IRRIGATION WATER DEMAND: PRICE ELASTICITIES AND CLIMATIC DETERMINANTS IN THE GREAT LAKES REGION By Ari Kornelis A THESIS Submitted to Michigan State University In partial fulfillment of the requirements for the degree of Agricultural, Food, and Resource Economics Ð Master of Science 2018 ABSTRACT IRRIGATION WATER DEMAND: PRICE ELASTICITIES AND CLIMATIC DETERMINANTS IN THE GREAT LAKES REGION By Ari Kornelis Even in a water abundant context, the spatial and temporal concentration of irriga- tion withdrawals can create water scarcity. Many studies have explored irrigation managem ent behavior in the western U.S. Comparatively, t he determinants of irri- gation behavior in a water abundant context have not been extensively studied . This paper explores the environmental and market determinants of irrigation management in a five -state Great Lakes region. I find evidence that corn, soyb ean, and potato irrigators respond to the cost of water at the intensive margin. Evidence of a water -price effect at the extensive margin is mixed. Additionally, this study is unique in its consideration of the water -use effects from extreme heat and preci pitation varia- bility. I find important effects of long -run average temperature on crop acreage allo- cation decisions and short -run extreme heat events on water application rates . Though I do not find evidence of a water -use response to intra -seas onal precip itation variability , I present a number of precipitation variability and drought measures that might be considered in future research. iii ACKNOWLEDGEMENTS I would like to extend my deepest gratitude to the many individuals who have contributed to making this study possible. I would like to thank my advisor, Dr. Patricia Norris , for countless hours of support and guidance, and my committee members, Dr. Cloe Garnache and Dr . Joe Herriges , for their thoughtful comments and advice throughout the research process . Furthermore, I would like to thank MSU faculty members , Scott Swinton and Jeff Andresen , as well as staff specialists , Steve Miller and Ben Russell, for their suggestions and respective expertise which improved the quality of the thesis. Additionally, this work would not have succeeded without the resources and staff at the USDA National Agricultural Statistics Service . In particular, I owe thanks to Kif Hurlbut and Matthew Fetter. Finally, I would like to thank the many faculty members in the Department of Agricultural , Food , and Resource Economics from whom I have learned so much, Dr. Soren Anderson, Dr. Eric Crawfo rd, Dr. John Hoehn, Dr. Frank Lupi, Dr. Nicole Mason, and Dr. David Schweikhardt . iv TABLE OF CONTENTS LIST OF TABLES ..... .............................................................................. ............... vi LIST OF FIGURES ................................................................ .............. ................ viii CHAPTER 1: INTRODUCTION ...... ..................................................... ................. 1 1.1 Background and Motivation .................................................................... 1 1.2 Climate Context ......................... .............................................. ............... 3 1.3 Water Management Institutions in the States ......... ......... ........ .............. 4 1.4 The Great Lakes Compact ....................................... ............................... 5 1.5 Study Objective ..................................................................... .................. 7 CHAPTER 2: THEORETICAL FRAMEWORK ..................... ........................... .. 10 2.1 Approaches in the Literature ................................... .................... ....... .. 10 2.2 Econometric Approaches in the Literature ......... ................................. .. 11 2.3 Theoretical Mode l .............................. ...................... .............................. 13 2.4 Empirical Model ................................................................................. ... 15 CHAPTER 3: DATA AND HYPOTHESES .. .......................... .............................. 17 3.1 Data Overview ........................................................ .............................. 17 3.2 FRIS ......................................... ......................... ........... ..................... .....18 3.3 Dependent Variables ............................................................................ . 24 3.4 Measuring the Cost of Water ................................................ ..... ........... 30 3.5 Climate and Weather Data .................................... ................ ............... 37 3.6 Measur es of Precipitation Variability ..................... ................. .............. 39 3.7 NRCS Soils Data .................................................... .................. ............. 41 3.8 Crop Price Data ...................................................... .............................. 43 3.9 Addressing Measurement Error ................................................... .......... 44 3.10 Regress ion Weights ................................................ .............................. 49 CHAPTER 4: RESULTS ......................................................... .............................. 51 4.1 Water Application Estim ation ..................... .............. ............................. 51 4.2 Crop Allocation Estimation ..................................... .............................. 55 4.3 Irrigation Investment Estimation ............................................. ............. 61 4.4 Effect of Precipitation Variability ........................... .............................. 62 v CHAPTER 5: CONCLUSIONS ............................................... .............................. 64 5.1 Price Effects ............. ............................................................. ................64 5.2 Climate and Weather Effects .................................. ............................. .64 5.3 Limitations ........................................................... ... ............................ ..67 APPENDICES ....................................................................................................... 69 Appendix A Robustn ess c hecks ........................................................... ....... 70 Appendix B Investment model weather effects ...................................... ..... 72 Appendix C Precipitation variability m easures ................................. ........ 73 REFERENCES ........... ..... ............................................. ......................................... 74 vi LIST OF TABLES Table 3.1 Number of farms in study sample, by year, s tate, and crop irrigated .... 22 Table 3.2 Total irrigated acres in study sample by state , year, and crop ........ ...... 23 Table 3.3 Farm level descriptive statistics: water applied to corn (in/acre) .. ........ 24 Table 3.4 Farm level descriptive statistics: water applied to soybeans (in/acre) .. . 25 Table 3.5 Farm level descriptive statistics : water applied to potato es (in/ acre) . .. 25 Table 3.6 Farm level descriptive statistics: corn irrigate d harvested acres ............ 26 Table 3.7 Farm level descriptive statistics : soybean irrigated harvested acres .. .... 27 Table 3.8 Farm level descriptive statistics: potato irrig ated harvested acres ......... 27 Table 3.9 Sampled firms by crop(s) irrigated ................................................... ...... 29 Table 3.10 Capital investment for new expansion among sampled firms ............... 29 Table 3.11 Farm level descriptive statistics: cost of water ....... .............................. 35 Table 3.12 Water cost: v alues in the literature .................. ...... .............................. 36 Table 3.13 Cost of water: mean comparison by surface water use ...... ................... 36 Table 3.14 Crop price correlation matrix .......................................................... ..... 44 Table 3.15 Water application model: check for measurement error ........... ............ 47 Table 4.1 Summa ry of variables: water application m odels ................... ... ..... ........ 51 Table 4.2 Wate r a ppli cation variables: conditional descriptions ..... ................... .... 52 Table 4.3 Water application models : estimated c oefficients .................... ... ........... . 53 vii Table 4.4 Water a pplication: point elasticity e stimates ....................... ... ............... 54 Table 4.5 Short -run water cost elasticities in the literature ................................... 54 Table 4.6 Summary of variables: crop allocatio n m odels .......... ............................. 55 Table 4.7 Crop allocation variables: conditional descriptions ................................ 56 Table 4.8 Crop acreage allocation: tobit average partial effects ............. ....... ... ...... 57 Table 4.9 Cost of w ater: mean comparison by potato indicator .................. ....... ... 59 Table 4.10 Crop acreage allocation: linear regression wit h restricted samples........ 60 Table 4.1 1 Summary of variables: investment models ................................. .......... 61 Table 4.12 Capital investment for new expansion : tobit average partial effects .... 62 Table A.1 Fixed effect estimates: water application ... ........................................... . 70 Table A.2 Fixed eff ect estimates: crop acreage allocation....................................... 71 Table B.1 Irrigation capital investment: lagged weather effects .... ......................... 72 Table C.1 Precipitation variability measures: corn water -application effects ........ 73 viii LIST OF FIGURES Figure 1.1 Agricultural irrigation water use by state .................... ........... ..... ........... 8 Figure 3 .1 Sample frame: irrigated acres by state and y ear ............... .................... 20 Figure 3.2 Spatial distribution of irrigated a cres , 2012 ........................ ........... ...... . 21 Figure 3.3 E nergy expense for p umping in sample frame by fuel type ........ ........... 33 Figure 3.4 Seasonal varia tion in w ater w ithdrawals .......................... ... .................. 38 Figure 3.5 Distribution of water cost by sample exclusion rule ............................. 48 Figure 3.6 Distribution of sample weights by sample exclusion rule ............ .......... 50 1 CHAPTER 1: !INTRODUCTION 1.1 Background and Motivation A relative abundance of r esearch explor es water management decisions within regions that suffer from particularly thorny resource challenges, for example, the activities of west- ern irrigation districts or the mining of the Ogallala Aquifer . Little is known , however, about the factors that drive the decisions of supplemental irrigators operating in the eastern U .S., a region characterized by relative water abundance. Yet, even these water -abundant regions are not free from water r esource concerns. In water -abundant regions, irrigation water with- drawals can lead to surface water scarcity, especially when they are seasonally and spatially concentrated (Mubako, Ruddell, and Mayer 2013) . The transferability of results from west- ern studies to a water -abundant context is limited by the structural differences in manage- ment behavior between regions (Moore, Gollehon, and Carey 1994) . A recent study noted that Òeven in relatively water -rich regions, withdrawal and consumption of water has the potential to create instream freshwater ecosystem water scar- city, especially at seasonal and local scalesÓ (Mubako, Ruddell, and Mayer 2013, 671) . This study explore d the irrigation management behavior of firms in the Western Great Lakes Basin Ð Illinois, Indiana, Michigan, Minnesota, and Wisconsin. Aquifers in the Great Lakes region tend to be shallow and connected to surface water resources, leading to sensitivity of surface water systems to groundwater withdrawals 2 (Walland er 2017) . Importantly , Mubako et al. found that in the Kalamazoo River watershed in Southwest Michigan , Òmost instream water scarcity is caused by localized consumptive uses of water in late summer months at small spatial scales of less than 300 km 2Ó (2013 , 678). The most extreme examples of scarcit y occurred where there were heightened concen- tration s of i rrigation withdrawals located specifically within a small -scale upland watershed. These inte nse localized withdrawals caused scarcity impacts that reve rberated through downstream segments including the main river stem. Mubako et al. note d that irrigation withdrawals are particularly important drivers of scarcity because they typically occur at sensitive times and locations. Irrigation withdrawals are most heavily concentrated during low -flow summer months, and , unlike other consumptive withdrawals, they are most often located in Òsmaller -scale upland agricultural watersheds, where stream baseflows are rela- tively small and more vulnerable to seasonal ch anges.