located in areas high in amenities then one would expect the same for agservices&ff, but it had a negative coefficient in both the population and rent (at 10 percent significance) growth regressions. Most of the micropolitan areas in the study with a significant concentration of jobs in agservices&ff would be expected to have majority of the jobs in the agservices sub industry but not forestry and fishing. It is of therefore of value to analyze agservices employment better. It includes: soil preparation services, crop services, veterinary services, animal services (except veterinary), farm labor and management services, landscape and horticultural services. Employment in the agservices subindustries declined 13.9 percent nationwide during the 1990’s and one would therefore expect that micropolitan areas with a large concentration of agservices employment to be declining too. Therefore it is plausible that the the negative coefficient had something to do with labor demand. The Fiscal and Other Policy group was relatively important in explaining the behavior in both the population and rent data. All the significant variables in the population regression (except county spending on education and highways) reduced migration, including state spending on health and hospitals, which had the largest impact (by far) of all the significant fiscal variables on population growth. That perhaps reflects 70 the Medicaid burden for states. Medicaid accounted for 19.2 percent of the average state budget in the US in the 1995 fiscal year, with the share of budget allocated to Medicaid ranging from a low of 5.1 percent in Alaska to a high of 38.2 percent in New Hampshire8. States with heavy Medicaid burdens can be expected to compensate with policy actions that make them less attractive, and that could explain the negative coefficient. High spending on health and hospitals could also reflect a relatively sickly population, which makes the area less attractive and deters migration. This indicates that high effective local tax burden is a drag on population growth and economic development. This is supported by some studies in the literature. Bartik (1992) finds that high local effective tax rates on average reduce economic growth. However, both the county government spending on highways and education had a positive impact on migration, which is also supported somewhat by the economic literature. Fisher (1997) found that that local government spending can have a positive impact on population and economic growth, especially spending on highway infrastructure and to a lesser degree on education. Both local and state spending on public safety reduced migration and rent. That could indicate that micropolitan areas with relatively high spending on public safety also had more crimes. The Demographic group was also relatively important explaining migration and rent growth. A high concentration of people in the 5064 age group increased both inmigration and rent, implying that this age group was most likely to migrate to 8The National Association of State Budget Officers 1995 State Expenditure Report: http://www.nasbo.org/Publications/StateExpenditureReport/tabid/79/Default.aspx 71 micropolitan areas during the 1990’s. This is supported by Plane et al (2005) who found that there was a substantial migration in the latter parts of the 1990’s by people in the 5064 age group from large metropolitan areas to micropolitan and rural areas. Stability as measured by the percent of married households locally was also attractive local characteristic for micropolitan migration, showing significant positive impact on the growth of both population and rent. Approximately 59.3 percent of all households in 1990 were married in the 511 micropolitan areas in the study, compared to 55.1 percent nationwide. It is reasonable to surmise that micropolitan areas are relatively safe, which is an attractive local characteristic for migration. Crime rates decline with higher household incomes and crime rates are in general higher in nonfamily households (householder not married)9. If micropolitan areas with less concentration of married households have higher crime rates resulting in relatively high spending on public safety then it would explain the negative relationship between local spending on public safety and migration that we discovered earlier when we analysed the fiscal and policy variables. A high concentration of Hispanics reduced both population and rent. The Hispanic population is one of the youngest populations in the US and two in five are foreign born10. Hispanics are furthermore one of the most nomadic populations in the US with 14.1 percent of all Hispanics in 2000 reporting they lived in a different county five years earlier, compared to 8.4 percent overall US average11. If stability is attractive locational characteristic for migration then a high concentration of Hispanics in a location 9 The Bureau of Justice Statistics report: http://bjs.ojp.usdoj.gov/index.cfm?ty=tp&tid=92 10 US Census Report: http://www.census.gov/prod/2003pubs/p20545.pdf 11 USCensus 72 would have negative effect on inmigration. The Hispanic population is also overall relatively unskilled and if areas with high concentration of unskilled people are unattractive for migration then that could as well explain why a concentration of Hispanics had a negative impact on both population and rent. However, the explanation could also include things like culture or funic avoidance behavior. The Amenity group was the fourth important group in explaining the behavior in both the population growth and rent data. High January temperatures were the natural amenity that stood out as being the most condusive for migration. An elevated, but generally level region was favored (at 10 percent significance). Humidity and high July temperatures had significant negative impact on migration and rents. The Education and the Urbanization groups were the least important variable groups explaining the behavior of the population and rent data, but still important. In general higher concentration of people with higher education increased migration and rent, and locations further away from metropolitan areas (especially small metropolitan areas) reduced migration and rent. That could indicate that being close to urban amenities was somewhat important. The fixed effect was very important explaining both population and rent growth. The Census division group was the second most important explaining the population data and the most important by far explaining the behavior in the rent data. All the Census divisions in the population growth regression, except the Pacific division (D9) and the Middle Atlantic division (D2) had significant fixed effects relative to the control division (New England) and that indicates there is something about the south and the west that is 73 attracting people. It is possible that the Census division group is picking up amenities not captured in the model. This is consistent with the findings in other studies in the economic literature (Mulligan and Vias, 2007). Manufacturing and average wages were the most important variables explaining growth in wages. Vias (1999) says that manufacturing was moving to areas in the 1990’s with low wages and the data in this study supported his findings. Therefore, it is of value to analyze manufacturing employment further. The 1990 average wage was 2.3 percent higher in the 218 micropolitan areas in the study that lost manufacturing jobs during the period than in the 293 micropolitan areas that added manufacturing jobs. Wages furthermore increased more in areas that added manufacturing jobs. Average wages increased 41 percent during the period in micropolitan areas that added manufacturing jobs, well above the 38.7 percent growth in micropolitan areas that lost manufacturing jobs. This explains partly the importance of average wages and manufacturing in wage growth. However, despite the higher growth of wages in micropolitan areas that added manufacturing jobs it was not enough to catch up to the wage differential. The average wage in micropolitan areas that added manufacturing jobs was still slightly below the average 2000 wage of micropolitan areas that lost manufacturing jobs. The Amenity group explained 8.1 percent of the increase in wages, with the mean July temperatures (at 10 percent significance) and square miles of water being most conducive to wage growth, but high mean January temperatures tend to reduce wage growth. It is interesting that a significant portion of the new manufacturing jobs added in 74 micropolitan areas during the period went to Census division 3 (East North Central), posting an increase in manufacturing jobs of 11.4 percent (well above the micropolitan average of 2.4 percent). Most of the states in that division have relatively low average January temperatures and all the states have access to navigable water ways through the Great Lakes, The other variable groups were much less important in explaining the data. Only the Mountain (D8) division and the Pacific division (D9) had significant fixed effects on wage growth relative to the control division (New England). The percent of people with Bachelor’s degree or higher, the percent of people in the 2549 age group (at 10 percent significance) and the percent of black population were all conducive to wage growth, but state spending on highways and all the incremental distance variables to the metropolitan hierarchy reduced growth in wages. The fact that all the incremental distance variables were significant and reduced wage growth (incremental distance to the next metropolitan area with 500,000 or less at 10 percent significance) indicates that one of the costs of distance for micropolitan areas is less productivity, which is consistent to findings in other studies in the economic literature (Partridge, et al 2010). 75 Growth Effects & Analysis The evolution of the explained and residual growth effects that induced growth of micropolitan areas during the period are analysed in next sections, with aid of the the GlaeserTobio growth model. The Amenity Growth Effect The evolution of the Amenity Growth effect ( ) is governed by the growth of expenditure on housing minus the growth of wages, given by , where α is the share of expenditure that goes toward housing and , are regression coefficients from the rent and wage regressions. There have been different values for α used in the literature, but a decision was made to use α = 0.2312 because it is a conservative value. The results show that micropolitan amenities were relatively attractive compare to the rest of the nation during the 1990’s ( vs ) 13. The regression estimates ( ’s) were then used to calculate the explained growth estimates ( ’s) for population, rent and wage growth for each micropolitan area. The ( ’s) were put into the growth model to estimate the explained Amenity (Productivity, Housing Supply) growth effect. The explained Amenity (Productivity, Housing Supply) growth effect was regressed on the total Amenity (Productivity, Housing Supply) effect and the adjusted R2 was analyzed. The results show that approximately 37.7 percent of 12 Rickman & Rickman (2011) 13 The average population, rent and wage growth for the 511 micropolitan areas, as well as nationwide, were put into the GlaeserTobio model to calculate the total amenity, productivity and housing supply effects. See Chapter 3 for detailed explanations of the model. bPh bW Ph b W b 511 0.27 micros 0.40 US b ˆy ˆy 76 the total variation in the amenity effect between the 511 micropolitan areas is explained by the regression. Next, the growth effects were calculated for each variable group14 and regressed on the total Amenity growth effect (one group at a time) in order to find out how important each group was in explaining the growth effects. Approximately 24.7 percent (see Table XVI) of the variation in the Amenity effect regression can be explained by the Economic variable group, 6.6 percent by the fixed effect (Census division variable group variables); 4.8 percent by the Education group variables; 4.4 percent by the Amenity group variables; 3.9 percent by the Fiscal and Other Policy group variables; 2.6 percent by the Demographic group variables; and only 0.6 percent by the Urbanization group variables. Table XVI Group: Specific Amenity Growth Effect Dependent Var : Total Amenity Effect Independent Var: Group Specific Amenity Effect Amenity Variable Group 0.044 Census Division Variable Group 0.066 Demographic Variable Group 0.026 Education Variable Group 0.048 Fiscal and Other Policy Variable Group 0.039 Economic Variable Group 0.247 Urbanization Variables Group 0.006 14 Only the variables belonging to the respective variable group are regressed on the dependent variables in each regression and the estimates ( ’s) are used to calculate the explained variable group growth estimates ( ’s) for each micropolitan area. The ( ’s) are then put into the growth model to estimate the explained group amenity (productivity/housing supply) effect. The group amenity effect is then regressed on the total amenity effect (the group productivity effect is regressed on the total productivity effect and the group housing supply effect is regressed on the total housing supply effect) and the R2 is analyzed. b ˆy ˆy 77 It is apparent that the Economic variable group is mostly important for the variation in the Amenity growth effect, explaining four times the variation in the Amenity effect compared to the second most important group. The Beta coefficients were analyzed in order to find out why that was the case. The Beta coefficients were adjusted by the coefficients that define the respective growth effects in the relevant regressions15 in order to assess their relative importance within each group. The average wage (in the Economic variable group in the wage regression) was by far the most important variable contributing to the variation in the Amenity growth effect, meaning that migrants were willing to accept relatively low wages to enjoy micropolitan amenities. The fact that the relative Amenity growth effect was favorable (compared to the US average) also indicates that migrants were willing to accept less than average nationwide growth in wages and higher than average growth in rental payments in order to enjoy micropolitan amenities. The Productivity Growth Effect The Glaeser and Tobio model indicates that strong growth of population and wages reflects increases in productivity. Thus, the growth of the productivity effect ( ) is a weighted growth of population and wages. It is characterized by the following equation , in which = share of labor in production, is the See the methodology section = = A (1 )bN (1 )bW A (1 ) (1 ) N W b b Ph W b b L 1 Ph N W b b b 78 share of capital and , are regression coefficients from the population and wage regressions. Productivity is an important factor in explaining demand sided migration. An increase in productivity in a given micropolitan area results in higher wages and that induces people to migrate to that micropolitan area. The model shows that productivity increased in micropolitan areas during the period, corroborating our earlier findings that the real wage increased. However, productivity increased significantly less in micropolitan areas than nationwide ( vs ). It is therefore unlikely that the migration to micropolitan areas was motivated by micropolitan productivity and by spatial differences in economic opportunity. Approximately 42.5 percent of the variation in the Productivity growth effect is explained by the regression (the explained Productivity growth effect regressed on the total Productivity growth effect). Table XVII shows that the Economic variable group explains 29.1 percent of the total variation in the N b W b 511 0.29 micros A 0.37 US A Table XVII: Group Specific Productivity Growth Effect Dependent Var : Total Productivity Effect Independent Var: Group Specific Productivity Effect Amenity Variable Group 0.017 Census Division Variable Group 0.030 Demographic Variable Group 0.005 Education Variable Group 0.020 Fiscal and Other Policy Variable Group 0.035 Economic Variable Group 0.291 Urbanization Variable Group 0.008 79 Productivity growth effect; Fiscal and Other Policy variable group, 3.5 percent; Census division variable group, 3.0 percent; Education variable group, 2.0 percent; Amenity variable group, 1.7 percent; Urbanization variable group, 0.8 percent; and the Demographic variable group, 0.5 percent. As expected then all the top factors that contribute to growth in wages (from the wage regression) were the most significant forces contributing to the positive and negative evolution of the Productivity growth effect during the period. The most important variable explaining the Productivity growth effect (by far) was average wages (Economic variable group), followed by; January temperatures (Amenity variable group); the Mountain division (Census division variable group); the percent of manufacturing jobs (Economic variable group – p value = 0.053); the percent of population with Baccalaureate degree or higher (Education variable group); July temperatures (Amenity variable group  p value = 0.059); percent jobs in construction (Economic variable group); and the percent of blacks in the local population (Demographic variable group). It is interesting how important the Mountain division is in explaining the growth in productivity. There must be some fixed factors in that division which are very conducive to growth in wages or perhaps the region is attracting productive firms. Housing Supply Growth Effect Glaeser (2007) finds in a study on urban megaregions that differences in housing supply due to differences in land use regulations was an important determinant of regional population growth. Therefore, the Housing Supply growth effect is important in explaining the growth of regions. The Housing Supply growth effect () is defined by L 80 the model to be equal to , where is the elasticity of housing supply. A robust growth in population and wages associated with relatively less growth in rents indicates a growth in the housing supply effect. An increase in population growth in a given area (ceterus paribus) will always increase housing prices and rents somewhat if land supply is limited. If housing supply is overly restricted because of some reason, then housing prices and rents will be even higher. That in turn could deter inmigration of people. That is because “housing costs”/rents are usually the single largest component of spending for households. This could also deter inmigration of firms because an increase in rents means higher unit cost of production and less profits. 