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FORECASTING WHEAT YIELD AND QUALITY CONDITIONAL ON WEATHER INFORMATION AND ESTIMATING CONSTRUCTION COSTS OF AGRICULTURAL FACILITIES By BYOUNGHOON LEE Bachelor of Science in Agricultural Economics Kangwon National University Chuncheon, Korea 1999 Master of Science in Agricultural Economics Korea University Seoul, Korea 2001 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 May, 2011 ii FORECASTING WHEAT YIELD AND QUALITY CONDITIONAL ON WEATHER INFORMATION AND ESTIMATING CONSTRUCTION COSTS OF AGRICULTURAL FACILITIES Dissertation Approved: Dr. Philip Kenkel Dissertation Adviser Dr. B. Wade Brorsen Dr. Rodney Holcomb Dr. Patricia RayasDuarte Dr. Mark E. Payton Dean of the Graduate College iii ACKNOWLEDGMENTS It is my great pleasure to thank all the people who made this dissertation possible. I wish to express my sincere appreciation to my academic advisor Dr. Philip Kenkel for his intelligent supervision and invisible guidance and encouragement through my Ph.D. program at Oklahoma State University. I also wish to thank all members of my academic committee Dr. Wade Brorsen, Dr. Rodney Holcomb, and Dr. Patricia RayasDuarte for their helpful advice invaluable comments during the final week of completing this dissertation. Especially Dr. Wade Brorsen provided thoughtful econometrics advice and hard training for great direction throughout my preparation of this dissertation. My appreciation is extended to Dr. Francis Epplin who has provided a research opportunity, great teaching and advice. Also Dr. Brain Adam, and Dr. Changjin Chung who have encouraged my academic success. I wish to thank my academic friends Inbae Ji, Jongsan Choi, Seongjin Park, Yoonsuk Lee, and Samarth Shah. Lastly, and most importantly, I wish to appreciate my parents SunTae Lee and JongSook Yoon for endless love and patience. My wife jiyeon Park and two daughters, Eunju, Kyuna, and the son, Donghoo who have helped me complete this program. Also, I always have appreciated my ancestors. iv TABLE OF CONTENTS I. Preharvest Forecasting of County Wheat Yield and Wheat Quality Conditional on Weather Information ..................................................................1 Introduction ..............................................................................................................1 Conceptual Framework ............................................................................................4 Data ........................................................................................................................10 Empirical Model Specification ..............................................................................16 Estimation Method and Procedures .......................................................................19 Empirical Results ...................................................................................................22 Summary and Conclusion ......................................................................................29 Appendices .............................................................................................................31 II. Improved Methods of Estimating Construction Costs of Agricultural Facilities .........................................................................................43 Introduction ............................................................................................................43 Conceptual Framework ..........................................................................................47 Empirical Model Specification and Procedures .....................................................50 The Structure of Economic Engineering Construction Cost Templates Model ....54 Collection of a list of the components and cost data .....................................54 The requirements of each component aspect .................................................58 Cost estimation of each aspect of components ..............................................65 Cost adjustments for size factors and time period .........................................70 Data ........................................................................................................................76 Empirical Results ...................................................................................................77 Summary and Conclusion ......................................................................................88 Appendices .............................................................................................................90 REFERENCES ............................................................................................................98 v LIST OF TABLES Table Page (Chapter I) Table 1. Descriptive Statistics for Wheat Quality Characteristics, 2004  2010 ............................ 14 Table 2. Tests of No Spatial Autocorrelation for Wheat Yield, Protein, and Test Weight ............ 22 Table 3. Yield Model and Spatial Yield Model Estimates, 19942009 ......................................... 23 Table 4. The Elasticity of Weather Variables ................................................................................ 24 Table 5. Out of Sample Forecast Error Statistics for Yield Models, 2010 .................................... 24 Table 6. Protein Model and Test Weight Model Estimates, 20042009 ........................................ 25 Table 7. The Elasticity of Weather Variables for Quality Model .................................................. 26 Table 8. Out of Sample Forecast Error Statistics of Wheat Quality, 2010 .................................... 27 Table 9. Out of Sample Fit Test using the Longer Period (FebMay) for Yield Models ............... 28 Table 10. Out of Sample Fit Test using the Shorter Period (FebApril) for Quality Models ........ 28 Appendix Table 1. Rsquared Estimated and Correlation Coefficients for Selecting Quality Variables riables ............................................................................................................................ 36 Appendix Table 2. Correlation Coefficients among Yield, Protein, Weight and Weather Variables ...................................................................................................................................................... 36 Appendix Table 3. Diagnostic Test Statistics: Yield, Protein, and Test Weight Response Models ...................................................................................................................................................... 37 Appendix Table 4. Yield Model and Spatial Yield Model Estimates, 19942009......................... 37 Appendix Table 5. Protein Model and Test Weight Model Estimates, 20042009 ...................... 37 Appendix Table 6. Descriptive Statistics for Yield Model Variables, 19942009 ........................ 38 Appendix Table 7. Descriptive Statistics for Quality Model Variables, 20042009 ..................... 38 Appendix Table 8. Comparing Actual and Prediction Values for Yield Models .......................... 38 Appendix Table 9. Comparing Actual and Prediction Values for Quality Models ....................... 39 Appendix Table 10. Yield Model and Spatial Yield Model Estimates using the Longer Period (FebMay), 19942009 ................................................................................................................... 40 vi (Chapter ІІ) Table 1. List of the Components and Units for Grain Bin Facilities Cost Estimation .................. 55 Table 2. List of the Components and Units for Warehouse Building Cost Estimation (Class S) .. 56 Table 3. List of the Components and Units for Pole Barn Cost Estimation (Class Dpole) ........... 57 Table 4. Estimated Auger Capacity and Horsepower Requirements ............................................ 60 Table 5. Grain Bin Formulas for Total Amount of Requirement and Cost Estimation ................ 67 Table 6. Warehouse Building Formulas for Total Amount of Requirement and Cost Estimation 68 Table 7. Pole Barn building Formulas for Total Amount of Requirement and Cost Estimation ... 69 Table 8. Cost adjustments by size factors (area & story height) ................................................... 71 Table 9. Grain bin and Warehouse Building Dimensions and Quotation for Size Factors ........... 72 Table 10. The Developed Cost Equations and Michigan Cost Equations Estimates for Grain Bin Comparison (loglog form) ............................................................................................ 81 Table 11. Total Cost Equation Estimates Using the Predicted Costs ($) for Warehouse .............. 81 Table 12. Chow Test for Parameter Stability of Grain Bin & Warehouse Cost Model ................ 82 Table 13. The Elasticity of Explanatory Variables and Correlation for Comparison ................... 83 Appendix Table 1. Predicted Total & Fan & Heater Costs for Diameter 105 ft and Eave Heights 25 to 105 ft. .................................................................................................................... 95 Appendix Table 2. Categorized Predicted Costs using „Economic Engineering Warehouse Building Construction Cost Templates Model‟ for Width 100, Lengths 100 to 300 ft ... 96 Appendix Table 3. Average cost ratio using „Economic Engineering Grain bin Construction Cost Templates Model‟ for diameter 105 ft, eave heights 25 to 105 ft. ................................ 97 Appendix Table 4. Average cost ratio using „Economic Engineering Warehouse Building Construction Cost Templates Model‟ for Width 100, Lengths 100 to 300 ft. ............................... 97 vii LIST OF FIGURES Figure Page (Chapter I) Figure 1. Wheat Growth and Development Stages .......................................................................... 6 Figure 2. The PGI Survey Area of Grain sheds basis .................................................................... 10 Figure 3. Location of 2010 Sample Elevators and Oklahoma Mesonet Stations ........................... 15 Figure 4. The Prediction procedure for Yield and Quality Models ............................................... 21 Appendix Figure 1. Plot Yield and Precipitation ........................................................................... 40 Appendix Figure 2. Plot Yield and Avg. Temp. ............................................................................ 40 Appendix Figure 2. Plot Yield and Avg. Temp. ............................................................................ 40 Appendix Figure 4. Plot Protein and Max. Temp. ......................................................................... 41 Appendix Figure 5. Plot Protein and Yield .................................................................................... 41 Appendix Figure 6. Plot Test Weight and Precipitation ................................................................ 41 Appendix Figure 7. Plot Test Weight and Maximum Temp. ......................................................... 41 Appendix Figure 8. Plot Test Weight and Mini. Temp. ................................................................ 41 Appendix Figure 9. Plot Test Weight and Yield ............................................................................ 41 Appendix Figure 10. Plot Protein and Solar Radiation ................................................................. 41 Appendix Figure 11. Plot Weight and Solar Radiation ................................................................ 42 Appendix Figure 12. Plot Yield and Solar Radiation ................................................................... 42 Appendix Figure 13. Calculated Relationship between Yield and Protein and Test Weight Using Elasticity ........................................................................................................................ 42 (Chapter II) Figure 1. Prediction & Evaluation Procedure for Economic Engineering Construction Cost Model ...................................................................................................................................................... 75 Figure 2. Predicted Total Cost Curve of bin Construction for Diameter 105 ft and Eave Heights 25 to 105 ft ..................................................................................................................... 77 Figure 3. Predicted Average Cost Curve of bin Construction for Diameter 105 ft and Eave Heights 25 to 105 ft ....................................................................................................... 78 viii Figure 4. Predicted Total Cost Curve of Warehouse Building Construction for Width 100 ft and Lengths 100 to 300 ft with Wall Height 24ft ................................................................. 79 Figure 5. Predicted Average Cost Curve of Warehouse Building Construction for Width 100 ft and Lengths 100 to 300 ft with Wall Height 24 ft ......................................................... 79 Figure 6. Average Percentages of Each Predicted Cost of Components ...................................... 80 Appendix Figure1. Grain bin construction basic components ....................................................... 91 Appendix Figure 11. Warehouse BuildingStorage (Average Class S) ........................................ 92 Appendix Figure 12. Pole Barn BuildingStorage (Average Class Dpole) .................................. 92 Appendix Figure 2. Economic Engineering Grain Bin Construction Cost Templates Model as spread sheet type model ................................................................................................. 93 Appendix Figure 3. Economic Engineering Warehouse Building Construction Cost Templates Model as spread sheet type model ................................................................................. 93 Appendix Figure 4. Economic Engineering Pole Barn Building Construction Cost Templates Model as spread sheet type model ................................................................................. 94 Appendix Figure 5. Comparsion for Required HP Between Tall Bin and Wide Short Bin ........... 94 1 CHAPTER I Preharvest Forecasting of County Wheat Yield and Wheat Quality Conditional on Weather Information Introduction Winter wheat production in the Southern Plains is a mostly dry land crop with substantial yeartoyear variation in yields and quality due to rainfall, temperature and other weather events. If wheat yield and wheat quality response to weather conditions could be predicted early and accurately, the information could be widely used. The information could be particularly important to farmers optimizing late season agronomic and marketing decisions and to grain elevators and millers for purchasing decisions. Thus, there has been increasing interest in the use and development of robust crop weather response models. Numerous models have been estimated to predict crop yield based on weather conditions. Two main prediction approaches are simulation models and multiple regression models. A number of comprehensive agricultural simulation models are now available to predict yield and variability of wheat. Jones and Kinir (1986) suggested a model to simulate the effects of genotype and weather conditions on crop yield, Duchon (1986), Claborn (1998), Bannayan, Crout, Hoogenboom (2003), and Tsvetsinskaya et al. (2003) predicted yields using weather forecasts and scenarios using the Crop Environment Resource Synthesis (CERES) simulation model. For the Great Plains, Eastering et al. (1998) and Wang et al. (2006) used the Erosion Productivity Impact Calculator (EPIC) model and Eastering et al. (1998) found spatial disaggregation of climate data2 enhance predictions. Using CERESWheat model, Weiss et al. (2003) investigated the responses of wheat yield and enduse quality by using nitrogen management and planting dates data. The simulated results depended on spatial locations and climate changes, and also soil water stress and management of nitrogen strongly influenced yield distributions and kernel nitrogen content. Walker (1989) combined simulation and multiple regression to develop physiologically and regionally weighted drought indices from temperature and precipitation data. The forecasts showed the indices well explain the variation of interregional and annual yield within a growing season. A simulation model is designed to simulate crop yield using details about crop biology. However, as noted by Walker (1989), a simulation approach requires extensive information such as soil type, plant parameters, and weather data related to the crop development stage, which are often not readily available. Tannura, Irwin, and Good (2008) argue that an important limitation of crop simulation models is that they are likely to ignore the influence of technology development over time. Bechter and Rutner (1978) and Just and Rausser (1981) found singleequation models forecast more accurately than large econometric models and we should expect a similar result for agronomic models. Thus, many previous studies have preferred a regression approach rather than a large simulation model when the goal is forecasting. Studies using the multiple regression approach include Yang, Koo, and Wilson (1992), Dixon et al. (1994), Kandiannan et al. (2002), and Chen and Chang (2005) who used various production functions to capture the effect of climate variables on observed crop yield level and to predict crop yield. Irwin, Good, and Tannura (2008) and Tannura, Irwin, and Good (2008) modified Thompson‟s (1964) corn and soybean regression model and found crop yield strongly related to weather conditions such as temperature, rainfall, technology, and other weather variables. As Tannura, Irwin, and Good (2008) and other studies have proven, multiple regression models have high explanatory power and can represent relationships between weather conditions and crop yield. Thus, the multiple regression model approach is not only easier to use, it is also likely more accurate than the simulation model approach. 3 Several studies investigated the influences of weather conditions, genotype, and their interaction on wheat quality. The crop maturation period, such as milk development, heading, and ripening stages are the critical stages in determining wheat quality (FAO, 2002). Graybosch et al. (1995), Johansson and Svensson (1998), Smith and Gooding (1999) and Guttieri et al. (2000), and Johansson, Prieto, and Gissen (2008) developed quality models that showed the effect of weather and environment strongly influenced protein content and test weight of wheat. Smith and Gooding (1999) argued predicting grain quality before wheat harvest would be important information to grain buyers, and to farmers to help optimize agronomic activity, particularly, a late application of nitrogen fertilizer to increase protein content (Woolfolk et al., 2002). Britt et al. (2002) estimated six yield and quality of cotton response functions and profit functions as a function of weather information and input and output prices. Regnier, Holcomb, and RayasDurate (2007) investigated the variations in flour and dough functionality traits associated with environmental factors and found the interaction between crop years and production regions was a significant factor for flour and dough qualities since growing conditions and climate conditions differ among the regions and across years. Unlike previous yield regression models, most qualityrelated model studies did not measure prediction performance of their models and also used analysis of variance (ANOVA), Spearman rank correlation analysis or simple regression models without precise diagnostic tests for model misspecification. Therefore their methods may lead to biased and inconsistent estimates (McGuirk, Driscoll, Alwang, 1993). The extensive previous studies have limitations. One is that the previous regression studies cited have solely estimated the impacts on yield and quality level, respectively, and did not deal with agronomic tradeoffs between yield and quality of wheat. Also few focused on prediction and most studies did not consider out of sample forecasts but measured in sample fit. Insample fit can be inaccurate because most models, including ours, are developed from pretesting over a large number of alternative specifications. 4 The other is that many of the above studies have either used data from a single location or have not used the extra information provided by spatial data. The increasing availability of spatial climate information makes it important to incorporate this new level of information to improve forecasts. Anselin (1988) explained that when using spatial data, the dependent variable at each location may be correlated with observations of the dependent variable at neighboring locations. This is defined as spatial contiguity (lag) effect. If this effect is ignored in a model specification, the estimates in the general model are likely to be biased. Therefore, in order to get more accurate forecasts, the crop response model using spatial data needs to include a spatial lag effect. Oklahoma has two unique resources for examining the relationship between weather and wheat yields and quality. The Oklahoma Mesonet consists of 120 automated stations covering Oklahoma with one or more stations in each of Oklahoma's 77 counties. Plains Grains, Inc. (PGI) is a private, nonprofit wheat marketing organization based in Stillwater, Oklahoma. PGI evaluates wheat quality, including milling and baking quality from an extensive network of samples at the county level. These two unique data sets provide the opportunity to examine the ability to predict wheat yield and quality with weather data. These two data sets (mesoscale weather data and elevator scale quality data) are highly disaggregated. Thus, the disaggregated data sets could provide more precise wheat yield and quality predictions than was possible with the data sets used in past research. The objective of the study is to develop wheat regression models to account for the impact of weather on wheat yield and quality and to predict (forecast) wheat yield and quality levels accurately. In other words, the primary purpose of the study is to use weather information to predict wheat yield and wheat quality and to select variables and functional forms to estimate parameters and then measure how well the developed models forecast. Conceptual framework Previous studies have used knowledge about biological development stages of crops to help select the explanatory variables. Dixon et al. (1994) and Kafumann and Snell (1997) specified weather 5 variables for their corn yield regression models that were based on biophysical stages of corn1. On the other hand, Yang, Koo, and Wilson (1992) and others used planting season and growing season precipitation and average temperature. Hansen (1991), Tannura, Irwin, and Good (2008) and others estimated the effect of calendar month precipitation and temperature variables on soybean and corn yield during crucial development periods to forecast potential crop yield. Even though biological stages of crops do not precisely correspond with calendar months, a number of previous regression response models have used weather variables defined on a monthly average calendar basis. Previous studies also assume every cross sectional location has the same development stages since it is very difficult to match the precise time point of crop development stages at every location. Another reason is the estimated results using monthly weather variables were similar with that of stage basis variables. For example, Dixon et al. (1994) compared weather variables based on biological stages with variables that based on fixed calendar months and found the forecasting performance and R2 of the two models only changed slightly. Weather strongly affects four stages2 of wheat development that determine wheat production level and qualities (FAO, 2002). Aitken (1974), Miralles and Slafer (1999), and Acevedo et al. (2002) argued mainly temperature and precipitation influence wheat development; the most crucial stages of wheat yield are from double ridge to anthesis (flowering) (GS2) and from anthesis to maturity (GS3) since kernel number and weight are being determined at that time (figure 1). 1 The corresponding weather variables were specified based on the six weeks before and three weeks after silking point rather than calendar months basis because corn is critically sensitive to precipitation in June and midJuly in Midwestern U.S. 2 The stages can be categorized as germination to emergence (E), from germination to double ridge (GS1), from double ridge to anthesis (GS2), and grain filling period from anthesis to maturity (GS3) (FAO, 2002). 6 Figure 1. Wheat Growth and Development Stages 7 Meanwhile, the influence of temperature and precipitation during grain filling are widely known to influence wheat quality characteristics. Graybosch et al. (1995), Johansson and Svensson (1998), Stone and Savin (1999), and Smith and Gooding (1999) found weather has deep impacts on grain quality; for instance, increased temperatures during grain filling tend to increase protein and reduce mean grain weight. Stone and Savin (1999) argued that 7080 % of total protein is accumulated during the grain filling period. Winter wheat of the southern Great Plains is typically planted in early September through the middle of November. In general winter wheat harvest begins toward the end of May in southern Oklahoma and continues until about the middle of July (IPM Center, 2005). According to crop weather summary in Oklahoma (DOA, 2000), wheat begins to double ridge and joint in February. Southwestern counties begin to head by the end of March. In April, anthesis is begun and some wheat in south Oklahoma begins the grain filling period, and finally wheat harvest begins approximately May 20th in the southern counties. Using the above described general relation of weather variables and wheat by growth stages, the study selects calendar months during GS2 and GS3 and specifies appropriate calendar month weather variables for growing periods that correspond to these biological wheat development stages. Eastering et al. (1998) used a fine spatial scale to reduce statistical bias from aggregation and confirmed the difference between the observed and estimated yield was greatly reduced when data scale was disaggregated to around 37mile × 50mile. Unfortunately, their method requires a very fine data scale and cannot be used with our data. On the other hand, Anselin (1988) assumed generally the dependent variable or residual at each location may be correlated with neighboring locations‟ dependent variables or residuals. For this spatially correlated data or residuals, the dependence is termed as spatial autocorrelation or spatial lag (contiguity) effect. This indicates that dependents or residuals are spatially autocorrelated and then violate the general assumption of statistically 8 independent explanatory variables and errors. If the spatial lag effect is not considered, estimates will be biased and inconsistent. Previous studies have often used regional models using regional crosssectional data. However, regional data such as observed yield, quality level, and weather variables are generally aggregated considerably beyond the county level. If point estimates (weather, yield, quality) are observed near the border of neighboring regions, there is an opportunity for spatial autocorrelation. For instance, grain produced in one county could be shipped to an adjoining county (this would only affect the quality data since the yield data are based on ARS (Agriculture Research Service) yields which are in turn based on producer reports of harvested production). Some cropland will be closer to a weather station in a neighboring county than weather stations in its own county. Thus, weather measures in a neighboring county should help predict yield. Thus, a spatial lag model should increase forecast accuracy. Anselin et al. (2008) and Anselin and Bera (1998) express the neighbor relation with a spatial weights matrix, and the elements of reflect the potential spatial relations between observations that correspond to the spatial weights structure. The spatial weights matrix can be expressed as binary contiguity sharing a common border, distance contiguity including nearest neighbor locations, and inverse distance between two observations. Anselin and Bera (1998) suggest two main alternative models of spatial autocorrelation: the spatial lag model, and the spatial error model. The main purpose of the former is to predict the spatial patterns such as cluster and random correlation, while the latter is to increase the efficiency of estimates (Bongiovanni and LowenbergDeBoer, 2001). A spatial lag model is used here since the explanatory variables in neighboring counties are expected to help predict our dependent variables. The general regression function can be expressed as: 9 where is a vector of dependent variables, is the matrix of independent variables, and is a vector of stochastic error terms. The spatial lag model is where is the spatial autoregressive coefficient, is a N × N spatial weight matrix (Greene, 2008). This is similar to including a lagged dependent variable in a time series model, except that endogeneity is created because the lagged effects go both directions. The weights matrix is standardized so that rows sum to 1 such as = where are elements of If , the dependent variable at each location is positively correlated with other location‟s dependent variables. Hence, the spatial lag model can be estimated with instrumental variables such as two stage least squares (2SLS) and generalized method of moments (GMM ) or with maximum likelihood (ML) (Lambert and LowenbergDeBoer, 2001), and 2SLS is used here (see appendix 1). 10 Data The wheat yield data (from 19942009) are from 67 counties in Oklahoma and were obtained from „Crop Production Report‟ of United States Department of Agriculture (USDA) National Agricultural Statistics Service (NASS). The adopted yield was based on Harvested acre. Oklahoma has 77 counties, but ten of them are not included due to having little wheat acreage. The crosssectional timeseries data is composed of 1,072 observations (16 years*67 counties). The wheat quality data are from Plains Grains, Inc (PGI)3. PGI tests 96 samples that were collected on a “grainshed” basis from grain elevators when at least 30% of the local harvest was completed. The term “grainshed” was developed by PGI and represents regions within each state in which the majority of the wheat is marketed through a terminal elevator, river elevator or train loading facility (figure 2). Figure 2. The PGI Survey Area of Grainsheds basis Source: 2009 Oklahoma wheat quality report. (2010) 3 Plains Grains Inc.(PGI) is located in Oklahoma and does a wheat quality survey and quality testing of hard red winter wheat to provide enduse quality information to the wheat buyer and producer and published Wheat Quality Report PGI (2009). 