Essays on Water Resource Economics and Agricultural Extension. Steven Charles Buck. A dissertation submitted in partial satisfaction of the

Transcription

1 Essays on Water Resource Economcs and Agrcultural Extenson By Steven Charles Buck A dssertaton submtted n partal satsfacton of the requrements of the degree of Doctor of Phlosophy n Agrcultural and Resource Economcs n the Graduate Dvson of the Unversty of Calforna, Berkeley Commttee n charge: Professor Maxmlan Auffhammer, Co-Char Professor Davd Sundng, Co-Char Professor Steven Raphael Professor Davd Zlberman Fall 2011

2 Essays on Water Resource Economcs and Agrcultural Extenson Copyrght Fall 2011 by Steven Charles Buck

3 Abstract Essays on Water Resource Economcs and Agrcultural Extenson by Steven Charles Buck Doctor of Phlosophy n Agrcultural and Resource Economcs Unversty of Calforna, Berkeley Professor Maxmlan Auffhammer, Co-Char Professor Davd Sundng, Co-Char Ths dssertaton dscusses topcs n the mcroeconomcs of water resource economcs and agrcultural extenson. In one chapter I use a hedonc model to explan the prce of land transactons, and from ths an mpled value of rrgaton water s nferred. In a separate chapter I develop measures of wllngness-to-pay for water supply relablty measures, and estmate how consumers respond to changes n the prce of resdental water. My fnal chapter develops a model of a farmer s decson to nvest n learnng from agrcultural techncans about a new ntegrated pest management technology that mproves yelds and reduces agrcultural run-off of pestcdes nto surface waterways. Each chapter s grounded n mcroeconomc models of decson-makng. Chapter 2 presents a hedonc analyss of farmland values to recover a value of rrgaton water. Irrgaton accounts for most freshwater dversons worldwde. Water avalable to farmers may be reduced n the long run by clmate change and other factors. We use dfferences n farmland prces to value the avalablty of rrgaton water. Usng panel data on a set of farm parcels, we estmate the value of rrgaton water usng a plot-level fxed effects desgn an approach to hedonc analyss that effectvely controls for unobservable factors and may be useful n numerous settngs. Our results suggest that the value of water for rrgaton s much larger than measured n prevous studes based on cross-sectonal analyss. Ths fndng has mportant mplcatons for the analyss of polces that nfluence water supply relablty, and for the assessment of clmate mpacts. Chapter 3 descrbes a method for evaluatng consumer wllngness-to-pay for water supply relablty when fxed costs are a large porton of the margnal prce of resdental water. We show that the wllngness-to-pay for water supply relablty s determned by consumer demand for water, how the utlty covers ts costs, and the source of unrelablty. The framework s appled to the case of 52 large urban water utltes n Calforna coverng the greater San Dego, Los Angeles, and San Francsco Bay Areas. We estmate resdental water demand usng a panel dataset trackng annual prce and consumpton data from for 82 Calforna water retalers. Based on our estmated prce elastctes along wth observed rates and the margnal costs of supply, we calculate 1

4 wllngness-to-pay (WTP) measures for relablty mprovements for segments of both Northern and Southern Calforna. Chapter 4 uses a smple utlty maxmzaton model to examne how trust atttudes affect farmer learnng durng an agrcultural tranng. Usng data orgnally collected n 2005 we examne f trust condtons a farmer s decson to learn durng an agrcultural tranng. We present a model of farmer behavor durng the agrcultural tranng n order to lnk trust measures to behavor n the feld. We fnd evdence that farmers who trust agrcultural techncans relatvely more than communty farmers learn more durng tranng. The results provde nsght nto the desgn of agrcultural extenson servces n Ecuador. 2

5 To Kathleen.

6 Contents 1 Introducton 1 2 The Economc Impact of Changes n the Avalablty of Irrgaton Water Economc Model Data Outcome Varable: Farmland Sale Prce Per Acre Explanatory Varable of Interest: Surface Water Delvery Rght Per Acre Control Varables Sample Selecton Emprcal Research Desgn Emprcal Challenge Estmatng Equatons Results and Dscusson Conclusons and Future Work The Value of Supply Relablty n Urban Water Systems Loss Framework Resdental Water Demand Estmaton Econometrc Specfcaton Data Estmaton Results Economc Losses of a Water Supply Dsrupton Parameterzng the Loss Functon Data for Calculaton of Losses Results of the Loss Analyss Conclusons Agrcultural Extenson, Trust and Learnng Defnng Trust The Trust Game Modelng Farmer Behavor n the Agrcultural Tranng Model of Learnng from Communty Farmers and Techncans Relatve Trust & Selecton nto Learnng Regmes Data Background

7 4.4.2 Sample Summary Summary Statstcs of Trust Measures Summary of Exam Scores Emprcal Framework Estmaton Strategy Senstvty analyss and sources of potental bas Standard Error and Pvotal Statstc Adjustments Results and Dscusson Conclusons

8 Lst of Fgures 3.1 Economc Losses Under Volumetrc Prces and Constant Unt Cost Hstograms of trust measures v

9 Lst of Tables 2.1 Comparson of plot characterstc means across samples Cross-sectonal sample: Regress prce/acre on federal water delveres Panel sample: Regress prce/acre on federal water delveres w/o plot-level fxed effects Panel sample: Regress prce/acre on federal water delveres w/ plot-level fxed effects Resdental water demand estmaton Controllng for weather n the resdental water demand estmaton Welfare losses due to shortages of 10%, 20% and 30% Summary statstcs for control and treatment groups Descrpton of trust measures Regress exam score on trust measures Regress exam score on relatve trust measures v