1 Ph N W b b b Table XVIII Group Specific Housing Supply Growth Effect Dependent Var : Total HS Effect Independent Var: Group Specific HS Effect Amenity Variable Group 0.139 Census Division Variable Group 0.436 Demographic Variable Group 0.159 Education Variable Group 0.114 Fiscal and Other Policy Variable Group 0.202 Economic Variable Group 0.210 Urbanization Variable Group 0.024 81 Many studies in the economic literature (McGranahan, 2007) have found that high “housing prices”/rents deter interregional migration. Other studies have found that job related migration is greatly affected by the state of housing markets. Most recently Valetta and Kuang (2010) find that part of the reason why people are not migrating for jobs is due to the state of housing markets. The state of housing markets has important implications for economic growth. Housing supply was significantly less flexible in the 511 micropolitan areas than on average nationwide as indicated by the Housing Supply growth effect ( vs ). Approximately, 72.7 percent of the total variation in the Housing Supply growth effect is explained by the model regression (the explained Housing Supply growth effect regressed on the total Housing Supply growth effect). The 511 1.12 micros L 0.75 US A Table XIX Net Contribution to the Housing Supply Effect Rent Regression Census Division Group Adj Beta Coef East North Central (D3) 3.6 West North Central (D4) 2.9 South Atlantic (D5) 2.7 Mountain (D8) 2.7 Pacific (D9) 2.5 East South Central (D6) 2.5 West South Central (D7) 2.2 Middle Atlantic (D2) 1.1 82 Census division variable group explains 43.6 percent of total variation in the housing supply effect (see Table XVIII); the Economic variable group, 21 percent; Fiscal and Other Policy variable group, 20.2 percent; Demographic variable group, 15.9 percent; Amenity variable group, 13.9 percent; Education variable group 11.4 percent; and the Urbanization variable group, 2.4 percent. The adjusted Beta coefficients (see table XIX) show that all the eight Census division variables in the rent regression were the most significant by far contributing to the negative Housing Supply growth effect, indicating that a significant portion of the impact that contributed to the unfavorable Housing Supply growth effect is unexplained by the variables in the regression. Interestingly, the Census divisions that contribute most to the negative Housing Supply growth effect (East North Central, West North Central and the South Atlantic divisions) also have the top three largest micropolitan populations and account for more than 51 percent of the population in micropolitan areas in the study. Analysis The growth effects model indicates that micropolitan areas benefitted from relatively attractive natural amenities that induced inmigration and population growth. Table XX Micropolitan Areas CD 3 CD 4 Avg. All Micros Wage9000 40.00% 42.50% 39.90% Pop9000 5.90% 6.00% 9.20% 83 The model shows that productivity increased in micropolitan areas, but well below the overall nationwide productivity growth, implying that productivity was not a significant catalyst for migration. Further analysis corroborates the results from the growth effect model. The micropolitan areas in both the East and West North Central divisions (Census divisions 3&4) had one of most robust growth in wages of all micropolitan areas in the study (see Table XX). Yet both divisions had population growth well below the micropolitan average. The model also indicated that the housing supply in micropolitan areas was significantly less flexible than the housing supply nationwide, which could be a major deterrent to micropolitan migration. The Census division group in the rent regression is by far the most important variable group contributing to the variation in the explained Housing Supply growth effect. The Census division group must be capturing regional attributes that affect the local housing supply. Next we will apply the GlaeserTobio model on the variation in the data that is not explained by the regressions in order to in order to understand better the overall sources of micropolitan growth. Unexplained Growth Effects, the Role of the Housing Supply and Unexplained Outliers Unexplained Growth Effects In order to get a deeper understanding on micropolitan growth in the 1990s the focus shifts now to the residual (unexplained) growth effects. Whereas the explained growth effects were obtained using , the residual growth effects are obtained using (see the methodology section). The regression variables did not explain all the variation ˆy ˆe 84 in the data. By analyzing the residual growth effects we get a more complete picture of the forces that contributed to the growth of the micropolitan areas in the 1990s. The residual growth effects will also help us to identify factors that help explain the growth of outliers. The residuals (’s) from each (population, wage and rent) regression were put into the growth effect model16 to calculate the residual Amenity (Productivity, Housing Supply) growth effect. The residual Amenity (Productivity, Housing Supply) growth effect was regressed on the total Amenity (Productivity, Housing Supply) effect and the adjusted R2 was analyzed. The residual Amenity growth effect explains 59 percent of the total Amenity growth effect in micropolitan growth during the period, the residual Productivity growth effect 59.3 percent and the residual Housing Supply growth effect 27.3 percent. It is important to find out how much unexplained population growth (errors in the population regression) is impacted by the three types of unexplained growth effects in order to identify important factors that contributed to the unexplained population growth. The residual population growth was therefore regressed on the residual innovations17 in 16 See the methodology section 17 errorpop = f( λUϕ, λUA, λUL), where errorpop = the error terms from the population regression, λUϕ, = the residual (unexplained) Amenity growth effect, λUA = the residual Productivity growth effect and λUL= the residual Housing Supply growth effect ˆe (1)(1) U A eNeW U PhW e e 1 U Ph L NW e e e 85 order to analyze residual population growth, but the degree of collinearity between the different growth effects made any inference impossible. Bivariate Pearson correlation analyses were therefore applied for analysis. The Pearson correlation matrix (see Table XXI) revealed that the errors in the population regression were significantly correlated with the residual (unexplained) Housing Supply growth effect (r =  0.20, p<0.0001), considerable less correlated with the residual Productivity growth effect and (r =  0.175, p<0.0001) and not significantly correlated with the residual Amenity growth effect (p=0.1319). In order to find out how much residual Productivity growth effect affected residual population growth we have to look better at residual wage growth. The correlation between the residual Productivity growth effect and residual wage growth (errors in the wage regression) is 0.99, however, the correlation between residual population growth and residual wage growth is not statistically significant which indicates that it is unlikely that the residual Productivity growth effect was an important factor explaining unexplained population growth. Table XXI Residual Residual Population P Productivity P Correlation Growth Value Effect Value Residual Amenity Effect 0.067 0.132 Residual Productivity Effect 0.175 <.0001 Residual l Housing Supply Effect 0.202 <.0001 Residual Wage Growth 0.054 0.222 0.993 <.0001 86 Next we look at the unexplained Housing Supply growth effect. Table XXII shows that the “residual population growth regressed on the residual Housing Supply growth effect" regression is statistically significant and has an R2 of 0.041. It is not a surprise because there is a significant 44.7 percent correlation between the residual population growth and the residual rent growth (which is the most significant contributor to the residual Housing Supply growth effect). Table XXII also shows that when the residual Housing Supply growth effect data is divided into groups of micropolitan areas with smaller and larger residual housing supply effects than the average for all the 511 micropolitan areas in the study, then both regressions are significant. It is interesting though that the R2 increases
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Title  Us Micropolitan Area Economies in the 1990's 
Date  20120701 
Author  Davidsson, Michael Erlingur 
Keywords  Amenity Effect, General Dominance Analysis, Housinig Supply Effect, Migration, Outlier Analysis, Productivity Effect 
Department  Economics 
Document Type  
Full Text Type  Open Access 
Abstract  This paper uses a hedonic growth model developed by Glaeser and Tobio (2008) and general dominance analysis to examine the forces contributing to the growth of micropolitan areas during the 1990's. The paper also analyses unexplained outliers of micropolitan growth. Micropolitan areas have been described by the US Census Bureau as emerging metropolitan areas and are therefore important for growth of regions. The results show that micropolitan growth benefitted from relatively attractive amenities compare to the rest of the nation during the 1990's. Micropolitan areas characterized by stability (high percentage of marriage households), high concentration of people in the "5064" year old age group, high relative concentration of people with higher education degrees, mild January temperatures and access to water and highways were preferred. However, local housing markets and the state of the local regulatory environment were also very important determinants of migration and economic growth. Relatively inflexible local housing markets and difficult local regulatory environment significantly retarded overall migration and economic growth, even in micropolitan areas with relatively high level of natural amenities. Most of the outliers' performance could be explained by the state of the local regulatory environment. 
Note  Dissertation 
Rights  © Oklahoma Agricultural and Mechanical Board of Regents 
Transcript  US MICROPOLITAN AREA ECONOMIES IN THE 1990’S By MICHAEL E. DAVIDSSON Bachelor of Arts in Economics Lewis & Clark College Portland, OR 1988 Master of Arts in Economics University of Central Oklahoma Edmund, OK 1990 Submitted to the Faculty of the Graduate College of the Oklahoma State University in partial fulfillment of the requirements for the Degree of DOCTOR OF PHILOSOPHY July, 2012 ii US MICROPOLITAN AREA ECONOMIES IN THE 1990’S Dissertation Approved: Dr. Dan Rickman Dissertation Adviser Dr. Lee Adkins Dr. Michael Applegate Dr. Michael Woods Dr. Sheryl A. Tucker Dean of the Graduate College iii TABLE OF CONTENTS Chapter Page I. INTRODUCTION ...................................................................................................1 Economic Performance of Micropolitan Counties in the 1990's .............................2 Purpose of the Study ................................................................................................3 Contribution .............................................................................................................5 II. REVIEW OF THE LITERATURE Urban & Natural Amenities .....................................................................................6 Outlier Studies .........................................................................................................9 III. METHODOLOGY The Roback Model .................................................................................................11 The GlaeserTobio Model ......................................................................................16 The Empirical Model Three Hedonic Cross Section Regressions ......................................................21 Econometric Issues ..........................................................................................25 Data Discussion and Description ...........................................................................28 Purging of the Data using the Method of the Hat Matrix ................................35 Purging of the Data using the Method of the “kClustering” ..........................36 Final Data and Variance Analysis....................................................................37 Variance Decomposition of the R2  Dominance Analysis ..............................39 Beta Coefficient Analysis ................................................................................45 IV. FINDINGS Empirical Results and Analysis Regression Results The Population Regression ..............................................................................47 The Rent Regression ........................................................................................51 The Wage regression........................................................................................53 Analysis............................................................................................................57 Dominance Analysis General Dominance – Population growth ..............................................................58 General Dominance – Rent Growth .................................................................62 General Dominance – Wage growth ................................................................65 Analysis............................................................................................................67 iv Growth Effects and Analysis The Amenity Growth Effect ............................................................................75 The Productivity Growth Effect .......................................................................77 The Housing Supply Growth Effect ................................................................79 Analysis............................................................................................................82 Unexplained Growth Effects, the Role of the Housing Supply and Unexplained Outliers Unexplained Growth Effects ............................................................................83 The Role of the Housing Supply on Economic Growth ..................................94 Unexplained Outliers .......................................................................................97 V. CONCLUSION Summary & Conclusions .......................................................................................99 REFERENCES ..........................................................................................................107 APPENDIXES APPENDIX A General Dominance Analysis for the Population Regression ........................111 APPENDIX B General Dominance Analysis for the Wage Regression ................................146 v LIST OF TABLES Tables Page I. Autocorrelation Analysis Regressions .............................................................26 II. Description of Data and Data Groups ..............................................................31 III. Variance Analysis of the Dependent Variables ...............................................38 IV. Generic Variance Decomposition – Stage I – Regression Algorithm .............42 V. Generic Variance Decomposition Stage II – Average Contribution to the R2 Calculations by Each Variable Group ........................................................43 VI. Generic Variance Decomposition Stage III– Average Contribution to the R2 – Final Calculations ....................................................................................44 VII. Results for the Population Regression .............................................................49 VIII. Results for the Rent Regression .......................................................................52 IX. Results for the Wages Regression ....................................................................55 X. General Dominance Analysis Result Population Growth Regressions ......................................................................................................59 XI. Significant Beta Coefficients – Population Regression by Variable Group ...............................................................................................................59 XII. General Dominance Analysis Result  Rent Growth Regressions ......................................................................................................63 XIII. Significant Beta Coefficients – Rent Regression by Variable Group.................................................................................................63 XIV. General Dominance Analysis Result  Wage Growth Regressions ......................................................................................................66 XV. Significant Beta Coefficients – Wage Regression by Variable Group.................................................................................................66 XVI. Group Specific Amenity Growth Effect R2 Analysis......................................76 XVII. Group Specific Productivity Growth Effect R2 Analysis ................................78 vi XVIII. Group Specific Housing Supply Growth Effect R2 Analysis ..........................80 XIX. Beta Coefficient Analysis – Net Contribution to the Housing Supply Effect .....................................................................................81 XX. Wage and Population Growth Analysis for Census Divisions 3 & 4....................................................................................82 XXI. Residual Population Growth Analysis for All the 511 Micropolitan Areas ..........................................................................................85 XXII. Residual Population Growth and Residual Housing Supply Growth Effect Analysis Broken Down by Two Groups: Above and Below the Average HSGE .............................................................86 XXIII. Residual Population Growth and Residual Housing Supply Growth Effect Analysis Broken Down by Groups Based on the Number of STD from the Average HSGE ...............................................................................87 XXIV. Directional Analysis on the Population Growth  Rent Growth Relationship ..................................................................................................88 XXV. Analysis on Micropolitan areas with Housing Supply Growth Effect that is two STD’s or More Below the Average Housing Supply Growth Effect................................................................................................90 XXVI. Analysis on Micropolitan areas with Housing Supply Growth Effect that is two STD’s or More Above the Average Housing Supply Growth Effect................................................................................................91 XXVII. Growth Analysis on Micropolitan Areas with the Rent Growth  Housing Supply Ratio Above and Below the Average Rent Growth  Housing Supply Ratio ...................................................................................95 XXVIII. Growth Analysis by Census Division on Micropolitan Areas with the Rent GrowthHousing Supply