Ó Mubako et al. selected the Kalamazoo River watershed as their study location using a set of criteria for generalizability. The Kalamazoo watershed possesses environmental and water -use characteristics that are typical of and thus reasonably gener alizable to other midsize watersheds in water -rich regions. The Mubako et al. study, among others (Luukkonen et al. 2004; Zorn, Seelbach, and Rutherford 2012; Watson, Mayer, and Reeves 2014) , suggest s that adaptive management of water scarcity in water -rich regions like the 3 Great Lakes Region must address the sensitivity of aquatic ecosystems within localized scales of space and time. 1.2 Climate Context A significant body of research explor es the effects of climate change on agricultural yields. Desch”nes and Greenstone (2007) found that climate change is likely to have a net positive effect on agricultural output and profit. In a conflicting result, Schlenker and Rob- erts (2009) found that yields are likely to diminish significantly before t he end of the century due to the damaging effects of extreme heat events. The exploration of potential nonlinear effects of climate and weather conditions has not spi lled over into the irrigation water de- mand literature. The typical approach in the irrig ation literature includes the estimation of linear temperature and precipitation effects. This approach excludes any important nonlinear tem- perature effects such as those identified by Schlenker and Roberts. Olen, Wu, and Langpap (2016) include d an indicator for counties that are historically drought prone in their model of irrigation application rates. The literature has not addressed the effect of extreme heat or precipitation variability on water application rates. This thesis introduces measures of extreme heat and precipitation variability to the liter ature on irrigation demand. 4 1.3 Water Management Institutions in the States Michigan, like most states in the relatively water abundant eastern United States, applies riparian doctrine to guide surface water allocation , an institution derived from the common law tradition (Lautenberger and Norris 2016). The three key provisions of riparian doctrine are as follows: Òonly riparians are legally entitled to make use of surface water; these water rights are not quantitatively fixed; each riparianÕs water use must be Ôreasona- bleÕ in relation to the water use of other riparians in the basinÓ (Griffin 2006, 121) . Under the principle of reasonable use, a landowner has the right to use water that is adjacent to his property as long as his use does not unreasonably harm the water use of other riparians . The application of the reasonable use principle to groundwater users emerged in Michigan common law to resolve conflicts between groundwater and surface water user s (Lautenberger and Norris 2016). The right to use groundwater is vested in those who own the overlying land. When conflict occurs between two or more riparian users, two or more groundwater users, or between riparians and groundwater users, the courts mus t apply the principle of reasonable use. Water law rooted in riparian doctrine and the principle of rea- sonable use typically lacks a predictable system for prioritizing uses (Griffin 2006) . This uncertainty leads to costly, unpredictable litigation for each unique case of conflict . The challenging nature of conflict resolution under MichiganÕs legal institutions is generalizable 5 to a ll Great Lakes St ates because the water use institutions in all Great Lakes States are rooted in the riparian tradition (Dellapenna 2005 ). 1.4 The Great Lakes Compact The Great Lakes Ð St. Lawrence River Basin Water Resources Compact calls upon the Parties Ð Illinois, Indiana, Michigan, Minnesota, New York, Ohio, Pennsylvania, and Wisconsin ! to Òdevelop and maintain a w ater resources inventory for the collection, inter- pretation, storage, retrieval , exchange, and dissemination of information concerning the wa- ter resources of the p arty Ó (Great Lakes ÑSt. Lawrence River Basin Water Resources Com- pact 2005) . The Parties are also obligated to manage water withdrawals and consumptive uses: Each Pa rty shall create a program for the management and regulation of New or Increased Withdrawals and Consumptive Uses by adopting and implementing Measures consistent with the Decision -Making Standard. Each Party, through a considered process, shall set and ma y modify threshold levels for the regulation of New or Increased Withdrawals in order to assure an effective and efficient Water management program that will ensure that uses overall are reasonable, that With- drawals overall will not result in significant i mpacts to the Waters and Water Dependent Natural Resources of the Basin, determined on the basis of significant impacts to the physical, chemical, and biological integrity of Source Watersheds É (Great Lakes ÑSt. Lawrence River Basin Water Resources Compact 2005, sec. 4.10.1) 6 The Compact outlines five criteria that collectively comprise the Decision -Making Standard for new withdrawals. In brief: withdrawn water must return to the source water- shed less an allowance for consumptive use; withdrawals must be implemented to insure n o significant individual or cumulative adverse resource impact; the withdrawal must incorpo- rate environmentally sound and economically feasible water conservation measures; the withdrawal must be in compliance with all relevant law; and the withdrawal must be rea- sonable , taking into consideration the hydrological interconnection of water sources and the balance between water -use benefits Ð economic development, social development , and en- vironmental protection. In accordance with the Compact, the S tates hav e implemented differing regulatory regimes for water withdrawal management. In 2008 Michigan implemented a series of new laws to comply with the compact . This statutory development, along with a preceding 2005 Michigan Court of Appeals deci- sion , expanded MichiganÕs legal structure to address the interaction between groundwater and surface water. These developments further changed the relations between water users and the public. ÒMichiganÕs recent water use statutes have established a new legal relation that assigns to large quantity water users a duty to limit water use in order to protect the right of the public to benefit from the stateÕs water resources. This new legal relation has no effect on the existing legal relations among water users, but it do es decrease the amount of water available for withdrawal .Ó 7 ÒThe new legal relation between the public and water users, administered through a cap on total withdrawals, increases the likelihood that conflicts will occur among water users.Ó (Lautenberger and Norris 2016, 916) Import antly, MichiganÕs new water use regime Òlimits the amount of available water, but it makes no effort to prioritize how available water should be usedÓ (Lautenberger and Norris 2016, 916) . 1.5 Study Objective Consider the importance of cropland irrigators, who cumulatively compose the larg- est consumptive water use sector in Michigan (Seedang and Norris 2011, 6) . Water resources are particularly sensitive to irrigation withdrawals because they tend to be tempora lly and spatially concentrated. Additionally, water use for agricultural irrigation has varied sig nifi- cantly in recent years , but, most notably in Michigan, there is an upward trend in agricul- tural water use in recent years. Due to limits in state reported water use data, the size and direction of a trend is less clear in the other states (see figure 1 .1) . Thus, an improved understanding of the conditions that drive i rrigation decisions will make water -use conflicts more predictable and may serve as a guide for estimating the marginal product of irrigation water use in a supplemental irrigation context. 8 Figure 1.1 Agricultural i rrigation water use by state Source: State water use reporting documents (multiple) IN: http://www.in.gov/dnr/water/4841.htm MI: http://www.michigan.gov/deq/0,4561,7 -135 -3313_3684_45331 -370128 --,00.html MN: https://www.dnr.state.mn.us/waters/watermgmt_section/appropriations/wateruse.html WI: https://dnr.wi.gov/topic/WaterUse/WithdrawalSummary.html The specific objective of this stu dy is to estimate the water -use response of irrigators in water abundant regions to various climatological, environmental, and price conditions . Secondary data sources, including the Farm and Ranch Irrigation Survey conducted every five years, were used for this study, which is focused on the response of irri gators across water application, crop acreage, and technology adoption decisions. The intensive margin estimation addresses the annual irrigation water application rate per acre . The extensive 9 margin estimation includes an acreage allocation decision and an irrigation investment de- cision. The crop acreage and water application results are related to provide an estimate of the long run elasticity of water use. 10 CHAPTER 2: !THEORETICAL FRAMEWORK 2.1 Approaches in the Literature The literature on irrigation demand has established a number of viable methods for demand estimation. Scheierling , Loomis, and Young (2006) distinguish ed between three broad categories of approach: mathematical programming, field experim ent, and economet- ric . Many early irrigation water demand studies employ ed mathematical programming methods, particularly linear programming, and deductive techniques (Frank and Bea ttie 1979) . This is partly due to the fact that , historically, irrigation data has been available in in only limited forms (Ogg and Gollehon 1989) . Mathematical programming approaches allow for great flexibility in extrapolating the model to produce results under hypothetical future conditions, but the reliability and accuracy of these results will depend on t he strength of the assumptions. Generally, l inear programmi ng approaches are sensitive to ass umptions about economic and technological conditions (Scheierling, Loomis, and Young 2006) . A second body of irrigation demand literature uses field experiments. These studies link agronomic data with economic production function s. The value marginal product of irrigation w ater can be estimated with the statistical relationship between plant yield and water application. Some studies also account for fertilizer application and weather 11 (Scheierling, Loomis, and Young 2006) . Field experiment studies are inductive, similar to econometric studies, b ut the results are generated from smaller collections of data. The results of field experiment studies are typically more constrained to a limited set of condi- tions than econometric or mathematical programming studies. In a review of irrigation water deman d research, Scheierling et. al. (2006) found that the price elasticities of water demand are generally very inelastic due to a lack of modeled adjustment possibilities . Econometric approaches encompass t he third major form of irrigation study. Early applications of this approach modeled total farm demand for irri gation water using price and fixed factor quantity data (Nieswiadomy 1985; Frank and Beattie 1979) . Later ap- proaches have used models of multi -output firms to allow for crop substitution (Moore, Gollehon, and Carey 1994; Hendricks and Peterson 2012; Mullen, Yu, and Hoogenboom 2009) . Econometric studies are inductive in nature, employing historical data to determine the demand for agricultural inputs within the range of observed historical conditions. This approach produces results that are not as readily extrapolated to new sets of con ditions when compared with mathematical programming approaches; however, the use of observed farm production data avoids the sensitivity to programming assumptions. 2.2 Econometric Approaches in the Literature The majority of the existing literature on i rrigation demand in the U .S. is confined to water -scarce western states. A national scale 2006 meta -analysis of irrigation demand 12 including studies dating from 1963 to 2004 did not include a single study east of the Mis- sissippi; over a third of the studies used data from California irrigators (Scheierling, Loomis, and Young 2006) . Recent notable studies have evaluated the effect of energy prices on agricultural groundwater extraction from the high plains aquifer and the effects of water scarcity and climate conditions on irrig ation decisions in the Wes tern U .S. (Olen, Wu, and Langpap 2016; Hendricks and Pet erson , 2012; Pfeiffer and Lin 2014) . Only a small number of irrigation demand studies have evaluated irrigation manage- ment decisions in the relatively water abundant eastern regions of the U .S. This geograph- ical imbalance is likely due to a number of factors: the scarcity and heightened water concern in western states, limitations in data availability, and a general assumption that the low cost of water in eastern states would lead to a near zero price elasticity for irrigation water. With evidence from Georgia, Gonzalez -Alvarez et al. (2006) concluded that even outside of the water scarce west, the cost of irrigation water is an important factor in farm irrigation decisions. There are a number of management choices that might be influenced by the cost o f irrigation water: ÒIrrigation efficiency can be improved, crops can be irrigated less, and farmers can pay closer attention to soil moisture and irrigation timingÓ (Gonzalez -Alvarez, Keeler, and Mullen 2006, 311) . One of the f ew irrigation management studies con- sidering firms east of the Mississippi found that irrigation water demand is Òmodestly af- fected by water price (with elasticities between -0.01 and -0.17) but more so by crop price 13 (with elasticities between 0.5 and 0.82)Ó (Mullen, Yu, and Hoogenboom 2009, 1421) . These studies used pump and well characteristics to estimate the marginal cost of irrigation. In contrast to agricultural inputs purchased in competitive markets , the own -price elasticity for irrigation water demand is uniquely challenging to measure where crop irriga- tors receive irrigation water from unpriced sources , most often on-site groundwater wells and occasionally surface -water pumps. Efforts to circumvent the lack of an explicit u nit price through the use of imputed irrigation costs suffer from bias issues (Mieno and Brozovi ! 