10 Acknowledgments There are many people that have helped me along the way, and I thank you all. Several people have played outstandng roles; I try to acknowledge them here. I ll start wth those who were there from the very begnnng: Mom, Dad, Barb, Dave, Mke and Nancy I am so lucky to have you all n my lfe. Jeffrey Alwang, whose patence as a co-author has been ncredble, provded wonderful gudance on my frst real research project and contnues to be a soundng board. Arrvng at Berkeley I met a brllant ARE cohort they helped me survve my frst year of the Ph.D. program, and made t lots of fun. Jenny, Kyrakos, Ben, Lesle, Santago and the rest of you made me a better researcher and person. Erck Gong and Kelly Jones were the perfect offcemates. They were always ready to answer a quck metrcs questons, offer support n tmes of dstress, and branstorm research deas you guys are amazng. Mara Bowman s wse, lovng and a metculous edtor; she s also fantastc frend, and I am so glad she joned me n Berkeley after studyng at Vrgna Tech together. Among the graduate students, I have to thank my soccer mates: One, Two.. Che!. And I thank Kate and Nel for ntroducng me to board games and plenty of thoughtful conversaton. I thank everyone n the Development Workshop for teachng me econometrcs, and specal thanks to Elsabeth Sadoulet and Ethan Lgon. I learned a great deal from them on how to pursue research. Thanks to all the ARE faculty especally, Bran Wrght, Peter Berck, Alan de Janvry, Gordon Rausser and Leo Smon who were great lsteners and were always ready to offer support f I knocked on ther doors. I thank my dssertaton commttee. Steven Raphael was a perfect IGERT mentor, and outsde commttee member. Davd Zlberman made me apprecate the mportance of usng a model, even a smple one, to motvate a research agenda and related emprcal analyses. I thank Max Auffhammer for hs encouragement and practcal advce. He s a natural teacher, and helped me resolve detals that mattered n my dssertaton he pushed me to the very end. I thank Davd Sundng for ntroducng me to Calforna water ssues. He has taught me to not be dstracted by too many detals and has helped me cultvate a bg pcture perspectve. He has also been a tremendous advocate for me; I could not ask for a more supportve advsor. I am sure mportant people have been left out, but I am grateful to them as well. Fnally, someone who I could never forget: Kathleen you have done so much to help me complete ths dssertaton, you receve the bggest thanks of all. v

11 Chapter 1 Introducton Both the allocaton of water and management of ts qualty are controversal ssues confrontng socetes worldwde, and they wll lkely contnue to be the cause of conflct for a long tme to come. Farmers n Inda overdraft ther groundwater reserves; ndustral actvty n Chna pollutes ther surface and groundwater; drought, agrculture and envronmental flows generate unrest n Australa s Murray-Darlng Basn. In Afrca water hungery fertlzer and new agrcultural technologes such as drought resstant crop varetes or rrgaton systems are not wdely used or are never adopted. Ths dssertaton adds to the lterature on water resource economcs wth two chapters on valung water n Calforna, and a thrd chapter that consders how Ecuadoran farmers learn about a new agrcultural technology whch has benefts for surface water qualty. All three of these chapters use mcroeconomc models to generate hypotheses and motvate subsequent emprcal analyss. In the remander of ths ntroducton I provde a bref overvew of each chapter. Chapter 2 presents a hedonc analyss of farmland values to recover a value of rrgaton water. Irrgaton accounts for most freshwater dversons worldwde. Water avalable to farmers may be reduced n the long run by clmate change and other factors. We use dfferences n farmland prces to value the avalablty of rrgaton water. Usng panel data on a set of farm parcels, we estmate the value of rrgaton water usng a plot-level fxed effects desgn an approach to hedonc analyss that effectvely controls for unobservable factors and may be useful n numerous settngs. Our results suggest that the value of water for rrgaton s much larger than measured n prevous studes based on cross-sectonal analyss. Ths fndng has mportant mplcatons for the analyss of polces that nfluence water supply relablty, and for the assessment of clmate mpacts. Chapter 3 descrbes a method for evaluatng consumer wllngness-to-pay for water supply relablty when fxed costs are a large porton of the margnal prce of resdental water. We show that the wllngness-to-pay for water supply relablty s determned by consumer demand for water, how the utlty covers ts costs, and the source of unrelablty. The framework s appled to the case of 52 large urban water utltes n Calforna coverng the greater San Dego, Los Angeles, and San Francsco Bay Areas. We estmate resdental water demand usng a panel dataset trackng annual prce and consumpton data from for 82 Calforna water retalers. Based on our estmated prce elastctes along wth observed rates and the margnal costs of supply, we calculate wllngness-to-pay (WTP) measures for relablty mprovements for segments of both Northern and Southern Calforna. Chapter 4 uses a smple utlty maxmzaton model to examne how trust atttudes affect farmer 1

12 learnng durng an agrcultural tranng. Usng data orgnally collected n 2005 we examne f trust condtons a farmer s decson to learn durng an agrcultural tranng. We present a model of farmer behavor durng the agrcultural tranng n order to lnk trust measures to behavor n the feld. We fnd evdence that farmers who trust agrcultural techncans relatvely more than communty farmers learn more durng tranng. The results provde nsght nto the desgn of agrcultural extenson servces n Ecuador. 2