11 Figure 21. The Oklahoma Samples of 8 Grainshed Basis Source: 2009 Oklahoma wheat quality report (2010) There are 8 grainsheds in Oklahoma (figure 21). PGI collects representative wheat quality samples from country or terminal elevators. Generally elevators take samples from each truckload arriving at the elevator and the grain is sampled using a hand grain probe. Each elevator directly tests these samples about test weight and moisture content and then these samples typically accumulate in a barrel. Lastly, the elevators barrel is sampled by PGI‟s representative using a hand grain probe. The samples from county and terminal elevators are sent to USDA, ARS hard winter wheat Quality Lab in Manhattan, KS. Twentyfive quality parameters are analyzed in order to provide data that specifically describes the quality of wheat (PGI, 2009). The available historical quality data are from 2004 to 2010 crop years. Table 1 shows a list of wheat quality characteristics over categories and basic descriptive statistics. PGI describes the characteristics specifically “… U.S. wheat grades are determined as based on characteristics such as test weight and includes defects on damaged kernels, foreign materials, shrunken and broken kernels. Test Weight (lb/bu.) is a measure of the density of the sample and may be an indicator of milling yield and the general condition of the sample, as problems that occur during the growing season or at harvest often reduce test weight. Defects (%) are damaged kernels, foreign materials, and shrunken and broken kernels. The sum of O6 169 177 177 177 183 183 183 259 259 266 270 270 270 270 271 277 271 277 281 281 281 283 283 287 412 412 412 56 59 59 59 59 60 60 60 60 62 62 62 62 64 64 64 64 64 64 64 69 69 69 70 70 75 75 75 77 77 81 81 81 Toll Toll Toll Toll Toll Toll Toll Toll 35 35 40 40 44 44 44 Chickasaw NRA Kiamichi River Illinois R. Little River Washita River Salt Fork Salt Fork Cimarron River Candadian R CANADIAN RIVER Cimmaron River L. Altus Atoka L. Broken Bow L. 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Foreign material is all matter other than wheat that remains in the sample after the removal of dockage and shrunken and broken kernels and shrunken and broken kernels are all matter that passes through a 0.064 x 3/8inch oblonghole sieve after sieving. Damaged kernels are kernels, pieces of wheat kernels, and other grains that are badly grounddamaged, badly weather damaged, diseased, frostdamaged, germ damaged, heatdamaged, insectbored, mold damaged, sproutdamaged, or otherwise materially damaged. Additionally, there are kernel quality data and other wheat characteristics in determining the value of the wheat, for instance, wheat protein content, wheat moisture, dockage, thousandkernel weight, and falling number. In the kernel quality data, kernel size (%) is a measure of the percentage by weight of large, medium and small kernels in a sample. Large kernels or more uniform kernel size may help improve milling yield. Single Kernel Characterization System (SKCS) measures 300 individual kernels from a sample for size (diameter), weight, hardness (based on the force needed to crush) and moisture. Thousandkernel weight (g) and kernel diameter provide measurements of kernel size and density important for milling quality. Simply put, it measures the mass of the wheat kernel. Millers tend to prefer larger berries, or at least berries with a consistent size. Wheat with a higher TKW can be expected to have a greater potential flour extraction. In the case of other wheat characteristics, protein content (12% mb: moisture base) relates to many important processing properties, such as water absorption and gluten strength, and to finished product attributes such as texture and appearance. Higher protein dough usually absorbs more water and takes longer to mix. Falling number (sec) is an index of enzyme activity in wheat or flour and is expressed in seconds. Falling numbers above 300 are desirable, as they indicate little enzyme activity and a sound quality product. Falling numbers below 300 are indicative of more substantial enzyme activity and sprout damage. Moisture content (%) is an indicator of grain condition and storability. Wheat or flour with low moisture content is more stable during storage. Ash content (12%mb or %asis) also indicates milling performance and how well the flour separates from the bran. Millers need to know the overall mineral content of the wheat to achieve desired or specified ash levels in flour. Ash 13 content can affect flour color. White flour has low ash content, which is often a high priority among millers. Dockage (%) is all matter other than wheat that can be removed from the original sample by use of an approved device according to procedures prescribed in FGIS (Federal Grain Inspection Service) Instructions…” PGI, 2009 Hard Red Winter Wheat Quality Report. 2010. P. 915. For several year data sets, most quality data has some missing values and provides different quality information based on different testing systems. For example, the Single Kernel Characterization System (SKCS) and the whole kernel nearinfrared (NIR) are rapid tests for wheat quality characteristics, however, the high equipment costs limits the adoption to only large grain operations. So several specific historical year data did not include these test measures. However, test weight (lb/bu) and protein (12% mb) observations have maintained more consistent samplings and also have more high correlations with weather variables than that of the other quality data. Also these two quality data have an important role in determining wheat grade and received price level respectively. Finally, these quality data were used for the quality models and correlation analysis. The ability to predict other wheat quality variables such as total defects and falling number which help determine grade and quality of wheat or flour was examined. These models were dropped because of low Rsquared (see appendix table 1). Moisture content was not examined because it was assumed to be strongly affected by the weather conditions immediately prior to harvest. For more precise analysis, the study matched elevators‟ quality data with weather data from the closest Mesonet stations. This means one weather station per elevator was used to estimate wheat quality models, not a county average. Finally, wheat quality characteristic data used in the model included protein content (% mb) and test weight (lb/bu); the quality data were from 96 elevators based on 2010 (figure 3). 14 Table 1. Descriptive Statistics for Wheat Quality Characteristics, 2004  2010 N Mean Maximum Minimum SD Wheat Grading Data Grade 410 1.73 5 1 0.93 Test Weight (lb/bu) 492 60.1 65 52.8 1.89 Test Weight (kg/hl) 411 79.0 85.4 69.6 2.41 Damage Kernels Total (%) 411 0.19 1.8 0 0.25 Foreign Material (%) 411 0.30 4.7 0 0.55 Shrunken & Broken Kernels (%) 411 1.38 5.1 0.2 0.67 Total Defects (%) 411 1.86 6.5 0.3 1.02 Protein (%) 344 12.4 16.4 9 1.28 HWWQL Test Wt (lb/bu) 176 60.0 65.3 54.7 1.99 HWWQL Test Wt (kg/hl) 176 79.0 85.8 72.1 2.57 Kernel Quality Data Kernel Size Large (%) 343 59.6 86.1 23.6 11.05 Kernel Size Med (%) 343 38.9 71.6 14.0 10.53 Kernel Size Small (%) 343 1.5 7.1 0.0 0.92 SKCS Avg. Wt (mg) 343 29.5 35.4 22.5 2.21 SKCS SD Wt 257 8.23 10.2 5.1 0.74 SKCS Avg. Diam (mm) 343 2.5 2.9 2.0 0.19 SKCS SD Diam 257 0.37 0.5 0.2 0.07 SKCS Avg. Hard 343 74.5 97.2 46.4 9.74 SKCS SD Hard 257 17.29 27.3 13.4 1.79 SKCS Moisture (%) 257 12.2 16.2 8.7 1.34 SKCS SD Moisture 257 0.40 1.2 0.2 0.10 Thousand Kernel Wt (g) 492 28.7 35.4 21.1 2.46 Other Wheat Characteristics NIR Moisture (%) 329 10.7 13.6 8.7 0.90 NIR Protein (%asis) 243 12.2 14.9 9.0 1.00 NIR Protein (12% mb) 492 12.2 16.0 8.8 1.30 Indv Wheat Ash (%asis) 472 1.6 4.0 1.1 0.17 Indv Wheat Ash (12%mb) 406 1.5 3.9 1.1 0.19 Dockage (%) 411 0.71 11.3 0 0.89 Falling Number (sec) 334 418.7 529 172 31.97 Note: KGIS (Kansas Grain Inspection Service), SKCS (Single Kernel Characterization System), NIR (nearinfrared). Mb ( moisture base), and SD(standard deviation). Weather data (from January 1, 1994 to May 31, 2010) were obtained from the Oklahoma Mesonet (figure 3). Each of Oklahoma‟s 77 counties has one or more Mesonet stations. The selected daily data are daily rainfall (in), daily maximum (minimum) air temperature (°F), daily average air temperature (°F), total solar radiation (MJ ), and growth degree days (GDD)4. For all 4 GDD=[(Tmax+Tmin)/2]Tb, 32˚F or 39.2˚F as the base temperature (Tb) for physiological process in wheat(Cao and Moss, 1989). The GDD vary with growing stage and allow a rough estimation of when a given growth stage is going to occur at a particular site. 15 Mesonet stations, the daily observations are aggregated to monthly averages. Generally there is one station per county. For counties with multiple stations an average of all stations in the county is used for yield models; however, quality models use only data from the closest weather station. Several weather stations were added during the study period so the closest weather station sometimes varied by year (see appendix table 6 and 7). Figure 3. Location of 2010 Sample Elevators and Oklahoma Mesonet Stations Notes: the study matched elevators‟ quality data (points) with Mesonet stations‟ weather data (flags) on each the closest distance basis. 16 Source: Oklahoma Mesonet Empirical model specification To specify accurately the underlying relationships between yield and quality variables and weather variables, the study first examined the relationships between weather variables and yield and quality level using the correlation coefficients and graphical displays using proc GAM in SAS (SAS Institute Inc. 2004). GAM allows exploration of data and visualizing structure, and is useful for investigating the relations between dependent and independent variables (see appendix table 2, figures 112). Appendix table 2 shows all weather variables have a high correlation with dependent variables: yield and quality level during the growing season. Precipitation shows less correlation with yield than do average temperature while both variables are associated with yield. Maximum temperature and minimum temperature have all low correlation coefficients and negatively signed with protein and test weight, however, the two variables in quality models were statistically significant. Even though solar radiation and GDD have high correlation coefficients, the variables in the models were not statistically significant and therefore those variables were excluded in the model specification. That disagrees with Dixon et al. (1994) since the solar radiation variable in their model specification is 17 essential. Precipitation is quadratically related with yield; however, temperature has a linear relation with yield. Thus, the yield response model used linear and quadratic terms of precipitation and a linear term for temperature (see appendix figures 1 and 2). On the other hand, in the quality response model there is no evidence that weather variables have a nonlinear relation with quality. Therefore, the quality response model used a linear specification. Meanwhile, the study considered several alternative functional forms such as parametric methods: linear, CobbDouglas, translog, square root, spline, and semiparametric method which do not assume a specific functional form. CobbDouglas and linear model estimates showed not only statistically significant individual coefficients, but also relatively high pseudo R2 (variance ratio) between in sample annual predicted yield and annual actual yield during 19942009, therefore, we selected linear form and CobbDouglas form for yield response model, meanwhile, the quality response model adopted a linear form. The models have the same individual fixed effect and random effect; the functional form can be written as5 and also can be expressed as spatial lag model form using spatial lag term: 5 Linear form equation (3) and CobbDouglas form equation (4) can be represented as matrices and vectors: and , and be also rewritten in expected mean form as and respectively. Therefore, when we compare predictions (expected values) between two functional forms accurately, these mean forms are carefully considered. 18 where is the wheat yield of county i and time t, are individual fixed effects for counties, are the weather variables, and is a N × N spatial weights for crosssectional dimension, is a stochastic error term, is year random effect, and these error terms are assumed to be independent and identically distributed. The yield response model is composed of county fixed effect, year random effect, and three weather variables from February to April such as monthly average rainfall, squared average rainfall, and average temperature that correspond to before and after the anthesis period in Oklahoma because yield is mostly determined before the grain filling stage. As discussed, wheat quality depends on the growth periods such as milk development, heading, and ripening stages. In Oklahoma the wheat growth stages during March to May or June in the northern region contribute to grain filling which relates strongly to wheat quality. Additionally, the quality model employed agronomic tradeoff relationship between yield and quality of wheat using the predicted yield level from yield response model and can be expressed as where is composed of either protein content (12 % mb: moisture base) and test weight (lb/bu), and is a N × N spatial weights for crosssectional dimension and time t since the number of elevators vary by year, therefore weight structure also varies from year to year, for protein; weather variables are monthly average maximum and the monthly average rainfall from March to May, for 19 test weight; weather variables used in this model included monthly average rainfall for March, April, and May and maximum and minimum temperatures for April and May were based on the heading and ripening period such as before and after anthesis stage. Estimation method and procedure The study first tests spatial autocorrelation using proc VARIOGRAM in SAS (SAS Institute Inc. 2004). The most generally used test for spatial autocorrelation is Moran‟s I test6 (Griffith, 1987). Proc VARIOGRAM is used to calculate the Moran's I statistic, Z score, and pvalue for testing the hypothesis of no spatial autocorrelation. The study second adopts maximum likelihood estimation method (Greene, 2008, p. 400) and tests the heteroskedasticity and nonnormality of residuals using a likelihood ratio test, and Shapiro–Wilk test. If hereroskedasticity is formed in the wheat response models‟ error terms, multiplicative heteroskedasticity7 will be assumed (Greene, 2008, p. 170). If nonnormality is formed, the GMM or alternative estimation ways which do not require specific distribution, or a transformation method can be used to modify. If the dependent variable values are correlated with values of nearby locations based on the Moran‟s I statistic results, the models will include the weighted dependent variable of equation (2) and be estimated using instrumental variables (see appendix 1). Using proc IML in SAS (SAS Institute Inc. 2004) spatial weights matrix for first ( ) and second order ( ) are constructed based on inverse distance between two observations and where inverse distance matrices: = up to cut off miles, otherwise 0. At that time, GeoDa software (Luc Anselin, 2004) was 6 Moran’s I statistic is where, is a vector of dependent values for each time period , is a spatial weights matrix, N is observations, and S is the aggregation of all elements in . In general, a Moran's I statistic positive and large near one indicates positive autocorrelation while that is negative near one indicates negative autocorrelation (ESRI 2006). 7 If residuals are heteroskedastic, residual term ( ) can be expressed as general multiplicative heteroskedasticity form: or where and are a vector of parameters and the matrix of independent variables. 20 used to measure Arc distances among observations for yield and cut off distance using the Oklahoma counties is 49.6 miles. For quality observations, cut off distances vary over every year since the number of elevators differs by year, and therefore actual distances were used. In addition, the developed models need to be evaluated for accuracy using outofsample forecasting test rather than only a fitness test using historical data. Since the models were selected by pretesting, in sample tests will overestimate their accuracy. To test the outofsample forecasting power for the developed models, the yield and quality forecasts will be evaluated for 2010 out of sample. Also the forecasts will benchmark against previous actual six year average. These tests are truly outof sample since the models were developed before the 2010 harvest. RMSE, MAE, and Theil‟s U1 coefficient8 as measures of forecasting accuracy for all developed models were used to evaluate the forecasting performance of the models. The first two forecast error statistics (RMSE and MAE) depend on the scale of the dependent variable as relative measures. The Theil coefficient is scale invariant and always lies between zero and one, that is, zero means a perfect fit (Eviews 2000). Finally, in order to measure how the weather in the period immediately before harvest impacts yield and quality, the study conducts additionally the out of sample fit test using the longer period of weather data for the additional month of weather data on the estimates. 8 = where and are the prediction value and the corresponding actual value of county i respectively (Eviews, 2000, p. 337). 21 Figure 4. The Prediction Procedure for Yield and Quality Models 22 Empirical Results The study first tested spatial autocorrelation for dependent variables. Table 2 shows a strong spatial lag effect with a Moran‟s I statistic of 0.0078 for yield and 0.0254 for protein with pvalues of 0.0001. For test weight data, however, the pvalue is 0.2642, indicating the null hypothesis no spatial lag effect could not be rejected. Therefore, the study needed to employ the yield response models in (3.1) and (4.1) spatial yield response models, and the protein response models in (5.1) spatial protein response models. Table 2. Tests of No Spatial Autocorrelation for Wheat Yield, Protein, and Test Weight Moran's Index Expected Index SD zscore pvalue Yield 0.00784 *** 0.00091 0.000512 17.09 <.0001 Protein 0.02540 *** 0.00219 0.00106 26.03 <.0001 Test Weight 0.00101 0.00219 0.00106 1.12 0.2642 Note: *** significant at 1%, Ho: no spatial autocorrelation. The study second estimated equations (3) – (5.1) using SAS proc MIXED (SAS Institute Inc. 2004) and then the residuals of the estimated models were tested for heteroskedasticity and nonnormality (appendix table3). The test results showed linear yield models‟ LR statistics are smaller than the critical value at the 5% level ( ) that is, the null hypothesis of homoskedasticity was not rejected for linear yield models; while, the CobbDouglas yield models‟ calculated LR statistics were 19.1 for the general model and 16.1 for the spatial model, and thus the null hypothesis of homoskedasticity was rejected at the 5% level. On the other hand, all quality models‟ LR statistics were greater than critical value at the 5% level ( ). The null that residuals are homoskedastic was rejected, we assume multiplicative heteroskedasticity (see Greene, 2008 p. 523). Nonnormality tests showed we can reject the null of normality for all models 23 except test weight, the only linear yield model that did not have heteroskedasticity. As appendix table 3 shows, normality of residuals is still present after correction for heteroskedasticity9. Comparing Yield Response Models and Spatial Yield Response Models Table 3 shows the estimated yield response models and spatial yield response models. Log likelihood statistics were used to select the proper model and in this case (2 log likelihood), smaller is better. LR test was also used to test for spatial lag effect in the models. The null hypothesis of no spatial lag effect ( ) was rejected. The estimated coefficients indicate how weather variables affect wheat yield. The weather variables were all significant at a critical level of 5% for all yield models. Precipitation has a positive relation with yield; while, squared precipitation and temperature are negatively related to yield. Table 3. Yield Model and Spatial Yield Model Estimates, 19942009 Yield Response Spatial Yield Response Linear CobbDouglas Linear CobbDouglas Variable Coeff. pvalue Coeff. pvalue Coeff. pvalue Coeff. pvalue Intercept 98.621 <.0001 12.732 <.0001 68.097 0.0010 10.128 0.0003 Precipitation 0.569 <.0001 0.379 <.0001 0.299 0.0020 0.176 0.0135 Precipitation2 0.008 <.0001 0.049 <.0001 0.005 0.0003 0.026 0.0019 Temperature 1.610 <.0001 2.605 <.0001 1.363 <.0001 2.557 <.0001 Spatial lag 0.742 0.0002 0.843 <.0001 2 Log Likelihood 6496.2 696.8 6481.7 713.6 Note: A firstorder and secondorder spatial weight matrices were used as instruments for the spatial lag term as WX, W2X. 9 However, proc MIXED procedure does not provide for nonnormal residuals. Hence, in order to handle nonnormality and heteroskedasticity of residuals proc GLIMMIX procedure in SAS (SAS Institute Inc. 2004) was used. If the EMPIRICAL option (FIRORES) is specified, the procedure provides MacKinnon and White (1985)’s heteroscedasticityconsistent covariance matrix estimators (HCMM) to estimate standard errors. The GMM procedures in GLIMMX only give OLS parameter estimates and those are not consistent. We use proc MIXED and correct for heteroskedasticity to increase efficiency. Our standard errors are not adjusted for nonnormality, but that is of less concern here since our objective is forecasting. 24 Finally, spatial yield response model‟s log likelihood statistic indicated the accuracy of the yield response models could be significantly improved by adding the spatially lagged dependent variable (appendix table 4). To measure readily how weather variables affect yield, the elasticity for weather variables was calculated. Table 4 shows the estimated coefficients in CobbDouglas form are elasticities. Therefore, precipitation elasticity at mean precipitation is calculated as 0.067 to 0.116 for yield response models and 0.069 to 0.144 for spatial yield response models, that is, as the precipitation is increased by 1%, the average yield level would be expected to rise by 0.067% to 0.12% and 0.069 % to 0.144% in the yield response models and the spatial response models respectively. Temperature elasticity was measured as 2.6 to 2.74 in yield models, that is,1% rise in temperature decreases the average yield level by 2.6% to 2.74%, however, for spatial yield models, temperature elasticity was estimated as 2.32 to 2.55, so we cannot decide which variables have a greater effect on yield level of wheat because the units on the variables are arbitrary. Table 4. The Elasticity of Weather Variables Yield Response Spatial Yield Response Linear CobbDouglas Linear CobbDouglas Precipitation 0.116 0.067 0.144 0.069 Temperature 2.738 2.605 2.316 2.547 Table 5. Out of Sample Forecast Error Statistics for Yield Models, 2010 Average (20052009) Yield Response Spatial Yield Response Forecast Errors wo/weather effectsa Linear CobbDouglas Linear CobbDouglas RMSE 7.436 6.715 5.535 6.321 5.464 MAE 6.136 5.425 4.272 5.020 4.225 Theil U1 0.0081 0.00676 0.00584 0.00647 0.00577 Note: see appendix table 8 for comparing actual and predicted values. a: and are county fixed effect and random year effect for yield. Forecast error statistics for all yield models are summarized in table 5. The calculated statistics showed forecasts from the CobbDouglas form of spatial yield response model were slightly more accurate than yield response models. The linear model was slightly less accurate out of sample 25 just as it was in sample. The models for yield performed better relative to the benchmark 5 year average. Protein Response Model and Weight Response Model The estimated quality response models of equations (5) and (5.1) for wheat characteristics: protein and test weight level are reported in table 6. Yield and weather variables were all significant at the 5% level. Precipitation and maximum temperature positively affect protein and test weight. Minimum temperature is negatively related with test weight. High yield reduces protein, while, yield positively influenced test weight. These relationships between weather variables and wheat quality are consistent with the findings of Johansson and Svensson (1998) and Smith and Gooding (1999), who found warm temperature affects crude protein positively and precipitation at the end of the season has significant positive correlation with protein concentration. Table 6. Protein Model and Test Weight Model Estimates, 20042009 Protein (12%, mb) Test Weight (lb/bu) NoSpatial Spatial NoSpatial Variable Coeff. pvalue Coeff. pvalue Coeff. pvalue Intercept 2.986 0.0587 2.708 0.1417 35.075 0.0058 Yield 0.103 <.0001 0.096 <.0001 0.1152 <.0001 Precipitation 0.014 0.0006 0.017 0.0009 0.0533 0.0003 Max. temp. 0.149 <.0001 0.130 <.0001 0.4651 0.0001 Min. temp. 0.2922 0.0108 Spatial lag 0.138 0.3843 2 Log Likelihood 1045.5 1019.1 1482.9 Note: A first and secondorder spatial weight matrices were used as instruments for the spatial lag term as WX, W2X. Temperature positively influences test weight and rainfall also is positively associated with test weight. Even though the spatial lag term was not significant using a Wald test, the more reliable likelihood ratio test does reject the null hypothesis of no spatial lag. The estimated results express the tradeoffs between quality of wheat and yield using the calculated elasticity (appendix figure13). The elasticity is similar to Dahl and Wilson (1997)‟s trade26 off coefficients, which take the derivative with respect to protein and then multiply by average yields10. It indicates how much protein levels affect yield, while, this study focuses on how yield affects quality levels. In other words, yield elasticity indicates that increases in yield lead to lower protein levels and higher test weight. Table 7 shows a 1% rise in yield decreases average protein by 0.25% and increases average test weight by 0.28%. Precipitation affects protein and test weight, however, maximum and minimum temperatures have a stronger influence on quality levels. Meanwhile, the spatial protein model is more sensitive to weather conditions than the no spatial protein model. Additionally, the study treated crop year as a random effect and the counties as fixed effects and the estimated results showed specific region or crop year of wheat also affects the quality level (appendix table 5). Table 7. The Elasticity of Weather Variables for Quality Model Protein response Test Weight Response NoSpatial Spatial NoSpatial Yield 0.247 0.266 0.275 Precipitation 0.039 0.052 0.144 Max. Temperature 0.924 0.940 2.747 Min. Temperature 1.434 Forecasting accuracy of the quality models was evaluated over the 2010 crop year. Table 8 shows the forecast error statistics with protein and test weight response models. Firstly, the study estimated the general quality models using predicted yield from yield response models. Secondly, the spatial quality models were estimated by using predicted yields. The forecast error values indicate that the accuracy of the quality models can be improved by adding predicted yield from the spatial protein response model rather than that of the no spatial protein response model. Also RMSE values showed that the forecasting performance of the models combining spatially predicted yield were improved. Additionally, average values (20042009) were used as benchmark forecasts and as expected, all forecast error values for average values were higher than those of the weather models. The models 10 The relationship between protein and yield was estimated using , and tradeoff coefficients = (Dahl and Wilson, 1997). 27 for protein performed better relative to the benchmark six year average than did the test weight models. In addition, the accuracy of the quality models was compared using the actual and predicted values. The forecasting values spatially predicted were closer to actual values, the results consists with that of table 8 (See appendix table 9) . Table 8. Out of Sample Forecast Error Statistics of Wheat Quality, 2010 Average (20042009) 2010 NoSpatial Spatial wo/weather effects W/ spatially predicted yield W/ generally predicted yield W/ spatially predicted yield W/ generally predicted yield Protein RMSE 1.080 0.727 0.731 0.702 0.717 MAE 0.870 0.588 0.594 0.582 0.583 Theil U1 0.0074 0.00530 0.00530 0.005135 0.005197 Test Weight RMSE 1.495 1.305 1.361 MAE 1.196 1.117 1.174 Theil U1 0.00041 0.000357 0.000372 Note: see appendix table 8 for comparing actual and predicted values. Implications of the Value of Additional Month of Weather Data on Estimates Including late growing season weather data in a forecast model is less desirable from a decision maker stand poing because the forecast are not available with enough lead time to make logistical and marketing decisions prior to harvest. Expanding the data series to include late season weather information does provide insights into how the weather conditions immediately prior to harvest impact yield and quality. In the case of yield model, the study calculated additionally out of sample fit test using the longer period of weather data for the additional month of weather data on the estimates. The extended weather data (FebMay) were used to estimate new estimates and predicted yields using the new estimates (see appendix table 10). Contrary to expectations, the forecast errors reported in table 9 were larger than those of the original yield models (FebApril) (compare with table 5). A likely explanation is that late season weather conditions such as rainfall and temperature have 28 different effects relative to earlier in the growing season. For example, higher temperatures early in the growing season may promote growth while excessive temperatures late in the growing season may interfere with grain development. The development of forecasting models incorporating early season and late season weather information as separate variables is an opportunity for further research. Table 9. Out of Sample Fit Test using the Longer Period (FebMay) for Yield Models Average (20052009) Yield Response Spatial Yield Response Forecast Errors wo/weather effects Linear CobbDouglas Linear CobbDouglas RMSE 7.436 7.776 6.831 6.762 6.557 MAE 6.136 6.205 5.400 5.357 5.124 Theil U1 0.0081 0.00759 0.00686 0.00679 0.00665 Note: see table 5 for comparison. The impact of late season weather on wheat quality was also examined by the out of sample fit test using the shorter period of weather data (MarchApril) with a longer period (MarchMay). It should be noted that the (MarchMay) weather data was used in the original quality estimates, so it this case the original estimates are being compared with estimated generated with a shorter period of weather data Forecast error statistics for new quality model (MarchApril) are summarized in table 10. The calculated statistics shows there is no significant difference between the original quality model and the new quality model; however new forecasts were slightly less accurate than original quality response models. Therefore, these results point out the weather in the period immediately before harvest have slight impacts on quality levels. Table 10. Out of Sample Fit Test using Shorter Period (Mar.April) for Quality Models Average (20042009) (MarchMay) (MarchApril) wo/weather effects Original Shorter Protein RMSE 1.080 0.727 0.736 MAE 0.870 0.588 0.616 Test Weight RMSE 1.495 1.305 1.411 MAE 1.196 1.117 1.184 Note: Original indicates nospatial quality model and obtained from table 8, and shorter represents nospatial quality model using shorter weather data (FebApril), respectively. 