Ratio (R/HS) Above and Below the Average Rent GrowthHousing Supply Ratio .....................................................................96vii LIST OF FIGURES Figure Page 1. The Basic Roback Model ......................................................................................13 2. Changes in the Level of Amenities or Productivity in the Roback Model ...........15 3. Census Regions and Divisions of the United States .............................................23 1 CHAPTER I INTRODUCTION The 1990’s were a period of prosperity in the U.S. and a period of the longest peacetime economic expansion in U.S. history. This period also marked the beginning of the “new economy” with advances in Internet, information, telecommunications and other production technology that set the stage for a decade that was characterized by robust economic growth. Economic growth and the ensuing prosperity affected every corner of the U.S., with private nonfarm employment growth remarkably even across the nation; employment growth was 22 percent for metropolitan counties, and 21.7 percent for nonmetropolitan counties. Many studies in the economic literature noticed a significant trend in migration to nonmetropolitan counties during the decade. The potential advantages that nonmetropolitan counties have over metropolitan counties for people are higher levels of natural amenities, and less urban disamenities, such as traffic congestion and crime. Nonmetropolitan counties offer lower production costs and wages for firms and when the cost of distance is less than the savings in production costs and wages and the business operations do not require face time with consumers, then a nonmetropolitan county can be a good business location.2 This trend in nonmetropolitan county growth prompted the Census Bureau to put forth a new classification of an urban area, called micropolitan area, which is based on the concept of urban clusters. Micropolitan statistical areas were first defined by the Office of Management and Budget (OMB) in 2000 as: “having at least one urban cluster with a population of at least 10,000 but less than 50,000. Under the standards, the county (or counties) in which at least 50 percent of the population resides within urban areas of 10,000 or more population, or that it contains at least 5,000 people residing within a single urban area of 10,000 or more population, is identified as a ‘central county’ (counties)1. Additional ‘outlying counties’ are included in the CBSA if they meet specified requirements of commuting to or from the central counties. Since the definition of micropolitan areas is fairly new, there are relatively few studies in the economic literature on the growth of micropolitan areas in the 1990’s. Therefore this study will analyze the sources of growth of micropolitan areas in the 1990’s. Economic Performance of Micropolitan Counties in the 1990's There are 3,087 counties and county equivalents in the continental US and of those 662 are classified as micropolitan counties. Approximately 10.6 percent of the continental population lived in these micropolitan counties in 1990, in which 13.6 percent of the population 25 years “old and over” had Bachelor’s, Master’s or Professional degrees (compared to 20.3 percent nationwide). The population increased overall by 9.8 percent in micropolitan areas in the continental US during the decade, compared to 13.2 percent population growth nationwide. The population increased much faster in 1 http://www.census.gov/population/www/metroareas/aboutmetro.html 3 micropolitan areas located in the west and south, than in micropolitan areas located in the east and north portion of the country. The center of gravity for the micropolitan population steadily drifted from northeast to southwest in the 1990’s (Mulligan & Vias, 2006). The economic performance of micropolitan counties was good during the decade, with private nonfarm employment increasing 22 percent (same as nationwide, but slightly more than the continental US). Furthermore, the employment/population ratio increased 3.2 percent points in micropolitan counties but declined 0.4 percent nationwide, which indicates that employment growth kept better pace with population growth in micropolitan areas. The manufacturing industries were moving out of metropolitan and rural counties into micropolitan counties during the decade, with manufacturing employment increasing 2.2 percent in micropolitan areas, but declining 2.9 percent nationwide. Average wages in micropolitan areas increased 40 percent (versus 51.1 percent nationwide), but rent (includes imputed rent2) increased 54 percent (versus 46.6 percent nationwide). This could indicate that the migration to micropolitan areas was amenity oriented since migrants to micropolitan areas were willing to accept less than national average growth in real wages and higher than the national average growth in rent in order to enjoy micropolitan amenities. Purpose of the Study Micropolitan areas are neither rural nor urban but can be thought of as emerging 2 See section 5.1 for methodology 4 metropolitan areas. So far the economic literature has focused mostly on the general determinants of growth of micropolitan areas, which explains the growth of the average micropolitan area. Some micropolitan areas with average level independent variables experienced growth well above the typical micropolitan area in the 1990’s. The purpose of this study is to analyze population growth that can be explained by regression analysis and unexplained outliers of population growth of micropolitan areas nationwide. Explained growth refers to the portion of the population growth that is explained by the independent variables in the population regression. Unexplained population growth refers to the portion that is not explained by the independent variables and becomes part of the residual error of the population regression. An unexplained outlier of population growth is a micropolitan area with exceptional (or extremely poor) population growth that cannot be explained by the variables in the population regression. The analysis in this study has two parts. The first part is an econometric study of micropolitan areas nationwide to identify the determinants of population growth of micropolitan areas overall (population growth explained by the regressions). The second part of the study will focus on examining the unexplained outliers of population growth of micropolitan areas nationwide. Systematic analysis will be applied in order to identify the factors that can explain the outlier performance. It is possible that the performance of micropolitan areas with outlier growth is due to factors such as economic policies not utilized elsewhere. This understanding is important in order for local governments to have effective policies that are conducive for economic growth. 5 Contribution Economic research on micropolitan areas has not been as extensive as it has been for metropolitan areas since the definition of micropolitan areas is fairly recent. Furthermore, most of the economic literature has focused on the on the average micropolitan area. This study attempts to analyze both the explained and residual sources of economic growth of micropolitan areas. The contribution of this paper to economic literature is to increase understanding of micropolitan growth and to bridge the gap in the economic literature of the knowledge of the determinants of growth between the average micropolitan area and micropolitan areas with outlier performance. 6 CHAPTER II REVIEW OF THE LITERATURE Urban & Natural Amenities Regional growth in the United States has historically been characterized by stark differences in growth between regions (Barro and SalaiMartin, 1991; Blanchard and Katz 1992). It is important for economic developers to understand the reasons for these differences in growth in order to have policies that are conducive to economic growth. The growth in jobs and incomes in rural areas has lagged behind, partly because of a decline in economic opportunities in traditional rural industries (McGranahan and Beale, 2002). There is a significant body of literature that states that historically an important factor in interregional labor migration was asymmetric regional demand shocks and lengthy adjustments in wage differentials across regions, meaning that the migration was driven by demand shocks and economic opportunities (Blanchard and Katz 1992). Many studies therefore used local wages and employment growth as the major determinant of migration (Greenwood and Hunt, 1989). Historically, regional growth and migration were thus labor demand driven. Migration was characterized by a step migration up the urban hierarchy with people moving to a bigger city/urban area for jobs (Plane et al, 2005). 7 This means that economic growth was driven by productivity. However, amenities gradually became more important in the migration decision as incomes increasedespecially urban amenities (Graves, 1983). Bigger cities have more urban amenities than small cities and towns because urban amenities are usually scale dependent. Amenities can affect both quality of life and productivity. The household utility function includes amenities and amenities are therefore capitalized into factor prices (Roback, 1988 & 1982). Many studies have found that “scale dependent” urban amenities are a normal good (Glaeser et al, 2000 and Roback, 1988) and important in migration of high skilled and educated people because these groups consume more of “scale dependent” urban amenities. Migration is therefore more likely to reflect the utility of the educated and highly skilled, rather than the low skilled (Bound and Holzer, 2000; Bartik, 1996 & 2001). This also means that cities with plentiful urban amenities are likely to have a larger portion of their labor force skilled and educated (Adamson et al, 2004). It stands to reason that changes in the household evaluation of amenities can be a catalyst for supply sided migration. Starting in the 1970’s, empirical studies began to show an increase in migration to nonmetropolitan areas (Wardwell & Brown, 1980). Improvements in the transportation infrastructure, environmental awareness, urban disamenities (crimes, congestion, etc), and increasing affluence were some of the factors that were the catalysts for this change (Chi and Marcouiller, 2011). This indicates that natural amenities became more important in the utility function for some households (especially for higher income households) and therefore the relative utility increased in high amenity areas for those households (Graves, 1979), resulting in nonmetropolitan high amenity areas to become more attractive for migration. 8 This trend continued into the 1990’s. Almost all the migration during the end of the 1990’s was down the urban hierarchy and the most significant migration flows were from the top of urban hierarchy to the bottom of the hierarchy (Plane et al, 2005). This is consistent with supply side migration for natural amenities. Supply side natural amenity migration analysis focuses on interregional differences in amenities and other specific locationbased attributes. Numerous studies using amenity models and hedonic pricing models have found that amenities affect regional growth significantly (Chen and Rosenthal, 2008; Gabriel and Rosenthal, 2004; Clark et al, 2003; Deller et al, 2001; Gyourko and Tracy, 1991; Roback, 1982). The demand for natural amenities in the south have also possibly increased because of the invention of air conditioning and other technological advances (Mueser & Graves, 1995). One can calculate the implicit value of natural amenities, if the amenities are fully capitalized into the labor market and the housing market (Gabriel et al, 2003; Beeson and Ebberts, 1989; Roback, 1980;). Distance can also affect the household amenity evaluation. Areas high in natural amenities tend to be further away from big cities and areas further away from big cities have less urban “scale dependent” household and production amenities. Two areas with the similar amenity variables can also have a different household amenity evaluation just because they differ in distance from a big city. There is evidence that preferences for more distant natural amenities are increasing. Partridge, et al. (2010) relate household amenities to distance in a study of counties in the 1990’s in order to understand how distance of counties from cities across the urban hierarchy contributes to agglomeration and they found that 9 preferences for natural amenities in rural, remote urban, and more remote metropolitan areas were increasing. Although natural amenities are important in population growth and migration, they are not all the same; a right mix of natural amenities (open land, water, forest and various type of topography) is most conducive to migration (McGranahan, 2007). Some studies on nonmetropolitan counties/areas have found that in order to increase economic growth in rural and micropolitan areas it is more important to attract people and increase the labor force rather than attract new firms and new jobs. That is because jobs follow people more than people follow jobs (Vias, 1999; Mulligan and Vias, 2006). The possible reason for that is that more workers usually mean higher density of skills which results in better labor matching, and better labor matching reduces training costs. The question about how important natural amenities are in regional economic growth and migration is still debated. Some studies continue to find that population growth in some regions was due to rising productivity (Caselli and Coleman, 2001). Furthermore, rents are seldom included in regional migration studies (Mueser and Graves, 1995). Recently however, there is new research emerging supporting the hypothesis that rents and flexible housing supply can be more important for growth of regions than amenities or productivity (Glaeser, Gyourko, and Saks, 2006). Outlier Studies Loveridge et al. (2007) argue that in order to get a deeper understanding of economic phenomena, it is of value for economic researchers to study outliers. It is a standard practice in econometrics to accept models that explain only 20 to 30 percent of the total variance in the data and the results from these models are used to explain the determinants of growth in 10 the respective areas. Therefore, a lot of variability remains unexplained in the data and the models are therefore susceptible to omitted variable bias, especially for outliers. They say that if a place is advancing more rapidly than other places with similar sociodemographics, geographic and industry characteristics, we ought to know why. Their research supplements a study by Anderson, et al. (2007) in which they used 1990 and 2000 county data in a crosssectional study to estimate the determinants of the growth in the proportion of working poor in the counties of the states in the North Central region of the U.S. In order to explain the performance of the outliers they systematically analyze the areas using economic, geographic and qualitative data (telephone surveys and interviews). They use the data to look for a group of factors that can explain the outlier performance. They are successful to explain the difference in many outliers. For example they find Michigan’s Upper Peninsula they find that the difference between the above and underperformance outliers are mostly in attitudes and policy. The above performance outliers are poised to grow within, but the underperformance outliers are counting on external growth and quick fix options for local growth. 11 CHAPTER III METHODOLOGY The Roback Model Charles Mills Tiebout (1956) observed and popularized the notion that people vote with their feet, relating migration to utilities. Sherwin Rosen (1979) expanded on this notion and related it to amenities and wages; and a few years later Jennifer Roback (1982) extended Rosen’s analysis and came out with a comprehensive model that has been widely accepted and used in the economic literature for studies on quality of life and migration. This model, now usually called the “Roback model” shows the effect of interregional differences in amenities and productivity on wages and rents. The Roback model assumes perfect competition. The regional value and cost functions are functions of wages, rents and amenities, which is a shifter: V(w,r;,s)= kv and C(w,r;s)=kc. This means that there are interregional utility and unit cost equilibriums that have to be maintained in the long run. The Roback model also assumes that people and firms sort themselves according to their preferences for amenities and other specific locational attributes. If amenities change then they will generate compensated variations in wages and rents through12 migration that will calibrate the region back into the interregional utility and cost equilibrium. Amenities are therefore a significant factor in explaining growth of regions. In the Roback model each individual maximizes his/her utility given the income constrains: max U(w,lc;s) subject to (w+l = p*x+r*lc) and firms produce a composite good X with a production function x=f(n,lp;s) where x=composite good, lc is land used by households, p=price of the composite good, r=rental costs, lp is land used in production and s = amenity. The utility function is increasing in wages, but declining in rents. The cost function is increasing in both wages and rents. The assumptions for the model are3: 1. Workers have identical tastes and are completely mobile between regions. 2. Capital is identical, completely mobile between regions 3. Production technologies are the same between regions 4. Cities are characterized as bundles of attributes, which can affect household utility and costs of production. 5. Household utility is the same in each region 6. Unit costs of production are the same in all regions. 