13 Chapter 2 The Economc Impact of Changes n the Avalablty of Irrgaton Water Agrculture accounts for most freshwater dversons worldwde (Foley, 2005). Irrgaton s essental for crop producton n ard parts of the developed and developng world. Changes n the avalablty of rrgaton water can have large welfare consequences snce water s an mportant nput nto agrcultural producton n these ard regons. Beyond natural fluctuatons n precptaton, water supply to agrculture can be affected by numerous factors. Clmate change has emerged as a sgnfcant threat to freshwater resources n many regons (McDonald, 2011). In Calforna, Hayhoe (2004) fnd that under certan scenaros clmate change wll reduce snow pack n the Serra Nevada mountans by 73-90%, thus, sgnfcantly reducng the man source of fresh water n the state. Beyond clmate change, envronmental regulatons can also mpact the avalablty of water for agrculture. For example, regulaton under the Endangered Speces Act has reduced the supply of rrgaton water to farmers n Calforna, Arzona, Texas and other locatons (Moore, Mulvlle, and Wenberg, 1996). Relable estmates of the economc mpacts of expected reductons n rrgaton water supples are of crucal mportance to the desgn of effcent water polcy. The welfare mplcatons of changes n water avalablty are dffcult to observe drectly snce water n agrcultural settngs s not allocated by a compettve prce mechansm n the vast majorty of agrcultural areas. Whle there s usually not a compettve market for water that establshes a market-clearng prce, there s a hghly compettve market for farmland. Ths paper explots dfferences n observed transacton-based farmland values among parcels wth dfferental access to rrgaton water delveres to nfer the value of water to producers. We base our analyss on a dataset of farmland transactons n Calforna s San Joaqun Valley, one of the most mportant agrcultural areas n the world. We contrbute to the larger hedoncs lterature, by estmatng a hedonc model usng a plot-level fxed effects desgn to control for unobservable tme-nvarant factors. Wth cross-sectonal data t s dffcult to adequately control for unobserved varables that may be correlated wth the explanatory varable of nterest and the outcome varable leadng to based coeffcents. Panel data on the repeated sale of the same parcel of farmland over tme would allow one to parse out any bas due to unobserved tme-nvarant characterstcs. We make a frst step n ths drecton by constructng a small panel dataset to estmate the value of water avalablty whle controllng for unobservables at the parcel level. Consstent wth theory, the panel analyss suggests that the value of rrgaton water n Calfor- 3

14 na agrculture s hgher than estmates obtaned from the pooled cross-sectonal analyss. Indeed, the estmates from our panel analyss usng a plot-level fxed effects desgn are several tmes the sze of cross-sectonal estmates. We provde evdence that ths result s not an artfact of a selecton process; we run the cross-sectonal analyss on the same set of plots that appear n the panel analyss. We fnd results are smlar to other studes and are consstent wth the presence of mportant unobservable cross-sectonal varaton that bases cross-sectonal estmates of the value of rrgaton water supples towards zero. Thus, farmers wllngness-to-pay for an addtonal acre-foot of water per acre appears to be much larger than pror estmates. The hedonc approach s commonly used for evaluatng envronmental polces; examples nclude the Clean Ar Act (Chong, Phpps, and Anseln, 2003; Chay and Greenstone, 2005) and the Superfund program for cleanup of hazardous waste stes (Greenstone and Gallagher, 2008). The approach s also used for valung natural resources such as water qualty (Leggett and Bockstael, 2000) and clmate (Mendelsohn, Nordhaus, and Shaw, 1994; Schlenker, Hanemann, and Fsher, 2006). Other examples of the hedonc method appled to polcy evaluaton and resource valuaton are numerous. Kumnoff, Parmeter, and Pope (2010) pont out that n the presence of omtted varables the hedonc prce functon can produce severely based estmates. Unobserved characterstcs that affect the sale prce of a good may also be correlated wth the explanatory varable of nterest; n ths paper we make ths pont explct. To do so, we evaluate the qualty of hedonc valuatons of rrgaton water supples usng cross-sectonal estmates compared to panel estmates usng plot-level fxed effects. Startng wth Selby (1945) and most recently Petre and Taylor (2007) emprcal studes have analyzed how access to rrgaton water s captalzed nto farmland value. Other examples nclude Hartman and Anderson (1962), Crouter (1987), and Faux and Perry (1999). Most smlar to ths study s the work of Schlenker, Hanemann, and Fsher (2007) SHF henceforth, who use crosssectonal data on self-reported plot-level land values from the June Agrcultural Survey. The survey s geo-referenced whch allows them to match farm-level data on the value of a farm wth clmate and sol databases. Ther study takes place over a smlar tme perod and locaton; therefore, ther results can be compared to ours. The remander of ths chapter s organzed as follows. In the next secton we present a smple economc model to motvate the emprcal analyss. Secton 2.2 descrbes the data sources. In secton 2.3 we present the man estmatng equatons. The subsequent secton shares the estmaton results along wth a dscusson. The fnal secton concludes and ndcates areas for future work. 2.1 Economc Model Ths secton presents the economc logc of the hedonc prce analyss for the valuaton of rrgaton water supples. Followng Crouter (1987) and others, we ntroduce a model of farmland prces applyng Rosen s theory of hedonc prce functons (1974). Rosen s theory allows one to nfer the market value of a good by examnng the prces of a composte good whch nclude the good of nterest. Applyng the theory, we nfer that there s an mplct market for rrgaton water delveres that works through the explct farmland market. The man economc concept exploted n the hedonc prce analyss s that the prce of farmland equals the net-present value (NPV) of economc rents expected from the farmland whle the prce of the dfferentated attrbute s the shadow value of the attrbute n terms of net present value. 4