29 Summary and Conclusions The study estimated wheat regression models to account for the effect of weather on wheat yield, protein, and test weight and to forecast wheat yield and the two wheat quality measures. The explanatory variables included precipitation and temperature for growing periods that correspond to biological wheat development stages. The models included county fixed effects, crop year random effects, and a spatial lag effect. Yield and quality level are strongly influenced by weather variables. For yield, precipitation has a positive relation with yield, while, precipitation squared and temperature are negatively related to yield. Precipitation and maximum temperature positively affect protein and test weight. Minimum temperature is negatively related with test weight. Yield affects negatively protein level, while, yield positively influenced test weight. In the forecast evaluation, the forecasting ability of both yield and protein models was enhanced by adding the spatial lag effect. Out of sample forecasting tests showed the developed models are more accurate than using a benchmark sixyear average. The study results or prediction information could be widely used and could be particularly important to producers optimizing late season agronomic and marketing decisions and to grain elevators and agribusiness for contracts or purchasing decisions. For examples, if the value of protein information to eliminate the reference to late application of fertilizer could be predicted early and accurately, the value are very useful. A good alternative rationale for value is that an agribusiness or producer might contract wheat and/or prepare shipping contingent on meeting minimum protein levels. The model prediction could help them anticipate not being able to meet the required protein levels and cancel the contracts and transportation and/or identify alternative markets. Limitations of the study could be summarized as follows. The study used just two weather variables information as rainfall and temperature for prediction because it is easier to interpret and 30 describe the impact of weather on yield and quality in a simple model. More complex models including interaction between weather variables might have the potential to increase forecast accuracy. The models examined also did not include measures for extreme weather events (example a late season freeze) that, while occurring infrequently, are known to have major impacts on quality and yield. There is also an obvious opportunity to expand this research by including a longer time series of wheat quality data as that data becomes available. A longer data series might make it possible to predict other important quality variables such as flour falling number or milling yield. An expanded time series might also make it possible to forecast additional quality variables and improve the forecast accuracy of the existing yield and quality models. A longer data series would also make it possible to conduct additional out of sample tests and to investigate the impact of trend and technology factors. 31 Appendix 1. The Estimation Procedures of Spatial Lag Model Anselin and Bera (1998) point out that with spatial data, the dependent variable may be influenced by spatially lagged dependent variables ( in the other locations. The spatially lagged term is also not only correlated with the same location‟s error term, but also the other locations‟ error terms. The consequence is violation of the assumption that error terms are assumed to be independent and identically distributed, therefore the OLS estimates of a spatial lag model will be biased and inconsistent (Land and Deane, 1992). Instead of OLS estimation, alternative estimation methods are needed to estimate consistent estimators. Equation (2) can be represented as a reduced form; a function of explanatory variables and error terms at all locations by using an inverse matrix11 under general assumptions, is independent of , and , therefore (A1) is rewritten in conditional mean form as and, specifically (A2) can be written as = = … and then (A1)  (A3) was used to empirically estimate (2), Anselin (1988), Land and Deane (1992), and Kelejian and Robinson (1993) suggested instrumental variables approach to estimation and the study selected Kelejian and Robinson (1993)‟s instrumental variables and twostage least squares estimation (2SLS) approach. Hence, equation (2) can be rewritten as 11 Inverse matrix can be expanded as = (1 + ) 32 where and , , and is a twostage least squares estimator and those can be expressed using (A2) and (A3) as and specifically (A5) can be rewritten as = = … where , are instrumental variables, and thus the 2SLS estimator ( is expressed as = where , indicating = and as a matrix of instruments, and then a matrix of fitted values can be rewritten as and also can be expressed as = . In addition, the variancecovariance matrix is where is residual variance and can be estimated from , thus, we can obtain consistent estimates and standard errors of spatial lag model. In summary, since OLS estimation of a spatial lag model leads to biased and inconsistent estimators, as the alternative method, 2SLS estimation was adopted here and empirically the procedures are as follows. In the first stage, regress equation (A5)‟s the right hand side spatially lagged dependent variable on all instrumental variables , which are a firstorder and secondorder spatial weight matrices were used as instruments for the spatial lag terms and draw out the estimated of 33 equation (A6), in other words, is obtained from that regress on and then in the second stage, replace in equation (2) with the estimated in the first stage, then rewrite (2) as and finally, regress (A9) on and and then obtain the 2SLS estimator ( of (A7) and (A8). The estimators is consistent and uncorrelated with error term ( and independent variables ( ). 34 Appendix 2. The Calculation Procedures of Elasticity of Weather Variables As is well known, the elasticity of dependent variable ( ) with respect to independent variables ( ) is equal to the slope value of the first derivative of dependent variable with respect to the independent variable (d /d ) multiplied by the means of ( ) and the elasticity of equation(1) can be written as and using equation (A1), the elasticity of equation (2) spatial lag model can be defined as and is similar to including long run coefficient in long run elasticity, on the other hand, in the CobbDouglas (CD) case12, (B1) and (B2) can be demonstrated by total differentiation: and in the spatial model, 12 For general CD form, , and for spatial CD form, 35 36 Appendix Table 1. Rsquared Estimated and Correlation Coefficients for Selecting Quality Variables Variables R Square a Observations Correlation coeffie. (Actual V.S. Prediction) Protein 0.622 415 0.789 Test weight 0.489 415 0.700 defect 0.228 412 0.480 Falling 0.318 334 0.566 Notes: a were obtained from equation (5) basis Appendix Table 2. Correlation Coefficients among Yield, Protein, Weight and Weather Variables Yield pvalue Protein pvalue Weight pvalue Yield 1.00 <.0001 0.47 <.0001 0.15 0.0019 Precipitation (in) February 0.49 <.0001 0.52 <.0001 0.06 0.1912 March 0.04 0.4098 0.20 <.0001 0.15 0.0014 April 0.05 0.3255 0.16 0.0005 0.08 0.1028 May 0.22 <.0001 0.09 0.0613 0.10 0.0406 Avg. temperature (˚F) February 0.43 <.0001 0.06 0.1734 0.05 0.2891 March 0.31 <.0001 0.02 0.6924 0.12 0.0094 April 0.42 <.0001 0.34 <.0001 0.20 <.0001 May 0.02 0.6899 0.00 0.9968 0.06 0.1994 Max. temperature (˚F) February 0.50 <.0001 0.29 <.0001 0.08 0.0815 March 0.35 <.0001 0.10 0.0396 0.07 0.1247 April 0.38 <.0001 0.45 <.0001 0.27 <.0001 May 0.19 <.0001 0.08 0.0742 0.13 0.0071 Min. temperature (˚F) February 0.14 0.0029 0.22 <.0001 0.13 0.0045 March 0.25 <.0001 0.11 0.0174 0.18 0.0001 April 0.35 <.0001 0.11 0.0171 0.10 0.0417 May 0.20 <.0001 0.16 0.0004 0.07 0.1368 Growing degree days February 0.55 <.0001 0.07 0.1295 0.12 0.0136 March 0.32 <.0001 0.01 0.8454 0.13 0.0069 April 0.39 <.0001 0.32 <.0001 0.22 <.0001 May 0.02 0.7532 0.06 0.1994 0.06 0.2246 Solar radiation (MJ m2d1) February 0.50 <.0001 0.35 <.0001 0.14 0.0027 March 0.51 <.0001 0.12 0.0129 0.13 0.0056 April 0.16 0.0013 0.22 <.0001 0.30 <.0001 May 0.40 <.0001 0.06 0.177 0.28 <.0001 37 Appendix Table 3. Diagnostic Test Statistics: Yield, Protein, and Test Weight Response Models Normality Normality Heteroskedasticity Method ShapiroWilk (1) ShapiroWilk (2) Likelihood ratio W pvalue W pvalue X2 Yield response modela Linear 0.9958 0.0047** 0.5** Cobb 0.9903 0.0001** 0.9884 0.0001** 19.1** Spatial yield response modela Linear 0.9965 0.0157* 0.1** Cobb 0.9895 0.0001** 0.9883 0.0001** 16.1** Quality response modelb Protein 0.9919 0.0231* 0.9890 0.0033** 27.7** Weight 0.9933 0.0614 0.9912 0.0150* 22.2** Spatial quality modelb Protein 0.9989 0.0030** 0.9856 0.0004** 26.6** Notes: *(*) significant at 1% ( 5%), critical value( =7.82) at the 5% level, critical value( =9.47) at the 5% level, and (1) and (2) indicate normality tests of standardized residuals before and after correction for heteroskedasticity, respectively. Appendix Table 4. Yield Model and Spatial Yield Model Estimates, 19942009 Yield Response Model Spatial Yield Response Model Linear CobbDouglas Linear CobbDouglas Variable F Value F Value F Value F Value Precipitation 79.26 43.94 14.48 20.97 Precipitation2 67.36 22.52 9.83 5.46 Average temperature 29.98 23.72 14.27 5.23 County fixed effect 3.8 3.41 3.71 3.25 Spatial lag 20.67 23.19 2 Log Likelihood 6496.2 696.8 6481.7 713.6 Notes: Values of precipitation variable was scaled by multiplying one hundred due to unit of rainfall. Appendix Table 5. Protein Model and Test Weight Model Estimates, 20042009 Protein Model Test Weight Model NoSpatial Spatial NoSpatial Variable F Value Pr > F F Value Pr > F F Value Pr > F Yield (bu/acre) 281.44 <.0001 110.94 <.0001 40.06 <.0001 Precipitation (in) 11.87 0.0006 11.25 0.0009 13.62 0.0003 Max. temperature (˚F) 101.61 <.0001 34.5 <.0001 15.28 0.0001 Min. temperature (˚F) 6.56 0.0108 County fixed effect 8.9 <.0001 7.25 <.0001 2.76 <.0001 Spatial lag 0.76 0.3843 2 Log Likelihood 1045.5 1019.1 1482.9 38 Appendix Table 6. Descriptive Statistics for Yield Model Variables, 19942009 Variable N Mean SD Minimum Maximum Year 1232 2002 4.61 1994 2009 Yield 1097 30.06 7.87 6.50 53.10 Precipitation(Feb.April) 1218 27.02 12.09 0.47 83.47 Avg. temp.(Feb.April) 1225 51.13 2.58 42.48 57.14 Precipitation2 1218 876.31 769.19 0.22 6966.68 Log yield 1097 3.36 0.29 1.87 3.97 Log precipitation 1218 3.16 0.59 0.76 4.42 Log Avg. temp. (Feb.April) 1225 3.93 0.05 3.75 4.05 Log precipitation2 1218 10.36 3.21 0.02 19.58 Appendix Table 7. Descriptive Statistics for Quality Model Variables, 20042009 Variable N Mean SD Minimum Maximum Year 457 2006.6 1.67 2004 2009 Longitude 457 98.72 1.32 102.50 94.80 Latitude 457 36.10 0.74 34.17 36.90 Protein 457 12.18 1.40 8.90 16.00 Test weight 453 59.79 1.96 52.80 64.60 Yield 421 29.45 7.80 6.50 46.00 Precipitation 454 27.40 13.54 3.40 65.97 Max. temp. (MarMay) 456 71.80 2.60 65.98 80.47 Min. temp. (MarMay) 456 46.27 3.36 35.68 55.43 Max. temp. (AprilMay) 456 75.81 3.52 69.05 85.88 Min. temp. (AprilMay) 456 50.41 3.10 39.78 59.53 Appendix Table 8. Comparing Actual and Prediction Values for Yield Models Actual Average Yield Response Spatial Yield Response Avg. (2010) (20052009) Linear CobbDouglas Linear CobbDouglas Yield(bu./acre) 31.6 27.3 33.9 32.3 33.3 32.3 Notes: 2010 actual value is weighted average based on production quantity basis. 39 Appendix Table 9. Comparing Actual and Prediction Values for Quality Models Protein (12% mb) Test weight (lb/bu) County No. 2010 Actual Value Average (20042009) Predict Value Spatial Predict Value 2010 Actual Value Average (20042009) Predict Value 2 11.9 12.6 11.7 11.5 60.1 60.0 59.2 4 12.6 14.1 13.3 13.5 61.5 59.5 59.1 6 12.2 11.7 11.3 11.3 62.7 60.2 60.5 8 11.3 13.1 11.5 11.2 61.8 58.9 60.1 9 11.1 12.2 10.3 10.3 61.2 60.5 62.5 13 12.4 13.5 12.8 12.5 61.8 60.0 58.9 17 12.1 12.0 11.4 11.3 60.0 60.1 60.6 20 11.4 12.1 11.6 11.0 62.7 60.2 61.5 22 11.5 10.4 10.0 10.0 60.0 58.2 60.3 23 12.2 12.2 12.1 11.9 60.4 58.5 58.7 24 12.3 11.9 11.2 11.3 59.2 59.5 59.3 27 12.2 11.8 11.7 11.6 59.6 59.1 58.5 28 11.8 13.7 12.1 12.0 62.2 61.0 61.2 29 11.2 12.1 12.4 12.5 63.3 60.8 62.1 30 11.9 13.1 12.2 12.0 60.2 59.7 58.7 33 11.6 12.6 12.3 12.1 61.7 61.6 60.9 38 11.5 11.9 11.4 11.2 62.2 60.0 60.6 42 11.5 12.0 11.6 11.6 60.2 59.4 59.4 44 12.0 12.1 11.4 11.4 60.0 59.4 59.7 52 12.3 12.2 11.6 11.6 57.2 58.6 57.9 70 11.7 13.2 12.6 12.3 61.0 59.9 60.2 71 11.6 12.6 11.6 11.5 60.9 61.2 61.2 75 10.0 12.7 11.4 10.9 62.2 60.4 61.3 76 12.5 11.8 11.5 11.5 60.6 60.4 59.6 77 11.8 12.1 11.7 11.4 59.3 59.0 58.9 Avg. 11.8 12.4 11.7 11.6 60.9 59.8 60.0 RMSE 1.080 0.727 0.702 1.495 1.305 MAE 0.870 0.588 0.582 1.196 1.117 40 Appendix Table 10. Yield Model and Spatial Yield Model Estimates using the Longer Period (FebMay), 19942009 Yield Response Spatial Yield Response Linear CobbDouglas Linear CobbDouglas Variable Coeff. pvalue Coeff. pvalue Coeff. pvalue Coeff. pvalue Intercept 129.340 <.0001 19.324 <.0001 65.138 0.0007 15.807 <.0001 Precipitation 0.540 <.0001 0.884 <.0001 0.140 0.0939 0.967 <.0001 Precipitation2 0.008 <.0001 0.131 <.0001 0.002 0.1412 0.149 <.0001 Temperature 2.049 <.0001 4.403 <.0001 1.535 <.0001 4.071 <.0001 Spatial lag 1.569 <.0001 0.632 0.0018 2 Log Likelihood 6445.4 683.6 6268.8 706.9 Note: A firstorder and secondorder spatial weight matrices were used as instruments for the spatial lag term as WX, W2X. Appendix Fig 1. Plot Yield and Precipitation Appendix Fig 2. Plot Yield and Avg. Temp. Appendix Fig 3. Plot Protein and Precipitation Appendix Fig 4. Plot Protein and Max. Temp. 41 Appendix Fig 5. Plot Protein and Yield Appendix Fig 6. Plot Test Weight and Precip. Appendix Fig 7. Plot Test Weight & Max.Temp. Appendix Fig 8. Plot Test Weight & Min.Temp. Appendix Fig 9. Plot Test Weight & Yield Appendix Fig 10. Plot Protein & Solar Radiation 42 Appendix Fig 11. Plot TestWeight & Solar Radi. Appendix Fig 12. Plot Yield & Solar Radi. Appendix fig. 13. Calculated Relationship between Yield and Protein and Test Weight Using Elasticity 43 CHAPTER II Improved Methods of Estimating Construction Costs of Agricultural Facilities Introduction A wide range of parties are interested in the costs of constructing agricultural facilities. Accurate prediction of costs of construction is very important to make decision for optimizing construction projects. Construction cost estimates are used in feasibility studies for agricultural projects, economic engineering analyses and decision tools assisting agricultural producers. Examples include estimating grain storage costs (Edwards, 2007; Uppal, 1997), grain storage rental (Hofstrand & Edwards, 2009), rental of other farm assets (Pershing & Atkinson, 1989). Agribusiness insurance companies, including farmerowned insurance cooperatives must estimate construction costs to price replacement cost insurance products. Agriculture specific construction cost information, particularly information formatted as easily updated indexes, would benefit agricultural economists and other researchers who are attempting to update and/or interpret previous studies involving building and infrastructure investments. The information would also allow agribusiness insurers to set actuarially efficient rates that would equitably reflect replacement costs. Several approaches have been used to estimate construction costs. Estimates or bids can be obtained from a representative set of vendors or firms that have recently completed projects. While this approach illustrates the variation in costs it is difficult to identify the sources of variation between projects. Moreover, unless the surveys are conducted on a regular basis, information from bids or 44 completed projects are difficult to update. Cost estimating software also can be used to estimate project cost, however, most of them support general construction and large projects or commercial systems available and therefore they are not suitable for agricultural industry or facilities. The bid/actual cost approach can be expanded by compiling and reporting cost of completed projects. The price indices of completed facilities reflect the price changes of construction output including all pertinent factors in the construction process. The building construction output indices compiled by Turner Construction Company and HandyWhitman Utilities are compiled in the U.S. Statistical Abstracts published each year. However this data does not provide prices of agricultural facilities. Even if a baseline price for an agricultural facility is known, price indices from completed construction projects may not accurately forecast the change in prices for an agricultural facility. An obvious example would be a steel grain bin where steel accounts for a much larger percentage of total material relative to most commercial buildings. If the bids or actual construction costs for a specific agricultural structure are obtained for one period in time, there are a number of approaches to updating historical construction cost information. These include the use of simple indexes and disaggregated indexes. The bestknown simple indexes of general price changes are the Gross Domestic Product (GDP) deflators compiled periodically by the U.S. Department of Commerce, and the consumer price index (CPI) compiled periodically by the U.S. Department of Labor. These broad gauges reflect overall changes in price levels may not accurately predict construction costs. Special price indices related to construction are also collected by industry sources since some input factors for construction and the outputs from construction may disproportionately outpace or fall behind general price indices. Examples of special price indices for construction input factors are the wholesale Building Material Price and Building Trades Union Wages, both compiled by the U.S. Department of Labor. In addition, the construction cost index and the building cost index are reported periodically in the Engineering NewsRecord (ENR) Index. The ENR index does not consider a productivity factor and so tends to increase at a more rapid rate than 45 the other indices (Uppal, 1997). Other specialized indexes, such as the Marshall Smith index (MSI), which is published monthly in Process Engineering, have been developed. The MSI is an indicator of the price changes for installed industrial chemical equipment over time (Hendrickson, 1998). The accuracy of index of construction cost can be increased by using a less aggregated index. These indexes are constructed based on aggregating particular material price and labor cost indexes using projectspecific weighting factors, which are typically collected through an industry survey (Earl, 1977). The composition of materials, components, equipment, and labor factors varies widely across the indexes. A number of periodicals and reference manuals publish unit prices on construction items. The most common indexes are for major building materials (concrete, structural steel, drywall, etc) and labor categories. As the degree of disaggregation increases (reporting costs at the subcomponent level) the index is better able to capture differential inflationary impacts on process plant construction costs from various materials and types of machinery and equipment (Earl, 1977). However, the disaggregated index approach requires information on the weighting factors or list of submaterial and equipment for the specific type of construction project. These are typically generated through a process known as economic engineering. Economic engineering involves mathematical or computerbased representations of production processes in which engineering and economic information are combined (Ferrell, Kenkel, & Holcomb, 2010). Economic engineering uses engineering data to estimate facility, equipment, labor and utility requirements. The economic component of the model determines the fixed and variable costs associated with constructing and operating the facility (Criner & Jacobs, 1992). Flores et al. (1993) used an economic engineering approach to estimate costs associated with building and operating flour mills of different sizes while Dale and Tyner (2006) employed a detailed economic engineering approach to determine the cost of a dry mill ethanol plant. For warehouse building, many studies have focused on cost optimization of warehouse design and operation. Francis & White (1974) developed computer algorithms to minimize total cost and found optimum dimensions of a rectangular warehouse. Park & Webster (1989) employed 46 conversion factor to compute warehouse building costs with factor based on the base area of the building, height, and required number of pieces of material, equipment. Cormier & Kersey (1995) provided several conceptual warehouse layouts and demonstrated the economic feasibility of a proposed project. The construction costs of a grain bin can be used to illustrate how economic engineering would be applied to agribusiness construction projects. There is a need for research specific to grain bins. Unlike other agricultural storage facilities, grain bins construction need to determine bin configuration which might allow them the necessary storage capacity while staying within their horse power and electrical power limitations. Geometric formulas would be used to calculate the area of the sides, foundation and roof of a grain bin of a given capacity. Engineering formulas would then be used to determine the weight and force exerted by the grain on the floor and sidewall which would in turn identify the depth of the concrete foundation and the gauge of metal required on sidewall panels. Once the type and amount of materials needed have been determined, the cost can be estimated for each component. In some cases, a proxy for a subcomponent is used. For example, after the linear feet of grain spouting has been determined the cost might be estimated on a per foot basis or by the pounds of steel represented rather than on a price listing for a specific piece of spouting. Modeling the construction cost of agribusiness structures using an economic engineering approach coupled with disaggregated construction cost indices has several advantages over using bids or the actual cost of recently completed projects. The configuration of the structure and associated structure is explicitly defined and the cost differences for various scales, configurations or complements of equipment can be explored. Because the economic engineering model provides a list of materials and equipment or proxies thereof, the costs can be updated by obtaining current costs for the materials and subcomponents. Alternatively, the output from the economic engineering estimates can be grouped into categories and changes in cost for the project can be estimated by examining the inflation index for each particular category. The object of this study is to create and evaluate a model for estimating construction costs of agricultural storage facilities. 47 Conceptual Framework Various construction cost estimation approaches suggested to date (appendix 1). Collier (1984), Hendrickson(1998), Hollman (1997), Peters and Timmerhaus (1991), and numerous studies suggested a unit cost method which is one of the most common economic engineering approaches when the project can be disaggregated into specific elements level lists for cost estimation. According to the definition, in the unit cost method the construction process is separating into a number of steps. The quantity of material and labor is then estimated for each step and the unit for measuring the amount of material or labor is defined. For example the unit for site grading might be acre while the unit for wallboard might be square feet. The cost for each unit is then estimated. A unit cost method can employ previous cost experience and be assigned to each of the construction components as represented by the construction bill of quantities. Thus, the total cost is the summation of the required quantities (material, labor, and equipment) multiplied by the corresponding unit costs. Therefore this method requires detailed estimates of purchase price obtained either from quotations or published data. The unit cost method can also be applied to engineering employee hours and materials quantities, equipment cost based on the drawings and specification. Unit cost can be based on recent project job specifications, where the material required can be determined and therefore the material unit cost matches the specifications. Hence, this method can be coupled with disaggregated construction cost from general cost information and recently completed projects. The costs can be updated by obtaining current cost information for the material unit cost and labor unit cost. Construction cost estimation is a very difficult task with substantial yeartoyear variation in unit cost estimates and bid estimates due to regions and supplydemand factors. Previous studies have used various type equations to apply unit costs to material, labor, and equipment needs. The 48 equations provide the characteristics of construction project and also readily keep track of each element in the project. Generally a cost equation is composed of material quantities, labor and equipment needs terms that correspond to unit cost in project and plus O&P (Overhead and Profit)13. Hendrickson(1998) suggest general total cost equation can be expressed as: where is the total cost, n is the number of units, is the quantity of the element and is the corresponding unit cost. Since the equation is simple, the construction site, skilled labor, management of the procedure, contractor‟s fee, and contingency for the estimated unit cost ( ) require appropriate adjustment. Alternatively Peters and Timmerhaus (1991) suggest approximate correction for adjustment by using a construction correction factor. The correction factor is estimated from previously completed projects and the correction factor help that the estimated model costs are closer to real costs. Hence the equation can be expressed by employing the correction factor to equation (1): where is the construction correction factor. Other studies have developed multiple regression models to predict cost estimates for long term or short term construction. Hwang (2009) employed linear regression models to predict construction project cost using a construction cost index series. Walker et al. (1990) developed a mathematical cost model to predict the major components of cost and sub components of cost for a grain bin system. Regression analysis was also used to determine these components cost and the relationship between cost values and total volume of storage (diameter and height). The method 13 O&P for the installing contractor may range from 5% to 15% of the bare total cost excluding O&P (RS Means Co., 2005) 49 provides the statistical inference and model‟s performance ability. For instance, significance of variables using Wald test and indicate the accuracy of the predicted costs. Therefore, predicted costs are useful to determine the range category cost or gross unit costs or special material cost which are not readily available. A disadvantage of this method is that it is difficult to determine the sources of variation between periods since the estimates are calculated for a given across year and location. Moreover, information from bids or completed projects are difficult to update. The regression model approach is based on neoclassical production theory14 suggested by Hall (1998). At a general level, if there exists a relation between inputs and output, the function that can be represented as where is single valued, that is, for any unique combination of inputs x, these corresponds a unique level of output (Chambers, 1988). Thus production function for construction employs the linear and quadratic input variables owing to the correspondence of maintained hypothesis with held the above production theory assumption (see footnote 14). The functional form (3) can be expressed in the matrix form as where is the vector of independent variables, is which is a stochastic error term. In other words, the volume of output of a production function for construction is coupled with the various inputs of materials, labor, equipments level etc. Therefore, in order to minimize the 14 Y= f(x), where x is input variables; a) x >=0 and finite( nonnegative); b) f(x) is finite, nonnegative, single valued for all possible combination of x variables; c) f(x) is everywhere continuous and everywhere twice continuously differentiable; d) f(x) is subject to the “law of diminishing returns” ( Hall, 1998). 