2016) . The various approaches to measuring water cost are discussed further in Chapter 3. 2.3 Theoretical Model This analysis focuses on firm irrigation management de cisions across a decision framework that includes expansion of irrigated acreage , crop allocation, and water applica- tion decisions . The problem is rooted in a simple total profit function for a multi -output irrigating firm (equation 1) . !(",#,$,%) (1) Where p is a vector of crop prices, b is the cost of irrigation water, and x is a vector of other exogenous environmental variables (climate, weather, soil quality ).1 N is the land constraint . Farms face an initial optimization problem that takes the following form: 1 Mathematical symbols are presented in itali c font. Symbols that represent vectors are also bold. 14 !(",#,$,%)=max &{!(",#,$,%):$=$'()+*} (2) In this form, t he optimization expresses the fi rmÕs decision to expand total irriga ted acreage . N is total irrigated acreage in a given year, which is the sum of last year 's irrigated acreage and any expansion (or reduction) happening in the given year , k. After each growing season , firms make irrigation expansion decisions with updated perceptions of climate -relate d risk and price conditions that ref lect the last growing season . To develop a theoretical framework for the crop allocation decision, the total profit function is decomposed into a set of individual irrigated crop profit functions , where i indi- cates a particular crop : +,(-.,#,/,0,%) (3) The optimization can be restated as a choice of irrigated acreage allocation for the individual crops, constrained by the total acreage under irrigation !"## $. !(",#,$,%)=max 12É1345+,(-.,#,/,0,%)6 7,=)5/,=$,88 0 7,=)9(4) The estimable forms for the crop allocation and water application decisions are derived from the crop level model of a multioutput irrigating firm . At the intensive margin, t he specific management behavior of interest is the volume of water applied to a particular crop Ð corn, soybeans, or potatoes Ð given that a firm is growing the crop on a field with irrigation infrastructure in place. 15 2.4 Empirical Model Assuming a norma lized quadratic profit function, t he estimable empirical functions are linear in the exogenous variables (Lau 1978; Moore and Negri 1992; Moore, Gollehon, and Carey 1994) . The equation for /, expansion of irrigated acreage, is presented as a func- tion of crop prices, water cost, total cropland, and environmental conditions . Due to data limitations, a proxy was used in place of the theorized dependent variable. Expenditure on irrigation equipment for new expansion, k (measured in dollars) , was used as the dependent variable in the expans ion estimation rather than an acreage measure. In equations 5 and 6, j indexes the output prices for the m crops. *=:+5;<-<+7<=)=#+>$+5?@A@'@=)(5) The empirical model for crop -acreage allocation is similar in structure, but with ef- fects that vary by crop i. /,0=:,+5;<, -<+7<=)=,#+>,$+5?@,A@'@=) B=1,É,C(6) This function is intended to capture the indirect water use response observed as the change in the allocation of irrigated land among the m crops, each of which has unique water requirements and favors certain environmental conditions. In the irrigation invest- ment and crop acreage models, the environmental and price variables, x and p, include weather and price conditions lagged one year with additional controls for long run climate 16 conditions . The variables were chosen to reflect the information available to the firm in the winter of the survey year when investment and planting decisions are made. Application of HotellingÕs lemma to the indi vidual crop profit function produces t he estimable intensive margin water demand function. (=+,(-.,#,/,0,%)=#= D,(-.,#,/,0,%) B=1,É,C(7) D,=E,+%,-,+=,#+>,$+5?@, A@'@=) B=1,É,C(8) The general forms for the two estimations are similar although cross prices do not appear in the empirical function for w. The price and environmental variables that appear in the water application models are selected to reflect the information and conditi ons available to the firm during the irrigation season . The construction and specifications of each variable are further explored in C hapter 3 . 17 CHAPTER 3: !DATA AND HYPOTHESES 3.1 Data Overview Individual response data from the USDA Farm and Ranch Irrigation Surv ey (FRIS) is the foundational data set for this analysis. It contains firm level responses on water application rates, irrigated acreage, expense for irrigation pumping, and other irrigation management topics . The sample used in this study is a subset of the national FRIS survey. The selected sample includes major irrigating states in the Great Lakes region Ð Illinois, Indiana, M ichigan, Minnesota, and Wisconsin, and it covers three years Ð 2003, 2008, and 2013. The FRIS data is supplemented with environmental and price data from a number of third party sources. Precipitation and temperature data were obtained from the PRISM Climate Group. Solar radiation, humidity, and wind speed data were obtained from the Department of EnergyÕs National Solar Radiation Database, Physical Solar Model 3.0. Soil quality data was derived from the NRCS STATSGO database. Finally, state level crop pr ice data was obtained using USDA Q uickstats. Due to limitations of the survey data used for th is study, each firm is geographically identified at the county level. The climate and soil data characteristics were aggregated and related to the FRIS response data at the county level. 18 3.2 FRIS Survey data on agricultural management decisions and firm characteristics was ob- tained from the USDA National Agricultural Statistics Service Farm and Ranch Irrigation Survey (FRIS) . FRIS is a supplement to the Census of Agriculture (COA) , a general farm management survey conducted on five -year cycles. The FRIS is collected in the years fol- lowing the COA from a sample frame of firms who reported having participated in irrigation in that particular COA . For this study, FRIS responses have been selected from 2003, 2008, and 2013 . In 2013, the national FRIS sampl e targeted 35,000 farms and obtained responses from 34,966. The targeted farms were selected via a stratification strategy. The major irri- gators in each State were assigned to a certainty stratum (i.e. probability=1). The remain- ing noncertainty strata (pro bability < 1) were sampled systematically by acreage. The boundaries of each strata were uniquely defined by State to reflect each StateÕs distribution of farm size measured as total acres irrigated. 2,095 farms were selected f rom the certainty stratum , an d t he remaining 32,871 farms were selected from the various noncertainty strata (FRIS 2013, Appendix A -1). This sampling strategy was also used for the 2003 and 2008 FRIS. The individual response data includes weights that are used to correct for the inher ent non -randomness of the sample selection strategy. 19 The three most recent survey cycles are a natural selection for this analysis because there were changes to certain relevant questions in the FRIS between 1998 and 2003 . This sample time frame also covers a dynamic period in the implementation of the Great Lakes ÑSt. Lawrence River Basin Water Resources Compact , to which each of the states in the study is a party . (Although only Michigan has almost all of its agricultural area within the Great Lakes Basin, Wisconsin and Minn esota treat in -basin and out -of-basin water use management the same .) The selected sample includes corn, soybean, and potato irrigators. These crops com- pose the majority of the irrigated acreage in the five states. Agricultural irrigation occurred on over 2.5 million acres acro ss the five -state region in 2012 . Figure 3.1 displays these acres by the share in each crop. The relative shares of irrigated acreage for each crop are similar across the states in the region with the exc eption of Wisconsin , where vegetables are par- ticularly dominant. This study does not consider vegetabl e irrigation because the data is limited in distinguishing between vegetable types. Additionally, there are relatively few farms g rowing individual vegetable types and management practices are likely to vary by type. 20 Figure 3.1 Sample frame: irrigated acres by state and y ear Source: FRIS summary reports 2003, 2008, 2013 Potato irrigation occurs on a very small percentage of irrigated acreage in the south- ern part of the region (i.e. Illinois and Indiana). Potato irrigation occurs on a larger share of acreage in the northern part of the region and is an important crop to ev aluate because it generally requires greater irrigation volume than the other crops addressed in this study. Figure 3.2 displays the spatial distribution of irrigated acres as reported in the COA 2012. The figure highlights the presence of several key irri gation areas within the sample region. Most notably, the largest concentrations of irrigating farms are in Southwest Lower Michigan/Northern Indiana and Central Minnesota. 21 Table 3.1 contains the number farms by year, state, and crop as they appear in the final study sample. The 4,750 farms are relatively evenly distributed over the three sample years and five sample states. Summing the number of firms over the three crops in a given state and year will not sum to the reported total number of firms because many firms irrigate more than one of the studied crops. !" Figure 3.2 Spatial distribut ion of irrigated a cres , 2012 Note: NA indicates counties where data was suppressed in published USDA COA summary tables to protect survey respondent confidentiality. 22 Table 3.1 Number of farms in study s ample, by year, state, and crop STATE IL IN MI MN WI Total 2003 All Crops 392 292 233 335 271 1,523 Corn 372 270 207 302 205 1,356 Soybean 301 207 138 228 131 1,005 Potato 10 8 39 40 91 188 2008 All Crops 336 309 288 362 228 1,523 Corn 324 288 269 328 182 1,391 Soybean 200 207 163 231 98 899 Potato 3 3 36 33 60 135 2013 All Crops 420 361 292 355 276 1,704 Corn 392 343 263 324 238 1,560 Soybean 255 227 177 204 111 974 Potato 8 8 38 23 67 144 Total All Crops 1,148 962 813 1,052 775 4,750 Corn 1,088 901 739 954 625 4,307 Soybean 756 641 478 663 340 2,878 Potato 21 19 113 96 218 467 Some firms in the sample can be matched across the several years using a unique firm identifier. In th e selected sample , approximately ten percent of unique firms appear in all three survey years, comprising twenty percent of the observations in the sample . Ap- proximately eighteen percent of unique firms appear in two years of the survey, comprising twenty five percent of the observations. 23 Table 3.2 contains the total irrigated acreage of firms observed in the sample by year, state, and crop. In 2013, the s ample includes firms covering approximately 1,060,000 irrigated acres of corn, soybeans or potatoes. This represents approximately 40% of the total irrigated acreage in the region in 2012 (all crops). That is to say, the sample includes a large portion of the total irrigation activity in the region. Table 3.2 Total irrigated acres in study sample by state, year, and crop STATE IL IN MI MN WI Total 2003 Corn 134.2 77.9 94.2 91.9 56.9 455.1 Soybean 63.7 38.4 34.9 48.6 26.0 211.7 Potato 2.0 0.8 31.7 41.1 59.6 135.3 2008 Corn 157.4 105.9 162.2 115.5 62.7 603.7 Soybean 50.1 44.8 44.1 45.6 19.9 204.4 Potato * (S) (S) 25.6 28.4 45.3 102.2 2013 Corn 206.9 163.5 158.4 126.4 89.1 744.3 Soybean 61.9 49.4 42.9 40.6 21.8 216.6 Potato * (S) (S) 26.5 14.3 54.3 100.6 Total Corn 498.5 347.3 414.9 333.8 208.7 1803.1 Soybean 175.7 132.6 121.9 134.8 67.6 632.6 Potato 9.7 1.7 83.8 83.8 159.1 338.1 Note: All values reported in thousands *S indicates values suppressed to protect response confidentiality in accordance with USDA publication standards. 