15 A potental buyer of a plot of farmland observes that the land comes wth a quantty of expected water avalablty and that ths land and water may be combned wth varable nputs to produce output n year t. We defne output n year t n terms of a producton functon, f (L,W,v t ) where L s land, W s water avalable to the plot and v t s some optmal quantty of a varable nput n tme perod t. The buyer assumes the prce of the output s p t and the cost of the varable nput to be c t n perod t; the cost of the land wth ts assocated water supply s q(l,w), whch s the hedonc prce functon. Based on these factors, the potental buyer consders the economc rents that may be derved n a year by choosng the optmal level of v t gven avalable land and water, and facng prces p t, c t, and q(l,w). Sad dfferently, she solves the followng proft maxmzaton problem: max Π = (v t ) δ t (p t f (L,W,v t ) c t v t ) q(l,w) (2.1) t=0 The resultng Π equals the expected economc rent to be obtaned from the land. Next we consder how to assess the shadow value of a permanent change n yearly water avalablty. Frst, we note that a change n W wll affect Π t ; ths change n Π t s the shadow value of addtonal water n a year of producton, λ. The shadow value of a permanent change n yearly water avalablty s the sum of dscounted shadow values of addtonal water for each year. The NPV of a permanent change n annual water supply can be wrtten as: λ W = t=0 δ t λ. In ths smple framework λ W s the value of an addtonal unt of rrgaton water delveres n perpetuty. To complete ths analyss we te λ W to changes n land prces assocated wth a unt change n rrgaton water delveres. Because land markets are compettve, all economc rents wll be bd away that s, the prce of land wll reflect the NPV of producton on the land. Therefore, any dfferences n land prces reflect dfferences n the NPV of the land. In summary, the partal dervatve of the hedonc prce functon wth respect to W s equvalent to the shadow value of a permanent ncrease n water avalablty: q(l,w) W = λ W = t=0 δ t λ (2.2) Importantly, the am of the emprcal analyss s to recover a consstent estmate of λ W. 2.2 Data We gather data on sale prces of all land transactons n eght Calforna countes between 2001 and 2008, water delveres and land acreage for rrgaton dstrcts, groundwater depth measurements, hstorcal temperature and precptaton, sol qualty measures, land classfcaton codes, and measures of populaton densty. All data resources are combned nto a sngle dataset for analyss. Ths fnal dataset s comprsed of 8 countes, 19 hydrologcal unt areas, and 28 rrgaton dstrcts Outcome Varable: Farmland Sale Prce Per Acre The farmland prce data were purchased from DataQuck, a prvate frm whch collects data on land sales, mostly from county court houses. Each observaton s geo-referenced wth lattude and longtude, and both the street address and lot sze are observed, whch allows for clear dentfcaton 5

16 of repeat observatons. In addton to land prces and the aforementoned varables, the transacton data nclude nformaton on transacton characterstcs such as whether the sale was a foreclosed property. Characterstcs related to structures on the property are n the dataset ncludng whether there s buldng on the property, total square footage of the buldng, the number of bedrooms, and the number of bathrooms, as well as an estmate of the percentage mprovements made to the property. Other property characterstcs nclude lot sze and a approxmate measure of the prmary use of the land accordng to a county admnstrator Explanatory Varable of Interest: Surface Water Delvery Rght Per Acre In 1933 the State of Calforna passed the Central Valley Project Act. Ths act authorzed the government to begn fundrasng for the constructon of water nfrastructure such as reservors, dams and canals to support rrgated agrculture. Due to the Great Depresson, the federal government made several fnancal transfers to the State of Calforna to complete the project. Today, the Unted States Bureau of Reclamaton s responsble for the admnstraton of the Central Valley Project (CVP) that delvers surface water to rrgaton dstrcts n Calforna s Central Valley. Farmland wthn an rrgaton dstrct has a contractual rght to buy a fxed amount of water n a gven year from the Bureau of Reclamaton. However, due to changng hydrologc condtons and other factors, the federal government does not guarantee that any specfc amount of surface water delveres wll be made n any gven year. Therefore, farmers may use the current year s surface water delveres as a best estmate of water rghts enttled to a plot of land. Surface water delveres from the Central Valley Project account for a sgnfcant share of agrcultural water use n Calforna. Data on federal surface water delveres come from the Bureau of Reclamaton whch records annual delveres at the rrgaton dstrct level. We make the strong assumpton that the rrgaton dstrct level delvery s evenly dvded among all land n the dstrct. Based on conversatons wth rrgaton dstrct managers ths s a vald approach gven that ths s how water rghts are allocated. Hence, to compute a per-acre measure of surface water delvery rghts we dvde the total quantty of surface water delveres by the total amount of land n acres wthn an rrgaton dstrct Control Varables Other sources of surface water delveres are the State Water Project and prvate projects whch are usually admnstered by local governments; both are observed n our dataset. The last major source of water for agrculture s groundwater, whch vares sgnfcantly across the State and wthn our sample. We gather data on groundwater avalablty from the Calforna Department of Water Resources. They record approxmated measures of groundwater levels n over 15,000 wells for several decades. Many wells are not measured regularly or durng the sample perod, and the wells used for groundwater measurements are not evenly dstrbuted across agrcultural land. Therefore, we use regonal averages of groundwater avalablty to create plot-level measures of groundwater avalablty; these are lkely measured wth error. Data on groundwater qualty and other hydrologcal characterstcs such as groundwater flow drecton are not easly collected and so are unobserved n ths analyss. However, hydrologsts have surveyed Calforna and defned 6