50 production cost for a specified level of output, proper a set of values for input factors such as diameter, height, width, length etc could be employed. Using the main two methods presented in this study, first, a unit cost method approach can be used to estimate construction costs. Second, regression equation approach will be employed to evaluate or measure the proposed economic engineering model‟s performance. Empirical model specification and procedure The construction costs of representative storage facilities are subdivided into major material and labor cost categories through review of detailed bid sheets and specific drawings. These subcategories are linked to specific data sets of published indexes of building materials, labor, and equipment rates. This required sorting across major or sub categories and detailed task elements for projects. As discussed, economic engineering approach is a mathematical representation of construction processes in which engineering and economic information are combined. Thus, this study used two group components (economic components and engineering components) basis to model and estimate costs associated with storage facilities of different sizes. The engineering component of the model used estimation of equipment, labor and materials requirements. The economic component of the model determined unit or fixed costs associated with constructing as follows. Economic Components: Grain Bin Cost of 77 separate components linked to reported prices in “RSMeans Building Construction Cost Data” Cost of aeration fan/motors for range of HP obtained from industry quotes Cost of elevator leg for range of height and bu/hr obtained from industry quotes 51 Cost of aeration duct and unloading system for range of sizes obtained from industry quotes on a per foot basis Engineering Components: Grain Bin Steel components and concrete determined by dimension and engineering requirements Capacity in cylinder based on diameter, height and pack factor which is function of grain and depth Height of cone based on angle of repose= f(grain type) Volume in cone = f(height of cone, diameter) Sidewall, floor and roof area = f(dimensions) Force on sidewall and foundation = f(grain weight and grain type) Gage/thickness of sidewall and floor= f(force) Aeration fan static pressure = f(grain, height, grain type and desired CFM/bu) Aeration fan HP = f(static pressure and total CFM delivered) Dimension of aeration ducts and unload trough based on bin dimension Cost multiplier = f(size factor= f(project capacity)) Economic Components: Warehouse Building Cost of 44 separate components linked to reported prices in “RSMeans Building Construction Cost Data” Cost of equipment, plumbing, heating, ventilating, air condition, and electrical installation as analyzed as percentage shares of total cost obtained from RSmeans database of completed projects. Engineering Components: Warehouse Building 52 Steel frame and siding and concrete determined by dimension and engineering requirements Capacity in warehouse based on width, length, and wall height Angle of repose for roof= f(engineering requirements) Floor, sidewall and roof area = f(dimensions) Force on stud, sidewall, frame, rafter, beam and foundation =f(dimension, wall height, and storage goods type in warehouse) Gage/thickness of stud, rafter, beam, frame, sidewall and floor=f(force) Electrical and Mechanical devices =f(dimension, storage goods type) Story height multiplier= f (wall height) Cost multiplier = f(size factor= f(project square foot)) As a specific economic engineering approach, a unit cost method was employed to predict project costs, the material, labor, equipment, and Q&P required were applied and therefore the these unit costs matches the drawings or specifications. Using (1) and (2) the cost equations can be modified as where is the total cost, n is the number of specific elements, is the material unit cost at specific element, is the material quantity of ith specific element, is the labor unit cost at specific element, is the labor required level for specific material, is the equipment unit cost for specific element, 53 is the equipment usage quantity of specific element, is the overhead and profit unit cost for specific element, is the specific element required level coupled with O&P, is cost multiplier based on size of facilities; one of correction factors15, and is story height multiplier based on height of warehouse; one of correction factors.16 The grain bin and warehouse building construction costs obtained from equation (5) can also be categorized as total cost (bare cost, including Q&P cost), major components cost, and cost per unit (bushel (bu), Square Foot (S.F.)) using presented unit cost method. For example, the grain bin system can be categorized as six main components as floor, wall, roof, fan& heating , auger& driver, and others (accessory) based on diameter, height, height of cone, and pack factor which is function of grain and depth. Warehouse building cost is composed of floor, wall, roof, electrical & mechanical, and office based on width, length, and wall height. Based on the above two group components basis and equation (5), the study developed “Economic Engineering Construction Cost Templates Model” spread sheet type model. The spread sheet is a two dimensional series of columns and rows with cells (see appendix figure 2, 3, and 4). The user can input the data, formulas, text, and functions which the most useful functions are VLOOKUP and MATCH function which is useful for semi automating unit cost spread sheet application. Especially, when a project is looking for an exact engineering component match based on unit cost value. The user just inputs detailed items as follows. In the case of the grain bin, the type of grain, diameter of bin Eave, height of bin aeration (none, 1/10 CFM/Bu, .25 CFM/Bu), angle 15 Cost multiplier: the larger grain bin & warehouse building will have the lower unit cost per bushel or square feet. This is mainly due to the decreasing contribution of the exterior walls plus the economy of scale usually achievable in larger buildings (R.S. Means, 2009) 16 Story height multiplier: wall height of warehouse building affect base cost for variation in average story height (14ft). Therefore, multipliers (0.882.84) multiply base cost by range of wall height (8ft80ft) respectively (State of Michigan Appraisers Manual, 2004) 54 of repose (23˚ 29˚), fan select (centrifugal, axial), heating system(yes, no), unloading system (yes, no), elevator leg (no, yes: height and Bu/min), sidewall stiffeners (yes, no), and current index (2009=100) are entered ( see also appendix figure 2). In the case of the warehouse building, the width (ft), length (ft), wall height (ft), overheaddoor (ea), HVAC electrical & mechanical (yes, no), office size (S.F.), current index (2009=100) are entered (see also appendix figure 3). In the case of the pole barn building, the width (ft), length (ft), wall height (ft), siding (yes, no), post spacing (O.C.), concrete floor (yes, no), and current index (2009=100) are entered (see also appendix figure 4). The Structure of Economic Engineering Construction Cost Templates Model As discussed previously, a unit cost method is the most common cost estimating economic engineering approach. Therefore, the construction costs were estimated by multiplying the disaggregated specific elements level lists by the corresponding unit prices. The next sections provide more detail on construction cost structure, assumption and methods used in the model. 1) Collection of a list of the components and cost data For grain bin, Floor, Wall, Roof, Fan & Heating, Auger & Driver, and Others (accessory) were categorized as major components based on diameter, height, height of cone, and pack factor. The warehouse building cost was divided into floor, wall, roof, HVAC (electrical & mechanical), and office components based on width, length, and wall height. The pole barn building was only divided into footing, wall, and roof. Table 1, 2, and 3 provide a list of used materials uses and unit, respectively. There are various items and sizes of components used in constructing bins and warehouse buildings. Most of them are available as disaggregated unit level. Some such as Auger & Drive and Fan & Heater components at grain bin facilities, and HVAC (Heating, Ventilating, and Air Conditioning) in warehouse building, and footing work in pole barn building are available as aggregated units. 55 Components Items Unit Unit Size Unit requirement by Size factors Source Floor FormsAnchor bolts ea Anchor bolts, Jtype, 1/2" diameter x 12" long 2 / bottom sheet R.S. Means formrod set Bolt, hex head, plain steel, 1/4" dia x 2" L, 2 / bottom sheet R.S. Means Forms in place L.F. Multiple use, to 6" high Perimeter of bin R.S. Means Reinforcing steel Ea Deformed, 2' long, #3 Floor area R.S. Means Concrete C.Y Slab on grade, 6" thick Diam. of bin R.S. Means Wall Stiffener L.F. 12ga ~ 18ga (2" flange) 2 / sheet R.S. Means stiffener_splice Ea 12ga ~ 18ga (15/8" flange) 2 / sheet R.S. Means Bolt & Nuts for fasten stiffener ea 5/16'' dia, 11/2''long 16 / sheet R.S. Means Bolt & Nuts for sheet ea 3/8'' dia, 1''long 30 / sheet R.S. Means Stiffener_anchor Bolt set ea Anchor bolts, Jtype, 1/2" diameter x 12" long 2 / bottom sheet R.S. Means Sheet S.F. 3''deep, galv, 20ga ~ 8ga 25 / sheet R.S. Means Rope chaulking L.F. 3/4" diam. 4.33 / sheet R.S. Means Roof Eave clip ea Clips to attach, 2"X2"X16ga 6 / top sheet R.S. Means Bolt & Nuts ea 3/8'' diam., 1''long 6 / top sheet R.S. Means Roof ring L.F. Steel pipe, 11/4'' dia 50% / perimeter of bin R.S. Means Roof ring bracket (bolts&nuts) ea Coupling rigid style 11/4"diam. 1 / top sheet R.S. Means Peak ring S.F. 71/2''deep, long span, 14ga 3.14*Diam.(20'')*deep(14") R.S. Means Roof hatch ea Gal. steel curb and cover 1 / bin R.S. Means Vents ea 1 per M.S.F, Maximum 0.5 / top sheet R.S. Means Roof Ladder Rung (cut) L.F. 8' high wall, 18 gax 4"24"O.C Eaveheight of bin R.S. Means Roof sheet S.F. 161/2''wide, standard finish, 24ga 3.14*.5*diam.* roof slope R.S. Means Accessory Door ea 24''x36'' 1 / bin R.S. Means Ladder V.L.F. Steel, 20'' wide, bolted w/cage Eave height Michigan Assessor's Manual V.L.F. Steel, 20'' wide, bolted WO/cage Eave height Michigan Assessor's Manual Auger & Drive Auger L.F. Auger 4" ~ 10" jet flow Diam. of bin AugerUSA drive( motor) ea Electric Motor 1/3 hp ~ 50 hp 3 phase Diam. of bin AugerUSA Speaders L.F. Auger and drive add $500 to $750 Diam. of bin Michigan Assessor's Manual Stirrators L.F. Auger and drive add $500 to $750 Diam. of bin Michigan Assessor's Manual Fan & Heater Fan ea Axial flow,# CFM, 1/2 HP ~ 10HP Diam. & eave height R.S. Means ea Centrifugal, # CFM, 1/2 HP ~ 10 HP Diam. & eave height R.S. Means Heater ea Unit heaters, 12 MBH ~ 404 MBH Diam. & eave height R.S. Means Note: L.F. (Linear Foot), S.F. (Square Foot), C.Y.(Cubic Yard), V.L.F.(Vertical Linear Foot) Table 1. List of the Components and Units for Grain Bin Facilities Cost Estimation 56 Components Items Unit Unit Size Unit requirement Source Floor Forms in place L.F. Multiple use, to 6" high Perimeter of floor R.S. Means Reinforcing steel Ea Deformed, 2' long, #3 Floor area R.S. Means Concrete in Place C.Y 6" thick Floor area R.S. Means wood block flooring S.F. End grain flooring, coated, 2" thick Floor area R.S. Means Wall Frameend wall Lower studs L.F. 2 X 6 stud 16" O.C. #' high steel 1/16" R.S. Means Frameend wall upper studs (back) L.F. 2 X 6 stud 16" O.C. #' high steel 1/16" R.S. Means Frameend wallupper studs (front) L.F. 2 X 6 stud 16" O.C. #' high steel 1/16" R.S. Means plate L.F. 2 X 6 stud 16" O.C. #' high steel Widedoor R.S. Means Door Lintel Ea 4 " X321" X 3", 1/4" thick, 9' long Door length R.S. Means Framing Anchors Ea 18 ga, 4 1/2" X 2 3/4" 2/stud R.S. Means Anchor Bolts Ea 3/4" diam X 12" long 1/stud R.S. Means Partition S.F. Metal studs 16" O.C., 35/8" wide 1/16" R.S. Means Sidinglining S.F. Corrugated. 0.019" thick painted, steel Lining area R.S. Means Siding S.F. Corrugated. 0.019" thick painted, steel Siding area R.S. Means Door S.F. Wood, 13/4" thick 12 X 12 Door/warehouse R.S. Means Roof Frameroof beam L.F. 18 ga X 6" deep beams 1 / 12' R.S. Means Rafters front L.F. 18 ga X 6" deep rafters, 2" Depend on repose R.S. Means Rafters back L.F. 18 ga X 6" deep rafters, 2" Depend on repose R.S. Means Framing joists (vertical) L.F. Joist, 2" flange 18ga X 6" deep 1/16" R.S. Means Framing joists (vertical) L.F. Joist, 2" flange 18ga X 6" deep 1/16" R.S. Means Framing joists (cross) L.F. Joist, 2" flange 12ga X 10" deep Wide level R.S. Means Fascia board L.F. 2" X 8" Length level R.S. Means Steel roofing panel S.F. Zinc aluminum alloy finish 22 ga Roof area R.S. Means Purins L.F. 2 X 4, 2' O.C. Length & rafter length R.S. Means Office Frame studs L.F. 2" x 6" studs, 16" O.C., 8' high 4/office R.S. Means Framing Anchors Ea 18 gauge, 41/2" x 23/4" 2/stud R.S. Means Anchor Bolts Ea Anchor bolt, Jtype, 3/4" dia x 12" L 1/stud R.S. Means Concrete block S.F. 8" X16" units. 4" thick Siding area R.S. Means Drywall (finished) S.F. 3/8" thick, on walls, standard Siding area R.S. Means Siding S.F. Corrugated. 0.019" thick painted, steel Office area R.S. Means Window Ea 2'0" x 3'0" high 1/office R.S. Means Door frame Ea Metal, 16 ga., deep, 6'8" h x 3'0" w 1/office R.S. Means Door Ea Steel, 2'8" x 6'8" 1/office R.S. Means HVAC Warehouse w/o or w office % Equipment 1.3%~2.0 %/ total cost R.S. Means Mechanical & electrical % Plumbing 5.2%~5.3 %/ total cost R.S. Means % Heating, ventilating, air condition 5.5 %~6.2%/ total cost R.S. Means % Electrical 7.9 %~8.8%/ total cost R.S. Means Note: Class S of warehouse represents steel frame, siding, providing heating and cooling system, interior finish and floor, good office, good lighting and adequate plumbing, etc. Table 2. List of the Components and Units for Warehouse Building Cost Estimation (Class S) 57 Components Items Unit Unit size Unit requirement Source Footing Post footing Ea 12" diameter incl. excav, backfill, tube 1/post(pole) R.S. Means Concrete for floor C.Y Slab on grade 4'' thick, incl. forms & reinforcing steel Area R.S. Means Wall FramePost (pole) L.F. 6" X 6" Framing , colums for wood post Post No. based on post spacing O.C. R.S. Means Wall girts L.F. 2" X 4", 2' O.C. pneumatic nailed Wall area and siding R.S. Means Skirt board L.F. 2" X 6", pneumatic nailed Perimeter R.S. Means Siding S.F. Corrugated. 0.019" thick painted, steel Siding area (three siding) except front siding R.S. Means On wood framing S.F. For siding on wood frame, deduct from above siding cost Deduct on wood frame R.S. Means Roof Frameroof beam L.F. 2 X 8 single wood, pneumatic nailed Height/12 R.S. Means Rafters right L.F. 2" X 6" wood Depend on repose R.S. Means Rafters left L.F. 2" X 6" wood Depend on repose R.S. Means Collar Beam Tie L.F. 2" X 4", 2' O.C. Half of truss span R.S. Means Ceiling joists (cross) L.F. 4" X 6" wood joist Wide level R.S. Means Ridge board L.F. 2" X 6" wood 1/warehouse's length R.S. Means Purins L.F. 2" X 4", 2' O.C. Rafter length & length R.S. Means End studs L.F. 2" X 6" stud 16" O.C. # wood 1/16" R.S. Means Roofing panel steel S.F. Corrugated. 0.0155" thick, steel Roof area R.S. Means On wood framing S.F. For roof on wood frame, deduct from above roof siding cost Roof area R.S. Means Table 3. List of the Components and Units for Pole Barn Cost Estimation (Class Dpole) 58 2) The requirements of each components aspect Based on the appropriate drawings and engineering charts obtained from industry quotes and building manuals etc., the requirements for specific components were determined as follows. A. Grain bin i. Floor (concrete foundation) : Grain bin Using slab on ground construction basis, floor work is composed of foundation forms, reinforcement in place, placing concrete and placing anchor bolt. Concrete thickness and reinforcement bar and the amount of concrete uses were estimated or determined across bin diameter sizes (1 cubic foot= 0.037 cubic yard). Also, diameter sizes were used in determining the number of sheets (2.66” corrugation) per ring as diameter † 3. The number of sheets per ring and diameter size was also used to determine the number of anchor bolts requirements. From table 5, Floor components of requirement could be estimated as (1) FormsAnchor bolts = diameter ÷ 3 × 2 = # ea * diameter ÷ 3 = sheet # per ring (2) formrod = diameter ÷ 3 × 2 = # set (3) Forms in place = perimeter of bin = # L.F. (4) Reinforcing steel = floor area of bin × 1 = # ea (5) Concrete = floor area of bin (S.F.) × thickness (') of floor×0.037 = # C.Y.. ii. Wall (sidewall sheet) : Grain bin Based on force basis by bin eave height (or ring) and diameter size, the various wall sheet gauges (8ga ~ 20ga) were selected by 2.66” standard bin sidewall gauges criterion. The thinnest gauge (20a) sheets should be assembled on the top ring of the bin, while the thickest gauge (8ga) sheets go on the bottom ring. The number of sheets required was calculated by diameter and eave height level. Optionally two stiffeners (splice) per every sheet were used and stiffeners gauge also were changed based on height of bin. From table 5, Wall components of requirement could be estimated as (6) Stiffener = diameter ÷ 3 × Ring # × 2.66 × 2 = # L.F. * ring # = eave height † 2.66” 59 (7) Stiffener_ Splice = diameter ÷ 3 × Ring # × 2 = # Ea (8) Bolt & Nuts for fasten stiffener = diameter ÷ 3 × Ring # × 16 = # Ea (9) Bolt & Nuts for sheet = diameter ÷ 3 × Ring # × 30 = # Ea (10) Stiffeneranchor Bolt set = diameter ÷ 3 × 2 = # Ea (11) Sheet area = diameter ÷ 3 × Ring # × 25 = # S.F. (12) Rope chaulking = diameter ÷ 3 × Ring # × 4.33 = # S.F. * 4.33 is length of sheet iii. Roof : Grain bin Under the angle of repose (tangent °) basis by grain type, roof erecting work was divided into roof sheet, peak ring assembling, and roof accessory (roof ring, ladder rung, vent, hatch, etc.). Roof sheet required area was calculated by area of cone (pi × radius × side) and optionally slope of roof was changed by angle of repose (tangent °). From table 5, Roof components of requirement could be estimated as (13) Eave clip = diameter ÷ 3 × 6 = # Ea * 6 required per top sheets (14) Bolt & Nuts = diameter ÷ 3 × 6 = # Ea * 6 required per top sheets (15) Roof ring = 50 % of perimeter of bin = # L.F. (16) Roof ring bracket (bolts& nuts) = diameter ÷ 3 × 1= # Ea (17) Peak ring = diameter 20” and deep 14” ring = # S.F. (18) Roof hatch = one of each bin = # Ea (19) Vents = diameter ÷ 3 × 0.5 = # Ea. * 1 required per 2 top sheets (20) Roof Ladder Rung = Eaveheight of bin = # L.F. * 4.33 is length of sheet (21) Roof sheet = area of roof = # S.F.. iv. Others (Accessory) : Grain bin Based on eave height of bin basis, outside steel ladder (20'' wide) bolted with or without cage and standard metal door (24" x 36") was used for one per bin. From table 5, Others(Accessory) components of requirement could be estimated as (22) Door = one of each bin = # Ea (23) Ladder w/ cage =eave height = # V. L.F. (24) Ladder wo/ cage =eave height = # V. L.F. v. Auger & drive (Unloading system) : Grain bin Based on the diameter and capacity of bin basis, the simplest tube auger (horizontal angle (0°)) was used and auger capacity and horsepower requirements were determined by diameter and RPM (speed). For example on 496,692 (105' by 58' 8'') bushel capacity grain bin, the estimated 60 capacity and required motor size could be calculated as follows. Table 4 provides 12''diameter auger running at 300 rpm, conveys 4,520 bu/hr of grain and requires 2.5 hp per 10' of auger length. Hence, total horsepower can be calculated as Total HP = (diameter' ÷ 2) ÷ 10') × hp per 10' = (105'÷ 2) ÷10') × 2.5 hp/10' = 13.1 hp Table 4. Estimated Auger Capacity and Horsepower Requirements Bin Capacity (bu) Auger Diam.(') RPM (Speed) bu/hr hp/10' 5,000 4 900 560 0.6 50,000 6 600 1,500 1 100,000 8 450 2,210 1.4 300,000 10 360 3,300 2 500,000 12 300 4,520 2.5 750,000 14 260 6,230 3.4 1,000,000 16 225 8,040 4.4 Source: incline angle is 0° and the table was modified from MWPS13 (1988). From table 5, Auger & Drive components of requirement could be estimated as (25) Auger = auger base cost(4"~10") + add($13~$64) per diam(') = # L.F. (26) Drive (motor) = Select motor correspond to estimated auger horsepower = # Ea. (27) Spreaders = base $500 + add($500 to $930) per diam(')= # L.F. (28) Stirrators = base $130 + add($130 to $250) per diam(')= # L.F vi. Fan & Heater (Aeration system) : Grain bin Based on the airflow rate and static pressure level for aeration, the fan H.P. and heater specification were selected as follow. Aeration and heater cost are a significant aspect variable costs as well as construction cost. Fan selection was the process for determining fan H.P. First, airflow required (CFM) was calculated and then proper air static pressure was determined based on grain type and bin height. Airflow rate could be selected as either 0.1 CFM/Bu or 0.25 CFM/Bu. Finally fan horsepower was calculated as 61 Air Horsepower = (CFM × static pressure) / (6,320 × fan efficiency)17. For example on 496,692 (105' by 58' 8'') bushel capacity bin with airflow rate 0.1 CFM/Bu, the total airflow and static pressure could be calculated as 49,692 CFM, 7.4 inch, and fan efficiency was assumed as 65% and then Air Horsepower = (49,692× 7.4) / (6,320 × 0.65) = 89.5. Hence the estimated air horsepower is 89.5 hp and the model selects one of two fan types optionally and heaters needs that correspond to this hp. From table 5, Fan & Heater components of requirement could be estimated as (29) Fan (Axial) = Select fan correspond to estimated fan horsepower = # Ea. (30) Fan (Centrifugal) = Select fan correspond to estimated fan horsepower = # Ea. (31) Heater = Select fan correspond to estimated fan horsepower = # Ea.. B. Warehouse building (Class S) i. Floor (concrete foundation) : Warehouse building Warehouse foundation floor were composed of structural concrete and slab on grade with 6" thick and included reinforcing steel. Also foundation walls employed 8" thick concrete and reinforcing steel. The amount of foundation concrete was calculated as the sum of foundation floor and foundation walls area. From table 6, Floor components of requirement could be estimated as (1) Forms in place = Width × 2 + Length × 2 = # L.F *Perimeter of floor (2) Reinforcing steel = floor area × 1 = # Ea (3) Concrete = floor area (S.F.) × thickness (') of floor×0.037 = # C.Y. (4) Wood block flooring = floor area = # S.F. 17Source: http://www.ag.ndsu.edu/pubs/plantsci/smgrains/ae7013.htm#Fans and see tables in MWPS13 (1988). 62 ii. Wall (end & sidewall) : Warehouse building Wall frame structure was divided into end wall and inside (partition) wall. 2×6 Steel studs 16" O.C. was mainly used as upper & lower studs. The amount of studs required was calculated based on the slope of rafters and inside wall spacing (12'). To tie studs and foundation wall, 2 framing anchors per stud was used and wall height, wide and length size of building were used to determine total amount of siding panel requirement. The number of overhead door and wall height level could be inputted as options. From table 6, Wall components of requirement could be estimated as (5) Frameend wall Lower studs = Wide ÷ spacing (16”) × 2 wall side = # L.F (6) Frameend wall upper studs (left) = the summation of left rafter support studs = # L.F. (7) Frameend wall upper studs (right)=the sum of right rafter support studs= # L.F. (8) Plate = two plates in front and behind of building = # L.F. (9) Door Lintel= Door length × # door = # Ea (10) Framing Anchors = 2 Ea required per stud 16" O.C. = # Ea (11) Anchor Bolts = 1 Ea required per stud 16" O.C. = # Ea (12) Partition = the summation of Area of partitions = # S.F. (13) Sidinglining = the area of sidinglining for front & behind lining = # S.F. (14) Siding = total wall area = # S.F. (15) Door = option = # Ea.. iii. Roof : Warehouse building Based on rafter slope basis, roofing frame work was divided into rafter erecting, frame joists, purins, and roofing panel. Roofing panel (truss span) required area was estimated based on rafter slope degree and length of building. From table 6, Roof components of requirement could be estimated as (16) Frameroof beam = the summation of beam length = # L.F (17) Rafters right side = the summation of the rafter side length O.C.12‟ = # L.F. (18) Rafters left side = the summation of the rafter side length O.C.12‟ = # L.F. (19) Framing joists (verticalR) = the sum of the joist right side length O.C.16” = # L.F. (20) Framing joists (verticalL) = the sum of the joist left side length O.C.16” = # L.F. (21) Framing joists (cross) = the summof the joist cross length based on width = # L.F. (22) Fascia board = 2 board required based on the length = # L.F. (23) Steel roofing panel = Roof area = # S.F. (24) Purins = the summation of the required based on length and rafter length = # L.F. 63 iv. Office : Warehouse building Based on height of office and S.F area, the amount of siding panel, frame studs, concrete block, etc. were determined. From table 6, office components of requirement could be estimated as (25) Frame studs = the summation of stud length = # L.F (26) Framing Anchors = 2 required per stud = # Ea (27) Anchor Bolts = 1 required per stud = # Ea (28) Concrete block = area of office = # S.F. (29) Drywall = Siding area = # S.F. (30) Siding = side area for in& out side = # S.F. (31) Window = 1 per office = # Ea (32) Door = 1 per office = # Ea v. HVAC (Electrical & Mechanical system) : Warehouse building HVAC costs were categorized as equipment, plumbing, heating, ventilating, and air conditioning cost. Categorized component costs were obtained by multiplying the whole bare total costs of warehouse building by the ratio (%) of categorized components (see table 6). HAVC‟s Q&P was calculated by assuming 10% for the sum of the bare material cost since O&P for the installing contractor may range from 5% to 15% of the bare total cost. From table 6, HVAC components of requirement could not be estimated as quantity, so correspond costs could be calculated by multiply proper ratios as (33) Equipment = multiplying the bare total costs by the ratio (%) of equipment = # $ (34) Plumbing = multiplying the bare total costs by the ratio (%) of Plumbing = # $ (35) HVAC = multiplying the bare total costs by the ratio (%) of HVAC = # $ (36) Electrical = multiplying the bare total costs by the ratio (%) of electrical = # $ C. Pole barn building (Class Dpole) i. Footing (option concrete floor) : Pole barn Footings thickness is same as post thickness and footing width (diameter) is twice of post thickness. The circular concrete footings with 6" thick and 12" diameter were used. The number of footing was calculated based on the sum of posts required. Optionally, concrete floor were used as 64 slab on grade with 4" thick and included reinforcing steel. The amount of concrete floor was calculated based on barn area. From table 7, Footing components of requirement could be estimated as (1) Post footing = the summation of pole required footing = # Ea (2) Concrete for floor = Width ×Length× 0.037 = # C.Y. * 0.037: conversion for C. Y ii. Wall ( post (pole) wall ) : Pole barn According to size, post spacing & eave wall height, width and length users may need, the amount of materials used was determined. The number of post frame was calculated based on post spacing and length of barn. For example on 40'×80' (width × length), post spacing 8' pole barn, the calculated the number of post is 22 ea. Post # = 4+ Round (Length of Barn ÷ Post spacing length1) × 2 = 4 + (80' ÷ 8'1) × 2 = 22 The model allows pole barn cost to be estimated with or without siding. Siding work was divided into wall girts & skirt board, and siding panel. Siding panel area was calculated for three sides with the front assumed to be open. Wall girts (skirt board) work used wood plate which untreated 2"×4"(2"×6"), pneumatic nailed 2' O.C. From table 7, Wall components of requirement could be estimated as (3) FramePost = the summation of pole length required = # L.F. (4) Wall girts = the summation of the wood penal for wall area = # L.F. (5) Skirt board = 2sides length plus and 1 side width of barn = # L.F. (6) Siding = siding area (three siding) = # S.F. (7) On wood framing = deduction for wood frame from siding = # S.F 65 iii. Roof: Pole barn Based on rafter slope and width of barn, roofing material uses were rafters, ceiling joists, collar beam tie, purins, end studs and roofing panel. Roofing panel (truss span) required area was estimated based on rafter slope degree and length of building. The aluminum panels, corrugated with 0.0155.thick were used. For example on 40'×80' (width × length), angle 18° pole barn, based on the square of the length of the rafter (hypotenuse) equals the sum of the squares of the lengths of the two other sides (half of width & peak height minus wall height), the calculated length of rafter is 21.0 (L.F.) C = ((A)2 + (B) 2)^0.5 Length of rafter = (((TAN (18 × 3.14 ÷ 180) × (width ÷ 2)))2 + (width ÷ 2) 2)^0.5 = [(0.3249 × 20) 2 + (20) 2] ^ 0.5 = 21.029 From table 7, Roof components of requirement could be estimated as (8) Frameroof beam = the summation of beam length = # L.F (9) Rafters right side = the summation of the rafter side length O.C. #‟ = # L.F. (10) Rafters left side = the summation of the rafter side length O.C. #‟ = # L.F. (11) Collar beam tie = the summation of multiply the half of width with O.C. #‟ = # L.F. (12) Ceiling joists (cross) = pole(post) # × width = # L.F. (13) Ridge board = the length = # L.F. * 1 board required per building (14) Purins = the summation of the required based on length and rafter length = # L.F (15) End studs = the summation of left & right rafter support studs = # L.F. (16) Roofing panel steel = Roof area = # S.F. (17) On wood frami
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Title  Forecasting Wheat Yield and Quality Conditional on Weather Information and Estimating Construction Costs of Agricultural Facilities 
Date  20110501 
Author  Lee, ByoungHoon 
Keywords  Prediction, protein, spatial lag, test weight, weather, wheat yield 
Department  Agricultural Economics 
Document Type  
Full Text Type  Open Access 
Abstract  Two studies were conducted. First study is preharvest forecasting of county wheat yield and wheat quality conditional on weather information and second study is improved methods of estimating construction costs of agricultural facilities. The first study estimated wheat regression models to account for the effect of weather on wheat yield, protein, and test weight and to forecast wheat yield and the two wheat quality measures. The explanatory variables included precipitation and temperature for growing periods that correspond to biological wheat development stages. The models included county fixed effects, crop year random effects, and a spatial lag effect. The second study developed and evaluated `Economic Engineering Construction cost templates model' for estimating construction costs of storage facilities. To verify model performance, the regression statistical inferences were used and the predicted costs of the developed cost templates model were benchmarked against previous two projects for grain bin and one example of RSMeans estimating costs for warehouse building. The results of first study indicated that wheat yield, protein, and test weight level are strongly influenced by weather variables. Study also found that the forecasting power of the yield and protein models was enhanced by adding the spatial lag effect. Out of sample forecasting tests confirm the models' usefulness in accounting for the variations in average wheat yield and qualities. The first study results or prediction information could be widely used and could be particularly important to producers optimizing late season agronomic and marketing decisions and to grain elevators and agribusiness for contracts or purchasing decisions. The results of second study represented the fitting ability of the model is very well and provide information which help to illustrate and quantify the project to project variation in construction costs. It allows producers and agribusiness managers to examine a wide variety of configurations and options and to update their estimates as current RSMeans data becomes available. So, a major contribution of the study is that it develops a method of estimation that can be continuously updated as new RSMeans data is published. 