3 Beeson & Ebberts (1989) 13 Figure 1. The Roback Model 14 The value function (indirect utility function) for the region is V(w,r;s)=k, where k is the interregional utility equilibrium. The value function is upward sloping (Figure 1) because the function is written for a fixed utility k and therefore if wages increase, rents have to increase also to offset the increase in utility from increasing wages in order to stay on the same utility curve. If amenities increase then the utility curve shifts to the right representing that when the labor supply increases in the region, ceterus paribus, it will cause wages to decline and rents to increase. The cost function for firms is C(w,r;s)=1 in which the interregional production cost equilibrium is normalized to 1. The cost function is downward sloping (Figure 1) because if wages increase then rents have to decrease to compensate in order to stay on the same cost curve. If productivity increases in the region then it will cause the cost function to shift right because now firms in the region can afford to pay both higher wages and higher rents. Amenity and Productivity Differences Between Regions Regions that have higher amenity than the region in Figure 1 will have their utility curves to the right of V(w,r;s) because they have lower wages and higher rents and regions that have less amenity will be on the left because they have higher wages and lower rents. Likewise, the cost curves for regions that are more productive than the region in the Figure I will be on the right of C(w,r;s) because firms in those regions can afford to pay higher wages and higher rents and regions that are less productive will be on the left. 15 Figure 2. Changes in the Level of Amenities or Productivity in the Roback Model 16 Changes in the Level of Amenity and/or Productivity Say that the Region in Figure II has the value function V(W0 ,R0;S0 ). Now amenities increase in the region and the utility curve shifts to the right to V(W1 ,R1;S1 ). Now wages are less and rents are higher, but the utility is restored to the same level it was before. Likewise, say that the cost function for firms in the region is C(W0 ,R0;S0 ). Now productivity increases in the region and the curve shifts to the right to C(W1 ,R1;S1 ). Firms in the region are now paying higher wages and rents, but the per unit costs are the same. The equilibrium wages increased from W1 to W3 and rents increased from R0 to R3. The total change in each variable is the sum of the impact from the change in both amenities and productivity. The Roback model shows that amenities generate compensated variations in wages and rents through migration, largely because people sort themselves according to their preferences for amenities and other specific locationbased attributes. Amenities are therefore a significant factor in explaining population growth of regions. The Glaeser & Tobio Model Glaeser & Tobio (2008), in a study on the population growth in the sunbelt states during the second half of the 20th century, noticed enormous growth in the housing supply since 1980 in the sunbelt but a slow pace of growth in housing prices relative to the rest of the country. This prompted them to hypothesize that the differences in local land use regulations between regions could have resulted in important differences in housing supply, which could have important consequences for population and employment growth. 17 Their model is based on the Roback model, in which growth of regions can be explained by differences in amenity and productivity. In the two sector Roback model, labor markets and housing markets always adjust perfectly so that if amenities change then wages and rents change to preserve the interregional utility equilibrium. Glaeser & Tobio expand the model by adding the “housing sector” to the model which was embedded into the Roback model but not modeled especially with equations describing the behavior of housing prices. Therefore the Glaeser & Tobio model also incorporates innovations in land and land prices in regional adjustment to an amenity shock and the model shows that the overall growth of regions can be explained by three effects on growth: Amenity growth effect; Productivity growth effect; and “Housing Supply” growth effect. Regional output is produced subject to the following production function: 1 Y AN KZ (1) in which “A” is an index on regional productivity,” N” is the number of workers,” K” is traded capital and “Z” is non traded capital (infrastructure, natural capital, etc). Maximizing the production function with respect to the firm’s budget gives the following inverse labor demand function: 1/(1 ) ( 1)/(1 ) (1 )/(1 ) /(1 ) W A N Z (2) in which “W” is wages, is the share of mobile capital inputs, and is the share of labor inputs. Regional households derive utility from the consumption of a traded good “C” (numeraire) and nontraded housing “H” according to the following utility function: 1 U C H (3) 18 in which “ ” represents a utility shifter and is the budget share of housing. Maximizing the utility function with respect to the household budget constraint gives the following indirect utility function: V WPh (1 )(1 ) (4) in which W is wages and Ph is price of housing. Housing suppliers use a fixed level of land “L” and structure on the land “h” in the production of housing. Housing suppliers maximize profits according to the profit function: ( ) ( ) L Ph hL h L PL (5) in which Ph is the selling price of housing, “ h ” is the cost of the housing structure ( is the elasticity of the housing supply), and” L P ” is the price of land. Maximizing the profit function to find the indirect housing supply function (assuming that land is fixed) and setting it equal to housing demand gives the inverse housing supply function at the equilibrium: ( 1)/ (1/ ) (1/ ) NW Ph h L (6) Taking the natural logs of the labor demand function, the indirect value function and the inverse housing supply function and solving simultaneously for static equilibrium gives us the static equilibrium equations: 19 ( ) ( ) (1 )( ( ) ( 1) log( ) log ( (1 ) ( 1)) N Log A Log L N K (7) ( 1) ( ) (1 )( ( ) ( 1) log( ) log ( (1 ) ( 1)) W Log A Log L W K (8) ( 1) ( ) ( ) (1 )log( ) log ( (1 ) ( 1)) P LogA Log L Ph K (9) Glaeser and Tobio assume that the evolution in amenities, productivity and housing supply are governed by the following growth equations: 1 log t A A A t A K S A (10) 1 log t A t K S (11) 1 log t L L L t L K S L (12) in which the variable S defines status. If equations 7,8, and 9 are made into a dynamic system in which equations 10,11, and 12 describe the dynamic process, then it implies the following evolution of labor, wages and housing prices: 1 ( ) (1 ) (1 ) ( 1) log ( (1 ) ( 1)) t A L N N t N S S S K N (13) 1 ( 1) (1 ) (1 ) ( 1) log ( (1 ) ( 1)) t A L W W t W S S S K W (14) 1 ( 1) ( 1) ( 1)(1 ) log ( (1 ) ( 1)) t A L Ph Ph t Ph S S S K Ph (15) 20 Where “ N K ”, “ W K ”, and “ Ph K ” are regional specific constants, the terms in the bracket are regional specific coefficients (that can be estimated by regressions) and “ N ”," W ”, and " Ph "are error terms. If we define the estimated regression coefficients on the S (status) variables as: ( ) (1 ) (1 ) ( 1) ( (1 ) ( 1)) A L N b (16) ( 1) (1 ) (1 ) ( 1) ( (1 ) ( 1)) A L W b (17) ( 1) ( 1) ( 1)(1 ) ( (1 ) ( 1)) A L Ph b (18) then we can solve the system and define the Amenity, the Productivity and the “Housing Supply” effects A , and L in terms of the regression coefficients ( N b , W b , and Ph b ) . A(1)bN(1)bW (19) Ph W b b (20) 1 Ph L N W b b b (21) N b , W b , and Ph b are regression coefficients which represent the Productivity, Amenity and “Housing Supply” effect that is explained by the population, wages and rent regressions. Since this study sets out to also analyze the residual effects (unexplained by the regressions)  the unexplained Productivity, Amenity, and “Housing Supply” effects 21 ” U A “,” U “and " U L ” are estimated with the following equations for the residuals: U (1 ) (1 ) A N W e e (22) U Ph W e e (23) 1 U Ph L N W e e e (24) In summary the theoretical model is used to identify the incentive behind the explained and unexplained growth of micropolitan areas. The regression estimates ( b ’s) are used to calculate the explained growth estimates ( ˆy ’s) for each micropolitan area. The ( ˆy ’s) are then decomposed into explained Amenity, Productivity and “Housing Supply” growth effects. The error terms are used like the ( ˆy ’s) in the model to explain the residual Amenity, Productivity and “Housing Supply effects. The Empirical Model Three Hedonic Cross Sectional Regressions In accordance with the economic literature (Glaeser & Tobio, 2008; Rickman & Rickman, 2011), three hedonic cross sectional regressions are run in order to obtain the regional specific estimates for the Amenity growth effect, Productivity growth effect and the “Housing Supply” growth effect: population growth regression; rent growth regression and wage growth regression. This paper uses the following vectors for each cross sectional regression using 1990 data to explain the growth of micropolitan areas in the 19902000 22 period: / Vector Vector Vector Vector Vector of of of of of Census Amenity Demographic Education Fiscal Policy District Variables Variables Variables Variabl Variables Growth Vector Vector of of Economic Urbanization es Variables Variables (25) The same variables were used for each regression except for the control variables (see Table II for complete data description). In the wage regression, the beginning rent is excluded; however, the beginning wages and population density are included. In the population regression, the beginning rent and beginning wages are excluded and the population density is included. In the rent regression, the beginning wages and population density are excluded, but beginning rent is included. The explained effects on the dependent variables not accounted for in the first six groups are accounted for by the Census division group, which measures the fixed effect that is attributed to the Census divisions. A map of the Census divisions can be seen in Figure III 23 Figure 3 24 Figure III Cont. 25 Econometric Issues Heteroskedasticity is often a problem in cross sectional data. Cross sectional data involves economic units of different sizes and it is likely that areas with larger economic units such as large firms or households have larger variation in the data because they have more members. This means that the variance (σ2) in the variancecovariance matrix is not constant due to structural/spatial instability. If micropolitan areas close to larger metropolitan areas tend to have larger population, it could result in a larger variation in their economic units and the overall data. This research study uses Ordinary Least Squares (OLS) model regressions and the consequences of spatial heteroskedasticity on the OLS estimates are incorrect standard errors and the variancecovariance matrix for the estimators is incorrect. The estimators are still unbiased but are not the best linear unbiased estimators (BLUE). In order to correct this problem, all the regressions in this study are ran using the White’s adjusted variance in the variancecovariance matrix which has been widely accepted and used in economic literature. Serial correlation can also be a problem in cross sectional data; although, unusual and typically not worrisome (Schmidt, 2005 P.225). If a data set includes both metropolitan and nonmetropolitan county data then a situation can occur where unexplained population (wage or rent) growth in metropolitan counties can cause unexplained population (wage or rent) growth in adjacent nonmetropolitan counties. Therefore, cov(eiej)≠0 indicating spatial dependence and autocorrelation, which means that the estimators are not BLUE. However, the data in this study includes only micropolitan areas that are fairly well scattered across the nation and are not adjacent to each other. 26 In order to analyze the extent of the problem with autocorrelation, the error terms for all the micropolitan areas in this study were regressed on the Census divisions for all three regressions (population growth, rent growth and wage growth) in order to determine if the Census divisions were able to explain the distribution of the error terms. The results show that there is no significant spatial dependency in the error terms (see Table I). Table I PopulationGroup Regression Dependent Variable: ehat Residual Number of Observations Read 511 Analysis of Variance F Value Pr > F <.0001 Parameter Estimates Variable DF Parameter Estimate Standard Error t Value Pr > t Intercept 1 3.60E13 0.88368 0 1 Division 1 5.62E14 0.16465 0 1 27 Table I Continued RentGroup Regression With Dependent Variable: ehat Residual Number of Observations Read 511 Analysis of Variance F Value Pr > F <.0001 Parameter Estimates Variable DF Parameter Estimate Standard Error t Value Pr > t Intercept 1 5.97E13 1.20417 0 1 Division 1 8.45E14 0.22437 0 1 WagesGroup Regression The REG Procedure Model: white Dependent Variable: ehat Residual Number of Observations Read 511 Analysis of Variance F Value Pr > F <.0001 Parameter Estimates Variable DF Parameter Estimate Standard Error t Value Pr > t Intercept 1 3.82E13 1.02181 0 1 Division 1 6.68E14 0.19039 0 1 28 Data Discussion and Description A decision was made to focus on the micropolitan areas that are located in the 48 contiguous continental states using the definition that was set out by the Office of Management and Budget in December of 2003. Going by that classification and after adjustments, the study started out with 554 micropolitan areas that encompass 662 counties in the lower 48 states. The study used 1990 and 2000 Census data for micropolitan areas (as defined by the Office of Management and Budget as of June 6, 2003  PHCT29). Due to the paucity of data collected for micropolitan areas, the study uses county level data that is aggregated into the Census micropolitan area definitions. The median gross rent is a weighted average of the median gross monthly rent for rental housing (complete count) and imputed rent for owner occupied housing (complete count), with the shares of renter and owner occupied houses as the weights. The median gross rent for rental housing is defined as contract rent plus the estimated average monthly cost of utilities (utilities are included, because they are sometimes included in the rental payment and therefore the median contract rent would be a biased estimator on median rent). The median imputed rent for owner occupied housing is calculated by converting the median value of owner occupied housing (complete count) using a discount rate of 7.85% (Peiser & Smith, 1985; Blomquist et al., 1988; Gabriel et al., 2003). The median gross rent does not control for differences in housing quality between regions. Average wages were calculated by dividing private nonfarm payroll by the private nonfarm employment. 29 Dividing the independent variables into groups enables broader analysis of the causational importance and better understanding of the growth effects. The data were therefore divided into seven groups (see Table II): 1. Amenity variable group (includes only natural amenities); 2. Demographics variable group; 3. Education variable group; 4. Fiscal and Other Policy variable group; 5. Economic variable group; 6. Urbanization variable group; 7. Census Division variable group. The Amenity variable group includes only natural amenities. The Amenity variable group includes: January and July temperatures; humidity; water area; and typography. The Demographic variable group includes: births per 1000 population; percent of married households; percent of African, Hispanic and Asian Americans; and percent of people in the 2549, 5064 and 65 plus age groups. The Educational variable group includes: percent of people with high school and “Bachelor’s, Master’s or Professional” degrees and the presence of a landgrant university to assess the education and accumulated knowledge in the area. 30 The Fiscal and Other Policy variable group includes: county and state property and sales taxes; county and state government spending on highway and safety; county spending on education; state spending on health and hospitals; state personal and corporation income taxes; and finally, right to work laws. All the state tax and spending variables are divided by the respective state personal income and all the county tax and spending variables are divided by the respective county personal income in order to access the effective burden of the policies to assure comparability between the different micropolitan areas. The Economic variable group includes: percent jobs in farming; agservice, forestry & fishing {from now on called agservices&ff}; mining; construction; manufacturing; services; government and the unemployment rate to control for the business cycle. Median gross rent is added in the rent regression and the average wage in the wage regression to control for beginning rents and wages in these regressions. The Urbanization variable group includes: the distance to nearest metropolitan area; and the incremental distance to the next metropolitan area with a population of 250 thousands, 500 thousands, and 1.5 million; and population density was included in the population and wage regressions to isolate the impact from industrial structure because industrial structure and population density can be correlated (Mueser & Graves, 1995). The Census division variable group includes Census divisions 29. 