17 areas wth smlar hydrologcal characterstcs, we reference these as hydrologcal unts. These are contguous areas smaller than a county, yet crossng county lnes; the land transactons n the sample are spread across 19 hydrologcal unts. We collect data on sol qualty from the Unted States Department of Agrculture s Natural Resources Conservaton Servce whch mantans both STATSGO and SSURGO2 sol databases. Nether of these sol databases are deal for plot-level analyss because, lke the groundwater measures, they are a weghted average of sol type over large swaths of land; ths mples sgnfcant varaton wthn each sol survey unt and non-trval measurement error. Ths poses a problem f the unmeasured component of sol qualty s correlated wth both delveres and land prce. For example, there may be a partcularly hgh qualty pece of land wthn a low average sol qualty area. If the hgh qualty land requres less rrgaton water to effectvely water plants, then ths source of measurement error would cause a downward bas n our pont estmate on delveres. In addton to rrgaton water avalablty and sol qualty, clmate s lkely to be another mportant determnant of farmland value. We use the same hgh-resoluton temperature and precptaton clmate data that has been employed by others (Schlenker, Hanemann, and Fsher, 2006). These clmate data were organzed by the Spatal Clmate Analyss Servce at Oregon State Unversty for the Natonal Oceanc and Atmospherc Admnstraton. Plot-level measures of clmate are nterpolated usng the PRISM model also developed by researchers at Oregon State. We use thrty-year hstorcal annual ranfall and both maxmum and mnmum temperatures to control for clmate n our analyss. There s evdence that alternatve clmate measures such as degree days and ranfall tmng wthn a year as well as durnal temperatures are more nformatve clmate measures than hstorcal means. However, we only use clmate measures n the cross-sectonal analyss the mpact of clmate on farmland values wll ultmately be parsed out n the panel data analyss because clmate does not vary n our sample tme perod. Another mportant factor to control for n any analyss of farmland values s urban development potental. Our approach to ths problem s to create a fve mle buffer zone around populaton centers. Vsual nspecton of these buffer zones usng ArcGIS confrms these are more densely populated areas Sample Selecton We proceed wth the crtera employed n sample selecton. For ncluson n the fnal sample we only use observatons whch satsfy several crtera. Frst, we drop all plots that also receve water from the State Water Project (SWP). Delveres from the SWP may be negatvely correlated wth CVP delveres and postvely correlated wth prce. We do not observe the actual quantty delvered from the SWP; n order to avod omtted varable bas we exclude these observatons. Second, varaton n urban development potental may stll be sgnfcant even after controllng for plots near populaton centers. Land prces over $20,000 per acre n year 1998 prces lkely represent plots of farmland wth urban development potental and so were removed from the sample. For smlar reasons we dropped land classfed as rural resdental by the Calforna Department of Conservaton. We also drop plots sold more than three tmes n our sample perod or sold twce wthn the same year. The concern s that property wth hgher turnover may also sgnal urban development potental, or other characterstcs unque to propertes whch are sold more than three tmes n a decade. Thrd, plots wth houses and other sgnfcant nfrastructure wll greatly affect the prce per acre. Smlar to urban development potental, plot attrbutes such as housng may 7

18 dwarf varaton n prces due to surface water delveres. To address ths ssue we drop all observatons wth bedrooms, bathrooms or wth buldngs larger than 1500 square feet (ths allows for servce sheds). We also had to drop sales whose recorded prce ncluded non-farmland parcels because nformaton on the non-farmland porton of the property were not reported n our data. Fnally, we drop plots of land that have relatvely lttle use for rrgaton water; farmland plots used for tmber, poultry or dary producton are removed. The admttedly small panel sample has 304 observatons representng 146 parcels of farmland. In order to evaluate the external valdty of our panel estmates we compare these plots of farmland for whch we have repeated observatons to all plots satsfyng the descrbed selecton crtera; we reference the latter as the non-panel sample. Table 1 reports the means and sample standard devatons for observable covarates by the nonpanel and panel samples. The samples are comparable although statstcally sgnfcant dfferences exst between them. The plots of land n the panel sample receve more ran, have hgher average maxmum daly temperatures, and are at a hgher elevaton than plots of land n the non-panel sample. 8

19 Table 2.1: Comparson of plot characterstc means across samples All Panel Only Mnmum Maxmum Mean Mean P-value Prce per acre (dollars) (4540) (3848) Delveres n year of sale (acre-feet) (.819) (.785) Lot sze (n thousands of acres) (.06) (.07) Buldng structure/storage shed (d) (.29) (.26) Square footage of buldng structure (916.3) ( ) Prvate water delveres access (d) (.5) (.5) No groundwater (d) (.49) (.49) Mean depth to groundwater (ft) (48.35) (45.38) Elevaton (meters) (37.53) (36.24) Hstorcal mean ranfall (.01) (.01) Hstorcal mean max temp ( C) (.07) (.06) Hstorcal mean mn temp ( C) (.04) (.03) Store Index for sol qualty (.03) (.03) Orchards (d) (.48) (.48) Vnyards (d) (.39) (.38) Dstance to freeway (.01) (.01) Rural resdental buffer (d) (.47) (.48) Partal property sale (d) (.16) (.12) Total Observatons Note: Sample standard devatons presented n parantheses. 9

20 2.3 Emprcal Research Desgn The man emprcal concern s that an unobservable plot characterstc s correlated wth both water delveres and land prces. We descrbe ths emprcal challenge n more detal and justfy the need for panel data to address the potental problem of omtted varable bas. Then we ndcate how we wll proceed wth the emprcal analyss and present the man estmatng equatons Emprcal Challenge To begn, we assume land and water are the only two factors of producton and that land qualty s homogeneous. Therefore, the hedonc prce equaton may be estmated usng: prce/acre t = β 0 + β 1 delveres t + ε t (2.3) In ths equaton, denotes the plot of land, the outcome varable s the prce per acre of the land sale, and delveres captures the expected stream of annual surface water to be delvered n perpetuty to plot. The parameter β 1 can be nterpreted as the shadow value of a permanent shock to water delveres supply (λ W ); β 1 s expected to be postve. If one observes land prce and volumetrc water delveres, then one can estmate β 1 consstently f the followng dentfyng assumpton holds: E[ε t delveres t ] = 0 (2.4) Assumng equaton (2.4) holds then β 1 can be estmated usng Ordnary Least Squares to recover the captalzed value of surface water delveres. However, the dentfyng condton can be volated n many ways. The most basc way s that there are unobservable envronmental qualty characterstcs of the plot that are correlated wth delveres so that: ε t = γ EQ + η t (2.5) where EQ s the underlyng envronmental qualty of plot. If EQ s observable then one can consstently estmate the coeffcent of nterest f the followng condton holds: E[η t delveres t, EQ ] = 0 (2.6) Ths s the assumpton mantaned n pooled cross-sectonal analyses such as n (SHF, 2007). Ths dentfyng assumpton s volated f there are plot specfc unobservable characterstcs, whch are correlated wth ether the other envronmental qualty measures or delveres. That s, the error term from equaton (2.3) may take the form: where, ε t = θ + γ EQ + ν t (2.7) E[θ EQ, delveres t ] 0. (2.8) Relaxng the assumpton of homogeneous land qualty and assumng the expressons n equatons (2.7) and (2.8) hold, then the only way to estmate β 1 consstently s usng a fxed effects estmator, whch requres repeat sales of the same plot. 10