Note  Dissertation 
Rights  © Oklahoma Agricultural and Mechanical Board of Regents 
Transcript  FORECASTING WHEAT YIELD AND QUALITY CONDITIONAL ON WEATHER INFORMATION AND ESTIMATING CONSTRUCTION COSTS OF AGRICULTURAL FACILITIES By BYOUNGHOON LEE Bachelor of Science in Agricultural Economics Kangwon National University Chuncheon, Korea 1999 Master of Science in Agricultural Economics Korea University Seoul, Korea 2001 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 May, 2011 ii FORECASTING WHEAT YIELD AND QUALITY CONDITIONAL ON WEATHER INFORMATION AND ESTIMATING CONSTRUCTION COSTS OF AGRICULTURAL FACILITIES Dissertation Approved: Dr. Philip Kenkel Dissertation Adviser Dr. B. Wade Brorsen Dr. Rodney Holcomb Dr. Patricia RayasDuarte Dr. Mark E. Payton Dean of the Graduate College iii ACKNOWLEDGMENTS It is my great pleasure to thank all the people who made this dissertation possible. I wish to express my sincere appreciation to my academic advisor Dr. Philip Kenkel for his intelligent supervision and invisible guidance and encouragement through my Ph.D. program at Oklahoma State University. I also wish to thank all members of my academic committee Dr. Wade Brorsen, Dr. Rodney Holcomb, and Dr. Patricia RayasDuarte for their helpful advice invaluable comments during the final week of completing this dissertation. Especially Dr. Wade Brorsen provided thoughtful econometrics advice and hard training for great direction throughout my preparation of this dissertation. My appreciation is extended to Dr. Francis Epplin who has provided a research opportunity, great teaching and advice. Also Dr. Brain Adam, and Dr. Changjin Chung who have encouraged my academic success. I wish to thank my academic friends Inbae Ji, Jongsan Choi, Seongjin Park, Yoonsuk Lee, and Samarth Shah. Lastly, and most importantly, I wish to appreciate my parents SunTae Lee and JongSook Yoon for endless love and patience. My wife jiyeon Park and two daughters, Eunju, Kyuna, and the son, Donghoo who have helped me complete this program. Also, I always have appreciated my ancestors. iv TABLE OF CONTENTS I. Preharvest Forecasting of County Wheat Yield and Wheat Quality Conditional on Weather Information ..................................................................1 Introduction ..............................................................................................................1 Conceptual Framework ............................................................................................4 Data ........................................................................................................................10 Empirical Model Specification ..............................................................................16 Estimation Method and Procedures .......................................................................19 Empirical Results ...................................................................................................22 Summary and Conclusion ......................................................................................29 Appendices .............................................................................................................31 II. Improved Methods of Estimating Construction Costs of Agricultural Facilities .........................................................................................43 Introduction ............................................................................................................43 Conceptual Framework ..........................................................................................47 Empirical Model Specification and Procedures .....................................................50 The Structure of Economic Engineering Construction Cost Templates Model ....54 Collection of a list of the components and cost data .....................................54 The requirements of each component aspect .................................................58 Cost estimation of each aspect of components ..............................................65 Cost adjustments for size factors and time period .........................................70 Data ........................................................................................................................76 Empirical Results ...................................................................................................77 Summary and Conclusion ......................................................................................88 Appendices .............................................................................................................90 REFERENCES ............................................................................................................98 v LIST OF TABLES Table Page (Chapter I) Table 1. Descriptive Statistics for Wheat Quality Characteristics, 2004  2010 ............................ 14 Table 2. Tests of No Spatial Autocorrelation for Wheat Yield, Protein, and Test Weight ............ 22 Table 3. Yield Model and Spatial Yield Model Estimates, 19942009 ......................................... 23 Table 4. The Elasticity of Weather Variables ................................................................................ 24 Table 5. Out of Sample Forecast Error Statistics for Yield Models, 2010 .................................... 24 Table 6. Protein Model and Test Weight Model Estimates, 20042009 ........................................ 25 Table 7. The Elasticity of Weather Variables for Quality Model .................................................. 26 Table 8. Out of Sample Forecast Error Statistics of Wheat Quality, 2010 .................................... 27 Table 9. Out of Sample Fit Test using the Longer Period (FebMay) for Yield Models ............... 28 Table 10. Out of Sample Fit Test using the Shorter Period (FebApril) for Quality Models ........ 28 Appendix Table 1. Rsquared Estimated and Correlation Coefficients for Selecting Quality Variables riables ............................................................................................................................ 36 Appendix Table 2. Correlation Coefficients among Yield, Protein, Weight and Weather Variables ...................................................................................................................................................... 36 Appendix Table 3. Diagnostic Test Statistics: Yield, Protein, and Test Weight Response Models ...................................................................................................................................................... 37 Appendix Table 4. Yield Model and Spatial Yield Model Estimates, 19942009......................... 37 Appendix Table 5. Protein Model and Test Weight Model Estimates, 20042009 ...................... 37 Appendix Table 6. Descriptive Statistics for Yield Model Variables, 19942009 ........................ 38 Appendix Table 7. Descriptive Statistics for Quality Model Variables, 20042009 ..................... 38 Appendix Table 8. Comparing Actual and Prediction Values for Yield Models .......................... 38 Appendix Table 9. Comparing Actual and Prediction Values for Quality Models ....................... 39 Appendix Table 10. Yield Model and Spatial Yield Model Estimates using the Longer Period (FebMay), 19942009 ................................................................................................................... 40 vi (Chapter ІІ) Table 1. List of the Components and Units for Grain Bin Facilities Cost Estimation .................. 55 Table 2. List of the Components and Units for Warehouse Building Cost Estimation (Class S) .. 56 Table 3. List of the Components and Units for Pole Barn Cost Estimation (Class Dpole) ........... 57 Table 4. Estimated Auger Capacity and Horsepower Requirements ............................................ 60 Table 5. Grain Bin Formulas for Total Amount of Requirement and Cost Estimation ................ 67 Table 6. Warehouse Building Formulas for Total Amount of Requirement and Cost Estimation 68 Table 7. Pole Barn building Formulas for Total Amount of Requirement and Cost Estimation ... 69 Table 8. Cost adjustments by size factors (area & story height) ................................................... 71 Table 9. Grain bin and Warehouse Building Dimensions and Quotation for Size Factors ........... 72 Table 10. The Developed Cost Equations and Michigan Cost Equations Estimates for Grain Bin Comparison (loglog form) ............................................................................................ 81 Table 11. Total Cost Equation Estimates Using the Predicted Costs ($) for Warehouse .............. 81 Table 12. Chow Test for Parameter Stability of Grain Bin & Warehouse Cost Model ................ 82 Table 13. The Elasticity of Explanatory Variables and Correlation for Comparison ................... 83 Appendix Table 1. Predicted Total & Fan & Heater Costs for Diameter 105 ft and Eave Heights 25 to 105 ft. .................................................................................................................... 95 Appendix Table 2. Categorized Predicted Costs using „Economic Engineering Warehouse Building Construction Cost Templates Model‟ for Width 100, Lengths 100 to 300 ft ... 96 Appendix Table 3. Average cost ratio using „Economic Engineering Grain bin Construction Cost Templates Model‟ for diameter 105 ft, eave heights 25 to 105 ft. ................................ 97 Appendix Table 4. Average cost ratio using „Economic Engineering Warehouse Building Construction Cost Templates Model‟ for Width 100, Lengths 100 to 300 ft. ............................... 97 vii LIST OF FIGURES Figure Page (Chapter I) Figure 1. Wheat Growth and Development Stages .......................................................................... 6 Figure 2. The PGI Survey Area of Grain sheds basis .................................................................... 10 Figure 3. Location of 2010 Sample Elevators and Oklahoma Mesonet Stations ........................... 15 Figure 4. The Prediction procedure for Yield and Quality Models ............................................... 21 Appendix Figure 1. Plot Yield and Precipitation ........................................................................... 40 Appendix Figure 2. Plot Yield and Avg. Temp. ............................................................................ 40 Appendix Figure 2. Plot Yield and Avg. Temp. ............................................................................ 40 Appendix Figure 4. Plot Protein and Max. Temp. ......................................................................... 41 Appendix Figure 5. Plot Protein and Yield .................................................................................... 41 Appendix Figure 6. Plot Test Weight and Precipitation ................................................................ 41 Appendix Figure 7. Plot Test Weight and Maximum Temp. ......................................................... 41 Appendix Figure 8. Plot Test Weight and Mini. Temp. ................................................................ 41 Appendix Figure 9. Plot Test Weight and Yield ............................................................................ 41 Appendix Figure 10. Plot Protein and Solar Radiation ................................................................. 41 Appendix Figure 11. Plot Weight and Solar Radiation ................................................................ 42 Appendix Figure 12. Plot Yield and Solar Radiation ................................................................... 42 Appendix Figure 13. Calculated Relationship between Yield and Protein and Test Weight Using Elasticity ........................................................................................................................ 42 (Chapter II) Figure 1. Prediction & Evaluation Procedure for Economic Engineering Construction Cost Model ...................................................................................................................................................... 75 Figure 2. Predicted Total Cost Curve of bin Construction for Diameter 105 ft and Eave Heights 25 to 105 ft ..................................................................................................................... 77 Figure 3. Predicted Average Cost Curve of bin Construction for Diameter 105 ft and Eave Heights 25 to 105 ft ....................................................................................................... 78 viii Figure 4. Predicted Total Cost Curve of Warehouse Building Construction for Width 100 ft and Lengths 100 to 300 ft with Wall Height 24ft ................................................................. 79 Figure 5. Predicted Average Cost Curve of Warehouse Building Construction for Width 100 ft and Lengths 100 to 300 ft with Wall Height 24 ft ......................................................... 79 Figure 6. Average Percentages of Each Predicted Cost of Components ...................................... 80 Appendix Figure1. Grain bin construction basic components ....................................................... 91 Appendix Figure 11. Warehouse BuildingStorage (Average Class S) ........................................ 92 Appendix Figure 12. Pole Barn BuildingStorage (Average Class Dpole) .................................. 92 Appendix Figure 2. Economic Engineering Grain Bin Construction Cost Templates Model as spread sheet type model ................................................................................................. 93 Appendix Figure 3. Economic Engineering Warehouse Building Construction Cost Templates Model as spread sheet type model ................................................................................. 93 Appendix Figure 4. Economic Engineering Pole Barn Building Construction Cost Templates Model as spread sheet type model ................................................................................. 94 Appendix Figure 5. Comparsion for Required HP Between Tall Bin and Wide Short Bin ........... 94 1 CHAPTER I Preharvest Forecasting of County Wheat Yield and Wheat Quality Conditional on Weather Information Introduction Winter wheat production in the Southern Plains is a mostly dry land crop with substantial yeartoyear variation in yields and quality due to rainfall, temperature and other weather events. If wheat yield and wheat quality response to weather conditions could be predicted early and accurately, the information could be widely used. The information could be particularly important to farmers optimizing late season agronomic and marketing decisions and to grain elevators and millers for purchasing decisions. Thus, there has been increasing interest in the use and development of robust crop weather response models. Numerous models have been estimated to predict crop yield based on weather conditions. Two main prediction approaches are simulation models and multiple regression models. A number of comprehensive agricultural simulation models are now available to predict yield and variability of wheat. Jones and Kinir (1986) suggested a model to simulate the effects of genotype and weather conditions on crop yield, Duchon (1986), Claborn (1998), Bannayan, Crout, Hoogenboom (2003), and Tsvetsinskaya et al. (2003) predicted yields using weather forecasts and scenarios using the Crop Environment Resource Synthesis (CERES) simulation model. For the Great Plains, Eastering et al. (1998) and Wang et al. (2006) used the Erosion Productivity Impact Calculator (EPIC) model and Eastering et al. (1998) found spatial disaggregation of climate data2 enhance predictions. Using CERESWheat model, Weiss et al. (2003) investigated the responses of wheat yield and enduse quality by using nitrogen management and planting dates data. The simulated results depended on spatial locations and climate changes, and also soil water stress and management of nitrogen strongly influenced yield distributions and kernel nitrogen content. Walker (1989) combined simulation and multiple regression to develop physiologically and regionally weighted drought indices from temperature and precipitation data. The forecasts showed the indices well explain the variation of interregional and annual yield within a growing season. A simulation model is designed to simulate crop yield using details about crop biology. However, as noted by Walker (1989), a simulation approach requires extensive information such as soil type, plant parameters, and weather data related to the crop development stage, which are often not readily available. Tannura, Irwin, and Good (2008) argue that an important limitation of crop simulation models is that they are likely to ignore the influence of technology development over time. Bechter and Rutner (1978) and Just and Rausser (1981) found singleequation models forecast more accurately than large econometric models and we should expect a similar result for agronomic models. Thus, many previous studies have preferred a regression approach rather than a large simulation model when the goal is forecasting. Studies using the multiple regression approach include Yang, Koo, and Wilson (1992), Dixon et al. (1994), Kandiannan et al. (2002), and Chen and Chang (2005) who used various production functions to capture the effect of climate variables on observed crop yield level and to predict crop yield. Irwin, Good, and Tannura (2008) and Tannura, Irwin, and Good (2008) modified Thompson‟s (1964) corn and soybean regression model and found crop yield strongly related to weather conditions such as temperature, rainfall, technology, and other weather variables. As Tannura, Irwin, and Good (2008) and other studies have proven, multiple regression models have high explanatory power and can represent relationships between weather conditions and crop yield. Thus, the multiple regression model approach is not only easier to use, it is also likely more accurate than the simulation model approach. 3 Several studies investigated the influences of weather conditions, genotype, and their interaction on wheat quality. The crop maturation period, such as milk development, heading, and ripening stages are the critical stages in determining wheat quality (FAO, 2002). Graybosch et al. (1995), Johansson and Svensson (1998), Smith and Gooding (1999) and Guttieri et al. (2000), and Johansson, Prieto, and Gissen (2008) developed quality models that showed the effect of weather and environment strongly influenced protein content and test weight of wheat. Smith and Gooding (1999) argued predicting grain quality before wheat harvest would be important information to grain buyers, and to farmers to help optimize agronomic activity, particularly, a late application of nitrogen fertilizer to increase protein content (Woolfolk et al., 2002). Britt et al. (2002) estimated six yield and quality of cotton response functions and profit functions as a function of weather information and input and output prices. Regnier, Holcomb, and RayasDurate (2007) investigated the variations in flour and dough functionality traits associated with environmental factors and found the interaction between crop years and production regions was a significant factor for flour and dough qualities since growing conditions and climate conditions differ among the regions and across years. Unlike previous yield regression models, most qualityrelated model studies did not measure prediction performance of their models and also used analysis of variance (ANOVA), Spearman rank correlation analysis or simple regression models without precise diagnostic tests for model misspecification. Therefore their methods may lead to biased and inconsistent estimates (McGuirk, Driscoll, Alwang, 1993). The extensive previous studies have limitations. One is that the previous regression studies cited have solely estimated the impacts on yield and quality level, respectively, and did not deal with agronomic tradeoffs between yield and quality of wheat. Also few focused on prediction and most studies did not consider out of sample forecasts but measured in sample fit. Insample fit can be inaccurate because most models, including ours, are developed from pretesting over a large number of alternative specifications. 4 The other is that many of the above studies have either used data from a single location or have not used the extra information provided by spatial data. The increasing availability of spatial climate information makes it important to incorporate this new level of information to improve forecasts. Anselin (1988) explained that when using spatial data, the dependent variable at each location may be correlated with observations of the dependent variable at neighboring locations. This is defined as spatial contiguity (lag) effect. If this effect is ignored in a model specification, the estimates in the general model are likely to be biased. Therefore, in order to get more accurate forecasts, the crop response model using spatial data needs to include a spatial lag effect. Oklahoma has two unique resources for examining the relationship between weather and wheat yields and quality. The Oklahoma Mesonet consists of 120 automated stations covering Oklahoma with one or more stations in each of Oklahoma's 77 counties. Plains Grains, Inc. (PGI) is a private, nonprofit wheat marketing organization based in Stillwater, Oklahoma. PGI evaluates wheat quality, including milling and baking quality from an extensive network of samples at the county level. These two unique data sets provide the opportunity to examine the ability to predict wheat yield and quality with weather data. These two data sets (mesoscale weather data and elevator scale quality data) are highly disaggregated. Thus, the disaggregated data sets could provide more precise wheat yield and quality predictions than was possible with the data sets used in past research. The objective of the study is to develop wheat regression models to account for the impact of weather on wheat yield and quality and to predict (forecast) wheat yield and quality levels accurately. In other words, the primary purpose of the study is to use weather information to predict wheat yield and wheat quality and to select variables and functional forms to estimate parameters and then measure how well the developed models forecast. Conceptual framework Previous studies have used knowledge about biological development stages of crops to help select the explanatory variables. Dixon et al. (1994) and Kafumann and Snell (1997) specified weather 5 variables for their corn yield regression models that were based on biophysical stages of corn1. On the other hand, Yang, Koo, and Wilson (1992) and others used planting season and growing season precipitation and average temperature. Hansen (1991), Tannura, Irwin, and Good (2008) and others estimated the effect of calendar month precipitation and temperature variables on soybean and corn yield during crucial development periods to forecast potential crop yield. Even though biological stages of crops do not precisely correspond with calendar months, a number of previous regression response models have used weather variables defined on a monthly average calendar basis. Previous studies also assume every cross sectional location has the same development stages since it is very difficult to match the precise time point of crop development stages at every location. Another reason is the estimated results using monthly weather variables were similar with that of stage basis variables. For example, Dixon et al. (1994) compared weather variables based on biological stages with variables that based on fixed calendar months and found the forecasting performance and R2 of the two models only changed slightly. Weather strongly affects four stages2 of wheat development that determine wheat production level and qualities (FAO, 2002). Aitken (1974), Miralles and Slafer (1999), and Acevedo et al. (2002) argued mainly temperature and precipitation influence wheat development; the most crucial stages of wheat yield are from double ridge to anthesis (flowering) (GS2) and from anthesis to maturity (GS3) since kernel number and weight are being determined at that time (figure 1). 1 The corresponding weather variables were specified based on the six weeks before and three weeks after silking point rather than calendar months basis because corn is critically sensitive to precipitation in June and midJuly in Midwestern U.S. 2 The stages can be categorized as germination to emergence (E), from germination to double ridge (GS1), from double ridge to anthesis (GS2), and grain filling period from anthesis to maturity (GS3) (FAO, 2002). 6 Figure 1. Wheat Growth and Development Stages 7 Meanwhile, the influence of temperature and precipitation during grain filling are widely known to influence wheat quality characteristics. Graybosch et al. (1995), Johansson and Svensson (1998), Stone and Savin (1999), and Smith and Gooding (1999) found weather has deep impacts on grain quality; for instance, increased temperatures during grain filling tend to increase protein and reduce mean grain weight. Stone and Savin (1999) argued that 7080 % of total protein is accumulated during the grain filling period. Winter wheat of the southern Great Plains is typically planted in early September through the middle of November. In general winter wheat harvest begins toward the end of May in southern Oklahoma and continues until about the middle of July (IPM Center, 2005). According to crop weather summary in Oklahoma (DOA, 2000), wheat begins to double ridge and joint in February. Southwestern counties begin to head by the end of March. In April, anthesis is begun and some wheat in south Oklahoma begins the grain filling period, and finally wheat harvest begins approximately May 20th in the southern counties. Using the above described general relation of weather variables and wheat by growth stages, the study selects calendar months during GS2 and GS3 and specifies appropriate calendar month weather variables for growing periods that correspond to these biological wheat development stages. Eastering et al. (1998) used a fine spatial scale to reduce statistical bias from aggregation and confirmed the difference between the observed and estimated yield was greatly reduced when data scale was disaggregated to around 37mile × 50mile. Unfortunately, their method requires a very fine data scale and cannot be used with our data. On the other hand, Anselin (1988) assumed generally the dependent variable or residual at each location may be correlated with neighboring locations‟ dependent variables or residuals. For this spatially correlated data or residuals, the dependence is termed as spatial autocorrelation or spatial lag (contiguity) effect. This indicates that dependents or residuals are spatially autocorrelated and then violate the general assumption of statistically 8 independent explanatory variables and errors. If the spatial lag effect is not considered, estimates will be biased and inconsistent. Previous studies have often used regional models using regional crosssectional data. However, regional data such as observed yield, quality level, and weather variables are generally aggregated considerably beyond the county level. If point estimates (weather, yield, quality) are observed near the border of neighboring regions, there is an opportunity for spatial autocorrelation. For instance, grain produced in one county could be shipped to an adjoining county (this would only affect the quality data since the yield data are based on ARS (Agriculture Research Service) yields which are in turn based on producer reports of harvested production). Some cropland will be closer to a weather station in a neighboring county than weather stations in its own county. Thus, weather measures in a neighboring county should help predict yield. Thus, a spatial lag model should increase forecast accuracy. Anselin et al. (2008) and Anselin and Bera (1998) express the neighbor relation with a spatial weights matrix, and the elements of reflect the potential spatial relations between observations that correspond to the spatial weights structure. The spatial weights matrix can be expressed as binary contiguity sharing a common border, distance contiguity including nearest neighbor locations, and inverse distance between two observations. Anselin and Bera (1998) suggest two main alternative models of spatial autocorrelation: the spatial lag model, and the spatial error model. The main purpose of the former is to predict the spatial patterns such as cluster and random correlation, while the latter is to increase the efficiency of estimates (Bongiovanni and LowenbergDeBoer, 2001). A spatial lag model is used here since the explanatory variables in neighboring counties are expected to help predict our dependent variables. The general regression function can be expressed as: 9 where is a vector of dependent variables, is the matrix of independent variables, and is a vector of stochastic error terms. The spatial lag model is where is the spatial autoregressive coefficient, is a N × N spatial weight matrix (Greene, 2008). This is similar to including a lagged dependent variable in a time series model, except that endogeneity is created because the lagged effects go both directions. The weights matrix is standardized so that rows sum to 1 such as = where are elements of If , the dependent variable at each location is positively correlated with other location‟s dependent variables. Hence, the spatial lag model can be estimated with instrumental variables such as two stage least squares (2SLS) and generalized method of moments (GMM ) or with maximum likelihood (ML) (Lambert and LowenbergDeBoer, 2001), and 2SLS is used here (see appendix 1). 10 Data The wheat yield data (from 19942009) are from 67 counties in Oklahoma and were obtained from „Crop Production Report‟ of United States Department of Agriculture (USDA) National Agricultural Statistics Service (NASS). The adopted yield was based on Harvested acre. Oklahoma has 77 counties, but ten of them are not included due to having little wheat acreage. The crosssectional timeseries data is composed of 1,072 observations (16 years*67 counties). The wheat quality data are from Plains Grains, Inc (PGI)3. PGI tests 96 samples that were collected on a “grainshed” basis from grain elevators when at least 30% of the local harvest was completed. The term “grainshed” was developed by PGI and represents regions within each state in which the majority of the wheat is marketed through a terminal elevator, river elevator or train loading facility (figure 2). Figure 2. The PGI Survey Area of Grainsheds basis Source: 2009 Oklahoma wheat quality report. (2010) 3 Plains Grains Inc.