31 Table II. Description of Data and Data Groups Amenity Variables Obs Mean Std Dev Minimum Maximum Data Source Humidity 511 57.10 13.69 18 79 USDA Land Surface Form Typography codes: 511 8.49 6.67 1 21 USDA Mean January Temperature 511 33.08 11.69 3.1 63.4 USDA Mean July Temperature 511 75.79 5.38 55.9 86.7 USDA Water Sq. Miles 511 3.87 8.95 0.01 66.13 USA Counties Program: US Census Demographic Variables Obs Mean Std Dev Minimum Maximum Data Source Births per 1,000 population 1990 511 14.88 2.40 9.1 26.4 USA Counties Program: US Census Percent African American 1990 511 8.71 13.87 0 64.6 USA Counties Program: US Census Percent Asian American 1990 511 0.52 0.48 0.04 3.57 USA Counties Program: US Census Percent Hispanic American 1990 511 4.31 10.94 0.2 84.4 USA Counties Program: US Census Percent of Married Households 1990 511 59.39 4.68 42.5 73.3 USA Counties Program: US Census Percent of Population in over 65 or Older 1990 511 14.51 2.88 5.1347 31.3137 USA Counties Program: US Census Percent of Population in the 2549 Age Group 1990 511 34.51 2.35 26.1 46.7 USA Counties Program: US Census Percent of Population in the 5064 Age Group 1990 511 13.66 1.57 7.8099 20.9226 USA Counties Program: US Census 32 Education Variables Obs Mean Std Dev Minimum Maximum Data Source Educational attainment  persons 25 years and over  Bachelor’s, Master’s, or Professional degree 1990 511 13.27 4.50 5.5 36.3 USA Counties Program: US Census Educational attainment  persons 25 years and over  percent high school graduate or higher 1990 511 69.75 8.68 42.9 89.1 USA Counties Program: US Census Pretense of a Land Grant University 511 0.03 0.17 0 1 Association of Public and Land Grant Universities Fiscal and Other Policy Variables Obs Mean Std Dev Minimum Maximum Data Source Local Per Capita Sales Tax Revenues 1992 511 0.00 0.00 0 0.023533 USA Counties Program: US Census Local Per Capita Spending on Health Care 1992 511 0.01 0.00 0.00435 0.015885 Economic Census 1992 Local Per Capita Spending on Highway Infrastructure 1992 511 0.01 0.00 0.000622 0.024515 Economic Census 1992 Local Per Capita Spending on Public Education 1992 511 0.05 0.01 0.02926 0.13888 Economic Census 1992 Local Per Capita Spending on Public Safety 1992 511 0.01 0.00 0.000804 0.021972 Economic Census 1992 Local Per Captia Property Tax Revenues 1992 511 0.03 0.01 0.00371 0.09937 USA Counties Program: US Census Right to Work State 511   0 1 Dr Rickman State Per Capita Spending on Highway Infrastructure 1992 511 0.01 0.00 0.007904 0.039311 Economic Census 1992 State Per Capita Spending on Public Safety 1992 511 0.01 0.00 0.007207 0.021361 Economic Census 1992 33 State Per Captia Corporate Income Tax Revenues 1992 511 0.00 0.00 0 0.0097879 Economic Census 1992 State Per Captia Income Tax Revenues 1992 511 0.02 0.01 0 0.039943 Economic Census 1992 State Per Captia Property Tax Revenues 1992 511 0.03 0.01 0.010091 0.060725 Economic Census 1992 State Per Captia Sales Tax Revenues 1992 511 0.02 0.01 0 0.051105 Economic Census 1992 Economic Variables Obs Mean Std Dev Minimum Maximum Data Source Average Wages 1990 511 16.88 2.38 10.4361 29.0493 USA Counties Program: US Census Employment in AgService: Percent of Total Jobs 511 1.20 1.11 0 12.6 USA Counties Program: US Census Employment in Farming: Percent of Total Jobs 511 6.26 3.64 0.4 20.8 USA Counties Program: US Census Jobs in Construction: Percent of Total Private Non Farm Jobs 511 4.77 1.78 0 14.9 USA Counties Program: US Census Jobs in Government: Percent of Total Employment 511 16.87 7.46 6.9 60.8 USA Counties Program: US Census Jobs in Manufacturing: Percent of Total Private Non Farm Jobs 511 18.35 10.25 1.3 47.6 USA Counties Program: US Census Jobs in Manufacturing: Percent of Total Private Non Farm Jobs 511 21.08 5.33 0 37.2 USA Counties Program: US Census Jobs in Mining: Percent of Total Private Non Farm Jobs 511 1.54 3.35 0 25.2 USA Counties Program: US Census Mean Gross Rent 1990 511 325.60 86.99 176.915 906.013 USA Counties Program: US 34 Census The Unemployment Rate 511 7.07 2.39 1.9 15.7 USA Counties Program: US Census Urbanization Variables Obs Mean Std Dev Minimum Maximum Data Source Distance to Next Metropolitan area 511 78.42 45.92 17.011 334.945 Partridge et al, 2010 Incremental Distance to the Next Metropolitan Area with a Population of 1.5 million or less 511 98.86 117.95 0 532.302 Partridge et al, 2010 Incremental Distance to the Next Metropolitan Area with a Population of 500,000 or less 511 34.42 55.11 0 362.772 Partridge et al, 2010 Incremental Distance to the Next Metropolitan Area with a Population of 250,000 or less 511 47.16 79.87 0 601.043 Partridge et al, 2010 Population Density 1990 511 62.38 41.68 1.787 265.301 USA Counties Program: US Census Census Division Variables Obs Mean Std Dev Minimum Maximum Data Source Census Divisions 29 511   0 1 US Census 35 A micropolitan area can be an outlier of growth because of two reasons: 1. Micropolitan areas with average level independent variables experiencing growth well above/below the typical micropolitan area. 2. Micropolitan areas with outlier independent variables The scope of this study includes the first reason, but not the second. Therefore the data were also purged of micropolitan areas with extreme outliers in the independent variables in order to be able to focus on outliers of micropolitan growth with average level independent variables. Purging of the Outliers using the Method of the Hat Matrix Analysis on the raw data revealed a significant variation in the data for the independent variables. A decision was made to purge the areas with disproportionate values of the independent variables, using the method of the Hat Matrix, in order to be able to focus on micropolitan areas that had outlier growth in the dependent variables, but more average level independent variables. The regression estimator b is based on both the X variables and the Y variable 1 ( ) T T b x x x y (26) and the hat matrix is defined as h = 1 ( ) T T x x x (27) bh*y (28) Therefore, the X variables in the hat matrix multiplied with dependent variable yield the 36 regression estimate. On way to purge the disproportionate X variables is based on leverage analysis on the Hat Diagonal Matrix (Belsley, Kuh, and Welsch, 1980). This method measures the influence of each observation on the regression estimates. The proposed cutoff for the influence statistic is: 2* p n (29) where “p” is number of parameters and “n” is the number of observations. Purging of the Outliers using the Method of kMeans Clustering The method of “kmeans” clustering was also used to identify outliers of micropolitan growth in the independent variables. The “kmeans” clustering method allocates all the data points in a set into k clusters in a way that minimizes the Euclidean distance between the average in the cluster (cluster center) and each point in the cluster4. This is an evolutionary algorithm which initially selects the k cluster means randomly from the data points and then it selects the closest points from the data to the kcluster means based on the Euclidean distance and then the cluster mean is recomputed. These steps are repeated until all the data points are allocated to clusters and reallocation of data between clusters is not going make any significant difference. The Fastclus procedure in SAS was used to do “five centroid” cluster analysis and micropolitan areas with extreme above and below growth performance in the dependent variables were identified for each dependent variable. Most of the outliers identified corresponded to outliers that were identified by the “Hat matrix” method. 4 http://support.sas.com/documentation/cdl/en/statugcluster/61777/PDF/default/statugcluster.pdf 37 Final Data and Variance Analysis The study started out with 554 micropolitan areas. After analyzing the data, there were four observations with data problems that were removed. The “Hat Matrix” method resulted in the purging of 40 observations and an additional three areas of observations were purged due to being extreme outliers in the cluster analysis. Therefore, data from 511 micropolitan areas were used for the study. This purging of disproportionate “X” variables resulted in a reduction of total variance of 25.2 percent in the population growth regression, 9.1 percent in the rent growth regression, and 20.3 percent in the wages growth regression. The data still show significant variation in the dependent variables as shown in Table III: population growth ranged from negative 17.1 percent to 73.6 percent during the period; negative 2.8 percent to 133.7 percent for rent (mean gross rent); and negative 2.9 percent to 97.9 percent for wages. 38 Table III. Variance Analysis of the Dependent Variables Dependent Variables N Min Max Mean STD Pop Growth 511 17.1% 73.6% 9.3% 11.2% Rent Growth 511 2.8% 133.7% 54.6% 19.2% Wages Growth 511 2.9% 97.9% 40.7% 11.1% 39 Variance Decomposition of the R2  Dominance Analysis It is of value to know the usefulness of the different variable groups for the dependent values and to find out which group is most important, the second most important, etc. Analyzing bivariate correlations between the dependent variables and the independent variables is not going to suffice because the bivariate correlation ignores other variables in the regression. In order to assess the contribution of the different variable groups to the explained behavior in the dependent variable it is possible to use some type of variance decomposition method to find out how big a portion of the total explained variation in the population, rent and the wage regressions is explained by the different variable groups. One way to do that is with dominance analysis based on the explained variance. The ideal method should meet three criteria: importance of a predictor should be defined in terms of a variance reduction error; the method should allow for direct comparison, rather than inferred measures; and importance of a predictor should reflect the direct effect (when considered by itself), total effect (conditional on all other variables) and the partial effect (conditional on a subset of predictors). Dominance analysis satisfies all these requirements and the results are transitive relationships and are not affected by any elimination of a subset of predictors from the model (Budescu, 1993). However, complete dominance cannot always be established between every pair of predictors. Complete dominance cannot be established if an additional contribution of a predictor to the R2 is greater than other predictors for some but not all of the subset models (X1 might dominate X2 independently, but X2 might contribute more when you add it to X1 40 than if you add X1 to X2). In that case, one can use “conditional dominance” or “general dominance.” Conditional dominance analysis focus on dominance between the different groups of the subset models and general dominance is based on the averaging of these conditional values. General dominance is therefore found by adding and averaging the conditional values and then the additional average contribution can be compared and it can be ordered. A predictor will generally dominate another predictor when it has a higher averaged additional contribution to the R2 and therefore accounts for a bigger portion of average explained variation of the dependent variable (Azen and Budescu, 2003). Complete dominance and conditional dominance analysis are outside the scope of this study and therefore general dominance analysis was undertaken to analyze the contribution of the different variable groups to explained variance in the data. With seven variable groups there are (271) = 127 possible different statistical combinations possible for the variable group regressions {combination (7,0)….combination (7, 6)}, which are the base regressions that have to be run to compare to. Furthermore, there are 63 additional regressions that have to be run for each group to find out the additional contributions to R2 when the respective variable group is added to the base regressions or a total 441 additional contribution regressions. Therefore, a total of 1450 regressions were run for all three models (population, wages and rent) for the general dominance analysis. Tables IV, V, & VI show the regression algorithm used for the variance decomposition to determine the order of general dominance for the variable groups in the population regression. Table IV shows a generic example of the calculations necessary to determine contributions for the X1 group (the Amenity variable group) for each line in the possible 64 variable group combinations (tables with complete results for all groups in all 41 regressions are listed in Appendix A). The variables in Table IV refer to: X1 = the Amenity variable group; X2 = the Demographics variable group; X3 = the Education variable group; X4 = the Fiscal and Other Policy variable group; X5 = the Economic variable group; the X6 = Urbanization variable group; and the X7 = Census division variable group (see Table II for description of the data). Table V shows how the average contribution was found for each of the seven combination subgroups (k=0..k=6) which then are also summed up and averaged. The average contribution to the R2 by the X1 group is {(0.120+ 0.097+ 0.074+ 0.056+ 0.044+ 0.035+ 0.027)/7}= 0.065. Similar regressions and calculations were run to get the contribution of each of the groups. Table VI shows how the average contribution to the R2 by each variable group is then summed up and equals 0.514 in the table. The relative contribution/general dominance for each variable group is then found by dividing the average R2 of each sub group into the total sum of R2 for all groups (Budescu, 1993). We can see that the X1 variable group has an average contribution to the explained variation in the population regression of 0.065 points, accounting for 12.6 percent of explained variation in the population data. The results from the dominance analysis will be analyised in detail the next section. Finally, this study used the adjusted R2 for the general dominance analysis rather than R2. That is because the adjusted R2 is preferable for decomposition when you have many variables and different number of variables in some groups between the models that are being compared. The adjusted R2 is a better estimate of the population R2, and that is what the R2 should be estimating (Wooldridge, 2005 p. 207). 42 Table IV. Generic Variance Decomposition Stage I – Regression Algorithm Generic Example Regressions and Calculations to Find the Average Contribution to the R2 by the X1 Group X1 X2  X2 X1 X3  X3 X1 X4  X4 X1 X5  X5 X1 X6  X6 X1 X7  X7 X1 X2 X3  X2 X3 X1 X2 X4  X2 X4 X1 X2 X5  X2 X5 X1 X2 X6  X2 X6 X1 X2 X7  X2 X7 X1 X3 X4  X3 X4 X1 X3 X5  X3 X5 X1 X3 X6  X3 X6 X1 X3 X7  X3 X7 X1 X4 X5  X4 X5 X1 X4 X6  X4 X6 X1 X4 X7  X4 X7 X1 X5 X6  X5 X6 X1 X5 X7  X5 X7 X1 X6 X7  X6 X7 X1 X2 X3 X4  X2 X3 X4 X1 X2 X3 X5  X2 X3 X5 X1 X2 X3 X6  X2 X3 X6 X1 X2 X3 X7  X2 X3 X7 X1 X2 X4 X5  X2 X4 X5 X1 X2 X4 X6  X2 X4 X6 X1 X2 X4 X7  X2 X4 X7 X1 X2 X5 X6  X2 X5 X6 X1 X2 X5 X7  X2 X5 X7 X1 X2 X6 X7  X2 X6 X7 X1 X3 X4 X5  X3 X4 X5 X1 X3 X4 X6  X3 X4 X6 X1 X3 X4 X7  X3 X4 X7 X1 X3 X5 X6  X3 X5 X6 X1 X3 X5 X7  X3 X5 X7 X1 X3 X6 X7  X3 X6 X7 X1 X4 X5 X6  X4 X5 X6 X1 X4 X5 X7  X4 X5 X7 X1 X4 X6 X7  X4 X6 X7 X1 X5 X6 X7  X5 X6 X7 X1 X2 X3 X4 X5  X2 X3 X4 X5 X1 X2 X3 X4 X6  X2 X3 X4 X6 X1 X2 X3 X4 X7  X2 X3 X4 X7 X1 X2 X3 X5 X6  X2 X3 X5 X6 X1 X2 X3 X5 X7  X2 X3 X5 X7 X1 X2 X3 X6 X7  X2 X3 X6 X7 X1 X2 X4 X5 X6  X2 X4 X5 X6 X1 X2 X4 X5 X7  X2 X4 X5 X7 X1 X2 X4 X6 X7  X2 X4 X6 X7 X1 X2 X5 X6 X7  X2 X5 X6 X7 X1 X3 X4 X5 X6  X3 X4 X5 X6 X1 X3 X4 X5 X7  X3 X4 X5 X7 X1 X3 X4 X6 X7  X3 X4 X6 X7 X1 X3 X5 X6 X7  X3 X5 X6 X7 X1 X4 X5 X6 X7  X4 X5 X6 X7 X1 X2 X3 X4 X5 X6  X2 X3 X4 X5 X6 X1 X2 X3 X4 X5 X7  X2 X3 X4 X5 X7 X1 X2 X3 X4 X6 X7  X2 X3 X4 X6 X7 X1 X2 X3 X5 X6 X7  X2 X3 X5 X6 X7 X1 X2 X4 X5 X6 X7  X2 X4 X5 X6 X7 X1 X3 X4 X5 X6 X7  X3 X4 X5 X6 X7 X1 X2 X3 X4 X5 X6 X7  X2 X3 X4 X5 X6 X7 X1 Total of 64 Lines 43 Table V. Generic Variance Decomposition Stage II – Average Contribution to the R2 Calculations by Each Variable Group Additional Number Base Adj. Contribution Contribution Combination Regr Regr R2 Regression Adj R2 Economic K=0 1 0 X1 0.120 0.120 K=1 X2 0.100 X2 X1 0.192 0.092 : : : : : K=1 Avg. (sum/6) 6 0.097 K=2 X2 X3 0.212 X2 X3 X1 0.295 0.084 : : : : : K=2 Avg. (sum/15) 15 0.074 K=3 X2 X3 X4 0.342 X2 X3 X4 X1 0.36 0.36 : : : : : K=3 Avg. (sum/20) 20 0.056 K=4 X2 X3 X4 X5 0.394 X2 X3 X4 X5 X1 0.435 0.435 : : : : : K=4 Avg. (sum/15) 15 0.044 K=5 X2 X3 X4 X5 X6 0.407 X2 X3 X4 X5 X6 X1 0.443 0.443 : : : : : K=5 Avg. (sum/6) 6 0.035 K=6 1 X2 X3 X4 X5 X6 X7 0.483 X2 X3 X4 X5 X6 X7 X1 0.51 0.027 Total/Overall Avg 64 (0.120+0.097+0.074+0.056+0.044+0.035+0.027)/7 0.065 44 Table VI Generic Variance Decomposition Stage III Avg. Contribution Simple Average R2 Percent X1 0.065 12.6% X2 0.086 16.8% X3 0.035 6.7% X4 0.087 17.0% X5 0.114 22.2% X6 0.022 4.3% X7 0.105 20.4% Sum 0.514 100% 45 Beta Coefficient Analysis Dominance analysis on the variable groups only tells us the relative importance of the respective variable groups. It is also of value to access the size and statistical significance of the coefficients to compare their relative importance within the respective variable groups. Achen (1982) states that “ j ” measures the potential influence of the variable and is independent of the sample; “ X “(where j X is the mean of the jth variable) measures the level importance and is dependent on the sample; and j j y (the Beta coefficient) measures the dispersion/relative importance because it is adjusted for the scale of the data. The regular OLS/GLS regression coefficients are sensitive to scale of the data and the standardized “Beta” coefficients were therefore used to analyze the relative importance of the different coefficients within each variable group. The impact is measured in terms of standard units rather than the original units of the independent and dependent variables. By doing that, all the variables are in the same equivalent standard deviation units and it brings out their relative importance (Achen, 1982). All the Beta coefficients from the 64 possible combinations for each variable in each group were added up and averaged to get the average standardized impact from each variable within the groups (The calculation of all the average Beta coefficients are listed in Appendix B). There are mostly two types of problems that have been discussed with the Beta coefficients (from now on they are sometimes referred to as BC) in the economic literature. 46 Firstly, some variables do not change a whole lot over time, while others do5. That is not a major obstacle here because this study uses crosssectional data. Secondly, some economic literature suggests that if there are positive and negative coefficients that are averaged, then there can be problems with the average impact and perhaps the directional effect (Azen and Budescu, 2009 p.304). Analyses were undertaken to find out the extent of alternate signs in all three models and to evaluate if there was a problem with averaging due to alternating positive/negative coefficients. The problem was found to be trivial because the alternating positive/negative coefficients were mostly in groups with little relative importance in the respective models and overall alternating signs only happened about 12.2 percent of the time. 5 Beta coefficients have been criticized because some variables are not possible to change while others are easy to change (Larry D. Schroeder, David L. Sjoquist, Paula E. Stephan. Understanding regression analysis, Sage Publications, 1986, ISBN 0803927584, p.3132. 47 CHAPTER IV FINDINGS Regression Results This chapter reviews the findings and analyses the viability of the regression results. The findings are also analysed in detail in the context of general dominance analysis and the GlaeserTobio model. The Population Regression The population growth regression included 50 variables and had an R2 of 55.8 percent. A total of 23 variables were significant at the 5 percent level and an additional 3 at the 10 percent level (see Table VII). The following variables induced population growth in micropolitan areas during the period: January temperatures, percent Bachelor’s degrees, birth rates, percent of 5064 age group, percent married households, per capita county highway spending, per capita spending on public education and Census divisions 36 & 8, (East North Central, West North Central, South Atlantic, East South Central and Mountain divisions) which are all significant at the 5 percent level. Typography (1=flat plains, the48 higher number the more hills and mountains), percent of farm jobs and Census division 7 (West South Central division) are significant at the 10 percent level). The fiscal variables should be interpreted cautiously. Taxes and government spending should be considered together because everything else being equal then taxes can be expected to have a negative impact on the attractiveness of an area wheras government spending is expected to have an positive impact. All the fiscal variables in the model should also be interpreted relative to the fiscal variables that are not in the model. Positive coefficients of the fiscal variables in the population regression in the context of the GlaeserTobio model framework contribute to local amenities, only if it also has the impact to increase rents and reduce wages (causing a decline in real wages). These variables decreased population growth: July temperatures, humidity, distance to next metropolitan area regardless of size, incremental distance to the next metropolitan area with a population of 250,000 or less, percent of agservice jobs, mining and manufacturing jobs, percent of Hispanics, county spending on safety, state spending on hospitals and the state income tax burden. 