21 2.3.2 Estmatng Equatons The emprcal analyss can be dvded nto two parts. In the frst part, followng prevous lterature we estmate the hedonc prce functon usng a cross-sectonal specfcaton wthout plot-level fxed effects. We also consder several cross-sectonal specfcatons wth varous controls, and estmate a model usng a random effects specfcaton clusterng at the hydrologcal unt level as ths s, n general, a more effcent estmator than Ordnary Least Squares (OLS) when usng clustered data. Second, we estmate a model usng plot-level fxed effects, and then run a Hausman test to evaluate the consstency of the random effects estmator clustered at the plot-level. For all specfcatons we measure expectatons about the stream of future water delveres usng delveres n the year of sale 1. In the sub-sectons that follow, we present the estmatng equatons and dscuss advantages and dsadvantages of each specfcaton. Pooled Cross-Sectonal Analyss We frst estmate the lnear relatonshp between prce per acre and acre-feet of water delveres per acre usng OLS ncludng controls for lot sze, whether there s buldng on the property, the buldng sze, alternatve surface water supply avalablty, groundwater depth, hstorcal ranfall and temperature, sol qualty, crop producton (orchards, vneyards and row crops/pasture land as the excluded group) populaton densty and transacton characterstcs such as whether the sale was a partal property sale. For a full lst of the control varables see table 2.1. In another specfcaton we estmate a random effects model wth spatal clusterng at the hydrologcal unt level. As mentoned earler, a hydrologcal unt s a regon of land (smaller than a county and larger than an rrgaton dstrct) wth smlar underlyng hydrologcal characterstcs. Because hydrologcal characterstcs are correlated wth sol, land wthn the same hydrologcal unt wll lkely have more smlar sol than land across hydrologcal unts. It s also true that plots wthn the same hydrologcal unts are lkely to experence smlar clmates. If ths s the case, then the random effects model wll produce nconsstent estmates. In a thrd specfcaton, we nclude hydrologcal unt fxed effects to account for groundwater avalablty, water qualty and flow drecton common to all land wthn n the hydrologcal unt. In fact, the hydrologcal unt fxed effects capture all characterstcs common to all land wthn the hydrologcal unt. For these reasons, hydrologcal unt fxed effects may be a better way to control for these mportant producton factors when usng cross-sectonal data. Perhaps the most compellng argument for ths spatal fxed effects estmator s that hydrologcal unts cross over rrgaton dstrcts lnes so that one can compare a plot n an rrgaton dstrct (.e., a plot that receves federal water delveres) to a plot that les just outsde the rrgaton dstrct but wthn the same hydrologcal unt. In ths sense, the estmaton s smlar to a border dscontnuty desgn; however, we cannot explctly employ a regresson dscontnuty approach snce we do not observe data delneatng borders. There s stll the potental that we could be omttng varables that vary across tme at the hydrologcal unt level such as changng urban development potental that, n turn, affect farmland prces. To partally control for ths possblty, we estmate a fourth specfcaton n whch we 1 We argue that current delveres s the correct measures of future delveres on the bass that water polcy n Calforna s n a constant state of evoluton, and that the recent past has been so unusual that t s a poor ndcator of water supply allocatons. 11

22 nteract the hydrologcal unt fxed effects wth a lnear tme trend. In a ffth specfcaton we add the set of hydrologcal unt fxed effects nteracted wth a quadratc tme trend. Ths fnal estmatng equaton s gven by: prce/acre jt = β 1 delveres t + β 2 X + β 3 Z t + µ j + τ t + µ j t + µ j t 2 + ε jt (2.9) where ndcates the plot; j ndcates the hydrologcal unt; t ndcates the year; delveres t represents the water delveres; X are tme-nvarant observables lke hstorcal mean temperature, ranfall, and sol qualty; Z t are tme-varyng transacton characterstcs; µ j s the hydrologcal unt fxed effect; τ t s the year fxed effect; µ t t + µ j t 2 s the hydrologcal unt fxed effect nteracted wth tme trends. It s worth notng that the nterpretaton of β 1 s that of λ W from equaton (2.1), the captalzed value of an acre-foot of water n perpetuty. The problem wth OLS and the spatal fxed estmators such as the model descrbed n equaton (2.9) s that they all ultmately rely on cross-sectonal varaton to dentfy the effect of rrgaton water avalablty on land prce. However, none of these estmators do an adequate job of addressng the man emprcal challenge: accountng for unobservable cross-sectonal varaton. Controllng for sol qualty usng SSURGO2 measures or through the use of spatal fxed effects s not suffcent as sol qualty measures are based on weghted averages over large areas and so, lke spatal fxed effects, assume homogeneous sol qualty for large regons of land. Furthermore, hydrologcal unts are large areas that encompass sgnfcant varaton n envronmental qualty. Thus, the use of hydrologcal unt spatal fxed effects does not satsfy the homogenety assumpton. As already descrbed, to overcome ths one could collect plot-level measures of sol qualty, although f there are remanng tme-nvarant omtted varables then the estmates may stll be based. For ths reason, an estmator employng panel data s attractve. Panel Analyss Envronmental qualty s slow to change over tme so one may consder t tme-nvarant over the sample perod; a plot-level fxed effects estmator wll parse out all varaton due to tme nvarant plot-level characterstcs. The estmatng equaton for the plot-level fxed effects analyss s gven by: prce/acre jt = δ 1 delveres t + δ 2 Z t + θ + τ t + µ j t + µ t 2 + ε jt (2.10) where, j and t are as before; θ s the plot-level fxed effect and Z t are tme-varyng transacton characterstcs; δ 1 s nterpreted as λ W from equaton (2.1), the captalzed value of an acre-foot of water n perpetuty. Ths specfcaton wll control for varaton n the outcome varable due to tme-nvarant characterstcs ncludng underlyng envronmental qualty of the land. Smlar to the cross-sectonal specfcaton, we estmate a hydrologcal unt specfc quadratc tme trend to account for tme varant omtted varables whch accounts for factors exhbtng a quadratc tme trend common wthn a hydrologcal unt. Standard Error and Pvotal Statstc Adjustments Statstcal nference s complcated due to the clustered structure of the data. To address clusterng and wthn-cluster heteroskedastcty we compute robust standard errors clustered at the county level (eght clusters). Bertrand, Duflo, and Mullanathan (2004) show that when there are a small 12