(PGI) is located in Oklahoma and does a wheat quality survey and quality testing of hard red winter wheat to provide enduse quality information to the wheat buyer and producer and published Wheat Quality Report PGI (2009). 11 Figure 21. The Oklahoma Samples of 8 Grainshed Basis Source: 2009 Oklahoma wheat quality report (2010) There are 8 grainsheds in Oklahoma (figure 21). PGI collects representative wheat quality samples from country or terminal elevators. Generally elevators take samples from each truckload arriving at the elevator and the grain is sampled using a hand grain probe. Each elevator directly tests these samples about test weight and moisture content and then these samples typically accumulate in a barrel. Lastly, the elevators barrel is sampled by PGI‟s representative using a hand grain probe. The samples from county and terminal elevators are sent to USDA, ARS hard winter wheat Quality Lab in Manhattan, KS. Twentyfive quality parameters are analyzed in order to provide data that specifically describes the quality of wheat (PGI, 2009). The available historical quality data are from 2004 to 2010 crop years. Table 1 shows a list of wheat quality characteristics over categories and basic descriptive statistics. PGI describes the characteristics specifically “… U.S. wheat grades are determined as based on characteristics such as test weight and includes defects on damaged kernels, foreign materials, shrunken and broken kernels. Test Weight (lb/bu.) is a measure of the density of the sample and may be an indicator of milling yield and the general condition of the sample, as problems that occur during the growing season or at harvest often reduce test weight. Defects (%) are damaged kernels, foreign materials, and shrunken and broken kernels. The sum of O6 169 177 177 177 183 183 183 259 259 266 270 270 270 270 271 277 271 277 281 281 281 283 283 287 412 412 412 56 59 59 59 59 60 60 60 60 62 62 62 62 64 64 64 64 64 64 64 69 69 69 70 70 75 75 75 77 77 81 81 81 Toll Toll Toll Toll Toll Toll Toll Toll 35 35 40 40 44 44 44 Chickasaw NRA Kiamichi River Illinois R. Little River Washita River Salt Fork Salt Fork Cimarron River Candadian R CANADIAN RIVER Cimmaron River L. Altus Atoka L. Broken Bow L. 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Foreign material is all matter other than wheat that remains in the sample after the removal of dockage and shrunken and broken kernels and shrunken and broken kernels are all matter that passes through a 0.064 x 3/8inch oblonghole sieve after sieving. Damaged kernels are kernels, pieces of wheat kernels, and other grains that are badly grounddamaged, badly weather damaged, diseased, frostdamaged, germ damaged, heatdamaged, insectbored, mold damaged, sproutdamaged, or otherwise materially damaged. Additionally, there are kernel quality data and other wheat characteristics in determining the value of the wheat, for instance, wheat protein content, wheat moisture, dockage, thousandkernel weight, and falling number. In the kernel quality data, kernel size (%) is a measure of the percentage by weight of large, medium and small kernels in a sample. Large kernels or more uniform kernel size may help improve milling yield. Single Kernel Characterization System (SKCS) measures 300 individual kernels from a sample for size (diameter), weight, hardness (based on the force needed to crush) and moisture. Thousandkernel weight (g) and kernel diameter provide measurements of kernel size and density important for milling quality. Simply put, it measures the mass of the wheat kernel. Millers tend to prefer larger berries, or at least berries with a consistent size. Wheat with a higher TKW can be expected to have a greater potential flour extraction. In the case of other wheat characteristics, protein content (12% mb: moisture base) relates to many important processing properties, such as water absorption and gluten strength, and to finished product attributes such as texture and appearance. Higher protein dough usually absorbs more water and takes longer to mix. Falling number (sec) is an index of enzyme activity in wheat or flour and is expressed in seconds. Falling numbers above 300 are desirable, as they indicate little enzyme activity and a sound quality product. Falling numbers below 300 are indicative of more substantial enzyme activity and sprout damage. Moisture content (%) is an indicator of grain condition and storability. Wheat or flour with low moisture content is more stable during storage. Ash content (12%mb or %asis) also indicates milling performance and how well the flour separates from the bran. Millers need to know the overall mineral content of the wheat to achieve desired or specified ash levels in flour. Ash 13 content can affect flour color. White flour has low ash content, which is often a high priority among millers. Dockage (%) is all matter other than wheat that can be removed from the original sample by use of an approved device according to procedures prescribed in FGIS (Federal Grain Inspection Service) Instructions…” PGI, 2009 Hard Red Winter Wheat Quality Report. 2010. P. 915. For several year data sets, most quality data has some missing values and provides different quality information based on different testing systems. For example, the Single Kernel Characterization System (SKCS) and the whole kernel nearinfrared (NIR) are rapid tests for wheat quality characteristics, however, the high equipment costs limits the adoption to only large grain operations. So several specific historical year data did not include these test measures. However, test weight (lb/bu) and protein (12% mb) observations have maintained more consistent samplings and also have more high correlations with weather variables than that of the other quality data. Also these two quality data have an important role in determining wheat grade and received price level respectively. Finally, these quality data were used for the quality models and correlation analysis. The ability to predict other wheat quality variables such as total defects and falling number which help determine grade and quality of wheat or flour was examined. These models were dropped because of low Rsquared (see appendix table 1). Moisture content was not examined because it was assumed to be strongly affected by the weather conditions immediately prior to harvest. For more precise analysis, the study matched elevators‟ quality data with weather data from the closest Mesonet stations. This means one weather station per elevator was used to estimate wheat quality models, not a county average. Finally, wheat quality characteristic data used in the model included protein content (% mb) and test weight (lb/bu); the quality data were from 96 elevators based on 2010 (figure 3). 14 Table 1. Descriptive Statistics for Wheat Quality Characteristics, 2004  2010 N Mean Maximum Minimum SD Wheat Grading Data Grade 410 1.73 5 1 0.93 Test Weight (lb/bu) 492 60.1 65 52.8 1.89 Test Weight (kg/hl) 411 79.0 85.4 69.6 2.41 Damage Kernels Total (%) 411 0.19 1.8 0 0.25 Foreign Material (%) 411 0.30 4.7 0 0.55 Shrunken & Broken Kernels (%) 411 1.38 5.1 0.2 0.67 Total Defects (%) 411 1.86 6.5 0.3 1.02 Protein (%) 344 12.4 16.4 9 1.28 HWWQL Test Wt (lb/bu) 176 60.0 65.3 54.7 1.99 HWWQL Test Wt (kg/hl) 176 79.0 85.8 72.1 2.57 Kernel Quality Data Kernel Size Large (%) 343 59.6 86.1 23.6 11.05 Kernel Size Med (%) 343 38.9 71.6 14.0 10.53 Kernel Size Small (%) 343 1.5 7.1 0.0 0.92 SKCS Avg. Wt (mg) 343 29.5 35.4 22.5 2.21 SKCS SD Wt 257 8.23 10.2 5.1 0.74 SKCS Avg. Diam (mm) 343 2.5 2.9 2.0 0.19 SKCS SD Diam 257 0.37 0.5 0.2 0.07 SKCS Avg. Hard 343 74.5 97.2 46.4 9.74 SKCS SD Hard 257 17.29 27.3 13.4 1.79 SKCS Moisture (%) 257 12.2 16.2 8.7 1.34 SKCS SD Moisture 257 0.40 1.2 0.2 0.10 Thousand Kernel Wt (g) 492 28.7 35.4 21.1 2.46 Other Wheat Characteristics NIR Moisture (%) 329 10.7 13.6 8.7 0.90 NIR Protein (%asis) 243 12.2 14.9 9.0 1.00 NIR Protein (12% mb) 492 12.2 16.0 8.8 1.30 Indv Wheat Ash (%asis) 472 1.6 4.0 1.1 0.17 Indv Wheat Ash (12%mb) 406 1.5 3.9 1.1 0.19 Dockage (%) 411 0.71 11.3 0 0.89 Falling Number (sec) 334 418.7 529 172 31.97 Note: KGIS (Kansas Grain Inspection Service), SKCS (Single Kernel Characterization System), NIR (nearinfrared). Mb ( moisture base), and SD(standard deviation). Weather data (from January 1, 1994 to May 31, 2010) were obtained from the Oklahoma Mesonet (figure 3). Each of Oklahoma‟s 77 counties has one or more Mesonet stations. The selected daily data are daily rainfall (in), daily maximum (minimum) air temperature (°F), daily average air temperature (°F), total solar radiation (MJ ), and growth degree days (GDD)4. For all 4 GDD=[(Tmax+Tmin)/2]Tb, 32˚F or 39.2˚F as the base temperature (Tb) for physiological process in wheat(Cao and Moss, 1989). The GDD vary with growing stage and allow a rough estimation of when a given growth stage is going to occur at a particular site. 15 Mesonet stations, the daily observations are aggregated to monthly averages. Generally there is one station per county. For counties with multiple stations an average of all stations in the county is used for yield models; however, quality models use only data from the closest weather station. Several weather stations were added during the study period so the closest weather station sometimes varied by year (see appendix table 6 and 7). Figure 3. Location of 2010 Sample Elevators and Oklahoma Mesonet Stations Notes: the study matched elevators‟ quality data (points) with Mesonet stations‟ weather data (flags) on each the closest distance basis. 16 Source: Oklahoma Mesonet Empirical model specification To specify accurately the underlying relationships between yield and quality variables and weather variables, the study first examined the relationships between weather variables and yield and quality level using the correlation coefficients and graphical displays using proc GAM in SAS (SAS Institute Inc. 2004). GAM allows exploration of data and visualizing structure, and is useful for investigating the relations between dependent and independent variables (see appendix table 2, figures 112). Appendix table 2 shows all weather variables have a high correlation with dependent variables: yield and quality level during the growing season. Precipitation shows less correlation with yield than do average temperature while both variables are associated with yield. Maximum temperature and minimum temperature have all low correlation coefficients and negatively signed with protein and test weight, however, the two variables in quality models were statistically significant. Even though solar radiation and GDD have high correlation coefficients, the variables in the models were not statistically significant and therefore those variables were excluded in the model specification. That disagrees with Dixon et al. (1994) since the solar radiation variable in their model specification is 17 essential. Precipitation is quadratically related with yield; however, temperature has a linear relation with yield. Thus, the yield response model used linear and quadratic terms of precipitation and a linear term for temperature (see appendix figures 1 and 2). On the other hand, in the quality response model there is no evidence that weather variables have a nonlinear relation with quality. Therefore, the quality response model used a linear specification. Meanwhile, the study considered several alternative functional forms such as parametric methods: linear, CobbDouglas, translog, square root, spline, and semiparametric method which do not assume a specific functional form. CobbDouglas and linear model estimates showed not only statistically significant individual coefficients, but also relatively high pseudo R2 (variance ratio) between in sample annual predicted yield and annual actual yield during 19942009, therefore, we selected linear form and CobbDouglas form for yield response model, meanwhile, the quality response model adopted a linear form. The models have the same individual fixed effect and random effect; the functional form can be written as5 and also can be expressed as spatial lag model form using spatial lag term: 5 Linear form equation (3) and CobbDouglas form equation (4) can be represented as matrices and vectors: and , and be also rewritten in expected mean form as and respectively. Therefore, when we compare predictions (expected values) between two functional forms accurately, these mean forms are carefully considered. 18 where is the wheat yield of county i and time t, are individual fixed effects for counties, are the weather variables, and is a N × N spatial weights for crosssectional dimension, is a stochastic error term, is year random effect, and these error terms are assumed to be independent and identically distributed. The yield response model is composed of county fixed effect, year random effect, and three weather variables from February to April such as monthly average rainfall, squared average rainfall, and average temperature that correspond to before and after the anthesis period in Oklahoma because yield is mostly determined before the grain filling stage. As discussed, wheat quality depends on the growth periods such as milk development, heading, and ripening stages. In Oklahoma the wheat growth stages during March to May or June in the northern region contribute to grain filling which relates strongly to wheat quality. Additionally, the quality model employed agronomic tradeoff relationship between yield and quality of wheat using the predicted yield level from yield response model and can be expressed as where is composed of either protein content (12 % mb: moisture base) and test weight (lb/bu), and is a N × N spatial weights for crosssectional dimension and time t since the number of elevators vary by year, therefore weight structure also varies from year to year, for protein; weather variables are monthly average maximum and the monthly average rainfall from March to May, for 19 test weight; weather variables used in this model included monthly average rainfall for March, April, and May and maximum and minimum temperatures for April and May were based on the heading and ripening period such as before and after anthesis stage. Estimation method and procedure The study first tests spatial autocorrelation using proc VARIOGRAM in SAS (SAS Institute Inc. 2004). The most generally used test for spatial autocorrelation is Moran‟s I test6 (Griffith, 1987). Proc VARIOGRAM is used to calculate the Moran's I statistic, Z score, and pvalue for testing the hypothesis of no spatial autocorrelation. The study second adopts maximum likelihood estimation method (Greene, 2008, p. 400) and tests the heteroskedasticity and nonnormality of residuals using a likelihood ratio test, and Shapiro–Wilk test. If hereroskedasticity is formed in the wheat response models‟ error terms, multiplicative heteroskedasticity7 will be assumed (Greene, 2008, p. 170). If nonnormality is formed, the GMM or alternative estimation ways which do not require specific distribution, or a transformation method can be used to modify. If the dependent variable values are correlated with values of nearby locations based on the Moran‟s I statistic results, the models will include the weighted dependent variable of equation (2) and be estimated using instrumental variables (see appendix 1). Using proc IML in SAS (SAS Institute Inc. 2004) spatial weights matrix for first ( ) and second order ( ) are constructed based on inverse distance between two observations and where inverse distance matrices: = up to cut off miles, otherwise 0. At that time, GeoDa software (Luc Anselin, 2004) was 6 Moran’s I statistic is where, is a vector of dependent values for each time period , is a spatial weights matrix, N is observations, and S is the aggregation of all elements in . In general, a Moran's I statistic positive and large near one indicates positive autocorrelation while that is negative near one indicates negative autocorrelation (ESRI 2006). 7 If residuals are heteroskedastic, residual term ( ) can be expressed as general multiplicative heteroskedasticity form: or where and are a vector of parameters and the matrix of independent variables. 20 used to measure Arc distances among observations for yield and cut off distance using the Oklahoma counties is 49.6 miles. For quality observations, cut off distances vary over every year since the number of elevators differs by year, and therefore actual distances were used. In addition, the developed models need to be evaluated for accuracy using outofsample forecasting test rather than only a fitness test using historical data. Since the models were selected by pretesting, in sample tests will overestimate their accuracy. To test the outofsample forecasting power for the developed models, the yield and quality forecasts will be evaluated for 2010 out of sample. Also the forecasts will benchmark against previous actual six year average. These tests are truly outof sample since the models were developed before the 2010 harvest. RMSE, MAE, and Theil‟s U1 coefficient8 as measures of forecasting accuracy for all developed models were used to evaluate the forecasting performance of the models. The first two forecast error statistics (RMSE and MAE) depend on the scale of the dependent variable as relative measures. The Theil coefficient is scale invariant and always lies between zero and one, that is, zero means a perfect fit (Eviews 2000). Finally, in order to measure how the weather in the period immediately before harvest impacts yield and quality, the study conducts additionally the out of sample fit test using the longer period of weather data for the additional month of weather data on the estimates. 8 = where and are the prediction value and the corresponding actual value of county i respectively (Eviews, 2000, p. 337). 21 Figure 4. The Prediction Procedure for Yield and Quality Models 22 Empirical Results The study first tested spatial autocorrelation for dependent variables. Table 2 shows a strong spatial lag effect with a Moran‟s I statistic of 0.0078 for yield and 0.0254 for protein with pvalues of 0.0001. For test weight data, however, the pvalue is 0.2642, indicating the null hypothesis no spatial lag effect could not be rejected. Therefore, the study needed to employ the yield response models in (3.1) and (4.1) spatial yield response models, and the protein response models in (5.1) spatial protein response models. Table 2. Tests of No Spatial Autocorrelation for Wheat Yield, Protein, and Test Weight Moran's Index Expected Index SD zscore pvalue Yield 0.00784 *** 0.00091 0.000512 17.09 <.0001 Protein 0.02540 *** 0.00219 0.00106 26.03 <.0001 Test Weight 0.00101 0.00219 0.00106 1.12 0.2642 Note: *** significant at 1%, Ho: no spatial autocorrelation. The study second estimated equations (3) – (5.1) using SAS proc MIXED (SAS Institute Inc. 2004) and then the residuals of the estimated models were tested for heteroskedasticity and nonnormality (appendix table3). The test results showed linear yield models‟ LR statistics are smaller than the critical value at the 5% level ( ) that is, the null hypothesis of homoskedasticity was not rejected for linear yield models; while, the CobbDouglas yield models‟ calculated LR statistics were 19.1 for the general model and 16.1 for the spatial model, and thus the null hypothesis of homoskedasticity was rejected at the 5% level. On the other hand, all quality models‟ LR statistics were greater than critical value at the 5% level ( ). The null that residuals are homoskedastic was rejected, we assume multiplicative heteroskedasticity (see Greene, 2008 p. 523). Nonnormality tests showed we can reject the null of normality for all models 23 except test weight, the only linear yield model that did not have heteroskedasticity. As appendix table 3 shows, normality of residuals is still present after correction for heteroskedasticity9. Comparing Yield Response Models and Spatial Yield Response Models Table 3 shows the estimated yield response models and spatial yield response models. Log likelihood statistics were used to select the proper model and in this case (2 log likelihood), smaller is better. LR test was also used to test for spatial lag effect in the models. The null hypothesis of no spatial lag effect ( ) was rejected. The estimated coefficients indicate how weather variables affect wheat yield. The weather variables were all significant at a critical level of 5% for all yield models. Precipitation has a positive relation with yield; while, squared precipitation and temperature are negatively related to yield. Table 3. Yield Model and Spatial Yield Model Estimates, 19942009 Yield Response Spatial Yield Response Linear CobbDouglas Linear CobbDouglas Variable Coeff. pvalue Coeff. pvalue Coeff. pvalue Coeff. pvalue Intercept 98.621 <.0001 12.732 <.0001 68.097 0.0010 10.128 0.0003 Precipitation 0.569 <.0001 0.379 <.0001 0.299 0.0020 0.176 0.0135 Precipitation2 0.008 <.0001 0.049 <.0001 0.005 0.0003 0.026 0.0019 Temperature 1.610 <.0001 2.605 <.0001 1.363 <.0001 2.557 <.0001 Spatial lag 0.742 0.0002 0.843 <.0001 2 Log Likelihood 6496.2 696.8 6481.7 713.6 Note: A firstorder and secondorder spatial weight matrices were used as instruments for the spatial lag term as WX, W2X. 9 However, proc MIXED procedure does not provide for nonnormal residuals. Hence, in order to handle nonnormality and heteroskedasticity of residuals proc GLIMMIX procedure in SAS (SAS Institute Inc. 2004) was used. If the EMPIRICAL option (FIRORES) is specified, the procedure provides MacKinnon and White (1985)’s heteroscedasticityconsistent covariance matrix estimators (HCMM) to estimate standard errors. The GMM procedures in GLIMMX only give OLS parameter estimates and those are not consistent. We use proc MIXED and correct for heteroskedasticity to increase efficiency. Our standard errors are not adjusted for nonnormality, but that is of less concern here since our objective is forecasting. 24 Finally, spatial yield response model‟s log likelihood statistic indicated the accuracy of the yield response models could be significantly improved by adding the spatially lagged dependent variable (appendix table 4). To measure readily how weather variables affect yield, the elasticity for weather variables was calculated. Table 4 shows the estimated coefficients in CobbDouglas form are elasticities. Therefore, precipitation elasticity at mean precipitation is calculated as 0.067 to 0.116 for yield response models and 0.069 to 0.144 for spatial yield response models, that is, as the precipitation is increased by 1%, the average yield level would be expected to rise by 0.067% to 0.12% and 0.069 % to 0.144% in the yield response models and the spatial response models respectively. Temperature elasticity was measured as 2.6 to 2.74 in yield models, that is,1% rise in temperature decreases the average yield level by 2.6% to 2.74%, however, for spatial yield models, temperature elasticity was estimated as 2.32 to 2.55, so we cannot decide which variables have a greater effect on yield level of wheat because the units on the variables are arbitrary. Table 4. The Elasticity of Weather Variables Yield Response Spatial Yield Response Linear CobbDouglas Linear CobbDouglas Precipitation 0.116 0.067 0.144 0.069 Temperature 2.738 2.605 2.316 2.547 Table 5. Out of Sample Forecast Error Statistics for Yield Models, 2010 Average (20052009) Yield Response Spatial Yield Response Forecast Errors wo/weather effectsa Linear CobbDouglas Linear CobbDouglas RMSE 7.436 6.715 5.535 6.321 5.464 MAE 6.136 5.425 4.272 5.020 4.225 Theil U1 0.0081 0.00676 0.00584 0.00647 0.00577 Note: see appendix table 8 for comparing actual and predicted values. a: and are county fixed effect and random year effect for yield. Forecast error statistics for all yield models are summarized in table 5. The calculated statistics showed forecasts from the CobbDouglas form of spatial yield response model were slightly more accurate than yield response models. The linear model was slightly less accurate out of sample 25 just as it was in sample. The models for yield performed better relative to the benchmark 5 year average. Protein Response Model and Weight Response Model The estimated quality response models of equations (5) and (5.1) for wheat characteristics: protein and test weight level are reported in table 6. Yield and weather variables were all significant at the 5% level. Precipitation and maximum temperature positively affect protein and test weight. Minimum temperature is negatively related with test weight. High yield reduces protein, while, yield positively influenced test weight. These relationships between weather variables and wheat quality are consistent with the findings of Johansson and Svensson (1998) and Smith and Gooding (1999), who found warm temperature affects crude protein positively and precipitation at the end of the season has significant positive correlation with protein concentration. Table 6. Protein Model and Test Weight Model Estimates, 20042009 Protein (12%, mb) Test Weight (lb/bu) NoSpatial Spatial NoSpatial Variable Coeff. pvalue Coeff. pvalue Coeff. pvalue Intercept 2.986 0.0587 2.708 0.1417 35.075 0.0058 Yield 0.103 <.0001 0.096 <.0001 0.1152 <.0001 Precipitation 0.014 0.0006 0.017 0.0009 0.0533 0.0003 Max. temp. 0.149 <.0001 0.130 <.0001 0.4651 0.0001 Min. temp. 0.2922 0.0108 Spatial lag 0.138 0.3843 2 Log Likelihood 1045.5 1019.1 1482.9 Note: A first and secondorder spatial weight matrices were used as instruments for the spatial lag term as WX, W2X. Temperature positively influences test weight and rainfall also is positively associated with test weight. Even though the spatial lag term was not significant using a Wald test, the more reliable likelihood ratio test does reject the null hypothesis of no spatial lag. The estimated results express the tradeoffs between quality of wheat and yield using the calculated elasticity (appendix figure13). The elasticity is similar to Dahl and Wilson (1997)‟s trade26 off coefficients, which take the derivative with respect to protein and then multiply by average yields10. It indicates how much protein levels affect yield, while, this study focuses on how yield affects quality levels. In other words, yield elasticity indicates that increases in yield lead to lower protein levels and higher test weight. Table 7 shows a 1% rise in yield decreases average protein by 0.25% and increases average test weight by 0.28%. Precipitation affects protein and test weight, however, maximum and minimum temperatures have a stronger influence on quality levels. Meanwhile, the spatial protein model is more sensitive to weather conditions than the no spatial protein model. Additionally, the study treated crop year as a random effect and the counties as fixed effects and the estimated results showed specific region or crop year of wheat also affects the quality level (appendix table 5). Table 7. The Elasticity of Weather Variables for Quality Model Protein response Test Weight Response NoSpatial Spatial NoSpatial Yield 0.247 0.266 0.275 Precipitation 0.039 0.052 0.144 Max. Temperature 0.924 0.940 2.747 Min. Temperature 1.434 Forecasting accuracy of the quality models was evaluated over the 2010 crop year. Table 8 shows the forecast error statistics with protein and test weight response models. Firstly, the study estimated the general quality models using predicted yield from yield response models. Secondly, the spatial quality models were estimated by using predicted yields. The forecast error values indicate that the accuracy of the quality models can be improved by adding predicted yield from the spatial protein response model rather than that of the no spatial protein response model. Also RMSE values showed that the forecasting performance of the models combining spatially predicted yield were improved. Additionally, average values (20042009) were used as benchmark forecasts and as expected, all forecast error values for average values were higher than those of the weather models. The models 10 The relationship between protein and yield was estimated using , and tradeoff coefficients = (Dahl and Wilson, 1997). 