49 TABLE VII Results for Population Regression Dependent Variable: GrPop9000 Number of Observations Read 511 Analysis of Variance F Value Pr > F <.0001 Parameter Estimates Variable DF Parameter Estimate Standard Error t Value Pr > t Intercept 1 36.47122 25.51977 1.43 0.1536 TempJan 1 0.5659 0.11155 5.07 <.0001 TempJuly 1 0.64762 0.19694 3.29 0.0011 Humidity 1 0.20592 0.08001 2.57 0.0104 Water 1 0.06641 0.04978 1.33 0.1829 Typography 1 0.16507 0.08574 1.93 0.0548 Dist to next Metro 1 0.02659 0.01065 2.5 0.0129 incmetgt250k 1 0.01723 0.00645 2.67 0.0078 incmetgt500k 1 0.00336 0.00769 0.44 0.6623 incmetgt1500k 1 0.00123 0.00471 0.26 0.7939 D2 1 5.04378 3.79443 1.33 0.1844 D3 1 9.93344 3.50554 2.83 0.0048 D4 1 10.57837 3.83796 2.76 0.0061 D5 1 18.05848 3.94865 4.57 <.0001 D6 1 10.92284 4.12424 2.65 0.0084 D7 1 7.95805 4.29385 1.85 0.0645 D8 1 14.78795 5.3179 2.78 0.0056 D9 1 1.9461 5.67182 0.34 0.7317 PopDens90 1 0.00095755 0.01442 0.07 0.9471 LandGrantU 1 0.54496 2.234 0.24 0.8074 PcFarmJobs90 1 0.3111 0.17017 1.83 0.0682 PcAgServ&ffJobs90 1 1.2743 0.44447 2.87 0.0043 PcMinJobs90 1 0.95969 0.16074 5.97 <.0001 PcConstJobs90 1 0.39792 0.2578 1.54 0.1234 PcMfgJobs90 1 0.19688 0.07875 2.5 0.0128 PcServsJobs90 1 0.11551 0.10111 1.14 0.2538 PcGovJobs90 1 0.1347 0.09807 1.37 0.1703 PcBA90 1 0.88382 0.19945 4.43 <.0001 PrcntHsch 1 0.03016 0.11761 0.26 0.7977 PcUnempl90 1 0.28651 0.27988 1.02 0.3065 Births90 1 0.72105 0.24772 2.91 0.0038 PcPopBlack90 1 0.01306 0.0658 0.2 0.8428 PcPopHisp90 1 0.13504 0.0566 2.39 0.0174 PcPopAsian90 1 0.40852 1.10754 0.37 0.7124 PcAge2549 1 0.24725 0.26248 0.94 0.3467 PcAge5064 1 1.20285 0.50468 2.38 0.0176 PcAge65plus 1 0.23504 0.29608 0.79 0.4277 PCMrdHH90 1 0.72772 0.16284 4.47 <.0001 50 cty92property 1 48.96037 53.11723 0.92 0.3571 cty92sales 1 196.10321 133.7142 1.47 0.1432 cty92highway 1 558.957 150.79019 3.71 0.0002 cty92safety 1 520.9902 227.21944 2.29 0.0223 cty92education 1 92.60638 45.06497 2.05 0.0404 stl92property 1 1.08845 96.87452 0.01 0.991 stl92sales 1 46.00734 86.19853 0.53 0.5938 stl92inctax 1 218.52629 67.00757 3.26 0.0012 stl92corptax 1 9.13939 292.02945 0.03 0.975 stl92hosp 1 604.83367 307.36527 1.97 0.0497 stl92highway 1 93.30443 143.22857 0.65 0.5151 stl92pblsfty 1 438.0431 324.02459 1.35 0.1771 Right to Work 1 0.06422 1.58681 0.04 0.9677 51 The Rent Regression The rent growth regression included 50 variables (see Table VIII) and had R2 of 71.77 percent. A total of 29 of the variables were significant at the 5 percent level and an additional 3 were significant at the 10 percent level. Thereof, 19 were also significant in the population regression. Interestingly, 18 of those had the same sign in both regressions. The significant variables common to both regressions with a positive sign were: Census divisions 38 (Census division 7 was significant at the 10 % level in the population regression), percent Bachelor’s degrees, percent of 5064 age group, percent married households, per capita county spending on highways and public education. The significant variables common to both regressions with a negative sign were: July temperatures, distance to next metropolitan area regardless of size, incremental distance to the next metropolitan area with a population of 250,000 or less, percent of mining jobs, percent of agservice jobs and manufacturing jobs (at 10 percent significance), and percent Hispanics. The only variable significant in both regressions with opposite sign to the population regression was the birth rate, which had a negative sign in the rent regression. The following variables with positive sign were significant in the rent regression, but not the population regression: water area, Census division 2 and 9 (the Middle Atlantic and Pacific Census divisons), county sales tax, and the right to work. 52 TABLE VIII Results for Rent Regression Dependent Variable: GrRent9000 Number of Observations Read 511 Analysis of Variance F Value Pr > F <.0001 Variable DF Parameter Estimate Standard Error t Value Pr > t Intercept 1 126.47013 34.58933 3.66 0.0003 TempJan 1 0.12653 0.1517 0.83 0.4047 TempJuly 1 1.20862 0.27016 4.47 <.0001 Humidity 1 0.14783 0.10979 1.35 0.1788 Water 1 0.33217 0.06614 5.02 <.0001 Typography 1 0.15657 0.11703 1.34 0.1816 Dist to next Metro 1 0.08026 0.01428 5.62 <.0001 incmetgt250k 1 0.0606 0.00882 6.87 <.0001 incmetgt500k 1 0.03601 0.01044 3.45 0.0006 incmetgt1500k 1 0.00394 0.00658 0.6 0.5498 D2 1 23.74669 5.65662 4.2 <.0001 D3 1 51.50236 5.38473 9.56 <.0001 D4 1 42.94197 5.73542 7.49 <.0001 D5 1 40.96864 5.84281 7.01 <.0001 D6 1 38.67004 6.08033 6.36 <.0001 D7 1 32.39297 6.3042 5.14 <.0001 D8 1 62.27736 7.61715 8.18 <.0001 D9 1 67.32323 7.9478 8.47 <.0001 MGR90 1 0.0923 0.01279 7.22 <.0001 LandGrantU 1 0.05374 3.04394 0.02 0.9859 PcFarmJobs90 1 0.30076 0.22947 1.31 0.1906 PcAgServJobs90 1 1.14988 0.60717 1.89 0.0589 PcMinJobs90 1 1.16698 0.22352 5.22 <.0001 PcConstJobs90 1 0.27303 0.3534 0.77 0.4402 PcMfgJobs90 1 0.19112 0.11024 1.73 0.0836 PcAgServ&ffJobs90 1 0.07885 0.13827 0.57 0.5688 PcGovJobs90 1 0.30236 0.13486 2.24 0.0254 PcBA90 1 1.10344 0.28983 3.81 0.0002 PrcntHsch 1 0.13439 0.1598 0.84 0.4008 PcUnempl90 1 0.88648 0.3922 2.26 0.0243 Births90 1 0.86789 0.33957 2.56 0.0109 PcPopBlack90 1 0.14546 0.09353 1.56 0.1206 PcPopHisp90 1 0.16669 0.07706 2.16 0.031 PcPopAsian90 1 3.59393 1.50481 2.39 0.0173 PcAge2549 1 0.5035 0.36879 1.37 0.1728 PcAge5064 1 1.81365 0.69043 2.63 0.0089 PcAge65plus 1 1.21424 0.40455 3 0.0028 53 PCMrdHH90 1 0.55723 0.23489 2.37 0.0181 cty92property 1 84.39263 73.3082 1.15 0.2502 cty92sales 1 394.74195 182.38784 2.16 0.031 cty92highway 1 455.18353 203.01268 2.24 0.0254 cty92safety 1 157.88553 308.85868 0.51 0.6095 cty92education 1 135.94803 61.35159 2.22 0.0272 stl92property 1 26.56184 135.47593 0.2 0.8446 stl92sales 1 204.71917 117.45434 1.74 0.082 stl92inctax 1 134.7349 91.23756 1.48 0.1404 stl92corptax 1 175.14744 405.41684 0.43 0.6659 stl92hosp 1 89.08006 415.72019 0.21 0.8304 stl92highway 1 95.77941 195.23795 0.49 0.624 stl92pblsfty 1 1337.89128 458.40038 2.92 0.0037 Right to Work 1 4.94588 2.16231 2.29 0.0226 The following variables with negative sign were significant in the rent regression, but not the population regression: incremental distance to the next metropolitan area with a population of 500,000 or less, average rent, percent of government jobs, percent of unemployment, percent of Asian population, percent of people over 65, spending on public safety, and state sales tax (at 10 percent significance). The Wage Regression The wage growth regression included 51 variables (see Table IX) and had R2 of 39.23 percent. A total of 12 variables were significant at the 5 percent level and an additional 5 variables were significant at the 10 percent level. Six of those variables were also significant in the population and the rent regressions. Percent of Bachelor's degree and Census division 8 (Mountain division) has a positive coefficient in all three regressions and incremental distance to the next metropolitan area with a population of 250,000 or less and percent agservices&ff jobs had negative coefficent in all three regressions. 54 July temperatures and percent of manufacturing jobs (at 10 % significance for both) had positive coefficient in the wage regressions, but negative in the other regressions. This makes sense because wages are overall lower in the south and manfacturing firms with standardized product seek out places with low wages to reduce unit costs. At the same time, very high July temperatures makes it more difficult to enjoy local natural amenities and reduce migration and rent. January temperatures was significant in the wage regression and the population regression. It had a negative sign in the wage regression, but a positive sign in the population regression. Four coefficients were significant in the wage regression and the rent regression. Water area and Census division 9 (the Pacific division) had positive coefficients in both regressions and percent unemployment and incremental distance to the next metropolitan area with 500,000 or less (10% significance) had negative coefficients. Six variables were significant only in the wage regression. Incremental distance to the next metropolitan area with 1.5 million or less, average wages and state highway spending (10 percent significance) had negative impact on wages. However, percent of construction jobs, percent of black population and percent of 2549 age group (at 10 percent significance) had a positive impact on wages. 55 TABLE IX WageRegression Dependent Variable: Grwage9000 Number of Observations Read 511 Analysis of Variance F Value Pr > F <.0001 Variable DF Parameter Estimate Standard Error t Value Pr > t Intercept 1 22.3544 29.58206 0.76 0.4502 TempJan 1 0.47141 0.12939 3.64 0.0003 TempJuly 1 0.43192 0.22799 1.89 0.0588 Humidity 1 0.07688 0.09262 0.83 0.407 Water 1 0.12748 0.05767 2.21 0.0276 Typography 1 0.02333 0.09949 0.23 0.8147 Dist to next Metro 1 0.01688 0.01233 1.37 0.1716 incmetgt250k 1 0.01811 0.00748 2.42 0.0159 incmetgt500k 1 0.01568 0.0089 1.76 0.0787 incmetgt1500k 1 0.01153 0.00546 2.11 0.0351 D2 1 0.55476 4.39495 0.13 0.8996 D3 1 4.74925 4.0582 1.17 0.2425 D4 1 2.34333 4.44419 0.53 0.5983 D5 1 1.02669 4.57362 0.22 0.8225 D6 1 3.79214 4.78308 0.79 0.4283 D7 1 5.52136 4.97295 1.11 0.2675 D8 1 16.24993 6.15748 2.64 0.0086 D9 1 13.44462 6.5658 2.05 0.0412 AvgWage90 1 2.86843 0.26085 11 <.0001 PopDens90 1 0.01009 0.0167 0.6 0.5463 LandGrantU 1 0.2277 2.58838 0.09 0.9299 PcFarmJobs90 1 0.16661 0.19785 0.84 0.4002 PcAgServ&ffJobs90 1 1.03119 0.51572 2 0.0461 PcMinJobs90 1 0.06999 0.19257 0.36 0.7164 PcConstJobs90 1 0.85484 0.30091 2.84 0.0047 PcMfgJobs90 1 0.1832 0.09455 1.94 0.0533 PcServsJobs90 1 0.09622 0.11709 0.82 0.4116 PcGovJobs90 1 0.13944 0.11455 1.22 0.2241 PcBA90 1 0.47593 0.23112 2.06 0.04 PrcntHsch 1 0.11461 0.13979 0.82 0.4127 PcUnempl90 1 0.68748 0.32809 2.1 0.0367 Births90 1 0.03462 0.28678 0.12 0.904 PcPopBlack90 1 0.1736 0.07644 2.27 0.0236 PcPopHisp90 1 0.03317 0.0656 0.51 0.6133 PcPopAsian90 1 1.29629 1.28328 1.01 0.313 PcAge2549 1 0.57519 0.30498 1.89 0.0599 PcAge5064 1 0.78115 0.58451 1.34 0.1821 PcAge65plus 1 0.28774 0.3428 0.84 0.4017 PCMrdHH90 1 0.22655 0.19092 1.19 0.236 56 cty92property 1 23.55257 61.519 0.38 0.702 cty92sales 1 69.01308 155.05052 0.45 0.6565 cty92highway 1 33.81344 174.90351 0.19 0.8468 cty92safety 1 36.95562 265.18802 0.14 0.8892 cty92education 1 76.33809 52.32938 1.46 0.1453 stl92property 1 60.63414 112.72005 0.54 0.5909 stl92sales 1 7.69884 100.15981 0.08 0.9388 stl92inctax 1 28.91794 77.56926 0.37 0.7095 stl92corptax 1 169.91916 338.04747 0.5 0.6155 stl92hosp 1 47.75289 355.83419 0.13 0.8933 stl92highway 1 289.30196 166.14442 1.74 0.0823 stl92pblsfty 1 109.43551 375.12284 0.29 0.7706 Right to Work 1 2.54241 1.85205 1.37 0.1705 57 Analysis Almost 56 percent of the total variance in the population data is explained by the regression, 72 percent in the rent regression and 39 perecent in the wage regression. The fact that the explained variation in the rent regression is almost two times that of the wage regression is not unusual. That is because rent regressions explain one way impacts from both population migration and firm migration on rents. Rent increases in both cases. Wage regressions usually have a lower R2 because they explain two way (offsetting) impacts from firm migration and population migration on wages. When companies move to an area it results in higher wages due to increased labor demand, ceterus paribus. Higher wages then induce people to move to the area and the labor supply increases in the area resulting in lower wages, ceteris paribus. To a certain degree these opposite effects cancel each other out resulting in a lower R2. All of the variables in all the three regressions had plausible or expected signs. The fact that 19 of the significant coefficients in the population regression were also significant in the rent regression with only one having different signs (local birth rates increased population growth, but decreased rents) is good because higher/lower population growth, ceterus paribus, usually results in higher/lower rent. General Dominance Analysis General dominance for the different variable groups in the regressions is established in the next three sections and followed by identificiation and analysis of the factors that induced migration and economic growth to micropolitan areas. 58 General Dominance – Population Growth The average contribution to the explained population growth by the different variable groups is shown in Table X. The Economic variable group had the highest contribution to the explained variation in the population regression with an average contribution of 11.4 percent points to the average adjusted R2, accounting for 22.2 percent of explained variation in the population data. As mentioned in the section about data discussion and description, then the Beta coefficients from the 64 possible combinations for each variable in each group for all three regressions were added up and averaged to get the average standardized impact from each variable within each group in order indicate the relative importance of the respective variable within the group (see Appendix B). The relative size of the average standardized Beta coefficients show that concentration of employment in the mining industry (BC = 0.299), and the manufacturing industry (BC = 0.201) are significant detriment in migration in micropolitan areas (see Table XI). Farming had a positive impact but was only significant at 10 percent level (BC= 0.056) and agservices&ff (BC = 0.08) reduced migration .59 TABLE X. General Dominance  Population Growth Regressions Combinations Amenity Demographics Education Fiscal Economic Urbanization Census Division K=0 0.120 0.100 0.012 0.165 0.139 0.035 0.159 K=1 0.097 0.104 0.040 0.157 0.146 0.030 0.138 K=2 0.074 0.099 0.045 0.096 0.138 0.027 0.116 K=3 0.056 0.091 0.045 0.068 0.122 0.023 0.097 K=4 0.044 0.082 0.041 0.050 0.104 0.018 0.083 K=5 0.035 0.071 0.034 0.040 0.085 0.013 0.073 K=6 0.027 0.057 0.025 0.035 0.064 0.008 0.067 Simple Avg. 0.065 0.086 0.035 0.087 0.114 0.022 0.105 Percent of Explained Variation 12.6% 16.8% 6.7% 17.0% 22.2% 4.3% 20.4% TABLE XI. Significant Beta Coefficients Population Regression Amenity Demographics Education TempJan 0.482 PCMrdHH90 0.266 PcBA90 0.257 CCTypogC 0.113 PcAge5064 0.205 Humidity 0.196 Births90 0.151 TempJuly 0.236 PcPopHisp90 0.113 Fiscal Economic Urbanization cty92highway 0.130 PcFarmJobs90 0.056 CDist 0.131 cty92education 0.053 PcAgServJobs90 0.083 incmetgt250k 0.143 cty92safety 0.141 PcMfgJobs90 0.201 stl92inctax 0.143 PcMinJobs90 0.299 stl92hosp 0.211 Census Division D5 0.464 D8 0.340 D6 0.293 D7 0.210 D4 0.194 D3 0.170 60 The Census division variable group accounts for 20.4 percent of the average explained variation; contributing 10.5 percent points to the average adjusted R2. Although, there is no variation in the fixed effect, a higher Beta coefficient shows higher importance within the group. The South Atlantic Census (D5) division (BC = 0.464) seems to have (by far) the most region specific characteristics that are conducive to inmigration and explained by the regression, followed by: the Mountain (D8) division (BC = 0.34); the East South Central (D6) division (BC = 0.293); the West South Central (D7) division (BC = 0.210 at 10 percent significance); the West North Central (D4) division (BC = 0.194); and the East North Central (D3) division (BC = 0.17). It is interesting that the Middle Atlantic division which includes high population density cities such as New York and Philadelphia did not have a significant impact on population growth of micropolitan areas. Perhaps there are spillover effects from these megacities on their own region that people who move to micropolitan areas do not like. The Fiscal and Other Policy variable group explains 17.0 percent of variation in population growth that is explained by the regression adding 8.7 percentage points to the average adjusted R2. As explained in section 4.1, all the spending and tax variables are divided by the local personal income to estimate the effective burden from these policies in order to be able to compare between micropolitan areas in the same state and different states. The county spending on highway infrastructure (BC = 0.13) was the most conducive for inmigration, followed by county spending on education (BC = 0.053). All the other significant state and local tax variables reduced the attractiveness of 61 micropolitan areas: county spending on safety (BC = 0.141); state income tax (BC = 0.143) and the state spending on health and hospitals (BC = 0.21) The Demographics variable group contributes about 16.8 percent to the explained variation in data with average adjusted R2 being 8.6 percent. The percentage of married households (BC = 0.266) is the most significant factor that is conducive to population growth/migration to micropolitan areas in the demographic group, followed by the percent of people in the 5064 age group (BC = 0.204); and the birth rate (BC = 0.151). The least conducive local demographic characteristics for migration is the percent of Hispanic population (BC = .011). The Amenity variable group contributed 6.5 percentage points to the average adjusted R2 and the group explained 12.6 percent of the explained variation in population growth. Mild January temperatures stand out as being the natural amenity that is conducive to migration to micropolitan areas (BC = 0.482) followed by topography (BC = 0.113 at 10 percent significance). High July temperatures reduce inmigration significantly (BC = 0.236) as well high humidity (BC = 0.196). The Education variable group accounted for 6.7 percent of all explained variation in the data, adding 3.5 percent to the average adjusted R2. The percent of the population with Bachelor’s degree or higher (BC = 0.257) seems to be the only variable within the group of real importance in making the micropolitan area more attractive for migration. Finally, the Urbanization group explained only 4.3 percent of total explained variation, contributing 2.2 percentage points to the average adjusted R2. Interestingly, all the coefficents showed that being further away from a metropolitan area reduced the 62 attractiveness of the micropolitan area for migration. Incremental distance to a metropolitan area with 