24 3.3 Dependent Variable s The FRIS questionnaire asks firms to report annual water applications to each irri- gated crop as an annual per -acre value. These reported values were used directly as the dependent variable in th e water application estimation. The following tables Ð 3.3, 3.4, and 3.5 Ðpresent descriptive stati stics for water applications by crop. Across all states and years, firms in the sample applied an average of 7.0 acre -inches of irrigation water to corn and 6.4 acre -inches to soybeans . Table 3.3 Farm level de scriptive statistics: w ater applied to corn (in /acre) STATE IL IN MI MN WI Total 2003 mean 7.7 5.5 6.2 7.4 7.6 6.9 sd 4.1 3.1 2.6 2.9 3.7 3.5 2008 mean 6.2 6.4 6.5 7.6 7.7 6.8 sd 3.8 3.1 2.4 2.6 3.5 3.2 2013 mean 7.9 6.5 6.5 7.3 7.7 7.2 sd 5.1 3.2 3.3 2.7 3.6 3.8 Total mean 7.3 6.2 6.4 7.4 7.7 7 sd 4.5 3.2 2.8 2.7 3.6 3.5 25 Table 3.4 Farm level descriptive statistics: w ater applied to soybeans (in /acre) STATE IL IN MI MN WI Total 2003 mean 7.6 4.8 5.3 7.2 6.7 6.5 sd 4.2 2.9 2.3 2.8 3.1 3.4 2008 mean 6.1 6.3 5.8 6.9 6.7 6.3 sd 3.8 7.6 2 2.4 3.6 4.5 2013 mean 7.5 5.6 5.2 6.6 7 6.4 sd 5.1 2.5 2.6 3.7 4.3 3.9 Total mean 7.1 5.6 5.4 6.9 6.8 6.4 sd 4.5 4.9 2.3 3 3.6 4 Table 3.5 Farm level descriptive statistics: w ater applied to potatoes (in /acre) STATE IL IN MI MN WI Total 2003 mean 10.3 7.1 9.8 9.7 10.4 10 sd 7.2 3.9 4.2 2.6 4.4 4.3 2008 mean 6.4 6.8 9.3 9.5 10.6 9.8 sd 1.8 1.4 3.5 2.6 6.9 5.2 2013 mean 5.6 9.8 8.3 8.1 9.7 8.9 sd 3.9 3.5 6.2 4 4.7 5 Total mean 7.9 8.1 9.1 9.3 10.2 9.6 sd 5.9 3.6 4.8 3 5.3 4.8 Potatoes are the most water intensive of the three crops , receiving an average of 9.6 inches per acre . The difference in water intensity provides the basis for the hypothesized 26 effects of water cost in the crop allocation model. In response to higher water prices, firms are expected to substitute away from potatoes and toward corn and soybeans. The dependent variables in the crop allocation models are the FRIS reported values for irrigated acreage of the specific crop. Descriptive statistics for each crop are present ed in tables 3.6, 3.7, and 3.8. For example, the average firm growing irrigated corn in Illinois in 2003 allocated 361 acres of irrigated land to corn. Table 3.6 Farm level descriptive statistics: corn irrigated harvested acres STATE IL IN MI MN WI Total 2003 mean 361 288 455 304 278 336 sd 399 266 498 435 346 399 2008 mean 486 368 603 352 344 434 sd 503 378 840 446 487 558 2013 mean 528 477 602 390 374 477 sd 602 536 908 671 556 663 Total mean 458 385 561 350 334 419 sd 515 427 789 531 476 560 27 Table 3.7 Farm level descriptive statistics: soybean irrigated harvested acres STATE IL IN MI MN WI Total 2003 mean 212 186 253 213 199 211 sd 216 156 264 291 295 244 2008 mean 250 216 270 197 203 227 sd 396 220 326 226 307 298 2013 mean 243 218 243 199 196 222 sd 313 215 333 297 239 285 Total mean 232 207 255 203 199 220 sd 305 200 312 272 281 276 Table 3.8 Farm level descriptive statistics: potato irrigated harvested acres STATE IL IN MI MN WI Total 2003 mean 201 108 813 1027 655 719 sd 225 131 1260 1598 865 1128 2008 mean (S) (S) 711 859 754 757 sd (S) (S) 1079 1800 1173 1315 2013 mean (S) (S) 698 622 810 699 sd (S) (S) 1423 1470 1251 1279 Total mean 462 88 742 872 730 724 sd 709 111 1255 1633 1079 1229 The mean irrigated potato acreage is significantly larger than the respective means for corn or soybean , indicating a greater degree of firm concentration in potato production. Table 3.9 contains the number of firms in the sample by crop(s) irrigated. The vast majority 28 of firms irrigated corn or both corn and soybeans in the observed years. This distribution is consistent with typical crop rotations where firms alternate between corn an d soybeans on two or three -year rotations. Similarly, a majority of the potato irrigators in the sample are also irrigating other crops. This is expected as potatoes are also t ypically grown on a two or three -year rotation. Considering the nature of typical crop rotations, it is likely that nearly all, if not all , firms in the sample regularly participate in irrigation of at least two of the studied crops. Thus, substitution eff ects in the crop allocation parameters are expected to appe ar as a decision to participate or not participate in growing irrigated potatoes. Potato production decisions are likely partially constrained by production contracts, but the FRIS lacks a useable identifier for firms operating with production contracts. Some firms in the sample may rotate through crops that are not addressed in this study. Notably, a significant share of potato producers are likely to rotate potato acreages with vegetables. Due t o the relatively small number of firms and potentially varied nature of vegetable production management, vegetables have been excluded from this study. 29 Table 3.9 Sampled firms by crop(s) i rrigated Firm Ty pe Count Percent Corn Only 1,777 33.66 Soybean Only 239 4.53 Potato Only 270 5.11 Corn & Soybean 2,717 51.47 Corn & Potato 108 2.05 Soybean & Potato 33 0.63 All 135 2.56 Total 5,279 100 The dependent variable in the third and final model is the FRIS reported expenditure on irrigation technology for new expansion that occurred in the year of t he survey. The majority of firms report zero for this variable, but the group of firms reporting non -zero values is large enough to fit an empirical model. Table 3.10 Capital investment for new e xpansion among sampled firms 2003 mean 73,819 sd 99,410 N 183 2008 mean 121 ,058 sd 154 ,492 N 280 2013 mean 173 ,469 sd 211 ,139 N 330 Total mean 131,967 sd 165 ,353 N 793 All values in CPI adjusted August 2013 dollars 30 3.4 Measuring the Cost of Water The primary variable of interest is the cost of irrigation water which is hypothesized to have a negative effect on water application r ates . Additionally, the cost of water is hy- pothesized to affect a substitution away from water intensive crops. There are three general approaches to measuring irrigation cost in the irrigation demand literature when water itself is unpriced . Here, they are ref erred to as the energy price approach, the engineering ap- proach , and the average cost approach. The energy price approach relies on variation in local energy prices applied as a proxy for the marginal w ater d elivery cost . Mieno and Brozovi ! (2016) showed that Òenergy price elasticity is identical to the irrigation cost elasticity of groundwater use when ground- water itself is not pricedÓ (Mieno and Brozovi ! 2016, 423) . The energy price approach is simple in construction, but it does not account for a number of firm technology character- istics that affect the cost of water (e.g., groundwater depth, pumping pressure, total dy- namic head). Additionally , t his me thod is only suitable if price varies sufficient ly across the sample. In the context of this study , the available measures of energy price do not provide sufficient variability to use the energy price approach. Mieno and Brozovi ! Õs sample included only el ectricity users. Adapting this approach to the c ontext of this study would require a firm specific composite energy price index relating the market price (dollars per million bt u) for electricity and diesel. The energy price 31 index is computed as an average of the energy prices weighted by the firmÕs ratio of ex- penditures on the two energy sources. Prior studies have tested various methods for assign- ing fuel type when clear data is not available and found intensive margin price elasticity of water to be robu st to the various energy price assignment methods (Pfeiffer and Lin 2014) . Pfeiffer and Lin (2014) applied this approach and tested three ru les for assigning energy price where firm energy source is unknown. In the base specification, the natural gas price was assigned to firms in counties with natural gas production and the diesel price to firms in other counties. In an alternative specificat ion, the natural gas price was assigned to firms in counties with natural gas production and the electricity p rice to firms in other counties. In a third alternative, the authors assigned the price of the predominant energy source Ð natural gas in their case Ð to all firms. The two general alternatives to the energy price approach, the engineering and av- erage cost approaches , leverage the additional variation between firms with un ique water delivery infrastructure. The engineering approach requires data on pump characteristics to impute cost parameters using engineering relationship s (Gonzalez -Alvare z, Keeler, and Mullen 2006; Moore, Gollehon, and Carey 1994; Hendricks and Peterson 2012) . Common parameters used in the engineering approach include well depth , pump technology, pump system pressure, etc. A number of irrigation demand studies using FRI S data have applied the engineering approach to impute pumping costs (Moore, Gollehon, and Carey 1994; 32 Mullen, Yu, and Hoogenboom 2009; Hendricks and Peterson 2012) . However , in a recent study, Mieno and Brozovic (2016) raised some potential problems with this approach . Olen et al. (2016) used FRIS data and applied the average cost approach. This approach requires individually reported irrigation expenditure data and is distin ct from the energy price and engineering approac hes which aim to exclude any fixed costs associated with irrigation. A rational profit maximizing firm with complete information would optimize water use as a function of the marginal cost of water, but firms in the context of this study may instead re spond to an average cost over the time scale of a regular billing cycle . This expectation applies particularly to farms that use primarily electricity as their energy source for pumping. 33 Figure 3.3 Energy expense for p umping in sample frame by fuel type Diesel expenditures compose a large portion of the total pumping expense for irriga- tion, but electricity is the majority source in most state -years in the sample. Findings fro m Ito (2014) suggest that electricity consumers may not effectively respond to marginal prices due to complicated signals from nonlinear pricing. Many utility rate plans include pricing structures that might obscure an irrigating firmÕs per ception of marginal cost (e.g. , demand charges, block rates). Thus, the average cost of water may be more relevant than marginal cost for irrigating firms. 34 In this study, firm level marginal cost of irrigation water was calculated as the total annual ener gy expenditure s for pumping , E, divided by the total number of acre i nches applied by summing the crop level products of acreage allocation, n, and water application, w, for each crop i. #=FGD,/,7,=) The average cost of water variable, b, may appro ximate the marginal cost of water when there are no significant changes in energy prices during the irrigation season and firms do not conflate fixe d and marginal costs. The majority of irrigation activity occurs in a relatively short time scale (see Figure 3.4 ), so large variation in within -season energy price is unlikely. The reported average cost of water might be a poor proxy for the marginal cost if irrigators were able to adjust a systemÕs e nergy mix in response to within -season changes in energ y price ratios. A subset of the sampled firms report s expenditure s on multiple types of energy, primarily electricity and diesel. These irrigators might be potential candidates for energy switching behavior , except the nature of irrigation pump technology makes this behavior unlikely. Irrigation systems are relatively long -term investments for agricultural firms in the Great Lakes Region , and the presence of redundant pumping systems for energy switching is not a known practice (B. Russell , personal communi cation , February 1 , 2018 ). 35 The distribution of cost estimates obtained from the sample appears in the table below. Water costs are somewhat higher in Michigan than the other states. Table 3.11 Farm level descriptive statistics: cost of w ater ($/acre -in*) STATE IL IN MI MN WI Total 2003 mean 2.8 3.18 4.37 3.12 3.95 3.39 sd 1.83 2.11 2.75 1.83 2.31 2.21 2008 mean 3.9 4.03 5.16 3.94 4.49 4.26 sd 2.51 2.58 2.78 2.03 2.74 2.55 2013 mean 4.04 4.16 5.09 4.14 4.41 4.33 sd 2.52 2.47 2.87 2.24 2.42 2.53 Total mean 3.57 3.82 4.91 3.75 4.27 4.01 sd 2.37 2.44 2.82 2.09 2.49 2.47 * P rices CPI adjusted to USD August 2013 The cost estimates obtained in th is study sample are somewhat higher than the estimates for groundwater pumping cost s in related literature. Table 3.12 contains water cost esti- mates from a selection of related literature. 