27 for protein performed better relative to the benchmark six year average than did the test weight models. In addition, the accuracy of the quality models was compared using the actual and predicted values. The forecasting values spatially predicted were closer to actual values, the results consists with that of table 8 (See appendix table 9) . Table 8. Out of Sample Forecast Error Statistics of Wheat Quality, 2010 Average (20042009) 2010 NoSpatial Spatial wo/weather effects W/ spatially predicted yield W/ generally predicted yield W/ spatially predicted yield W/ generally predicted yield Protein RMSE 1.080 0.727 0.731 0.702 0.717 MAE 0.870 0.588 0.594 0.582 0.583 Theil U1 0.0074 0.00530 0.00530 0.005135 0.005197 Test Weight RMSE 1.495 1.305 1.361 MAE 1.196 1.117 1.174 Theil U1 0.00041 0.000357 0.000372 Note: see appendix table 8 for comparing actual and predicted values. Implications of the Value of Additional Month of Weather Data on Estimates Including late growing season weather data in a forecast model is less desirable from a decision maker stand poing because the forecast are not available with enough lead time to make logistical and marketing decisions prior to harvest. Expanding the data series to include late season weather information does provide insights into how the weather conditions immediately prior to harvest impact yield and quality. In the case of yield model, the study calculated additionally out of sample fit test using the longer period of weather data for the additional month of weather data on the estimates. The extended weather data (FebMay) were used to estimate new estimates and predicted yields using the new estimates (see appendix table 10). Contrary to expectations, the forecast errors reported in table 9 were larger than those of the original yield models (FebApril) (compare with table 5). A likely explanation is that late season weather conditions such as rainfall and temperature have 28 different effects relative to earlier in the growing season. For example, higher temperatures early in the growing season may promote growth while excessive temperatures late in the growing season may interfere with grain development. The development of forecasting models incorporating early season and late season weather information as separate variables is an opportunity for further research. Table 9. Out of Sample Fit Test using the Longer Period (FebMay) for Yield Models Average (20052009) Yield Response Spatial Yield Response Forecast Errors wo/weather effects Linear CobbDouglas Linear CobbDouglas RMSE 7.436 7.776 6.831 6.762 6.557 MAE 6.136 6.205 5.400 5.357 5.124 Theil U1 0.0081 0.00759 0.00686 0.00679 0.00665 Note: see table 5 for comparison. The impact of late season weather on wheat quality was also examined by the out of sample fit test using the shorter period of weather data (MarchApril) with a longer period (MarchMay). It should be noted that the (MarchMay) weather data was used in the original quality estimates, so it this case the original estimates are being compared with estimated generated with a shorter period of weather data Forecast error statistics for new quality model (MarchApril) are summarized in table 10. The calculated statistics shows there is no significant difference between the original quality model and the new quality model; however new forecasts were slightly less accurate than original quality response models. Therefore, these results point out the weather in the period immediately before harvest have slight impacts on quality levels. Table 10. Out of Sample Fit Test using Shorter Period (Mar.April) for Quality Models Average (20042009) (MarchMay) (MarchApril) wo/weather effects Original Shorter Protein RMSE 1.080 0.727 0.736 MAE 0.870 0.588 0.616 Test Weight RMSE 1.495 1.305 1.411 MAE 1.196 1.117 1.184 Note: Original indicates nospatial quality model and obtained from table 8, and shorter represents nospatial quality model using shorter weather data (FebApril), respectively. 29 Summary and Conclusions The study estimated wheat regression models to account for the effect of weather on wheat yield, protein, and test weight and to forecast wheat yield and the two wheat quality measures. The explanatory variables included precipitation and temperature for growing periods that correspond to biological wheat development stages. The models included county fixed effects, crop year random effects, and a spatial lag effect. Yield and quality level are strongly influenced by weather variables. For yield, precipitation has a positive relation with yield, while, precipitation squared and temperature are negatively related to yield. Precipitation and maximum temperature positively affect protein and test weight. Minimum temperature is negatively related with test weight. Yield affects negatively protein level, while, yield positively influenced test weight. In the forecast evaluation, the forecasting ability of both yield and protein models was enhanced by adding the spatial lag effect. Out of sample forecasting tests showed the developed models are more accurate than using a benchmark sixyear average. The study results or prediction information could be widely used and could be particularly important to producers optimizing late season agronomic and marketing decisions and to grain elevators and agribusiness for contracts or purchasing decisions. For examples, if the value of protein information to eliminate the reference to late application of fertilizer could be predicted early and accurately, the value are very useful. A good alternative rationale for value is that an agribusiness or producer might contract wheat and/or prepare shipping contingent on meeting minimum protein levels. The model prediction could help them anticipate not being able to meet the required protein levels and cancel the contracts and transportation and/or identify alternative markets. Limitations of the study could be summarized as follows. The study used just two weather variables information as rainfall and temperature for prediction because it is easier to interpret and 30 describe the impact of weather on yield and quality in a simple model. More complex models including interaction between weather variables might have the potential to increase forecast accuracy. The models examined also did not include measures for extreme weather events (example a late season freeze) that, while occurring infrequently, are known to have major impacts on quality and yield. There is also an obvious opportunity to expand this research by including a longer time series of wheat quality data as that data becomes available. A longer data series might make it possible to predict other important quality variables such as flour falling number or milling yield. An expanded time series might also make it possible to forecast additional quality variables and improve the forecast accuracy of the existing yield and quality models. A longer data series would also make it possible to conduct additional out of sample tests and to investigate the impact of trend and technology factors. 31 Appendix 1. The Estimation Procedures of Spatial Lag Model Anselin and Bera (1998) point out that with spatial data, the dependent variable may be influenced by spatially lagged dependent variables ( in the other locations. The spatially lagged term is also not only correlated with the same location‟s error term, but also the other locations‟ error terms. The consequence is violation of the assumption that error terms are assumed to be independent and identically distributed, therefore the OLS estimates of a spatial lag model will be biased and inconsistent (Land and Deane, 1992). Instead of OLS estimation, alternative estimation methods are needed to estimate consistent estimators. Equation (2) can be represented as a reduced form; a function of explanatory variables and error terms at all locations by using an inverse matrix11 under general assumptions, is independent of , and , therefore (A1) is rewritten in conditional mean form as and, specifically (A2) can be written as = = … and then (A1)  (A3) was used to empirically estimate (2), Anselin (1988), Land and Deane (1992), and Kelejian and Robinson (1993) suggested instrumental variables approach to estimation and the study selected Kelejian and Robinson (1993)‟s instrumental variables and twostage least squares estimation (2SLS) approach. Hence, equation (2) can be rewritten as 11 Inverse matrix can be expanded as = (1 + ) 32 where and , , and is a twostage least squares estimator and those can be expressed using (A2) and (A3) as and specifically (A5) can be rewritten as = = … where , are instrumental variables, and thus the 2SLS estimator ( is expressed as = where , indicating = and as a matrix of instruments, and then a matrix of fitted values can be rewritten as and also can be expressed as = . In addition, the variancecovariance matrix is where is residual variance and can be estimated from , thus, we can obtain consistent estimates and standard errors of spatial lag model. In summary, since OLS estimation of a spatial lag model leads to biased and inconsistent estimators, as the alternative method, 2SLS estimation was adopted here and empirically the procedures are as follows. In the first stage, regress equation (A5)‟s the right hand side spatially lagged dependent variable on all instrumental variables , which are a firstorder and secondorder spatial weight matrices were used as instruments for the spatial lag terms and draw out the estimated of 33 equation (A6), in other words, is obtained from that regress on and then in the second stage, replace in equation (2) with the estimated in the first stage, then rewrite (2) as and finally, regress (A9) on and and then obtain the 2SLS estimator ( of (A7) and (A8). The estimators is consistent and uncorrelated with error term ( and independent variables ( ). 34 Appendix 2. The Calculation Procedures of Elasticity of Weather Variables As is well known, the elasticity of dependent variable ( ) with respect to independent variables ( ) is equal to the slope value of the first derivative of dependent variable with respect to the independent variable (d /d ) multiplied by the means of ( ) and the elasticity of equation(1) can be written as and using equation (A1), the elasticity of equation (2) spatial lag model can be defined as and is similar to including long run coefficient in long run elasticity, on the other hand, in the CobbDouglas (CD) case12, (B1) and (B2) can be demonstrated by total differentiation: and in the spatial model, 12 For general CD form, , and for spatial CD form, 35 36 Appendix Table 1. Rsquared Estimated and Correlation Coefficients for Selecting Quality Variables Variables R Square a Observations Correlation coeffie. (Actual V.S. Prediction) Protein 0.622 415 0.789 Test weight 0.489 415 0.700 defect 0.228 412 0.480 Falling 0.318 334 0.566 Notes: a were obtained from equation (5) basis Appendix Table 2. Correlation Coefficients among Yield, Protein, Weight and Weather Variables Yield pvalue Protein pvalue Weight pvalue Yield 1.00 <.0001 0.47 <.0001 0.15 0.0019 Precipitation (in) February 0.49 <.0001 0.52 <.0001 0.06 0.1912 March 0.04 0.4098 0.20 <.0001 0.15 0.0014 April 0.05 0.3255 0.16 0.0005 0.08 0.1028 May 0.22 <.0001 0.09 0.0613 0.10 0.0406 Avg. temperature (˚F) February 0.43 <.0001 0.06 0.1734 0.05 0.2891 March 0.31 <.0001 0.02 0.6924 0.12 0.0094 April 0.42 <.0001 0.34 <.0001 0.20 <.0001 May 0.02 0.6899 0.00 0.9968 0.06 0.1994 Max. temperature (˚F) February 0.50 <.0001 0.29 <.0001 0.08 0.0815 March 0.35 <.0001 0.10 0.0396 0.07 0.1247 April 0.38 <.0001 0.45 <.0001 0.27 <.0001 May 0.19 <.0001 0.08 0.0742 0.13 0.0071 Min. temperature (˚F) February 0.14 0.0029 0.22 <.0001 0.13 0.0045 March 0.25 <.0001 0.11 0.0174 0.18 0.0001 April 0.35 <.0001 0.11 0.0171 0.10 0.0417 May 0.20 <.0001 0.16 0.0004 0.07 0.1368 Growing degree days February 0.55 <.0001 0.07 0.1295 0.12 0.0136 March 0.32 <.0001 0.01 0.8454 0.13 0.0069 April 0.39 <.0001 0.32 <.0001 0.22 <.0001 May 0.02 0.7532 0.06 0.1994 0.06 0.2246 Solar radiation (MJ m2d1) February 0.50 <.0001 0.35 <.0001 0.14 0.0027 March 0.51 <.0001 0.12 0.0129 0.13 0.0056 April 0.16 0.0013 0.22 <.0001 0.30 <.0001 May 0.40 <.0001 0.06 0.177 0.28 <.0001 37 Appendix Table 3. Diagnostic Test Statistics: Yield, Protein, and Test Weight Response Models Normality Normality Heteroskedasticity Method ShapiroWilk (1) ShapiroWilk (2) Likelihood ratio W pvalue W pvalue X2 Yield response modela Linear 0.9958 0.0047** 0.5** Cobb 0.9903 0.0001** 0.9884 0.0001** 19.1** Spatial yield response modela Linear 0.9965 0.0157* 0.1** Cobb 0.9895 0.0001** 0.9883 0.0001** 16.1** Quality response modelb Protein 0.9919 0.0231* 0.9890 0.0033** 27.7** Weight 0.9933 0.0614 0.9912 0.0150* 22.2** Spatial quality modelb Protein 0.9989 0.0030** 0.9856 0.0004** 26.6** Notes: *(*) significant at 1% ( 5%), critical value( =7.82) at the 5% level, critical value( =9.47) at the 5% level, and (1) and (2) indicate normality tests of standardized residuals before and after correction for heteroskedasticity, respectively. Appendix Table 4. Yield Model and Spatial Yield Model Estimates, 19942009 Yield Response Model Spatial Yield Response Model Linear CobbDouglas Linear CobbDouglas Variable F Value F Value F Value F Value Precipitation 79.26 43.94 14.48 20.97 Precipitation2 67.36 22.52 9.83 5.46 Average temperature 29.98 23.72 14.27 5.23 County fixed effect 3.8 3.41 3.71 3.25 Spatial lag 20.67 23.19 2 Log Likelihood 6496.2 696.8 6481.7 713.6 Notes: Values of precipitation variable was scaled by multiplying one hundred due to unit of rainfall. Appendix Table 5. Protein Model and Test Weight Model Estimates, 20042009 Protein Model Test Weight Model NoSpatial Spatial NoSpatial Variable F Value Pr > F F Value Pr > F F Value Pr > F Yield (bu/acre) 281.44 <.0001 110.94 <.0001 40.06 <.0001 Precipitation (in) 11.87 0.0006 11.25 0.0009 13.62 0.0003 Max. temperature (˚F) 101.61 <.0001 34.5 <.0001 15.28 0.0001 Min. temperature (˚F) 6.56 0.0108 County fixed effect 8.9 <.0001 7.25 <.0001 2.76 <.0001 Spatial lag 0.76 0.3843 2 Log Likelihood 1045.5 1019.1 1482.9 38 Appendix Table 6. Descriptive Statistics for Yield Model Variables, 19942009 Variable N Mean SD Minimum Maximum Year 1232 2002 4.61 1994 2009 Yield 1097 30.06 7.87 6.50 53.10 Precipitation(Feb.April) 1218 27.02 12.09 0.47 83.47 Avg. temp.(Feb.April) 1225 51.13 2.58 42.48 57.14 Precipitation2 1218 876.31 769.19 0.22 6966.68 Log yield 1097 3.36 0.29 1.87 3.97 Log precipitation 1218 3.16 0.59 0.76 4.42 Log Avg. temp. (Feb.April) 1225 3.93 0.05 3.75 4.05 Log precipitation2 1218 10.36 3.21 0.02 19.58 Appendix Table 7. Descriptive Statistics for Quality Model Variables, 20042009 Variable N Mean SD Minimum Maximum Year 457 2006.6 1.67 2004 2009 Longitude 457 98.72 1.32 102.50 94.80 Latitude 457 36.10 0.74 34.17 36.90 Protein 457 12.18 1.40 8.90 16.00 Test weight 453 59.79 1.96 52.80 64.60 Yield 421 29.45 7.80 6.50 46.00 Precipitation 454 27.40 13.54 3.40 65.97 Max. temp. (MarMay) 456 71.80 2.60 65.98 80.47 Min. temp. (MarMay) 456 46.27 3.36 35.68 55.43 Max. temp. (AprilMay) 456 75.81 3.52 69.05 85.88 Min. temp. (AprilMay) 456 50.41 3.10 39.78 59.53 Appendix Table 8. Comparing Actual and Prediction Values for Yield Models Actual Average Yield Response Spatial Yield Response Avg. (2010) (20052009) Linear CobbDouglas Linear CobbDouglas Yield(bu./acre) 31.6 27.3 33.9 32.3 33.3 32.3 Notes: 2010 actual value is weighted average based on production quantity basis. 39 Appendix Table 9. Comparing Actual and Prediction Values for Quality Models Protein (12% mb) Test weight (lb/bu) County No. 2010 Actual Value Average (20042009) Predict Value Spatial Predict Value 2010 Actual Value Average (20042009) Predict Value 2 11.9 12.6 11.7 11.5 60.1 60.0 59.2 4 12.6 14.1 13.3 13.5 61.5 59.5 59.1 6 12.2 11.7 11.3 11.3 62.7 60.2 60.5 8 11.3 13.1 11.5 11.2 61.8 58.9 60.1 9 11.1 12.2 10.3 10.3 61.2 60.5 62.5 13 12.4 13.5 12.8 12.5 61.8 60.0 58.9 17 12.1 12.0 11.4 11.3 60.0 60.1 60.6 20 11.4 12.1 11.6 11.0 62.7 60.2 61.5 22 11.5 10.4 10.0 10.0 60.0 58.2 60.3 23 12.2 12.2 12.1 11.9 60.4 58.5 58.7 24 12.3 11.9 11.2 11.3 59.2 59.5 59.3 27 12.2 11.8 11.7 11.6 59.6 59.1 58.5 28 11.8 13.7 12.1 12.0 62.2 61.0 61.2 29 11.2 12.1 12.4 12.5 63.3 60.8 62.1 30 11.9 13.1 12.2 12.0 60.2 59.7 58.7 33 11.6 12.6 12.3 12.1 61.7 61.6 60.9 38 11.5 11.9 11.4 11.2 62.2 60.0 60.6 42 11.5 12.0 11.6 11.6 60.2 59.4 59.4 44 12.0 12.1 11.4 11.4 60.0 59.4 59.7 52 12.3 12.2 11.6 11.6 57.2 58.6 57.9 70 11.7 13.2 12.6 12.3 61.0 59.9 60.2 71 11.6 12.6 11.6 11.5 60.9 61.2 61.2 75 10.0 12.7 11.4 10.9 62.2 60.4 61.3 76 12.5 11.8 11.5 11.5 60.6 60.4 59.6 77 11.8 12.1 11.7 11.4 59.3 59.0 58.9 Avg. 11.8 12.4 11.7 11.6 60.9 59.8 60.0 RMSE 1.080 0.727 0.702 1.495 1.305 MAE 0.870 0.588 0.582 1.196 1.117 40 Appendix Table 10. Yield Model and Spatial Yield Model Estimates using the Longer Period (FebMay), 19942009 Yield Response Spatial Yield Response Linear CobbDouglas Linear CobbDouglas Variable Coeff. pvalue Coeff. pvalue Coeff. pvalue Coeff. pvalue Intercept 129.340 <.0001 19.324 <.0001 65.138 0.0007 15.807 <.0001 Precipitation 0.540 <.0001 0.884 <.0001 0.140 0.0939 0.967 <.0001 Precipitation2 0.008 <.0001 0.131 <.0001 0.002 0.1412 0.149 <.0001 Temperature 2.049 <.0001 4.403 <.0001 1.535 <.0001 4.071 <.0001 Spatial lag 1.569 <.0001 0.632 0.0018 2 Log Likelihood 6445.4 683.6 6268.8 706.9 Note: A firstorder and secondorder spatial weight matrices were used as instruments for the spatial lag term as WX, W2X. Appendix Fig 1. Plot Yield and Precipitation Appendix Fig 2. Plot Yield and Avg. Temp. Appendix Fig 3. Plot Protein and Precipitation Appendix Fig 4. Plot Protein and Max. Temp. 41 Appendix Fig 5. Plot Protein and Yield Appendix Fig 6. Plot Test Weight and Precip. Appendix Fig 7. Plot Test Weight & Max.Temp. Appendix Fig 8. Plot Test Weight & Min.Temp. Appendix Fig 9. Plot Test Weight & Yield Appendix Fig 10. Plot Protein & Solar Radiation 42 Appendix Fig 11. Plot TestWeight & Solar Radi. Appendix Fig 12. Plot Yield & Solar Radi. Appendix fig. 13. Calculated Relationship between Yield and Protein and Test Weight Using Elasticity 43 CHAPTER II Improved Methods of Estimating Construction Costs of Agricultural Facilities Introduction A wide range of parties are interested in the costs of constructing agricultural facilities. Accurate prediction of costs of construction is very important to make decision for optimizing construction projects. Construction cost estimates are used in feasibility studies for agricultural projects, economic engineering analyses and decision tools assisting agricultural producers. Examples include estimating grain storage costs (Edwards, 2007; Uppal, 1997), grain storage rental (Hofstrand & Edwards, 2009), rental of other farm assets (Pershing & Atkinson, 1989). Agribusiness insurance companies, including farmerowned insurance cooperatives must estimate construction costs to price replacement cost insurance products. Agriculture specific construction cost information, particularly information formatted as easily updated indexes, would benefit agricultural economists and other researchers who are attempting to update and/or interpret previous studies involving building and infrastructure investments. The information would also allow agribusiness insurers to set actuarially efficient rates that would equitably reflect replacement costs. Several approaches have been used to estimate construction costs. Estimates or bids can be obtained from a representative set of vendors or firms that have recently completed projects. While this approach illustrates the variation in costs it is difficult to identify the sources of variation between projects. Moreover, unless the surveys are conducted on a regular basis, information from bids or 44 completed projects are difficult to update. Cost estimating software also can be used to estimate project cost, however, most of them support general construction and large projects or commercial systems available and therefore they are not suitable for agricultural industry or facilities. The bid/actual cost approach can be expanded by compiling and reporting cost of completed projects. The price indices of completed facilities reflect the price changes of construction output including all pertinent factors in the construction process. The building construction output indices compiled by Turner Construction Company and HandyWhitman Utilities are compiled in the U.S. Statistical Abstracts published each year. However this data does not provide prices of agricultural facilities. Even if a baseline price for an agricultural facility is known, price indices from completed construction projects may not accurately forecast the change in prices for an agricultural facility. An obvious example would be a steel grain bin where steel accounts for a much larger percentage of total material relative to most commercial buildings. If the bids or actual construction costs for a specific agricultural structure are obtained for one period in time, there are a number of approaches to updating historical construction cost information. These include the use of simple indexes and disaggregated indexes. The bestknown simple indexes of general price changes are the Gross Domestic Product (GDP) deflators compiled periodically by the U.S. Department of Commerce, and the consumer price index (CPI) compiled periodically by the U.S. Department of Labor. These broad gauges reflect overall changes in price levels may not accurately predict construction costs. Special price indices related to construction are also collected by industry sources since some input factors for construction and the outputs from construction may disproportionately outpace or fall behind general price indices. Examples of special price indices for construction input factors are the wholesale Building Material Price and Building Trades Union Wages, both compiled by the U.S. Department of Labor. In addition, the construction cost index and the building cost index are reported periodically in the Engineering NewsRecord (ENR) Index. The ENR index does not consider a productivity factor and so tends to increase at a more rapid rate than 45 the other indices (Uppal, 1997). Other specialized indexes, such as the Marshall Smith index (MSI), which is published monthly in Process Engineering, have been developed. The MSI is an indicator of the price changes for installed industrial chemical equipment over time (Hendrickson, 1998). The accuracy of index of construction cost can be increased by using a less aggregated index. These indexes are constructed based on aggregating particular material price and labor cost indexes using projectspecific weighting factors, which are typically collected through an industry survey (Earl, 1977). The composition of materials, components, equipment, and labor factors varies widely across the indexes. A number of periodicals and reference manuals publish unit prices on construction items. The most common indexes are for major building materials (concrete, structural steel, drywall, etc) and labor categories. As the degree of disaggregation increases (reporting costs at the subcomponent level) the index is better able to capture differential inflationary impacts on process plant construction costs from various materials and types of machinery and equipment (Earl, 1977). However, the disaggregated index approach requires information on the weighting factors or list of submaterial and equipment for the specific type of construction project. These are typically generated through a process known as economic engineering. Economic engineering involves mathematical or computerbased representations of production processes in which engineering and economic information are combined (Ferrell, Kenkel, & Holcomb, 2010). Economic engineering uses engineering data to estimate facility, equipment, labor and utility requirements. The economic component of the model determines the fixed and variable costs associated with constructing and operating the facility (Criner & Jacobs, 1992). Flores et al. (1993) used an economic engineering approach to estimate costs associated with building and operating flour mills of different sizes while Dale and Tyner (2006) employed a detailed economic engineering approach to determine the cost of a dry mill ethanol plant. For warehouse building, many studies have focused on cost optimization of warehouse design and operation. Francis & White (1974) developed computer algorithms to minimize total cost and found optimum dimensions of a rectangular warehouse. Park & Webster (1989) employed 46 conversion factor to compute warehouse building costs with factor based on the base area of the building, height, and required number of pieces of material, equipment. Cormier & Kersey (1995) provided several conceptual warehouse layouts and demonstrated the economic feasibility of a proposed project. The construction costs of a grain bin can be used to illustrate how economic engineering would be applied to agribusiness construction projects. There is a need for research specific to grain bins. Unlike other agricultural storage facilities, grain bins construction need to determine bin configuration which might allow them the necessary storage capacity while staying within their horse power and electrical power limitations. Geometric formulas would be used to calculate the area of the sides, foundation and roof of a grain bin of a given capacity. Engineering formulas would then be used to determine the weight and force exerted by the grain on the floor and sidewall which would in turn identify the depth of the concrete foundation and the gauge of metal required on sidewall panels. Once the type and amount of materials needed have been determined, the cost can be estimated for each component. In some cases, a proxy for a subcomponent is used. For example, after the linear feet of grain spouting has been determined the cost might be estimated on a per foot basis or by the pounds of steel represented rather than on a price listing for a specific piece of spouting. Modeling the construction cost of agribusiness structures using an economic engineering approach coupled with disaggregated construction cost indices has several advantages over using bids or the actual cost of recently completed projects. The configuration of the structure and associated structure is explicitly defined and the cost differences for various scales, configurations or complements of equipment can be explored. Because the economic engineering model provides a list of materials and equipment or proxies thereof, the costs can be updated by obtaining current costs for the materials and subcomponents. Alternatively, the output from the economic engineering estimates can be grouped into categories and changes in cost for the project can be estimated by examining the inflation index for each particular category. The object of this study is to create and evaluate a model for estimating construction costs of agricultural storage facilities. 47 Conceptual Framework Various construction cost estimation approaches suggested to date (appendix 1). Collier (1984), Hendrickson(1998), Hollman (1997), Peters and Timmerhaus (1991), and numerous studies suggested a unit cost method which is one of the most common economic engineering approaches when the project can be disaggregated into specific elements level lists for cost estimation. According to the definition, in the unit cost method the construction process is separating into a number of steps. The quantity of material and labor is then estimated for each step and the unit for measuring the amount of material or labor is defined. For example the unit for site grading might be acre while the unit for wallboard might be square feet. The cost for each unit is then estimated. A unit cost method can employ previous cost experience and be assigned to each of the construction components as represented by the construction bill of quantities. Thus, the total cost is the summation of the required quantities (material, labor, and equipment) multiplied by the corresponding unit costs. Therefore this method requires detailed estimates of purchase price obtained either from quotations or published data. The unit cost method can also be applied to engineering employee hours and materials quantities, equipment cost based on the drawings and specification. Unit cost can be based on recent project job specifications, where the material required can be determined and therefore the material unit cost matches the specifications. Hence, this method can be coupled with disaggregated construction cost from general cost information and recently completed projects. The costs can be updated by obtaining current cost information for the material unit cost and labor unit cost. Construction cost estimation is a very difficult task with substantial yeartoyear variation in unit cost estimates and bid estimates due to regions and supplydemand factors. Previous studies have used various type equations to apply unit costs to material, labor, and equipment needs. The 48 equations provide the characteristics of construction project and also readily keep track of each element in the project. Generally a cost equation is composed of material quantities, labor and equipment needs terms that correspond to unit cost in project and plus O&P (Overhead and Profit)13. Hendrickson(1998) suggest general total cost equation can be expressed as: where is the total cost, n is the number of units, is the quantity of the element and is the corresponding unit cost. Since the equation is simple, the construction site, skilled labor, management of the procedure, contractor‟s fee, and contingency for the estimated unit cost ( ) require appropriate adjustment. Alternatively Peters and Timmerhaus (1991) suggest approximate correction for adjustment by using a construction correction factor. The correction factor is estimated from previously completed projects and the correction factor help that the estimated model costs are closer to real costs. Hence the equation can be expressed by employing the correction factor to equation (1): where is the construction correction factor. Other studies have developed multiple regression models to predict cost estimates for long term or short term construction. Hwang (2009) employed linear regression models to predict construction project cost using a construction cost index series. Walker et al. (1990) developed a mathematical cost model to predict the major components of cost and sub components of cost for a grain bin system. Regression analysis was also used to determine these components cost and the relationship between cost values and total volume of storage (diameter and height). The method 13 O&P for the installing contractor may range from 5% to 15% of the bare total cost excluding O&P (RS Means Co., 2005) 49 provides the statistical inference and model‟s performance ability. For instance, significance of variables using Wald test and indicate the accuracy of the predicted costs. Therefore, predicted costs are useful to determine the range category cost or gross unit costs or special material cost which are not readily available. A disadvantage of this method is that it is difficult to determine the sources of variation between periods since the estimates are calculated for a given across year and location. Moreover, information from bids or completed projects are difficult to update. The regression model approach is based on neoclassical production theory14 suggested by Hall (1998). At a general level, if there exists a relation between inputs and output, the function that can be represented as where is single valued, that is, for any unique combination of inputs x, these corresponds a unique level of output (Chambers, 1988). Thus production function for construction employs the linear and quadratic input variables owing to the correspondence of maintained hypothesis with held the above production theory assumption (see footnote 14). The functional form (3) can be expressed in the matrix form as where is the vector of independent variables, is which is a stochastic error term. In other words, the volume of output of a production function for construction is coupled with the various inputs of materials, labor, equipments level etc. Therefore, in order to minimize the 14 Y= f(x), where x is input variables; a) x >=0 and finite( nonnegative); b) f(x) is finite, nonnegative, single valued for all possible combination of x variables; c) f(x) is everywhere continuous and everywhere twice continuously differentiable; d) f(x) is subject to the “law of diminishing returns” ( Hall, 1998). 