23 number of clusters (ten or less), the performance of statstcal nference usng cluster-robust standard errors s unrelable. Cameron, Gelbach, and Mller (2008) fnd the same result and consder a varety of standard error adjustments for clustered data and then evaluate whch adjustments offer relable performance for statstcal nference. They suggest usng the wld cluster-bootstrap method to obtan pvotal t-statstcs as ths offers asymptotc refnement. We follow ther advce, and compute a wld cluster-bootstrap pvotal t-statstc for each regresson coeffcent; then the analytcally computed cluster-robust standard error s used wth the adjusted pvotal t-statstc to perform hypothess testng. 2.4 Results and Dscusson We begn wth the results presented n table 2.2, whch presents the results of the cross-sectonal analyss usng the pooled non-panel sample. As we move across columns we see pont estmates from dfferent regresson specfcatons. In column (1) we present the smple OLS estmate of $219 for the captalzed value of an acre-foot of water. In the second specfcaton we present the random effects model clustered at the hydrologcal unt level. Surprsngly, the random effects pont estmate s dentcal to the OLS estmate. Ths suggests that there s no dependence between error terms wthn a hydrologcal unt (the level at whch the random effects model s clustered). Notably, ths random effects specfcaton s most smlar to the specfcaton employed by SHF (2007). The pont estmate of $219 s less than the pont estmate of $656 obtaned n ther study; however, dfferences between the samples may account for the observed dfference n pont estmates. Furthermore, the standard errors on pont estmates from SHF and our cross-sectonal analyss are not small enough to reject the null hypothess that they are dentcal. In column (3) of table 2.2 we present the results from the hydrologcal unt fxed effects estmaton. The pont estmate s slghtly larger, although we cannot reject a Hausman test that the pont estmates from the random effects and fxed effects models are dfferent. Ths evdence aganst clusterng s consstent wth the fndngs of SHF s results n whch they favor a random effects model over a fxed effects model, and wth the result that the OLS and random effects pont estmates are dentcal. In subsequent columns we test f hydrologcal unt specfc tme trends affect the pont estmates and we fnd no sgnfcant dfferences. 13

24 Table 2.2: Cross-sectonal sample: Regress prce/acre on federal water delveres Dependent varable: Prce per acre-foot/acre of water (Mean: 9,521, S.D.: 5,802) (1) (2) (3) (4) (5) Captalzed value of one acre-foot/acre federal surface water of ( λ W ) (170) (170) (185) (175) (201) # of observatons 1,702 1,702 1,702 1,702 1,702 R Year fxed effects Yes Yes Yes Yes Yes Tme varant controls Yes Yes Yes Yes Yes Hydrologcal unt fxed effects No No Yes Yes Yes Hydro. unt fxed effects*lnear Trend No No No Yes Yes Hydro. unt fxed effects*quadratc Trend No No No No Yes Robust standard errors clustered at the county level n parentheses. *** p<0.01, ** p<0.05, * p<0.1. In table 2.3 we see the results of the cross-sectonal analyss usng the panel sample. The regresson specfcatons n each column are the same as those n the correspondng columns of table 2.2. The pont estmates n the frst two columns are dentcal, ths s consstent wth what we observed n the prevous table there s lttle spatal dependence between observatons wthn a hydrologcal unt. The subsequent columns represent specfcatons ncludng the hydrologcal fxed effects. These models produce larger pont estmates for the value of rrgaton water, all estmates are greater than $1,000. However, we cannot reject the Hausman test s null hypothess that the random effects estmate s consstent. As before, ths result corroborates prevous evdence that there s lttle spatal dependence across observatons wthn a hydrologcal unt. Based on ths cross-sectonal analyss, we have no evdence that the value of rrgaton water s dfferent than the $656 estmate obtaned by SHF (2007). Table 2.3: Panel sample: Regress prce/acre on federal water delveres w/o plot-level fxed effects Dependent varable: Prce per acre-foot/acre of water (Mean: 9,339, S.D.: 5,779) (1) (2) (3) (4) (5) Captalzed value of one acre-foot/acre of federal surface water (λ W ) (129) (129) (423) (573) (585) # of observatons R Year fxed effects Yes Yes Yes Yes Yes Tme varant controls Yes Yes Yes Yes Yes Hydrologcal unt fxed effects No No Yes Yes Yes Hydro. unt fxed effects*lnear Trend No No No Yes Yes Hydro. unt fxed effects*quadratc Trend No No No No Yes Robust standard errors clustered at the county level n parentheses. *** p<0.01, ** p<0.05, * p<