250,000 people (BC = 0.143) reduced attractiveness of microplitan areas more than any other distance variable, followed by the distance to the next metropolitan area (BC = 0.131). The other distance variables were not significant. It is especially noteworthy that the population density variable was not significant. General Dominance – Rent Growth The general dominance analysis on the rental regressions shows that the most important factor contributing to the explained behaviour in the rental data is the Census division group, which accounts for 40.8 percent of the explained variation of the rental data and adds 28.0 percentage points to the average adjusted R2 (see Table XII). All the Census divisions have relatively large Beta coefficents, indicating that the fixed effects are very important in explaining growth in rent for all regions (see Table XIII). It is difficult to say why the Census divisons fixed effect are so significant, but the analysis of the explained and residual (unexplained) growth effects later will help us understand that. Not surprisingly the Economic variable group ranks number two in explanatory importance, contributing 16.5 percent to the overall average explained variation, adding 11.3 percentage points to the average adjusted R2. All the significant variables in the group had a negative impact on rent growth. The most significant variables within the group are the median gross contract rent in 1990 (BC = 0.373) followed by the percent of jobs in mining (BC = 0.262); the percent of jobs in government (BC = 0.165); the unemployment rate (BC = 0.1); percent agservice jobs (BC = 0.067 at 10 percent 63 Table XIII Significant Beta Coefficients  Rent Regression Amenity Demographics Education Water 0.102 PcAge5064 0.161 PcBA90 0.004 TempJuly 0.365 PCMrdHH90 0.059 PcPopAsian90 0.071 Births90 0.141 PcPopHisp90 0.177 PcAge65plus 0.283 Fiscal Economic Urbanization cty92highway 0.133 PcMfgJobs90 0.066 incmetgt500k 0.025 RTW 0.132 PcAgServJobs90 0.067 CDist 0.127 cty92education 0.034 PcUnempl90 0.100 incmetgt250k 0.189 cty92sales 0.024 PcGovJobs90 0.165 stl92sales 0.064 PcMinJobs90 0.262 stl92pblsfty 0.111 MGR90 0.373 Census Division D3 1.202 D4 0.981 D5 0.885 D8 0.884 D9 0.837 D6 0.836 D7 0.742 D2 0.380 Table XII. General Dominance  Rent Growth Regressions Combinations Amenity Demographics Education Fiscal Economic Urbanization Census Division K=0 0.104 0.130 0.076 0.153 0.164 0.024 0.405 K=1 0.107 0.100 0.039 0.122 0.151 0.020 0.365 K=2 0.105 0.079 0.021 0.099 0.136 0.027 0.327 K=3 0.095 0.064 0.011 0.077 0.116 0.036 0.285 K=4 0.079 0.050 0.007 0.056 0.096 0.044 0.240 K=5 0.060 0.039 0.007 0.035 0.075 0.049 0.193 K=6 0.040 0.027 0.009 0.017 0.054 0.049 0.146 Simple Avg. 0.085 0.070 0.024 0.080 0.113 0.035 0.280 Percent of Explained Variation 12.3% 10.2% 3.5% 11.6% 16.5% 5.2% 40.8% 64 significance); and the percent of jobs in manufacturing (BC = 0.066 at 10 percent significance). The Amenity variable group accounted for 12.3 percent of the variation in the rent data, with the average adjusted R2 equal to 8.5 percent (which is close to the impact it had on population growth). The water area variable (BC = 0.102) is the most important variable in the group that explains increases in rent and the July temperatures (BC = 0.365) was the most important explaining lack of growth in rent. The other amenity variables do not seem to have much impact. The Fiscal and Other Policy variable group contributed 11.6 percentage points to the explained variation, adding 8.0 percentage points to the avarage adjusted R2. County spending on highway infrstructure (BC = 0.133) was the most important variable contributing to growth in rent, followed by right to work (BC = 0.132); county spending on education (BC = 0.034), and county sales taxes (0.024). State spending on public safety seems to reduce rent (BC = 0.11) as well as state sales taxes (BC =  0.064 at 10 percent significance). The Demographics variable group accounted for 10.2 percent of explained variation in the data, contributing 7.0 percentage points to the average adjusted R2. Percent of people over 65 (BC = 0.283) had the largest impact to reduce rent, followed by the percent of Hispanics (BC = 0.177), the birth rate (BC = 0.14) and the percent of the Asian population (BC 0.071). Two variables increased rent. The “percent of people in the 5064 age group” variable (BC = 0.161), which had a relatively large impact on rent growth and the percent of married households (BC = 0.059). 65 The Urbanization and the Education variable groups did not seem very important in explaining the variation in the rent data, contributing 5.2 and 3.5 percentage points to the explained variation in rent growth and adding average adjusted R2 of 3.5 percent and 2.4 respectively. All of the variables, except incremental distance to a metropolitan area with 1.5 million or less, were significant with negative coefficients in the Urbanization group, but only the percent of the population with Bachelor’s degree or higher was significant in the Education group and it had the impact of increasing rent. General Dominance – Wage Growth Factors that affect productivity, such as industry structure, affect wage increases significantly. There is, therefore, no surprise that the Economic Group is ranked on top in explaining wage growth in micropolitan areas (see Table XIV). However, what is a surprise is that the Economic Group accounts for 77.4 percent of all explainied variation in the wage data, contributing 25.1 percent to the R2 (far more than any other group). The most important variables in the group conducive to increase in producivity and wages (see Table VX) are the percent of jobs in manufacturing (BC = 0.201 pvalue = 5.3 percent) and construction (BC = 0.16). Average wages in 1990 (BC = 0.579) had the largest negative impact on wage growth followed by the unemployment rate (0.152) and the percent of jobs in agservices&ff (BC = 0.106). 66 Table XIV General Dominance  Wages Growth Regressions Combinations Amenity Demographics Education Fiscal Economic Urbanization Census Division K=0 0.019 0.009 0.013 0.007 0.256 0.002 0.011 K=1 0.025 0.003 0.015 0.012 0.262 0.001 0.015 K=2 0.028 0.004 0.015 0.014 0.263 0.005 0.018 K=3 0.030 0.009 0.014 0.014 0.259 0.008 0.019 K=4 0.030 0.013 0.011 0.011 0.251 0.010 0.018 K=5 0.028 0.014 0.007 0.006 0.240 0.011 0.015 K=6 0.025 0.014 0.002 0.002 0.229 0.012 0.011 Simple Avg. 0.026 0.006 0.011 0.009 0.251 0.006 0.015 Percent of Explained Variation 8.1% 1.9% 3.3% 2.7% 77.4% 1.9% 4.7% Table XV Significant Beta Coefficients  Wage regression Amenity Demographics Education TempJuly 0.178 PcPopBlack90 0.119 PcBA90 0.194 Water 0.099 PcAge2549 0.080 TempJan 0.399 Fiscal Economic Urbanization stl92highway 0.117 PcMfgJobs90 0.201 incmetgt500k 0.074 PcConstJobs90 0.160 incmetgt1500k 0.093 PcAgServJobs90 0.106 incmetgt250k 0.096 PcUnempl90 0.152 AvgWage90 0.579 Census Division D8 0.218 D9 0.101 67 Analysis in the earlier section on the “Economic Performance of Micropolitan Counties in the 1990's” indicated that the Manufacturing industries were moving out of metropolitan areas and rural areas to micropolitan areas. It is likely that the type of manufacturing that is moving into micropolitan areas is mature with a standardized product and therefore not affected much by urbanization economies. The Manufacturing industry is therefore likely moving out of metropolitan areas to areas with low wages (Vias, 1999) and it might be moving out of rural areas due to cost of distance. The second most important group is the Amenity group which contributes 8.1 percentage points to average explained variation and adds 2.6 percent to the average adjusted R2. It is interesting that “the percent water area” variable (BC = 0.100) has the largest significant positive impact on wage growth (perhaps because of access to navigable water transportation systems which is a firm amenity). July temperatures (BC = 0.178) also increased wages at the 10 percent significance level. High January temperatures (BC = 0.399) reduced the growth in wages. Other groups have negligible contribution to the average explained variation in the data. Analysis These results indicate that the migration to micropolitan areas was related to amenities. That is not a surprise because other studies have found natural amenities important in nonmetropolitan migration in the 1990s (Rappaport 2003 , Deller et al 2001, McGranahan 2007). The Economics Group is very important explaining the growth of population and rent (most important explaining population growth and the second most important 68 explaining rent growth). If the migration was demand sided and driven by job opportunities then relatively high percent of employment in manufacturing would be expected to affect inmigration and rent in a positive way because high levels of manufacturing employment may serve as an indicator of economic health (Gunderson et al, 2008). Relatively high wages also induce demand sided migration (Blanchard and Katz, 1992). However, all the significant employment variables in both regressions reduced migration and rent, except for farming employment in the population regression. Both manufacturing and mining have strong negative impact on migration and rent, which is consistent with amenity oriented migration. Both of these industries are often associated with pollution and environmental degradation and have a negative public perception  one that brings to mind pollution, low wages, assemblyline work and layoffs6. The average population growth was furthermore 10.8 percent in the 317 micropolitan areas that had less than average wage of all the 511 micropolitan areas in the study in 1990, well above the 7.2 percent growth of the 194 micropolitan areas that had higher than the average wage. Furthermore, these 317 locations have higher average amenity scale7 which is consistent with the GlaeserTobio model which clearly shows that locations high in amenities have lower wages than areas with low level of amenities in order to maintain the regional utility equilibrium. 6 See negative perception of manufacturing work at http://wtnnews.com/articles/2464 7 See USDA Natural Amenity Index at http://www.ers.usda.gov/Browse/view.aspx?subject=NaturalResourcesEnvironment 69 The percent of farm jobs had a positive coefficient in the population growth regression. Numerous studies have determined that farming is an amenity and some of these studies estimated the amenity value of farmland by calculating the implicit value of amenities associated with farming or with contingent studies (Bergstrom and Ready, 2009). The percent of agservices&ff jobs variable had a negative coefficient. If farming is generally located in areas high in amenities then one would expect the same for agservices&ff, but it had a negative coefficient in both the population and rent (at 10 percent significance) growth regressions. Most of the micropolitan areas in the study with a significant concentration of jobs in agservices&ff would be expected to have majority of the jobs in the agservices sub industry but not forestry and fishing. It is of therefore of value to analyze agservices employment better. It includes: soil preparation services, crop services, veterinary services, animal services (except veterinary), farm labor and management services, landscape and horticultural services. Employment in the agservices subindustries declined 13.9 percent nationwide during the 1990’s and one would therefore expect that micropolitan areas with a large concentration of agservices employment to be declining too. Therefore it is plausible that the the negative coefficient had something to do with labor demand. The Fiscal and Other Policy group was relatively important in explaining the behavior in both the population and rent data. All the significant variables in the population regression (except county spending on education and highways) reduced migration, including state spending on health and hospitals, which had the largest impact (by far) of all the significant fiscal variables on population growth. That perhaps reflects 70 the Medicaid burden for states. Medicaid accounted for 19.2 percent of the average state budget in the US in the 1995 fiscal year, with the share of budget allocated to Medicaid ranging from a low of 5.1 percent in Alaska to a high of 38.2 percent in New Hampshire8. States with heavy Medicaid burdens can be expected to compensate with policy actions that make them less attractive, and that could explain the negative coefficient. High spending on health and hospitals could also reflect a relatively sickly population, which makes the area less attractive and deters migration. This indicates that high effective local tax burden is a drag on population growth and economic development. This is supported by some studies in the literature. Bartik (1992) finds that high local effective tax rates on average reduce economic growth. However, both the county government spending on highways and education had a positive impact on migration, which is also supported somewhat by the economic literature. Fisher (1997) found that that local government spending can have a positive impact on population and economic growth, especially spending on highway infrastructure and to a lesser degree on education. Both local and state spending on public safety reduced migration and rent. That could indicate that micropolitan areas with relatively high spending on public safety also had more crimes. The Demographic group was also relatively important explaining migration and rent growth. A high concentration of people in the 5064 age group increased both inmigration and rent, implying that this age group was most likely to migrate to 8The National Association of State Budget Officers 1995 State Expenditure Report: http://www.nasbo.org/Publications/StateExpenditureReport/tabid/79/Default.aspx 71 micropolitan areas during the 1990’s. This is supported by Plane et al (2005) who found that there was a substantial migration in the latter parts of the 1990’s by people in the 5064 age group from large metropolitan areas to micropolitan and rural areas. Stability as measured by the percent of married households locally was also attractive local characteristic for micropolitan migration, showing significant positive impact on the growth of both population and rent. Approximately 59.3 percent of all households in 1990 were married in the 511 micropolitan areas in the study, compared to 55.1 percent nationwide. It is reasonable to surmise that micropolitan areas are relatively safe, which is an attractive local characteristic for migration. Crime rates decline with higher household incomes and crime rates are in general higher in nonfamily households (householder not married)9. If micropolitan areas with less concentration of married households have higher crime rates resulting in relatively high spending on public safety then it would explain the negative relationship between local spending on public safety and migration that we discovered earlier when we analysed the fiscal and policy variables. A high concentration of Hispanics reduced both population and rent. The Hispanic population is one of the youngest populations in the US and two in five are foreign born10. Hispanics are furthermore one of the most nomadic populations in the US with 14.1 percent of all Hispanics in 2000 reporting they lived in a different county five years earlier, compared to 8.4 percent overall US average11. If stability is attractive locational characteristic for migration then a high concentration of Hispanics in a location 9 The Bureau of Justice Statistics report: http://bjs.ojp.usdoj.gov/index.cfm?ty=tp&tid=92 10 US Census Report: http://www.census.gov/prod/2003pubs/p20545.pdf 11 USCensus 72 would have negative effect on inmigration. The Hispanic population is also overall relatively unskilled and if areas with high concentration of unskilled people are unattractive for migration then that could as well explain why a concentration of Hispanics had a negative impact on both population and rent. However, the explanation could also include things like culture or funic avoidance behavior. The Amenity group was the fourth important group in explaining the behavior in both the population growth and rent data. High January temperatures were the natural amenity that stood out as being the most condusive for migration. An elevated, but generally level region was favored (at 10 percent significance). Humidity and high July temperatures had significant negative impact on migration and rents. The Education and the Urbanization groups were the least important variable groups explaining the behavior of the population and rent data, but still important. In general higher concentration of people with higher education increased migration and rent, and locations further away from metropolitan areas (especially small metropolitan areas) reduced migration and rent. That could indicate that being close to urban amenities was somewhat important. The fixed effect was very important explaining both population and rent growth. The Census division group was the second most important explaining the population data and the most important by far explaining the behavior in the rent data. All the Census divisions in the population growth regression, except the Pacific division (D9) and the Middle Atlantic division (D2) had significant fixed effects relative to the control division (New England) and that indicates there is something about the south and the west that is 73 attracting people. It is possible that the Census division group is picking up amenities not captured in the model. This is consistent with the findings in other studies in the economic literature (Mulligan and Vias, 2007). Manufacturing and average wages were the most important variables explaining growth in wages. Vias (1999) says that manufacturing was moving to areas in the 1990’s with low wages and the data in this study supported his findings. Therefore, it is of value to analyze manufacturing employment further. The 1990 average wage was 2.3 percent higher in the 218 micropolitan areas in the study that lost manufacturing jobs during the period than in the 293 micropolitan areas that added manufacturing jobs. Wages furthermore increased more in areas that added manufacturing jobs. Average wages increased 41 percent during the period in micropolitan areas that added manufacturing jobs, well above the 38.7 percent growth in micropolitan areas that lost manufacturing jobs. This explains partly the importance of average wages and manufacturing in wage growth. However, despite the higher growth of wages in micropolitan areas that added manufacturing jobs it was not enough to catch up to the wage differential. The average wage in micropolitan areas that added manufacturing jobs was still slightly below the average 2000 wage of micropolitan areas that lost manufacturing jobs. The Amenity group explained 8.1 percent of the increase in wages, with the mean July temperatures (at 10 percent significance) and square miles of water being most conducive to wage growth, but high mean January temperatures tend to reduce wage growth. It is interesting that a significant portion of the new manufacturing jobs added in 74 micropolitan areas during the period went to Census division 3 (East North Central), posting an increase in manufacturing jobs of 11.4 percent (well above the micropolitan average of 2.4 percent). Most of the states in that division have relatively low average January temperatures and all the states have access to navigable water ways through the Great Lakes, The other variable groups were much less important in explaining the data. Only the Mountain (D8) division and the Pacific division (D9) had significant fixed effects on wage growth relative to the control division (New England). The percent of people with Bachelor’s degree or higher, the percent of people in the 2549 age group (at 10 percent significance) and the percent of black population were all conducive to wage growth, but state spending on highways and all the incremental distance variables to the metropolitan hierarchy reduced growth in wages. The fact that all the incremental distance variables were significant and reduced wage growth (incremental distance to the next metropolitan area with 500,000 or less at 10 percent significance) indicates that one of the costs of distance for micropolitan areas is less productivity, which is consistent to findings in other studies in the economic literature (Partridge, et al 2010). 