36 Table 3.12 Water c ost : values in the l iterature ($/acre inch) * Data Years Region Source Mean Mieno et al. 2016 2007 -09, 2011 -12 Nebraska Ground 2.80 Olen et al. 2016 2008 U.S. West Coast Surface 4.76 Hendricks et al. 2012 1992 -2007 Kansas Ground 1.09 Mullen et al. 2009 2000 Georgia Ground 2.73 Gonzalez -Alvarez et al. 2006 1988 -2003 Georgia Ground 2.76 Schoengold et al. 2006 1994 -2001 California Surface 6.96 Moore et al. 1994 1984, 1988 Western U.S. /Plains Ground 2.99 Scheierling et al. 2006 Mean =1975 Various West/Plains Various 4.35 * Prices CPI adjusted to USD 2013 The difference between the estimates found in this sample and the somewhat lower estimates in the literature may be driven by short run fixed costs of irrigation. Additionally, the difference may be partially explained by greater irrigation efficiency in regions with greater irrigation water demand (e.g. , Western U.S. and Ogallala). Evidence from a t -test suggests that average water cost is highe r for the sampled firms that use surface water . This difference in water cost may be caused by differences in the average pump efficiency. Table 3.13 Cost of water : mean comparison by surface water use Use of On -Farm Surface Water N Mean = 0 3,748 3.87 (0.04) > 0 1,002 4.52 (0.09) Difference -0.66 (0.09)** 37 3.5 Climate and Weather Data Precipitation and temperature data were obtained from the PRISM Climate Group. ÒPRISM (Parameter -elevation Regressions on Independent Slopes Model) is a climate anal- ysis system that uses point data, a digital elevation model (DEM), and other spatial datase ts to generate gridded estimates of annual, monthly and event -based climatic parametersÓ (Daly, Taylor, and Gibson 1997, 1) . Daily precipitation and temperature records are avai l-able at a 4km grid resolution. Current year and lagged year temperature and precipitation variables used in all models were d erived using daily prec ipitation, maximum temperature, and minimum tem- perature data. Additional degree day and precipitation variability measures were produced with modifications to the daily PRISM values. PRISM also publishes 30 -year normal climate variables at the same 4km raster scale. The 30 -year precipitation and temperature condi- tions were included in the crop allocation and irrigation investment models . The specificat ions for the climate variables used in this study were guided by infor- mation from a gricultural irriga tion extension specialists at Michigan State University . Spe- cifically, MSU irrigation specialists indicated that May 1 st -September 31 st is a sufficiently wide growing season window during which environmental conditions would affect irrigation decisions, with July and August being the heaviest irrigation months (S. Miller, personal 38 communication , September 17, 2017 ). Irrigation would only occur outside the growing sea- son window under exceptional circumstances (e.g. to Òwater -inÓ a cover crop) . The season- ality of irrigation water demand is also apparent in Wisconsin water use reports presented in Figure 3.5 . Temperature is hypoth esized to have a positive effect and precipitation volume is hypothesized to have a negative effect on water applicat ion. Due to the relative sensitivity of potato es, higher temperature s are hypothesized to cause a substitution away from potato production . Figure 3.4 Seasonal variation in w ater withdrawals Source: Wisconsin Water Use Report 2013 http://dnr.wi.gov/topic/WaterUse/documents/WithdrawalReportDetail2013.pdf With the growing season calendar in mind, the preferred climate specification in- cludes variables for peak irrigation season precipitation volume and average temperature. Peak irrigation season is defined as the months of July and August. These variables were generated by converting the 4km cells in the raw daily PRI SM data to their central points 39 and then t aking the mean of all points that fall within the county to generate a county level aggregate . The daily, county -level precipitation data was summed to generate the cumula- tive values over a given time period . The mean of the daily, county -level temperature data gives the average daily max temperature over the same time period . An additional measure was designed to account for nonlinear temperature effects. The measure, Heat ing Degree Days (HDD), is similar to specifications for growing degree days that are common in the crop yield literature. It was calculated as the count of degrees in excess of an extreme heat threshold (34¡ C), summed over days D. In the following equation, ti is the maximum temperature on day i. HII = 5max (J,,34)(34K, The 34¡ C threshold has been identified as the threshold at which additional heat reduces crop yields (Deschenes and Greenstone 2007; Ritchie and NeSmith 1991) . Irrigation appli- cations are hypothesized to be increasing in HDD because irrigation is a potential strategy to mitigate heat s tress. 3.6 Measures of Precipitation Variability Literature on the effects of climate change in the Great Lakes region note that pre- dicted changes in precipitation are somewhat less certain than expectations about temper- ature changes. Yet, there is some evidence that precipitation will become more variable across multiple time scales ranging from daily, to seasonal, annual, and even decadal 40 (Pe ndergrass et al. 2017; Hatfield et al. 2014) . This thesis tests the hypothesis that precip- itation variability increases the demand for irrigation water using measures of precipitation variability at numerous time -scales. The predominant precipitation measures in the existing econometric irrigation d e-mand literature include seasonal and annual precipitation volume. These broad measures do not account for the important factor of precipitation timing. Simply stated, between two locations that receive the same total precipitation over a given time period (e.g. , one month), the location that receives that precipitation distributed most evenly throughout the month is expected to use less irrigation water. This expectation is a result of the limited capacity of the soil for water retention. To test this hy pothesis, three precipitation variability measures were considered. The first is the ordinary standard deviation of daily precipitation volume, calculated for all days with positive precipitation values over a given time period. This measure was applied ov er a growing season time -scale (May -September) and at a monthly time -scale for the peak irrigation months (July and August). The second measure is the Shannon Index . The Shannon index is a mathematical formula used to measure how closely a given distribu tion approximates a uniform distribu- tion. In this study, it was applied to daily precipitation rates during the growing season. For a given daily precipitation time series, t he Shannon Index produces a single continuous 41 value between 0 and 1 (inclusive) in dicating the relative uniformity of a distribution , where 1 is perfectly uniform. The Index was developed and has been used extensively in biology literature to measure specie s diversity within ecosystems (Bronikowski and Webb 1996; Ramezani 2012) . This thesis appears to be the first time that the Shannon Index has been applied to an analysis of water resource management. The Shannon index value, S, for a time period with total number of days, D, is calculated as a function of pi, the percentage of total time period precipitati on that falls on day i. L= (G-,K,=)ln (-,)ln (I) In this study, the Shannon Index was calculated using a May -September time period. The third measure of precipitation variabilit y is a count of drought events during the growing season. For this va riable specification , a d rought event was defined as a window of days , d, in which cumulative rainfall did not exceed five millimeters. The variable was considerable for two identifications for d, ten days and twenty days. 3.7 NRCS Soil s Data The s oil s data used in this paper is drawn from the USDA STATSGO database. The STATSGO Òlevel of mapping is designed for broad planning and management uses covering 42 state, regional, and multi -state areas.Ó 2 Variables for this analysis were generated from the Soil Ca pability Class layer, which groups soils Òaccording to their limitations for field crops, the risk of damage if they are used for crops, and the way they respond to management.Ó Class 1 soils have few limit ations that restrict their use. Class 2 soils have moderate limitations that reduce the choice of plants or that require moderate conservation practices. Class 3 soils have severe limitations that reduce the choice of plants or that require special conservation practices, or both. Class 4 soils have very severe limitations that reduce the choice of plants or that require very careful management, or both. Class 5 soils are subject to little or no erosion but have other limitations, imprac- tical to remove, that restrict their use mainly to pastur e, rangeland, forestland, or wildlife habitat. Class 6 soils have severe limitations that make them generally unsuitable for cul- tivation and that restrict their use mainly to pasture, rangeland, forestland, or wildlife habitat. Class 7 soils have very se vere limitations that make them unsuitable for cultivation and that restrict their use mainly to grazing, forestland, or wildlife habitat. Class 8 soils and miscellaneous areas have limitations that preclude commercial plant production and that restrict t heir use to recreational purposes, wildlife habi- tat, watershed, or esthetic purposes .3 For this analysis, the soil capability class data was converted to create a county level soil quality variable. Soil quality is measured as the percentage of land that falls into either class 1 or class 2 in each county . This specification is similar to the approach used by Olen 2 Source: https://www.nrcs.usda.gov/wps/portal/nrcs/detail/soils/survey/geo/?cid=nrcs142p2_053629 3 Source: https://www.nrcs.usda.gov/wps/portal/nrcs/detail/soils/survey/geo/?cid=nrcs142p2_053629 43 et al. (2016) . The expected effect of soil quality on water use at the intensive margin is negative. Higher quality soils that better retain moisture would reduce the need for irriga- tion. At the extensive margin, soil quality is hypothesized to have a positive effect on acre- age allocations of water intensive crops (i.e. potatoes) and a negative effect on acreage alloca tions of less water -intensive crops (i.e. soybeans). The direction of this effect may be confounded by differences in soil types that are not captured by the capability class soil quality measure. Potato growers are generally expected to prefer sandy soils (or other soils with good drainage) because potatoes require careful control of soil moisture and can be easily damaged in overly wet or overly dry soils. Given this sensitivity, land with few im- pediments (as measured with the capability class data) may b e a necessary, but not suffi- cient , condition for a typical firm to participate in potato production. 3.8 Crop Price Data The USDA National Agricultural Statistics Service publishes monthly state level values for price received by crop. Price variables selected from this data were included in the water application, crop allocation, and irrigation investment models. In the water ap- plication estimation, a variable indicating same -year, July price received was used to meas- ure firm expectations at the time irrigation decisions are made. Lagged marketing -year prices were included in the crop allocation and investment models to capture price expec- tations at the time planting and investment decisions are made. 44 Importantly, spatial var iation in the state -level price data is limited , so the estima- tion of price effects relies on variation between years. Corn and soybean prices are highly correlated in the sample, so their effects cannot be distinguished in the crop allocation models. Tab le 3.14 Crop price correlation m atrix Corn Price Soybean Price Potato Price Corn Price 1 Soy bean Price 0.971 1 Potato Price 0.787 0.781 1 To address the correlation between corn and soybean prices, a composite price was calculated as the average of the corn and soybean prices faced by each firm. This composite variable is used in the crop allocation and capital investment models in place of separate corn and soybean prices. 3.9 Addressing Measurement Error The distribution of marginal energy cost is skewed with a number of extreme values . The outliers with unexp ectedly large average water cost values may be attributable to errors in the FRIS responses or data entry errors for either total energy expense or irrigation volume. 