50 production cost for a specified level of output, proper a set of values for input factors such as diameter, height, width, length etc could be employed. Using the main two methods presented in this study, first, a unit cost method approach can be used to estimate construction costs. Second, regression equation approach will be employed to evaluate or measure the proposed economic engineering model‟s performance. Empirical model specification and procedure The construction costs of representative storage facilities are subdivided into major material and labor cost categories through review of detailed bid sheets and specific drawings. These subcategories are linked to specific data sets of published indexes of building materials, labor, and equipment rates. This required sorting across major or sub categories and detailed task elements for projects. As discussed, economic engineering approach is a mathematical representation of construction processes in which engineering and economic information are combined. Thus, this study used two group components (economic components and engineering components) basis to model and estimate costs associated with storage facilities of different sizes. The engineering component of the model used estimation of equipment, labor and materials requirements. The economic component of the model determined unit or fixed costs associated with constructing as follows. Economic Components: Grain Bin Cost of 77 separate components linked to reported prices in “RSMeans Building Construction Cost Data” Cost of aeration fan/motors for range of HP obtained from industry quotes Cost of elevator leg for range of height and bu/hr obtained from industry quotes 51 Cost of aeration duct and unloading system for range of sizes obtained from industry quotes on a per foot basis Engineering Components: Grain Bin Steel components and concrete determined by dimension and engineering requirements Capacity in cylinder based on diameter, height and pack factor which is function of grain and depth Height of cone based on angle of repose= f(grain type) Volume in cone = f(height of cone, diameter) Sidewall, floor and roof area = f(dimensions) Force on sidewall and foundation = f(grain weight and grain type) Gage/thickness of sidewall and floor= f(force) Aeration fan static pressure = f(grain, height, grain type and desired CFM/bu) Aeration fan HP = f(static pressure and total CFM delivered) Dimension of aeration ducts and unload trough based on bin dimension Cost multiplier = f(size factor= f(project capacity)) Economic Components: Warehouse Building Cost of 44 separate components linked to reported prices in “RSMeans Building Construction Cost Data” Cost of equipment, plumbing, heating, ventilating, air condition, and electrical installation as analyzed as percentage shares of total cost obtained from RSmeans database of completed projects. Engineering Components: Warehouse Building 52 Steel frame and siding and concrete determined by dimension and engineering requirements Capacity in warehouse based on width, length, and wall height Angle of repose for roof= f(engineering requirements) Floor, sidewall and roof area = f(dimensions) Force on stud, sidewall, frame, rafter, beam and foundation =f(dimension, wall height, and storage goods type in warehouse) Gage/thickness of stud, rafter, beam, frame, sidewall and floor=f(force) Electrical and Mechanical devices =f(dimension, storage goods type) Story height multiplier= f (wall height) Cost multiplier = f(size factor= f(project square foot)) As a specific economic engineering approach, a unit cost method was employed to predict project costs, the material, labor, equipment, and Q&P required were applied and therefore the these unit costs matches the drawings or specifications. Using (1) and (2) the cost equations can be modified as where is the total cost, n is the number of specific elements, is the material unit cost at specific element, is the material quantity of ith specific element, is the labor unit cost at specific element, is the labor required level for specific material, is the equipment unit cost for specific element, 53 is the equipment usage quantity of specific element, is the overhead and profit unit cost for specific element, is the specific element required level coupled with O&P, is cost multiplier based on size of facilities; one of correction factors15, and is story height multiplier based on height of warehouse; one of correction factors.16 The grain bin and warehouse building construction costs obtained from equation (5) can also be categorized as total cost (bare cost, including Q&P cost), major components cost, and cost per unit (bushel (bu), Square Foot (S.F.)) using presented unit cost method. For example, the grain bin system can be categorized as six main components as floor, wall, roof, fan& heating , auger& driver, and others (accessory) based on diameter, height, height of cone, and pack factor which is function of grain and depth. Warehouse building cost is composed of floor, wall, roof, electrical & mechanical, and office based on width, length, and wall height. Based on the above two group components basis and equation (5), the study developed “Economic Engineering Construction Cost Templates Model” spread sheet type model. The spread sheet is a two dimensional series of columns and rows with cells (see appendix figure 2, 3, and 4). The user can input the data, formulas, text, and functions which the most useful functions are VLOOKUP and MATCH function which is useful for semi automating unit cost spread sheet application. Especially, when a project is looking for an exact engineering component match based on unit cost value. The user just inputs detailed items as follows. In the case of the grain bin, the type of grain, diameter of bin Eave, height of bin aeration (none, 1/10 CFM/Bu, .25 CFM/Bu), angle 15 Cost multiplier: the larger grain bin & warehouse building will have the lower unit cost per bushel or square feet. This is mainly due to the decreasing contribution of the exterior walls plus the economy of scale usually achievable in larger buildings (R.S. Means, 2009) 16 Story height multiplier: wall height of warehouse building affect base cost for variation in average story height (14ft). Therefore, multipliers (0.882.84) multiply base cost by range of wall height (8ft80ft) respectively (State of Michigan Appraisers Manual, 2004) 54 of repose (23˚ 29˚), fan select (centrifugal, axial), heating system(yes, no), unloading system (yes, no), elevator leg (no, yes: height and Bu/min), sidewall stiffeners (yes, no), and current index (2009=100) are entered ( see also appendix figure 2). In the case of the warehouse building, the width (ft), length (ft), wall height (ft), overheaddoor (ea), HVAC electrical & mechanical (yes, no), office size (S.F.), current index (2009=100) are entered (see also appendix figure 3). In the case of the pole barn building, the width (ft), length (ft), wall height (ft), siding (yes, no), post spacing (O.C.), concrete floor (yes, no), and current index (2009=100) are entered (see also appendix figure 4). The Structure of Economic Engineering Construction Cost Templates Model As discussed previously, a unit cost method is the most common cost estimating economic engineering approach. Therefore, the construction costs were estimated by multiplying the disaggregated specific elements level lists by the corresponding unit prices. The next sections provide more detail on construction cost structure, assumption and methods used in the model. 1) Collection of a list of the components and cost data For grain bin, Floor, Wall, Roof, Fan & Heating, Auger & Driver, and Others (accessory) were categorized as major components based on diameter, height, height of cone, and pack factor. The warehouse building cost was divided into floor, wall, roof, HVAC (electrical & mechanical), and office components based on width, length, and wall height. The pole barn building was only divided into footing, wall, and roof. Table 1, 2, and 3 provide a list of used materials uses and unit, respectively. There are various items and sizes of components used in constructing bins and warehouse buildings. Most of them are available as disaggregated unit level. Some such as Auger & Drive and Fan & Heater components at grain bin facilities, and HVAC (Heating, Ventilating, and Air Conditioning) in warehouse building, and footing work in pole barn building are available as aggregated units. 55 Components Items Unit Unit Size Unit requirement by Size factors Source Floor FormsAnchor bolts ea Anchor bolts, Jtype, 1/2" diameter x 12" long 2 / bottom sheet R.S. Means formrod set Bolt, hex head, plain steel, 1/4" dia x 2" L, 2 / bottom sheet R.S. Means Forms in place L.F. Multiple use, to 6" high Perimeter of bin R.S. Means Reinforcing steel Ea Deformed, 2' long, #3 Floor area R.S. Means Concrete C.Y Slab on grade, 6" thick Diam. of bin R.S. Means Wall Stiffener L.F. 12ga ~ 18ga (2" flange) 2 / sheet R.S. Means stiffener_splice Ea 12ga ~ 18ga (15/8" flange) 2 / sheet R.S. Means Bolt & Nuts for fasten stiffener ea 5/16'' dia, 11/2''long 16 / sheet R.S. Means Bolt & Nuts for sheet ea 3/8'' dia, 1''long 30 / sheet R.S. Means Stiffener_anchor Bolt set ea Anchor bolts, Jtype, 1/2" diameter x 12" long 2 / bottom sheet R.S. Means Sheet S.F. 3''deep, galv, 20ga ~ 8ga 25 / sheet R.S. Means Rope chaulking L.F. 3/4" diam. 4.33 / sheet R.S. Means Roof Eave clip ea Clips to attach, 2"X2"X16ga 6 / top sheet R.S. Means Bolt & Nuts ea 3/8'' diam., 1''long 6 / top sheet R.S. Means Roof ring L.F. Steel pipe, 11/4'' dia 50% / perimeter of bin R.S. Means Roof ring bracket (bolts&nuts) ea Coupling rigid style 11/4"diam. 1 / top sheet R.S. Means Peak ring S.F. 71/2''deep, long span, 14ga 3.14*Diam.(20'')*deep(14") R.S. Means Roof hatch ea Gal. steel curb and cover 1 / bin R.S. Means Vents ea 1 per M.S.F, Maximum 0.5 / top sheet R.S. Means Roof Ladder Rung (cut) L.F. 8' high wall, 18 gax 4"24"O.C Eaveheight of bin R.S. Means Roof sheet S.F. 161/2''wide, standard finish, 24ga 3.14*.5*diam.* roof slope R.S. Means Accessory Door ea 24''x36'' 1 / bin R.S. Means Ladder V.L.F. Steel, 20'' wide, bolted w/cage Eave height Michigan Assessor's Manual V.L.F. Steel, 20'' wide, bolted WO/cage Eave height Michigan Assessor's Manual Auger & Drive Auger L.F. Auger 4" ~ 10" jet flow Diam. of bin AugerUSA drive( motor) ea Electric Motor 1/3 hp ~ 50 hp 3 phase Diam. of bin AugerUSA Speaders L.F. Auger and drive add $500 to $750 Diam. of bin Michigan Assessor's Manual Stirrators L.F. Auger and drive add $500 to $750 Diam. of bin Michigan Assessor's Manual Fan & Heater Fan ea Axial flow,# CFM, 1/2 HP ~ 10HP Diam. & eave height R.S. Means ea Centrifugal, # CFM, 1/2 HP ~ 10 HP Diam. & eave height R.S. Means Heater ea Unit heaters, 12 MBH ~ 404 MBH Diam. & eave height R.S. Means Note: L.F. (Linear Foot), S.F. (Square Foot), C.Y.(Cubic Yard), V.L.F.(Vertical Linear Foot) Table 1. List of the Components and Units for Grain Bin Facilities Cost Estimation 56 Components Items Unit Unit Size Unit requirement Source Floor Forms in place L.F. Multiple use, to 6" high Perimeter of floor R.S. Means Reinforcing steel Ea Deformed, 2' long, #3 Floor area R.S. Means Concrete in Place C.Y 6" thick Floor area R.S. Means wood block flooring S.F. End grain flooring, coated, 2" thick Floor area R.S. Means Wall Frameend wall Lower studs L.F. 2 X 6 stud 16" O.C. #' high steel 1/16" R.S. Means Frameend wall upper studs (back) L.F. 2 X 6 stud 16" O.C. #' high steel 1/16" R.S. Means Frameend wallupper studs (front) L.F. 2 X 6 stud 16" O.C. #' high steel 1/16" R.S. Means plate L.F. 2 X 6 stud 16" O.C. #' high steel Widedoor R.S. Means Door Lintel Ea 4 " X321" X 3", 1/4" thick, 9' long Door length R.S. Means Framing Anchors Ea 18 ga, 4 1/2" X 2 3/4" 2/stud R.S. Means Anchor Bolts Ea 3/4" diam X 12" long 1/stud R.S. Means Partition S.F. Metal studs 16" O.C., 35/8" wide 1/16" R.S. Means Sidinglining S.F. Corrugated. 0.019" thick painted, steel Lining area R.S. Means Siding S.F. Corrugated. 0.019" thick painted, steel Siding area R.S. Means Door S.F. Wood, 13/4" thick 12 X 12 Door/warehouse R.S. Means Roof Frameroof beam L.F. 18 ga X 6" deep beams 1 / 12' R.S. Means Rafters front L.F. 18 ga X 6" deep rafters, 2" Depend on repose R.S. Means Rafters back L.F. 18 ga X 6" deep rafters, 2" Depend on repose R.S. Means Framing joists (vertical) L.F. Joist, 2" flange 18ga X 6" deep 1/16" R.S. Means Framing joists (vertical) L.F. Joist, 2" flange 18ga X 6" deep 1/16" R.S. Means Framing joists (cross) L.F. Joist, 2" flange 12ga X 10" deep Wide level R.S. Means Fascia board L.F. 2" X 8" Length level R.S. Means Steel roofing panel S.F. Zinc aluminum alloy finish 22 ga Roof area R.S. Means Purins L.F. 2 X 4, 2' O.C. Length & rafter length R.S. Means Office Frame studs L.F. 2" x 6" studs, 16" O.C., 8' high 4/office R.S. Means Framing Anchors Ea 18 gauge, 41/2" x 23/4" 2/stud R.S. Means Anchor Bolts Ea Anchor bolt, Jtype, 3/4" dia x 12" L 1/stud R.S. Means Concrete block S.F. 8" X16" units. 4" thick Siding area R.S. Means Drywall (finished) S.F. 3/8" thick, on walls, standard Siding area R.S. Means Siding S.F. Corrugated. 0.019" thick painted, steel Office area R.S. Means Window Ea 2'0" x 3'0" high 1/office R.S. Means Door frame Ea Metal, 16 ga., deep, 6'8" h x 3'0" w 1/office R.S. Means Door Ea Steel, 2'8" x 6'8" 1/office R.S. Means HVAC Warehouse w/o or w office % Equipment 1.3%~2.0 %/ total cost R.S. Means Mechanical & electrical % Plumbing 5.2%~5.3 %/ total cost R.S. Means % Heating, ventilating, air condition 5.5 %~6.2%/ total cost R.S. Means % Electrical 7.9 %~8.8%/ total cost R.S. Means Note: Class S of warehouse represents steel frame, siding, providing heating and cooling system, interior finish and floor, good office, good lighting and adequate plumbing, etc. Table 2. List of the Components and Units for Warehouse Building Cost Estimation (Class S) 57 Components Items Unit Unit size Unit requirement Source Footing Post footing Ea 12" diameter incl. excav, backfill, tube 1/post(pole) R.S. Means Concrete for floor C.Y Slab on grade 4'' thick, incl. forms & reinforcing steel Area R.S. Means Wall FramePost (pole) L.F. 6" X 6" Framing , colums for wood post Post No. based on post spacing O.C. R.S. Means Wall girts L.F. 2" X 4", 2' O.C. pneumatic nailed Wall area and siding R.S. Means Skirt board L.F. 2" X 6", pneumatic nailed Perimeter R.S. Means Siding S.F. Corrugated. 0.019" thick painted, steel Siding area (three siding) except front siding R.S. Means On wood framing S.F. For siding on wood frame, deduct from above siding cost Deduct on wood frame R.S. Means Roof Frameroof beam L.F. 2 X 8 single wood, pneumatic nailed Height/12 R.S. Means Rafters right L.F. 2" X 6" wood Depend on repose R.S. Means Rafters left L.F. 2" X 6" wood Depend on repose R.S. Means Collar Beam Tie L.F. 2" X 4", 2' O.C. Half of truss span R.S. Means Ceiling joists (cross) L.F. 4" X 6" wood joist Wide level R.S. Means Ridge board L.F. 2" X 6" wood 1/warehouse's length R.S. Means Purins L.F. 2" X 4", 2' O.C. Rafter length & length R.S. Means End studs L.F. 2" X 6" stud 16" O.C. # wood 1/16" R.S. Means Roofing panel steel S.F. Corrugated. 0.0155" thick, steel Roof area R.S. Means On wood framing S.F. For roof on wood frame, deduct from above roof siding cost Roof area R.S. Means Table 3. List of the Components and Units for Pole Barn Cost Estimation (Class Dpole) 58 2) The requirements of each components aspect Based on the appropriate drawings and engineering charts obtained from industry quotes and building manuals etc., the requirements for specific components were determined as follows. A. Grain bin i. Floor (concrete foundation) : Grain bin Using slab on ground construction basis, floor work is composed of foundation forms, reinforcement in place, placing concrete and placing anchor bolt. Concrete thickness and reinforcement bar and the amount of concrete uses were estimated or determined across bin diameter sizes (1 cubic foot= 0.037 cubic yard). Also, diameter sizes were used in determining the number of sheets (2.66” corrugation) per ring as diameter † 3. The number of sheets per ring and diameter size was also used to determine the number of anchor bolts requirements. From table 5, Floor components of requirement could be estimated as (1) FormsAnchor bolts = diameter ÷ 3 × 2 = # ea * diameter ÷ 3 = sheet # per ring (2) formrod = diameter ÷ 3 × 2 = # set (3) Forms in place = perimeter of bin = # L.F. (4) Reinforcing steel = floor area of bin × 1 = # ea (5) Concrete = floor area of bin (S.F.) × thickness (') of floor×0.037 = # C.Y.. ii. Wall (sidewall sheet) : Grain bin Based on force basis by bin eave height (or ring) and diameter size, the various wall sheet gauges (8ga ~ 20ga) were selected by 2.66” standard bin sidewall gauges criterion. The thinnest gauge (20a) sheets should be assembled on the top ring of the bin, while the thickest gauge (8ga) sheets go on the bottom ring. The number of sheets required was calculated by diameter and eave height level. Optionally two stiffeners (splice) per every sheet were used and stiffeners gauge also were changed based on height of bin. From table 5, Wall components of requirement could be estimated as (6) Stiffener = diameter ÷ 3 × Ring # × 2.66 × 2 = # L.F. * ring # = eave height † 2.66” 59 (7) Stiffener_ Splice = diameter ÷ 3 × Ring # × 2 = # Ea (8) Bolt & Nuts for fasten stiffener = diameter ÷ 3 × Ring # × 16 = # Ea (9) Bolt & Nuts for sheet = diameter ÷ 3 × Ring # × 30 = # Ea (10) Stiffeneranchor Bolt set = diameter ÷ 3 × 2 = # Ea (11) Sheet area = diameter ÷ 3 × Ring # × 25 = # S.F. (12) Rope chaulking = diameter ÷ 3 × Ring # × 4.33 = # S.F. * 4.33 is length of sheet iii. Roof : Grain bin Under the angle of repose (tangent °) basis by grain type, roof erecting work was divided into roof sheet, peak ring assembling, and roof accessory (roof ring, ladder rung, vent, hatch, etc.). Roof sheet required area was calculated by area of cone (pi × radius × side) and optionally slope of roof was changed by angle of repose (tangent °). From table 5, Roof components of requirement could be estimated as (13) Eave clip = diameter ÷ 3 × 6 = # Ea * 6 required per top sheets (14) Bolt & Nuts = diameter ÷ 3 × 6 = # Ea * 6 required per top sheets (15) Roof ring = 50 % of perimeter of bin = # L.F. (16) Roof ring bracket (bolts& nuts) = diameter ÷ 3 × 1= # Ea (17) Peak ring = diameter 20” and deep 14” ring = # S.F. (18) Roof hatch = one of each bin = # Ea (19) Vents = diameter ÷ 3 × 0.5 = # Ea. * 1 required per 2 top sheets (20) Roof Ladder Rung = Eaveheight of bin = # L.F. * 4.33 is length of sheet (21) Roof sheet = area of roof = # S.F.. iv. Others (Accessory) : Grain bin Based on eave height of bin basis, outside steel ladder (20'' wide) bolted with or without cage and standard metal door (24" x 36") was used for one per bin. From table 5, Others(Accessory) components of requirement could be estimated as (22) Door = one of each bin = # Ea (23) Ladder w/ cage =eave height = # V. L.F. (24) Ladder wo/ cage =eave height = # V. L.F. v. Auger & drive (Unloading system) : Grain bin Based on the diameter and capacity of bin basis, the simplest tube auger (horizontal angle (0°)) was used and auger capacity and horsepower requirements were determined by diameter and RPM (speed). For example on 496,692 (105' by 58' 8'') bushel capacity grain bin, the estimated 60 capacity and required motor size could be calculated as follows. Table 4 provides 12''diameter auger running at 300 rpm, conveys 4,520 bu/hr of grain and requires 2.5 hp per 10' of auger length. Hence, total horsepower can be calculated as Total HP = (diameter' ÷ 2) ÷ 10') × hp per 10' = (105'÷ 2) ÷10') × 2.5 hp/10' = 13.1 hp Table 4. Estimated Auger Capacity and Horsepower Requirements Bin Capacity (bu) Auger Diam.(') RPM (Speed) bu/hr hp/10' 5,000 4 900 560 0.6 50,000 6 600 1,500 1 100,000 8 450 2,210 1.4 300,000 10 360 3,300 2 500,000 12 300 4,520 2.5 750,000 14 260 6,230 3.4 1,000,000 16 225 8,040 4.4 Source: incline angle is 0° and the table was modified from MWPS13 (1988). From table 5, Auger & Drive components of requirement could be estimated as (25) Auger = auger base cost(4"~10") + add($13~$64) per diam(') = # L.F. (26) Drive (motor) = Select motor correspond to estimated auger horsepower = # Ea. (27) Spreaders = base $500 + add($500 to $930) per diam(')= # L.F. (28) Stirrators = base $130 + add($130 to $250) per diam(')= # L.F vi. Fan & Heater (Aeration system) : Grain bin Based on the airflow rate and static pressure level for aeration, the fan H.P. and heater specification were selected as follow. Aeration and heater cost are a significant aspect variable costs as well as construction cost. Fan selection was the process for determining fan H.P. First, airflow required (CFM) was calculated and then proper air static pressure was determined based on grain type and bin height. Airflow rate could be selected as either 0.1 CFM/Bu or 0.25 CFM/Bu. Finally fan horsepower was calculated as 61 Air Horsepower = (CFM × static pressure) / (6,320 × fan efficiency)17. For example on 496,692 (105' by 58' 8'') bushel capacity bin with airflow rate 0.1 CFM/Bu, the total airflow and static pressure could be calculated as 49,692 CFM, 7.4 inch, and fan efficiency was assumed as 65% and then Air Horsepower = (49,692× 7.4) / (6,320 × 0.65) = 89.5. Hence the estimated air horsepower is 89.5 hp and the model selects one of two fan types optionally and heaters needs that correspond to this hp. From table 5, Fan & Heater components of requirement could be estimated as (29) Fan (Axial) = Select fan correspond to estimated fan horsepower = # Ea. (30) Fan (Centrifugal) = Select fan correspond to estimated fan horsepower = # Ea. (31) Heater = Select fan correspond to estimated fan horsepower = # Ea.. B. Warehouse building (Class S) i. Floor (concrete foundation) : Warehouse building Warehouse foundation floor were composed of structural concrete and slab on grade with 6" thick and included reinforcing steel. Also foundation walls employed 8" thick concrete and reinforcing steel. The amount of foundation concrete was calculated as the sum of foundation floor and foundation walls area. From table 6, Floor components of requirement could be estimated as (1) Forms in place = Width × 2 + Length × 2 = # L.F *Perimeter of floor (2) Reinforcing steel = floor area × 1 = # Ea (3) Concrete = floor area (S.F.) × thickness (') of floor×0.037 = # C.Y. (4) Wood block flooring = floor area = # S.F. 17Source: http://www.ag.ndsu.edu/pubs/plantsci/smgrains/ae7013.htm#Fans and see tables in MWPS13 (1988). 62 ii. Wall (end & sidewall) : Warehouse building Wall frame structure was divided into end wall and inside (partition) wall. 2×6 Steel studs 16" O.C. was mainly used as upper & lower studs. The amount of studs required was calculated based on the slope of rafters and inside wall spacing (12'). To tie studs and foundation wall, 2 framing anchors per stud was used and wall height, wide and length size of building were used to determine total amount of siding panel requirement. The number of overhead door and wall height level could be inputted as options. From table 6, Wall components of requirement could be estimated as (5) Frameend wall Lower studs = Wide ÷ spacing (16”) × 2 wall side = # L.F (6) Frameend wall upper studs (left) = the summation of left rafter support studs = # L.F. (7) Frameend wall upper studs (right)=the sum of right rafter support studs= # L.F. (8) Plate = two plates in front and behind of building = # L.F. (9) Door Lintel= Door length × # door = # Ea (10) Framing Anchors = 2 Ea required per stud 16" O.C. = # Ea (11) Anchor Bolts = 1 Ea required per stud 16" O.C. = # Ea (12) Partition = the summation of Area of partitions = # S.F. (13) Sidinglining = the area of sidinglining for front & behind lining = # S.F. (14) Siding = total wall area = # S.F. (15) Door = option = # Ea.. iii. Roof : Warehouse building Based on rafter slope basis, roofing frame work was divided into rafter erecting, frame joists, purins, and roofing panel. Roofing panel (truss span) required area was estimated based on rafter slope degree and length of building. From table 6, Roof components of requirement could be estimated as (16) Frameroof beam = the summation of beam length = # L.F (17) Rafters right side = the summation of the rafter side length O.C.12‟ = # L.F. (18) Rafters left side = the summation of the rafter side length O.C.12‟ = # L.F. (19) Framing joists (verticalR) = the sum of the joist right side length O.C.16” = # L.F. (20) Framing joists (verticalL) = the sum of the joist left side length O.C.16” = # L.F. (21) Framing joists (cross) = the summof the joist cross length based on width = # L.F. (22) Fascia board = 2 board required based on the length = # L.F. (23) Steel roofing panel = Roof area = # S.F. (24) Purins = the summation of the required based on length and rafter length = # L.F. 63 iv. Office : Warehouse building Based on height of office and S.F area, the amount of siding panel, frame studs, concrete block, etc. were determined. From table 6, office components of requirement could be estimated as (25) Frame studs = the summation of stud length = # L.F (26) Framing Anchors = 2 required per stud = # Ea (27) Anchor Bolts = 1 required per stud = # Ea (28) Concrete block = area of office = # S.F. (29) Drywall = Siding area = # S.F. (30) Siding = side area for in& out side = # S.F. (31) Window = 1 per office = # Ea (32) Door = 1 per office = # Ea v. HVAC (Electrical & Mechanical system) : Warehouse building HVAC costs were categorized as equipment, plumbing, heating, ventilating, and air conditioning cost. Categorized component costs were obtained by multiplying the whole bare total costs of warehouse building by the ratio (%) of categorized components (see table 6). HAVC‟s Q&P was calculated by assuming 10% for the sum of the bare material cost since O&P for the installing contractor may range from 5% to 15% of the bare total cost. From table 6, HVAC components of requirement could not be estimated as quantity, so correspond costs could be calculated by multiply proper ratios as (33) Equipment = multiplying the bare total costs by the ratio (%) of equipment = # $ (34) Plumbing = multiplying the bare total costs by the ratio (%) of Plumbing = # $ (35) HVAC = multiplying the bare total costs by the ratio (%) of HVAC = # $ (36) Electrical = multiplying the bare total costs by the ratio (%) of electrical = # $ C. Pole barn building (Class Dpole) i. Footing (option concrete floor) : Pole barn Footings thickness is same as post thickness and footing width (diameter) is twice of post thickness. The circular concrete footings with 6" thick and 12" diameter were used. The number of footing was calculated based on the sum of posts required. Optionally, concrete floor were used as 64 slab on grade with 4" thick and included reinforcing steel. The amount of concrete floor was calculated based on barn area. From table 7, Footing components of requirement could be estimated as (1) Post footing = the summation of pole required footing = # Ea (2) Concrete for floor = Width ×Length× 0.037 = # C.Y. * 0.037: conversion for C. Y ii. Wall ( post (pole) wall ) : Pole barn According to size, post spacing & eave wall height, width and length users may need, the amount of materials used was determined. The number of post frame was calculated based on post spacing and length of barn. For example on 40'×80' (width × length), post spacing 8' pole barn, the calculated the number of post is 22 ea. Post # = 4+ Round (Length of Barn ÷ Post spacing length1) × 2 = 4 + (80' ÷ 8'1) × 2 = 22 The model allows pole barn cost to be estimated with or without siding. Siding work was divided into wall girts & skirt board, and siding panel. Siding panel area was calculated for three sides with the front assumed to be open. Wall girts (skirt board) work used wood plate which untreated 2"×4"(2"×6"), pneumatic nailed 2' O.C. From table 7, Wall components of requirement could be estimated as (3) FramePost = the summation of pole length required = # L.F. (4) Wall girts = the summation of the wood penal for wall area = # L.F. (5) Skirt board = 2sides length plus and 1 side width of barn = # L.F. (6) Siding = siding area (three siding) = # S.F. (7) On wood framing = deduction for wood frame from siding = # S.F 65 iii. Roof: Pole barn Based on rafter slope and width of barn, roofing material uses were rafters, ceiling joists, collar beam tie, purins, end studs and roofing panel. Roofing panel (truss span) required area was estimated based on rafter slope degree and length of building. The aluminum panels, corrugated with 0.0155.thick were used. For example on 40'×80' (width × length), angle 18° pole barn, based on the square of the length of the rafter (hypotenuse) equals the sum of the squares of the lengths of the two other sides (half of width & peak height minus wall height), the calculated length of rafter is 21.0 (L.F.) C = ((A)2 + (B) 2)^0.5 Length of rafter = (((TAN (18 × 3.14 ÷ 180) × (width ÷ 2)))2 + (width ÷ 2) 2)^0.5 = [(0.3249 × 20) 2 + (20) 2] ^ 0.5 = 21.029 From table 7, Roof components of requirement could be estimated as (8) Frameroof beam = the summation of beam length = # L.F (9) Rafters right side = the summation of the rafter side length O.C. #‟ = # L.F. (10) Rafters left side = the summation of the rafter side length O.C. #‟ = # L.F. (11) Collar beam tie = the summation of multiply the half of width with O.C. #‟ = # L.F. (12) Ceiling joists (cross) = pole(post) # × width = # L.F. (13) Ridge board = the length = # L.F. * 1 board required per building (14) Purins = the summation of the required based on length and rafter length = # L.F (15) End studs = the summation of left & right rafter support studs = # L.F. (16) Roofing panel steel = Roof area = # S.F. (17) On wood frami 



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