25 We now turn to the results of the panel analyss usng plot-level fxed effects. Table 2.4 presents the results of these regressons. The frst column presents a random effects specfcaton wth the cluster at the plot-level. The pont estmate s -$369, and has a large standard error, especally gven the large bootstrapped crtcal t statstc. Subsequent columns nclude plot-level fxed effects. The second column reports a pont estmate of $2,655 and s sgnfcant at the 99% level; we strongly reject the Hausman test. We obtan a smlar result n column (3) when we control for the percentage of captal mprovements on the land. In the subsequent columns we add a hydrologcal unt lnear and quadratc tme trends, respectvely. Addng these regon specfc tme trends substantally ncreases the pont estmate on delveres to over $4,000. All of these estmates are sgnfcantly dfferent than zero at the 99% level when usng the robust standard errors clustered at the county level and our wld cluster bootstrapped crtcal t statstcs for hypothess testng. Based on SHF (2007) we also consder the null hypothess that the captalzed value of an acre-foot of water s $656; we are able to reject the null at the one percent level for columns (2) and (3), and at the fve percent level for columns (4) and (5). Based on our own data, the largest cross-sectonal estmate for the captalzed value of an acre-foot of water s $1,210. If we test our pont estmates from the plot-level fxed effects models aganst ths as the null hypothess we stll reject the null at the one percent level for the specfcatons n columns (2) and (3). Ths ndcates that f one beleves the plot-level fxed effects specfcaton consstently estmates the shadow value of expected future delveres then the estmates from the cross-sectonal analyss exhbt a large downward bas. Table 2.4: Panel sample: Regress prce/acre on federal water delveres w/ plot-level fxed effects Dependent varable: Prce per acre-foot/acre of water (Mean: 9,339, S.D.: 5,779) (1) (2) (3) (4) (5) Captalzed value of one acre-foot/acre *** 2603*** 4611*** 4286*** of federal surface water ( λ W ) (369) (380) (379) (1680) (2029) [4.59] [1.82] [1.74] [1.81] [1.69] # of Observatons R Plot-level fxed effects (146 plots) No Yes Yes Yes Yes Year fxed effects Yes Yes Yes Yes Yes Controls No No Yes Yes Yes Hydro. unt fxed effects*lnear Trend No No No Yes Yes Hydro. unt fxed effects*quadratc Trend No No No No Yes Robust standard errors clustered at the county level n parentheses. Wld cluster bootstrapped crtcal t-statstc for 99th percentle. *** p<0.01, ** p<0.05, * p<0.1. In terms of magntude, our estmates of $2,603 to $4,611 per captalzed acre-foot of water are two and a half to four tmes the sze of the cross-sectonal estmates usng the same data. The estmates are roughly the same degree of magntude larger than those of SHF who put the 15

26 captalzed value of rrgaton water at $656 per acre-foot. Second, the average prce of an acre of land n our sample s $9,339 wth the average plot recevng acre-feet per acre. Our estmate of $4,286 suggests that, on average, rrgaton water rghts account for approxmately 20% of the sale prce. Taken together our results suggest 1) that farmers have a much hgher wllngness-to-pay for water than prevously thought, and 2) that ths result plays a non-trval role n the determnaton of rrgated farmland prces. One may wonder how clmate change wll affect landowners wth rghts to surface water. To address ths, we consder the work of Chung (2005) and Vcuna (2006) who use the CALSIM 2 smulaton model to make predctons of the mpact of clmate change on CVP surface water delveres south of the Delta between 2035 and 2064, and between 2070 and Ther analyses are based on the A2 emsson scenaro modeled usng the Geophyscal Flud Dynamcs Laboratory global clmate model, detals can be found n Hanemann et al. (2006) and Cayan et al. (2008). Under the GFDL A2 emsson scenaro, Chung (2005) fnd that medan expected CVP surface water delveres are 2,435 thousand acre-feet (TAF) between 2035 and 2064, 14.5% less than base delveres durng the same tme perod. Usng the same GFDL A2 emsson scenaro, Vcuna (2006) fnds medan expected delveres are 1,944 TAF, 31.4% less than base delveres between 2070 and As an exercse, we assume these mpacts are not currently captalzed nto farmland values and generate an estmate of the net present value (NPV) of clmate change s aggregate mpact va water reductons on landowners wth rghts to CVP water. We calculate: Welfare = 58 t=24 δ t λ (Base TAF 1 Reduced TAF 1 ) + 88 t=59 δ t λ (Base TAF 2 Reduced TAF 2 ) (2.11) In ths welfare loss calculaton δ s the dscount factor and s based on a fve percent dscount rate; λ s the mpled value of an acre-foot of water. The change n welfare s the sum of losses from the perod and the perod ; t represents the number of years from 2011 that the loss wll be realzed. Based on a captalzed value for one acre-foot of $4,286, then assumng a 5% dscount rate, the mpled value of an acre-foot of water, λ, s $204. The base allocaton n the perod s assumed to be 2,716 TAF whle the reduced allocaton s 2,435 TAF. The base allocaton n the perod s assumed to be 2,833 TAF whle the reduced allocaton s 1,944 TAF. A substtuton of the relevant numbers nto equaton (2.11) ndcates the clmate change aggregate welfare loss to Calforna farmers due to reduced water delveres s $460 mllon dollars. Notably, ths fgure s based on the assumpton that clmate change has no mpact on delveres untl Nor does the calculaton consder water reductons beyond 2099 although these may be consderable. One fnal caveat s that these predctons are the outcome of one smulated clmate model and a partcular dscount rate, other scenaros wll lead to dfferent predctons. 2.5 Conclusons and Future Work Usng a small sample of repeated sales of agrcultural land n Calforna, we fnd evdence that exstng cross-sectonal estmates of the value of water delveres to agrculture are sgnfcantly downward based. Usng a plot-level fxed effects estmaton we account for unobserved factors correlated wth delveres and farmland prces, and obtan novel estmates of the value of water 16