45 Measurement error in the dependent variable of the water application function, D,, would be especially problematic because t hat term also appears in the denominator of the formula for constructing the water cost variable. #=FGD,/,7,=) E is the total energy expenditure for pumping. The water cost variable, b, is a primary covariate of interest in the both the intensive a nd extensive margin estimations. Measure- ment error in wi would introduce amplification bias in the estimated parameter on b, whereas measurement error in the numerator term E would introduce attenuation bias. The FRIS response data allows two possible met hods for measuring total volume of irrigation water applied. The first method involves summing over responses on the volume applied by water source Ð ground water, on -farm surface water, or off -farm water. The second approach involves aggregating the respo nses for acre -inches applied by crop, multi- plied by the irrigated acres of each crop. The second approach was used to produce the preferred total water use measure because the crop level questions are more narrowly fo- cused. The targeted nature of these questions reduces the likelihood of recollection error and other sources of survey response error (e.g. , lack of clarity in reported units) . As ex- pected, the variance of the cost of water variable under the second approach is significantly smaller. By comp aring the preferred values (summed by crop applications) to the second source (summe d by water source) , the sample can be restricted to the subset of observations 46 that report consistent total water quantity values (difference between the two values < 5%). If measurement error is driving amplification bias in the full sample, the parameter of interest estimated with the reduced sample would be expected to be smaller in magnitude. However, when the general model was estimated with the limited sample, the esti mated parameter on b was slightly larger in magnitude. This suggests the results are unlikely to be significantly biased by measurement error in wi. The model estimated with the restricted sample appears in the second column of Table 3.15. Measurement erro r in the responses for expenditures by energy source is also possible. These responses are summed to produce E, total energy expenditures for pumping. Firms may misreport energy expenditures for a variety of reasons, including but not limited to a blurred differentiation between irrigation -related expenditures and other energy -related ex- penditures. Consider two illustrative examples. First, a firm using primarily electricity for irrigation may receive a single bill for irrigation -related and non -irrigation -related energy use. A second firm using primarily diesel fuel for irrigation may buy diesel fuel in bulk for numerous uses. When later asked to report total energy expenditures by energy source, firms may fail to accurately distinguish between these compet ing uses. 47 Table 3.15 Water application model: check for measurement e rror Full Restrict on Water Restrict on Cost Water Cost -0.211 -0.271 -0.531 (0.037)** (0.044)** (0.026)** Precipitation -0.224 -0.204 -0.239 (0.039)** (0.048)** (0.036)** Temperature 0.264 0.163 0.232 (0.092)** (0.129) (0.092)* Soil Quality -0.010 -0.016 -0.014 (0.003)** (0.004)** (0.003)** 2008 0.289 0.272 0.588 (0.196) (0.275) (0.192)** 2013 0.365 1.153 0.586 (0.235) (0.332)** (0.230)* IN -0.345 -0.555 -0.388 (0.215) (0.245)* (0.211) MI -0.472 -0.731 -0.306 (0.264) (0.352)* (0.262) MN -0.002 0.023 0.011 (0.247) (0.327) (0.241) WI 0.019 -0.168 -0.086 (0.291) (0.407) (0.286) Constant 2.167 5.651 4.523 (2.808) (3.868) (2.812) R2 0.15 0.22 0.19 N 4,729 2,571 4,307 * p<0.05; ** p<0.01 Measurement error in the numerator term of the equation for b would lead to atten- uation bias of the estimated parameter on b. The distribution of the variable b, measured in $/acre -inch and displayed in Figure 3.5, has some extreme values in the tails (<0.7 and >12.5). Unfortunately, the survey questionnaire lacks an y second set of questions that might be used to check for consistency in reported expenditure levels. 48 Figure 3.5 Distribution of water cost by sample exclusion rule Note: The left panel is truncated at co st = 20 . Additional outlyin g observations appear between 20 and 200. To address the measurement error in the numerator of the equation for b, firms reporting extreme values were removed from the sample. The firms above the 95 th percentile and below the 5 th percentile for average cost of water, b, were removed from the sample for all subsequent analysis. The third column in Table 3.15 reports parameter estimates for a basic model after this exclusion. As expected, the estimated coefficient on b has increas ed due to the reduction of attenuation bias from measurement error. 49 3.10 Regression Weights All regressions are reported using the USDA -provided sample weights to correct for the non -randomness in the sampling method. The probability weights denote the inverse of the probability that a farm in the sample frame has been included in the sample. In a simple sense, probability weights can be interpreted as the number of unobserved firms of a similar size that are represented by a single firm in the sample. In this context, the farms selected into the certainty strata would take a weight of 1. The farm s from the non -certainty strata receive weights greater than 1. All models throughout the paper are estimated using the provided weights interpreted in Stata as probability weights. The distribution of the sample weights within the group of observations culled from the sample closely mirrors the distribution of weights in the kept sample. Figure 3.6 displays these distributions. The figure is presented as evidence that the original sample weights have not been meaningfully biased by the data filtering rul e. 50 Figure 3.6 Distribution of sample weights by sample exclusion rule 51 CHAPTER 4: !RESULTS 4.1 Water Application Estimation Table 4.1 con tains definitions and hypothesized effects of the variables that appear in the water application model s. Table 4.2 contains the mean and standard deviation for each variable in the sample conditioned by participation in irrigated production of the par- ticular crop. At the intensive margin, cross prices for the alte rnative crops are expected to have no effect. They were excluded from the crop specific models. Table 4.1 Summary of v ariables: water application m odel s Variable Variable Definition (units) Mean (sd) Expecte d Effect Dependent Corn irrigation Inches applied per acre 7.0 (3.5) Soybean irrigation Inches applied per acre 6.4 (4.0) Potato irrigation Inches applied per acre 9.6 (4.8) Cost / Price Cost of Water Dollar/Acre Inch 4.01 (2.47) Ð Corn Price July price received ($/bu) 5.13 + Soybean Price July price received ($/bu) 12.58 + Potato Price July price received ($/cwt) 9.26 + Environmental Precipitation July -August accumulation (inches) 5.8 2 (2.26) Ð Temperature July -August mean daily maximum (¡C) 27.8 4 (1.13) + Humidity July -August mean relative Humidity (%) 76.24 (7.35) Ð HDD Extreme Heat Degree Days 1.81 (3.15) + Soil Quality Percent of county area in soil capability class 1 or 2 61.23 (28.48) Ð 52 Table 4.2 Water application v ariables: conditional means and (standard deviations) Variable Full Sample Corn Soybean Potato Dependent Irrigation NA 7.0 (3.5) 6.4 (4.0) 9.6 (4.8) Cost/Price Cost of Water 4.01 (2.47) 3.9 7 ( 2.4 4) 3.89 (2.40) 4.53 (2.70) Crop Price NA 5.13 12.58 9.26 Environment Precipitation 5.82 (2.26) 5.8 2 (2.26 5.94 (2.32) 5.46 (1.60) Temperature 27.84 (1.13) 27.8 8 (1.11) 27.99 (1.14) 27.15 (1.05) Humidity 76.24 (7.35) 76.23 (7.35) 75.81 (7.45) 76.48 (6.62) HDD 1.81 (3.15) 1.86 (3.19) 2.02 (3.33) 0.60 (1.45) Percent 1&2 61.23 (28.48) 62.41 (27.84) 63.54 (26.28) 32.99 (27.71) N 4,750 4,307 2,878 467 Table 4.3 contains results for the intensive margin s pecification where crop specific water application rate (inch es/acre) was regressed as a linear function of price and environ- mental conditions. In this and all subsequent models, standard errors are clustered at the individual firm level. As hypothesized , the relationship between water cost and water ap- plication rate is significant and negative across all three crops. Precipitation, temperature, and humidity variables were included at a peak irrigation season time scale (aggregated over July and August). The coefficient on precipitation is negative and significant for corn and soybean. Similarly, the effect of humidity is negative and significant across all three crops. The effect of temperature is positive and significant for soybean and potato. HDD has the expected positive effect and is significant for corn and soybean. The soil quality measure has the expected sign and is significant across all crops. 53 Finally, the coefficient for crop price has the expected positive sign for all crops and is significant across the corn and soybean models. Table 4.3 Water a pplication models: estimated c oefficients Corn Soybean Potato Water Cost -0.527 -0.442 -0.523 (0.026)** (0.033)** (0.099)** Peak Season Precipitation -0.178 -0.118 0.021 (0.037)** (0.058)* (0.154) Temperature 0.093 0.424 1.027 (0.090) (0.100)** (0.298)** Humidity -0.035 -0.056 -0.101 (0.011)** (0.013)** (0.049)* HDD 0.106 0.111 -0.133 (0.027)** (0.042)** (0.248) Soil Quality -0.015 -0.020 -0.050 (0.003)** (0.004)** (0.011)** Crop Price 0.198 0.133 0.339 (own -price) (0.062)** (0.028)** (0.232) Constant 9.816 0.527 -10.220 (2.483)** (2.777) (9.188) R2 0.20 0.15 0.27 N 4,307 2,878 467 * p<0.05; ** p<0.01 The estimated elasticities are similar across the three crops (see table 4.4) . These elasticities are within the range of those found in existing literature, although elasticities reported in the literature vary widely (see table 4.5) . The elasticities estimated in this study are somewhat larger than elasticities estimated in a relatively water abundant context else- where (Mullen, Yu, and Hoogenboom 2009) . It is intuitive that water demand is somewhat 54 less price elastic for potatoes because potatoes have the greatest water sensitivity of t he three crops. Table 4.4 Water application : point elasticity e stimates Corn Soybean Potato Water Cost Coefficient -0.53 -0.44 -0.52 Elasticity -0.30 -0.30 -0.24 Crop Price Coefficient 0.20 0.13 0.3 4 Elasticity 0.15 0.26 0.35 To check for robustness , the model was estimated with state and year fixed effects to control for unobserved heterogeneity. The results are reported in Appendix A. The esti- mated coefficients on precipitation attenuate som ewhat in the fixed effect s model. Price variables that only vary at the state and year level are not significant in the fixed effect s model. The water -cost effects and other weather effects are robust to the fixed effect s spec- ification. Table 4.5 Short -run water c ost elasticities in the l iterature Data Years Region Elasticity * Mieno et al. 2016 2007 -09, 2011 -12 Nebraska -0.53 Hendricks et al. 2012 1992 -2007 Kansas -0.10 Mullen et al. 2009 2000 Georgia -0.095(0.07) Schoengold et al. 2006 1994 -2001 California -0.30(0.17) Moore et al. 1994 1984, 1988 Western U.S./Plains 0.01(0.10) Scheierling et al. 2006 197 5 Various West/Plains -0.48(0.53) *Where multiple elasticities are reported, values in table are mean(standard deviation) 55 4.2 Crop Allocation Estimation Table 4.6 contains a summary of the variables and hypothesized effects for the crop allocation models. Crop allocation decisions are assumed to be driven by long te rm climate conditions with adjustments made at the margins in response to updated perceptions of envi ronmental conditions. Table 4.6 Summary of v aria bles: crop allocation m odels Variable Variable Definition (units) Mean (sd) Expected Effect &'Dependent Corn Acres Irrigated Acres 419 (560 ) Soybean Acres Irrigated Acres 220 (276 ) Potato Acres Irrigated Acres 724 (1229 ) Cost / Price Cost of Water Dollar/Acre Inch 4.01 (2.47) Ð Composite Price * Marketing year price received corn soybean average ($/bu) 8.12 (2.35) Ð Potato Price * Marketing year price received ($/cwt) 8.53 (1.36) + Environmental 30yr Precipitation 30-year normal growing season precipitation 19.28 (1.19 ) + 30yr Temperature 30-year normal growing season average daily max temperature 25.47 (1.43 ) Ð Peak Temperature * July -August mean maximum daily temperature (¡C) 29.17 (1.83 ) Ð Peak Precipitation * July August accumulation (inches) 7.67 (3.61 ) + HDD * Heating Degree Days 13.87 (22.68 ) Ð Soil Quality Percent of county area in soil capability class 1 or 2 61.23 (28.48) + *Starred variables are lagged by one year öExpected effects indicate substitution toward greater (+) or less ( Ð) potato production 56 Table 4.7 contains the means and standard deviations for the variables that appear in the crop allocation models conditioned on participation in the given crop . Table 4.7 Crop allocation variables: c onditional means a nd standard deviations Variable Corn Soybean Potato Dependent Irrigated Acres 419 (560) 220 (276) 724 (1229) Cost/Price Cost of Water 3.9 7 ( 2.4 4) 3.89 (2.40) 4.53 (2.70) Composite Price 8.12 (2.35) 7.9 7 ( 2.38 ) 7.5 9 ( 2.36 ) Potato Price 8.53 (1.36 ) 8.49 ( 1.3 7) 8.97 ( 1.1 9) Environment 30yr Temperature 25.47 (1.4 4) 25.60 (1 .46 ) 24.13 (1.20 ) 30yr Precipitation 19.28 (1.19) 19.34 (1.16 ) 18.76 (1.34) Peak Temperature 29.17 (1.8 3) 29.26 (1.87 ) 27.93 (1.46 ) Peak Precipitation 7.67 (3.61 ) 7.7 4 ( 3.59 ) 7.45 (2.84 ) HDD 13.87 (22.69) 14.58 (23.95) 5.97 (11.80 ) Soil Quality 62.41 (27.84) 63.54 (26.28) 32.99 (27.71) N 4,307 2,878 467 Note: Each column includes the subset of the sample that irrigates the given crop. Standard deviations appear in parentheses. Table 4.8 contains results for the extensive margin estimation where crop -specific irrigated land allocation (acres) was estimated as a function of price and environmental conditions. The crop specific allocation models were estimated using the tobit estimation procedure to account for the pool of observations who allocate d zero irrigated acres to a particular crop. 57 Tabl e 4.8 Crop acreage allocation: tobit average partial effects Corn Soy bean Potato Water Cost -9.12 -6.77 29.65 (1.68)** (1.76)** (10.80)** Total Irrigated Acres 0.38 0.14 0.38 (0.01)** (0.02)** (0.04)** Composite Price Lag 21.17 -4.70 -42.95 (1.78)** (2.29)* (13.83)** Potato Price Lag 9.38 6.13 63.93 (3.96)* (4.41) (27.18)* Soil Quality 1.11 0.40 -4.14 (0.17)** (0.19)* (1.29)** 30yr Grow -season Max 61.02 68.75 -276.96 (8.45)** (11.06)** (80.31)** 30yr Grow -season Precip itation 9.18 5.37 18.36 (4.57)* (4.64) (28.78) Peak Temperature Lag -23.59 -44.68 27.07 (8.04)** (10.80)** (70.07) Peak Precipitation Lag 3.72 -1.04 -40.20 (1.49)* (1.69) (11.58)** HDD Lag -1.09 1.23 1.93 (0.35)** (0.37)** (3.11) N 4,750 4,750 4,750 * p<0.05; ** p<0.01 The effect of water cost is significant and negative for corn and soybeans. The effect of water cost on potato acreage is positive, significant, and larger in magnitude than for corn or soybean s. These results indicate that increasing water cost causes farms to sub- stitute from corn and soybean production toward potato production. This is unexpected due to the water intensity of potato production. However, potatoes are a higher value crop than corn or soybeans , receiving an estimated $3,900/acre in revenue in 2017 compared to 58 $530 and $400 for corn and soybeans respectively. 