75 Growth Effects & Analysis The evolution of the explained and residual growth effects that induced growth of micropolitan areas during the period are analysed in next sections, with aid of the the GlaeserTobio growth model. The Amenity Growth Effect The evolution of the Amenity Growth effect ( ) is governed by the growth of expenditure on housing minus the growth of wages, given by , where α is the share of expenditure that goes toward housing and , are regression coefficients from the rent and wage regressions. There have been different values for α used in the literature, but a decision was made to use α = 0.2312 because it is a conservative value. The results show that micropolitan amenities were relatively attractive compare to the rest of the nation during the 1990’s ( vs ) 13. The regression estimates ( ’s) were then used to calculate the explained growth estimates ( ’s) for population, rent and wage growth for each micropolitan area. The ( ’s) were put into the growth model to estimate the explained Amenity (Productivity, Housing Supply) growth effect. The explained Amenity (Productivity, Housing Supply) growth effect was regressed on the total Amenity (Productivity, Housing Supply) effect and the adjusted R2 was analyzed. The results show that approximately 37.7 percent of 12 Rickman & Rickman (2011) 13 The average population, rent and wage growth for the 511 micropolitan areas, as well as nationwide, were put into the GlaeserTobio model to calculate the total amenity, productivity and housing supply effects. See Chapter 3 for detailed explanations of the model. bPh bW Ph b W b 511 0.27 micros 0.40 US b ˆy ˆy 76 the total variation in the amenity effect between the 511 micropolitan areas is explained by the regression. Next, the growth effects were calculated for each variable group14 and regressed on the total Amenity growth effect (one group at a time) in order to find out how important each group was in explaining the growth effects. Approximately 24.7 percent (see Table XVI) of the variation in the Amenity effect regression can be explained by the Economic variable group, 6.6 percent by the fixed effect (Census division variable group variables); 4.8 percent by the Education group variables; 4.4 percent by the Amenity group variables; 3.9 percent by the Fiscal and Other Policy group variables; 2.6 percent by the Demographic group variables; and only 0.6 percent by the Urbanization group variables. Table XVI Group: Specific Amenity Growth Effect Dependent Var : Total Amenity Effect Independent Var: Group Specific Amenity Effect Amenity Variable Group 0.044 Census Division Variable Group 0.066 Demographic Variable Group 0.026 Education Variable Group 0.048 Fiscal and Other Policy Variable Group 0.039 Economic Variable Group 0.247 Urbanization Variables Group 0.006 14 Only the variables belonging to the respective variable group are regressed on the dependent variables in each regression and the estimates ( ’s) are used to calculate the explained variable group growth estimates ( ’s) for each micropolitan area. The ( ’s) are then put into the growth model to estimate the explained group amenity (productivity/housing supply) effect. The group amenity effect is then regressed on the total amenity effect (the group productivity effect is regressed on the total productivity effect and the group housing supply effect is regressed on the total housing supply effect) and the R2 is analyzed. b ˆy ˆy 77 It is apparent that the Economic variable group is mostly important for the variation in the Amenity growth effect, explaining four times the variation in the Amenity effect compared to the second most important group. The Beta coefficients were analyzed in order to find out why that was the case. The Beta coefficients were adjusted by the coefficients that define the respective growth effects in the relevant regressions15 in order to assess their relative importance within each group. The average wage (in the Economic variable group in the wage regression) was by far the most important variable contributing to the variation in the Amenity growth effect, meaning that migrants were willing to accept relatively low wages to enjoy micropolitan amenities. The fact that the relative Amenity growth effect was favorable (compared to the US average) also indicates that migrants were willing to accept less than average nationwide growth in wages and higher than average growth in rental payments in order to enjoy micropolitan amenities. The Productivity Growth Effect The Glaeser and Tobio model indicates that strong growth of population and wages reflects increases in productivity. Thus, the growth of the productivity effect ( ) is a weighted growth of population and wages. It is characterized by the following equation , in which = share of labor in production, is the See the methodology section = = A (1 )bN (1 )bW A (1 ) (1 ) N W b b Ph W b b L 1 Ph N W b b b 78 share of capital and , are regression coefficients from the population and wage regressions. Productivity is an important factor in explaining demand sided migration. An increase in productivity in a given micropolitan area results in higher wages and that induces people to migrate to that micropolitan area. The model shows that productivity increased in micropolitan areas during the period, corroborating our earlier findings that the real wage increased. However, productivity increased significantly less in micropolitan areas than nationwide ( vs ). It is therefore unlikely that the migration to micropolitan areas was motivated by micropolitan productivity and by spatial differences in economic opportunity. Approximately 42.5 percent of the variation in the Productivity growth effect is explained by the regression (the explained Productivity growth effect regressed on the total Productivity growth effect). Table XVII shows that the Economic variable group explains 29.1 percent of the total variation in the N b W b 511 0.29 micros A 0.37 US A Table XVII: Group Specific Productivity Growth Effect Dependent Var : Total Productivity Effect Independent Var: Group Specific Productivity Effect Amenity Variable Group 0.017 Census Division Variable Group 0.030 Demographic Variable Group 0.005 Education Variable Group 0.020 Fiscal and Other Policy Variable Group 0.035 Economic Variable Group 0.291 Urbanization Variable Group 0.008 79 Productivity growth effect; Fiscal and Other Policy variable group, 3.5 percent; Census division variable group, 3.0 percent; Education variable group, 2.0 percent; Amenity variable group, 1.7 percent; Urbanization variable group, 0.8 percent; and the Demographic variable group, 0.5 percent. As expected then all the top factors that contribute to growth in wages (from the wage regression) were the most significant forces contributing to the positive and negative evolution of the Productivity growth effect during the period. The most important variable explaining the Productivity growth effect (by far) was average wages (Economic variable group), followed by; January temperatures (Amenity variable group); the Mountain division (Census division variable group); the percent of manufacturing jobs (Economic variable group – p value = 0.053); the percent of population with Baccalaureate degree or higher (Education variable group); July temperatures (Amenity variable group  p value = 0.059); percent jobs in construction (Economic variable group); and the percent of blacks in the local population (Demographic variable group). It is interesting how important the Mountain division is in explaining the growth in productivity. There must be some fixed factors in that division which are very conducive to growth in wages or perhaps the region is attracting productive firms. Housing Supply Growth Effect Glaeser (2007) finds in a study on urban megaregions that differences in housing supply due to differences in land use regulations was an important determinant of regional population growth. Therefore, the Housing Supply growth effect is important in explaining the growth of regions. The Housing Supply growth effect () is defined by L 80 the model to be equal to , where is the elasticity of housing supply. A robust growth in population and wages associated with relatively less growth in rents indicates a growth in the housing supply effect. An increase in population growth in a given area (ceterus paribus) will always increase housing prices and rents somewhat if land supply is limited. If housing supply is overly restricted because of some reason, then housing prices and rents will be even higher. That in turn could deter inmigration of people. That is because “housing costs”/rents are usually the single largest component of spending for households. This could also deter inmigration of firms because an increase in rents means higher unit cost of production and less profits. 1 Ph N W b b b Table XVIII Group Specific Housing Supply Growth Effect Dependent Var : Total HS Effect Independent Var: Group Specific HS Effect Amenity Variable Group 0.139 Census Division Variable Group 0.436 Demographic Variable Group 0.159 Education Variable Group 0.114 Fiscal and Other Policy Variable Group 0.202 Economic Variable Group 0.210 Urbanization Variable Group 0.024 81 Many studies in the economic literature (McGranahan, 2007) have found that high “housing prices”/rents deter interregional migration. Other studies have found that job related migration is greatly affected by the state of housing markets. Most recently Valetta and Kuang (2010) find that part of the reason why people are not migrating for jobs is due to the state of housing markets. The state of housing markets has important implications for economic growth. Housing supply was significantly less flexible in the 511 micropolitan areas than on average nationwide as indicated by the Housing Supply growth effect ( vs ). Approximately, 72.7 percent of the total variation in the Housing Supply growth effect is explained by the model regression (the explained Housing Supply growth effect regressed on the total Housing Supply growth effect). The 511 1.12 micros L 0.75 US A Table XIX Net Contribution to the Housing Supply Effect Rent Regression Census Division Group Adj Beta Coef East North Central (D3) 3.6 West North Central (D4) 2.9 South Atlantic (D5) 2.7 Mountain (D8) 2.7 Pacific (D9) 2.5 East South Central (D6) 2.5 West South Central (D7) 2.2 Middle Atlantic (D2) 1.1 82 Census division variable group explains 43.6 percent of total variation in the housing supply effect (see Table XVIII); the Economic variable group, 21 percent; Fiscal and Other Policy variable group, 20.2 percent; Demographic variable group, 15.9 percent; Amenity variable group, 13.9 percent; Education variable group 11.4 percent; and the Urbanization variable group, 2.4 percent. The adjusted Beta coefficients (see table XIX) show that all the eight Census division variables in the rent regression were the most significant by far contributing to the negative Housing Supply growth effect, indicating that a significant portion of the impact that contributed to the unfavorable Housing Supply growth effect is unexplained by the variables in the regression. Interestingly, the Census divisions that contribute most to the negative Housing Supply growth effect (East North Central, West North Central and the South Atlantic divisions) also have the top three largest micropolitan populations and account for more than 51 percent of the population in micropolitan areas in the study. Analysis The growth effects model indicates that micropolitan areas benefitted from relatively attractive natural amenities that induced inmigration and population growth. Table XX Micropolitan Areas CD 3 CD 4 Avg. All Micros Wage9000 40.00% 42.50% 39.90% Pop9000 5.90% 6.00% 9.20% 83 The model shows that productivity increased in micropolitan areas, but well below the overall nationwide productivity growth, implying that productivity was not a significant catalyst for migration. Further analysis corroborates the results from the growth effect model. The micropolitan areas in both the East and West North Central divisions (Census divisions 3&4) had one of most robust growth in wages of all micropolitan areas in the study (see Table XX). Yet both divisions had population growth well below the micropolitan average. The model also indicated that the housing supply in micropolitan areas was significantly less flexible than the housing supply nationwide, which could be a major deterrent to micropolitan migration. The Census division group in the rent regression is by far the most important variable group contributing to the variation in the explained Housing Supply growth effect. The Census division group must be capturing regional attributes that affect the local housing supply. Next we will apply the GlaeserTobio model on the variation in the data that is not explained by the regressions in order to in order to understand better the overall sources of micropolitan growth. Unexplained Growth Effects, the Role of the Housing Supply and Unexplained Outliers Unexplained Growth Effects In order to get a deeper understanding on micropolitan growth in the 1990s the focus shifts now to the residual (unexplained) growth effects. Whereas the explained growth effects were obtained using , the residual growth effects are obtained using (see the methodology section). The regression variables did not explain all the variation ˆy ˆe 84 in the data. By analyzing the residual growth effects we get a more complete picture of the forces that contributed to the growth of the micropolitan areas in the 1990s. The residual growth effects will also help us to identify factors that help explain the growth of outliers. The residuals (’s) from each (population, wage and rent) regression were put into the growth effect model16 to calculate the residual Amenity (Productivity, Housing Supply) growth effect. The residual Amenity (Productivity, Housing Supply) growth effect was regressed on the total Amenity (Productivity, Housing Supply) effect and the adjusted R2 was analyzed. The residual Amenity growth effect explains 59 percent of the total Amenity growth effect in micropolitan growth during the period, the residual Productivity growth effect 59.3 percent and the residual Housing Supply growth effect 27.3 percent. It is important to find out how much unexplained population growth (errors in the population regression) is impacted by the three types of unexplained growth effects in order to identify important factors that contributed to the unexplained population growth. The residual population growth was therefore regressed on the residual innovations17 in 16 See the methodology section 17 errorpop = f( λUϕ, λUA, λUL), where errorpop = the error terms from the population regression, λUϕ, = the residual (unexplained) Amenity growth effect, λUA = the residual Productivity growth effect and λUL= the residual Housing Supply growth effect ˆe (1)(1) U A eNeW U PhW e e 1 U Ph L NW e e e 85 order to analyze residual population growth, but the degree of collinearity between the different growth effects made any inference impossible. Bivariate Pearson correlation analyses were therefore applied for analysis. The Pearson correlation matrix (see Table XXI) revealed that the errors in the population regression were significantly correlated with the residual (unexplained) Housing Supply growth effect (r =  0.20, p<0.0001), considerable less correlated with the residual Productivity growth effect and (r =  0.175, p<0.0001) and not significantly correlated with the residual Amenity growth effect (p=0.1319). In order to find out how much residual Productivity growth effect affected residual population growth we have to look better at residual wage growth. The correlation between the residual Productivity growth effect and residual wage growth (errors in the wage regression) is 0.99, however, the correlation between residual population growth and residual wage growth is not statistically significant which indicates that it is unlikely that the residual Productivity growth effect was an important factor explaining unexplained population growth. Table XXI Residual Residual Population P Productivity P Correlation Growth Value Effect Value Residual Amenity Effect 0.067 0.132 Residual Productivity Effect 0.175 <.0001 Residual l Housing Supply Effect 0.202 <.0001 Residual Wage Growth 0.054 0.222 0.993 <.0001 86 Next we look at the unexplained Housing Supply growth effect. Table XXII shows that the “residual population growth regressed on the residual Housing Supply growth effect" regression is statistically significant and has an R2 of 0.041. It is not a surprise because there is a significant 44.7 percent correlation between the residual population growth and the residual rent growth (which is the most significant contributor to the residual Housing Supply growth effect). Table XXII also shows that when the residual Housing Supply growth effect data is divided into groups of micropolitan areas with smaller and larger residual housing supply effects than the average for all the 511 micropolitan areas in the study, then both regressions are significant. It is interesting though that the R2 increases 



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