4 Firms may optimally increase potato production in re sponse to higher water costs because, despite the greater water intensity of potato production, water costs are a smaller percentage of per acre production costs. Relat- edly, the marginal value product of irrigation water for potato production is greater th an corn or soybean production. It is possible that unobserved environmental factors that are favorable for potato production are positively correlated with water cost. Alternatively, unobserved heterogene- ity in production contract participation may be aff ecting the result. Potato producers com- monly operate under production contracts that may require a certain level of irrigation capac ity. It is possible that potato -producing firms tend to have greater irrigation capacity and subsequently face higher short -run fixed costs of irrigation (e.g. , greater fixed electric charges). Unfortunately, the FRIS data does not provide a viable indication of whether a firm operates under a production contract. The results of a mean comparison t -test indicate that potato pro ducers pay higher costs for water (see table 4.9). 4 Source: https://www.nass.usda.gov/Quick_Stats/Ag_Overview/stateOverview.php?state=MICHIGAN 59 Table 4.9 Cost of w ater : mean c omparison by potato indicator N Mean Potato Producer 467 4.53 (0.13) Other 4,283 3.9 5 (0.04) Difference -0.58 (0.12)** * p<0.05; ** p<0.01 Table 4.10 contains the results of a linear regression of crop acreage, conditional on irrigating a positive acreage of the particular crops. Excluding the effects of water cost and potato price on potato acreage, the effects are similar in magnitude and direction to the tobit effects (Table 4.8 ). This indicates that the effects of water cost and potato price on potato production are sensitive to functional form. The remaining effects in the corn and soybean models are robust to the differing function al forms. The interpretation of the sub- stitution effects is also limited by the difficulty in capturing potential subst itu tions toward crops (e.g. , vegetables) or other land uses that are not addressed in this study. Importantly, long -run average temperature has a large and statistically significant effect across both sets of models. This effect indicates that the acreage allocation to potato production is highly sensitive to average temperature . Long -run average temper ature is the most important factor affecting substitution decisions between potatoes and corn/soybeans. Coefficients for the climate, weather, and price variables generally indicate the ex- pected effects. There is a large, positive, and significant effect of the composite price on 60 corn acreage. The effect of the composite price on soybean acres is negative. It may be that the soybean acreage substitution effect is dominated by the corn effect. Potato price has a large positive and signi ficant effect on pot ato acreage, but this effect does not persist in the linear specification. Table 4.10 Crop acreage a llocation: linear r egression with crop -specific sub -samples Corn Soybean Potato Water Cost -4.483 -1.189 -3.224 (1.298)** (0.908) (3.398) Total Irrigated Acres 0.503 0.216 0.438 (0.028)** (0.018)** (0.040)** Composite Price Lag 12.985 -2.719 -6.879 (1.432)** (1.381)* (5.807) Potato Price Lag 10.193 1.921 -6.340 (3.111)** (2.528) (18.229) Soil Quality 1.028 0.161 0.851 (0.143)** (0.114) (0.698) 30yr Grow -season Max Temp erature 34.954 22.608 -53.507 (8.415)** (6.953)** (24.388)* 30yr Grow -season Precip itation 7.824 -6.123 -17.151 (2.691)** (2.507)* (14.507) Peak Temperature Lag -18.508 -13.787 1.943 (7.353)* (6.538)* (21.821) Peak Precipitation Lag -0.233 -1.293 2.004 (1.029) (0.955) (6.696) HDD Lag -0.474 0.526 1.538 (0.254) (0.230)* (1.890) Constant -678.847 -2.251 1,612.758 (90.983)** (73.812) (602.954)** R2 0.72 0.54 0.73 N 4,307 2,878 467 * p<0.05; ** p<0.01 61 4.3 Irrigation Investment Estimation The irrigation investment model was estimated using the reported expenditure on irrigation capital for new expansion (as opposed to maintenance and re pair or efficiency improvement) and a subset of the variables that appear in the crop allocation estimation. Table 4.11 contains a summary of variables and hypothesized effects for the investment models. Table 4.12 contains tobit marginal effects (average partial effects) for models of investment and the natural log of investment. Table 4.11 Summary of variables: investment models Variable Mean (sd) by investment Expected Effect ' >0 =0 Investment 132,000 (165,000) 0 Cost of Water 4.30 (2.55) 3.95 (2.46) Ð Irrigated Acres 969 (1179) 684 (1063) + Composite Price* 8.52 (2.34) 8.00 (2.37) + Potato Price* 8.99 (1.48) 8.46 (1.31) + 30yr Precipitation 19.25 (1.17) 19.25 (1.22) Ð 30yr Temperature 25.40 (1.44) 25.40 (1.45) + Soil Quality 58.75 (28.41) 61.73 (28.47) Ð N 793 3,957 *Starred variables are lagged by one year 62 Table 4.12 Capital Investment for new e xpansion : tobit average partial effects Investment Log(Investment) Water Cost 409.73 0.09 (2,505.71) (0.20) Irrigated Acres 57.79 0.00 3 (9.65)** (0.00 04)** Composite Price Lag 11,403.30 0.62 (2,984.51)** (0.23)** Potato Price Lag 30,638.68 2.13 (5,800.13)** (0.40)** Soil Quality -416.96 -0.04 (272.37) (0.02) Temperature 12,946.93 1.09 30-year normal (5,363.80)* (0.41)** Precipitation -1,889.71 -0.17 30-year normal (6,011.57) (0.48) N 4,750 4,750 * p<0.05; ** p<0.01 After controlling for firm size, measured in irrigated acres, investment is increasing in the composite (corn and soybean) and potato prices. Models exploring the effects of same year and lagged year weather conditions did not produce significant effects w ith the expected signs. The results of these models are reported in Appendix B 4.4 Effect of Precipitation Variability Despite the hypothesized effect of precipitation variability on water application rates , the estimated effects are not significant. Water application rate s for corn were estimated with the introduction of a number of precipitation variability measures Ð peak season stand- 63 ard deviation, Shannon index, and drought measures. The estimated effects are either sta- tistically insignificant or, i n the case of the Shannon index, have a direction that is incon- sistent with theory. The estimated effects of precipitation variabilit y measures appear in Appendix C . 64 CHAPTER 5: !CONCLUSIONS 5.1 Price E ffects Firms respond to the cost of water by adjusting water application rates at the inten- sive margin. In the Great Lakes region , the intensive margin response to water cost domi- nates the extensive crop allocation response. This result aligns with the conclusion s of Mul- len et al. (2009) who found that the intra -seasonal water application effect dominates the crop allocation effect in the South eastern U.S. This appears to be a distinction between water -abundant and water -scarce regions where crop allocation decisions appear to domi- nate the response to water cost (Moore, Gollehon, and Carey 1994) . Firms in the sample are somewhat less responsive to crop prices than firms in the South eastern U.S . (Mullen, Yu, and Hoogenboom 2009) . 5.2 Climate and Weather Effects Nonlinear effects of temperature and precipitation on crop yields have received some attention in the literature on climate change and agricultur e (Zhang, Zh ang, and Chen 2017; Schlenker and Roberts 2009; Ritchie and NeSmith 1991) . These effect s have been un- addressed in much of the existing irrigation water demand literature. The results of the water application model s indicate that extreme heat has an important effect on irrigation water demand. The effect of extreme heat on water application r ates indicates that increas- ing summer temperatures due to changing climate conditions would likely increase water 65 demand throughout the region. The explored measures of precipitation variability do not significantly affect water demand in the context of th is study, but future research should explore their effects on water demand in other settings. Long -run climate conditions are significantly predictive of crop allocation decisions. Potato production is particularly sensitive to climatic temperature. This result indicates that summer temperatures may reduce the favorability for potato production in the region and may cause producers to substitute toward corn, soybeans, or other crops not addressed in this study. The following hypothetical scenarios are i llustrative examples of potential effects of climate change on irrigation demand. First, consider an increase in long -run average tem- perature. Hayhoe et al. (2010) conclude d that average temperatures in the Great Lakes Region are likely to increase by at least 1.3¡C under lower and up to 4¡C under higher emissions scenarios by midcentury (2040 Ð2069). All else equal, the projected increase in average temperature is likely to cause firms to substitute away from potato production. This effect is expected to reduce per -acre water appl ications by approximately 25 %. The average potato producer would use 505 fewe r acre -inches (42 acre -feet) farm -wide per year after switching all potato acreage to corn and soybeans. Without addressing general equi- librium effects, it is difficult to extrapolate this e xpectation to a regional scale. 66 This reduction would likely be ou tweighed by a second important effect. Vavrus and Van Dorn (2010) conclude d that the number of extreme days (daily max temperature > 32 ¡C) is likely to increase from 15 days/year in the late 20th century to 36 days under low or 72 days under high emission scenarios by the end of this century. Under an additional eight days that exceed the threshold for extreme heat by one degree (measured in this stud y as daily maximum temperature > 34¡C), firms are expected to increase wa ter applications on Corn and Soybeans by 15%. 5 For the average firm this would amount to 293 acre inc hes (24.4 acre feet) farm -wide . To understand the total combined effects of extreme heat and average temperature, consider a statistically representative firm that irrigates 245 acres of corn, 88 acres of soy- beans, and 33 acres of potatoes in the current year. All else equal, this firm is expected to respond to the hypothetical mid -century temperature scenario by increasing corn and soy- bean water applicati ons by the amounts discussed above. The firm is expected to convert the 33 potato acres to corn/soybeans and reduce overall water applications on those acres by 27 acre inches. For this statistically representative firm , total water application would incre ase from 2,483 acre inches to 2,749 acre inches. Thus, the expected total regional effect 5 The expected effect (for eight additional 35¡C days) is equivalent to the expected effect for 4 additional days where the maximum temperature reaches 36 ¡C. 67 for the given temperature scenario is a 10% increase in water application overall. The in- crease will be somewhat larger than 10% in counties where potatoes are not cu rrently grown. In regions where the spatial distribution of such increases in water demand aligns with the spatial distribution of limited water availability, including areas where total withdrawals are restricted as a result of Great Lake Compact implementation, there is a heightened likelihood of conflict over water access. Other regions , where potato production is highly concentrated , may experience net reductions in water applications if the observed substitu- tion effect persists. In sum, a gricultural activity and ir rigation practices in the region are likely to be affected by changes in both long -run average climate conditions and short -run weather events. This study provides evidence that temperature is an important contributing factor of irrigation water demand bot h in terms of long run average conditions and short run extreme heat events. At watershed scales, the net water use effects depend on th e regional production patterns. 5.3 Limitations The results of the study should be understood in the context of the re levant limita- tions of the models and underlying data. Importantly, observations are spatially identified at the county level. Some firms that operate in multiple counties are identified by their 68 primary county. This spatial proxy for firm location introduc es some error in all environ- mental and price variables which may attenuate the resulting effects. Additionally, general equilibrium effects and developments of new adaptation strategies may confound the ex- pected effects over longer time periods. The FRIS questionnaire distinguishes between sweet corn, corn for silage or green -chop, and corn for grain or seed. Production for grain or seed was addressed in this study because the majority of the regionÕs irrigated corn acreage is in this category. This group ing, however, does not allow for identification of seed vs . grain producers. There may be signif- icant differences in management practices between these two types of producers. Seed pro- ducers commonly operate under productions contracts (tournament style or other struc- tures ), which are likely to affect firm expectations of crop price and may change irrigation management decisions. Production contracts are also unidentified for potato producers. Fu- ture research might explore the effects of tournament style or other production contract structures on the incentives to irrigate. 69 APPENDICES 70 Appendix A Robustness c hecks Table A.1 Fixed effect estimates: water a pplication Corn Soybean Potato Water Cost -0.526 -0.436 -0.534 (0.026)** (0.033)* * (0.096)** Peak Precipitation -0.182 -0.078 0.011 (0.039)** (0.068) (0.172) Peak Temperature 0.103 0.270 0.977 (0.107) (0.129)* (0.329)** HDD 0.130 0.103 0.227 (0.034)** (0.047)* (0.304) Soil Quality -0.014 -0.018 -0.045 (0.003)** (0.004)** (0.011)** Peak Humidity -0.041 -0.045 -0.092 (0.017)* (0.021)* (0.080) 2008 2.057 -2.508 0.950 (0.742)** (2.036) (1.793) 2013 2.221 -2.819 0.027 (1.040)* (2.177) (1.922) IN 0.051 -0.810 2.455 (0.227) (0.377)* (1.364) MI 0.057 -0.752 2.803 (0.269) (0.356)* (1.794) MN -0.200 0.034 2.009 (0.317) (0.393) (1.831) WI 0.340 0.174 3.117 (0.297) (0.417) (1.487)* Crop Price -0.367 0.470 0.165 (own) (0.248) (0.282) (0.569) Constant 11.284 1.490 -11.052 (2.948)** (3.786) (14.023) R2 0.20 0.16 0.28 N 4,307 2,878 467 * p<0.05; ** p<0.01 71 Table A.2 Fixed effect estimates: crop acreage a llocation Corn Acres Soy Acres Potato Acres Water Cost -9.25 -5.70 28.39 (1.69)** (1.75)** (10.93)** Total Irrigated Acres 0.38 0.15 0.37 (0.01)** (0.02)** (0.04)** Composite Price Lag 63.50 -12.78 -24.95 (44.70) (46.01) (316.74) Potato Price Lag -2.58 16.51 -34.61 (6.49) (9.25) (60.54) Soil Quality 0.86 0.04 -3.58 (0.17)** (0.20) (1.29)** 30yr Grow -season Max Temp 1.66 45.87 -234.86 (5.69) (6.19)** (58.90)** 30yr Grow -season Precip itation 36.06 16.87 -27.75 (4.88)** (4.96)** (37.43) 2008 -137.66 19.55 15.39 (135.87) (140.48) (941.03) 2013 -292.38 13.92 167.89 (254.15) (259.74) (1,790.69) IN -31.87 39.95 51.47 (16.53) (16.05)* (190.86) MI 34.49 20.16 190.31 (32.55) (37.66) (243.20) MN -4.80 127.99 -181.53 (21.79) (21.96)** (166.48) WI -138.16 -34.49 148.89 (28.56)** (33.07) (226.60) N 4,750 4,750 4,750 * p<0.05; ** p<0.01 72 Appendix B Investment model weather effects Table B.1 Irrigation capital i nvestment : lagged weather e ffects Base Weather Water Cost 0.09 0.04 (0.20) (0.20) Total Irrigated Acres 0.00 0.00 (0.00)** (0.00)** Composite Price Lag 0.62 0.78 (0.23)** (0.29)** Potato Price Lag 2.13 2.56 (0.40)** (0.44)** Soil Quality -0.04 -0.04 (0.02) (0.02)* 30yr Grow -season Max Temp 1.09 3.63 (0.41)** (1.33)** 30yr Grow -season -0.17 0.06 Precip itation (0.48) (0.53) Temperature Lag -2.70 (1.34)* Precipitation Lag -0.26 (0.21) HDD 0.03 (0.04) N 4,750 4,750 * p<0.05; ** p<0.01 73 Appendix C Precipitation variability measures Table C.1 Precipitation variability measures: corn water -application effects Peak Precip sd Shannon Drought 10-day Drought 20-day Water Cost -0.527 -0.528 -0.527 -0.527 (0.026)** (0.026)** (0.026)** (0.026)** Peak Precipitation -0.189 -0.200 -0.178 -0.185 (0.061)** (0.039)** (0.037)** (0.038)** Peak Temperature 0.091 0.138 0.093 0.114 (0.090) (0.095) (0.090) (0.090) Peak Humidity -0.035 -0.029 -0.035 -0.037 (0.011)** (0.012)* (0.012)** (0.011)** HDD 0.106 0.112 0.106 0.115 (0.028)** (0.028)** (0.028)** (0.029)** Soil Quality -0.015 -0.015 -0.015 -0.015 (0.003)** (0.003)** (0.003)** (0.003)** Corn Price 0.193 0.159 0.198 0.205 (0.067)** (0.067)* (0.062)** (0.062)** Peak Precip sd 0.240 (1.018) Shannon 1.595 (1.044) Drought 10 0.002 (0.054) Drought 20 -0.136 (0.110) Constant 9.887 7.333 9.805 9.470 (2.500)** (3.046)* (2.550)** (2.458)** R2 0.20 0.20 0.20 0.20 N 4,307 4,307 4,307 4,307 * p<0.05; ** p<0.01 74 REFERENCES 75 REFERENCES Bronikowski, Anne, and Colleen Webb. 1996. ÒA Critical Examination of Rainfall Variability Measures Used in Behavioral Ecology Studies.Ó Behavioral Ecology and Sociobiology 39 (1): 27 Ð30. Daly, Christopher, G. H. Taylor, and W. P. Gibson. 1997. ÒThe PRISM Approach to Mapping Precipitation and Temperature.Ó In Proc., 10th AMS Conf. on Applied Climatology , 20 Ð23. ftp://rattus.nacse.org/pub/prism/docs/appclim97 -pris mapproach -daly.pdf. Del lapenna, Joseph. 2005. ÒWater Law in the Eastern United States: No Longer a Hypothetical Issue.Ó In Proceedings of the Twenty -Sixth Annual Energy and Mineral Law Institute , Ch. 11 , edited by Sharon J. Daniels . Deschenes, Olivier, and Michael Greenston e. 2007. ÒThe Economic Impacts of Climate Change: Evidence from Agricultural Output and Random Fluctuations in Weather.Ó American Economic Review 97 (1): 354 Ð385. Frank, Michael, and Bruce Beattie. 1979. ÒThe Economic Value of Irrigation Water In the Western United States: An Application of Ridge Regression.Ó Technical Report 99. Texas Water Resources Insitute: Texas A&M University. Gonzalez -Alvarez, Yassert, Andrew G. Keeler, and Jeffrey D. Mullen. 2006. ÒFarm -Level Irrigation and the Marginal Cost of Water Use: Evidence from Georgia.Ó Journal of Environmental Management 80 (4): 311 Ð17. https://doi.org/10.1016/j.jen vman.2005.09.012. Great Lakes ÑSt. Lawrence River Basin Water Resources Compact . 2005. Griffin, Ronald C. 2006. Water Resource Economi cs: The Analysis of Scarcity, Policies, and Projects . Cambridge, Mass. "; London, England: MIT Press. Hayhoe, Katharine, Jeff VanDorn, Thomas Croley, Nicole Schlegal, and Donald Wue bles. 2010. ÒRegional Climate Change Projections for Chicago and the US Great Lakes.Ó Journal of Great Lakes Research 36 (January): 7 Ð21. https://doi.org/10.1016/j.jglr.2010.03.012. 76 Hendricks, Nathan P., and Jeffrey M. Peterson. 2012. ÒFixed Effects Estimation of the Intensive and Extensive Margins of Irrigation Water Demand.Ó Journal of Agricultural and Resource Economics , 1 Ð19. Ito, Koichiro. 2014. Ò Do Consumers Respond to Marginal or Average Price? Evidence from Nonlinear Electricity Pricing.Ó American Economic Review 104 (2): 537 Ð63. https://doi.org/10.1257/aer.104.2.537. Jerry L. Hatfield, Daniel Brown, Jeffrey A. Andres en, David Bidwell, and Julie A. Winkler. 2014. Climate Change in the Midwest: A Synthesis Report for the National Climate Assess ment . Island Press. Lau, Lawrence. 1978. ÒApplications of Profit Functions.Ó In Productions Economics: A Dual Approach to Theory and Applications, Chapter 3 . Vol. 1. Lautenberger, M. C., and P. E. Norris. 2016. ÒPrivate Rights, Public Interests and Wate r Use Conflicts: Evolving Water Law and Policy in Michigan.Ó Water Policy 18 (4): 903 Ð17. https://doi.org/10.2166/wp.2016.037. Luukkonen, Carol, Stephen Blumer, T.L. Weaver, and Julie Jean. 2004. ÒSimulation of the Ground -Water -Flow System in the Kalam azoo County Area, Michigan.Ó Scientific Investigations Report 2004 Ð5054. U.S. Department of the Interior, U.S. Geological Survey. Mieno, Taro, and Nicholas Brozovi ! . 2016. ÒPrice Elasticity of Groundwater Demand: Attenuation and Amplification Bias du e to Incomplete Information.Ó American Journal of Agricultural Economics , December, aaw089. https://doi.org/10.1093/ajae/aaw089. Moore, Michael R., Noel R. Gollehon, and Marc B. Carey. 1994. ÒMulticrop Production Decisions in Western Irrigated Agriculture: The Role of Water Price.Ó American Journal of Agricultural Economics 76 (4): 859. https://doi.org/10.2307/1243747. Moore, Michael R., and Donald H. Negri. 1992. ÒA Multicrop Production Model of Irrigated Agri culture, Applied to Water Allocation Policy of the Bureau of Reclamation.Ó Journal of Agricultural and Resource Economics , 29 Ð43. 77 Mubako, Stanley T., Benjamin L. Ruddell, and Alex S. Mayer. 2013. ÒRelationship between Water Withdrawals and Freshwater Ecosystem Water Scarcity Quantified at Multiple Scales for a Great Lakes Watershed.Ó Journal of Water Resources Planning and Management 139 (6): 671 Ð681. Mullen, Jeffrey D., Yingzhuo Yu, and Gerrit Hoogenboom. 2009. ÒEstimating the Demand for Irrigatio n Water in a Humid Climate: A Case Study from the Southeastern United States.Ó Agricultural Water Management 96 (10): 1421 Ð28. https://doi.org/10.1016/j.agwat.2009.04.003. Nieswiadomy , Michael. 1985. ÒThe Demand for Irrigation Water in the High Plains of Texas, 1957 -80.Ó American Journal of Agricultural Economics 67 (3): 619. https://doi.org/10.2307/1241084. Ogg, Clayton, and Noel Gollehon. 1989. Ò Western Irrigation Response to Pump ing Costs: A Water Demand Analysis Using Climatic Regions Ó Water Resources Research 25 (5): 767 Ð73. Olen, Beau, JunJie Wu, and Christian Langpap. 2016. ÒIrrigation Decisions for Major West Coast Crops: Water Scarcity and Climatic Determinants.Ó America n Journal of Agricultural Economics 98 (1): 254 Ð75. https://doi.org/10.1093/ajae/aav036. Pendergrass, Angeline G., Reto Knutti, Flavio Lehner, Clara Deser, and Benjamin M. Sanderson. 2017. ÒPrecipitation Variability Increases in a Warmer Climate.Ó Scientific Reports 7 (1). https://doi.org/10.1038/s41598 -017 -17966 -y. Pfeiffer, L., and C. - Y. Cynthia Lin. 2014. ÒThe Effects of Energy Prices on Agricultural Groundwater Extraction from the High Plains Aquifer.Ó American Journal of Agricultural Economics 96 (5): 1349 Ð62. https://doi.org/10.1093/ajae/aau020. Ramezani, Habib. 2012. ÒA Note on the Normalized Definition of ShannonÕs Diversity Index in Landscape Pattern Analysis.Ó Environment and Natural Resources Research 2 (4). https://doi.org/ 10.5539/enrr.v2n4p54. Ritchie, Joe T., and D. S. NeSmith. 1991. ÒTemperature and Crop Development.Ó In Modeling Plant and Soil Systems , edited by John Hanks and J. T. Ritchie, 5 Ð29. American Society of Agronomy. 78 Scheierling, Susanne M., John B. Loomis, and Robert A. Young. 2006. ÒIrrigation Water Demand: A Meta -Analysis of Price Elasticities.Ó Water Resources Research 42 (1): W01411. https://doi.org/10.1029/2005WR004009. Schlenker, Wolfram, and Michael J. Roberts. 2009. ÒNonlinear Temperature Effects Indicate Severe Damages to US Crop Yields under Climate Change.Ó Proceedings of the National Academy of Sciences 106 (37): 15594 Ð15598. Seedang, Saichon, and Patricia E. Norris. 2011. ÒWater Withdrawals and Water Use in Michigan.Ó Extension Bulletin WQ-62. Michigan State University. http://nrconser vation.msu.edu/uploads/files/105/MSUE_BulletinWQ62_WaterWithdrawalsand WaterUseinMichigan.pdf. Vavrus, Steve, and Jeff Van Dorn. 2010. ÒProjected Future Temperature and Precipita tion Extremes in Chicago.Ó Journal of Great Lakes Research 36 (January): 22 Ð32. https://doi.org/10.1016/j.jglr.2009.09.005. Wallander, Steven. 2017. ÒUSDA Water Conservation Efforts Reflect Regional Differences.Ó Choices , no. Quarter 4. http://www.choicesmagazine.org/choices - magazine/theme -articles/inducing -water -conservation -in-agriculture -institutional - and -behavioral -drivers/usda -water -conservation -efforts -reflect -regional -differences. Watson, Katelyn A., Alex S. Mayer, and Howard W. Reeves. 2014. ÒGroundwater Availability as Constrained by Hydrogeology and Environmental Flows .Ó Groundwater 52 (2): 225 Ð38. https://doi.org/10.1111/gwat.12050 . Zhang, Peng, Junjie Zhang, and Minpeng Chen. 2017. ÒEconomic Impacts of Climate Change on Agriculture: The Importance of Additional Climatic Variables Other than Temperature and Precipitation.Ó Journal of Environmental Economics and Management 83 (May): 8 Ð31. https://doi.org/10.1016/j.jeem.2016.12.001 . Zorn, Troy G., Paul W. Seelbach, and Edward S. Rutherford. 2012. ÒA Regional -Scale Habitat Suitability Model to Assess the Effects of Flow Reduction on Fish Assemblages in Michigan Streams.Ó JAWRA Journal of the American Water Resources Association 48 (5): 871 Ð895.