Do farmers value the environment? Evidence from a conservation reserve program auction

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1 Avalable onlne at Internatonal Journal of Industral Organzaton 26 (2008) Do farmers value the envronment? Evdence from a conservaton reserve program aucton Tomslav Vukna a,, Xaoyong Zheng a, Mchele Marra a, Armando Levy b a Department of Agrcultural and Resource Economcs, North Carolna State Unversty, Ralegh, NC , Unted States b Brattle Group, San Francsco, Unted States Receved 7 August 2007; receved n revsed form 4 January 2008; accepted 7 January 2008 Avalable onlne 15 January 2008 Abstract The paper uses data from one Conservaton Reserve Program (CRP) aucton to elct farmers' atttudes toward the envronment by analyzng ther bds. The CRP pays farmers to remove chosen plots of land from agrcultural producton and put them to a conservaton use. An nterestng aspect of ths aucton s that wnners are determned by a combnaton of low bds and envronmental scores of ndvdual plots. Usng decson theoretc approach to model ths aucton we show that farmers condton ther bds on the strength of ther envronmental scores and that they value envronmental benefts, especally those that ncrease future sol productvty of ther land Elsever B.V. All rghts reserved. JEL classfcaton: D44; D81; Q51; Q58 Keywords: Government auctons; Decson theory; Envronmental benefts evaluaton 1. Introducton In ths paper, we study the strateges of bdders n an aucton sponsored by the U.S. Department of Agrculture (USDA) to determne partcpants n the Conservaton Reserve Program (CRP). The CRP pays farmers to remove land from producton and put t to a conservaton use. Farmers wshng to partcpate bd the prce per acre they wll receve f accepted nto the program. In addton, an envronmental score s calculated whch attempts to The authors want to thank Rob Innes, Guy Lacrox, Dean Lueck, Bruce Shearer, Matt Shum, an anonymous referee and semnar partcpants at the Unversty of Arzona and Unversté Laval. Correspondng author. Tel.: ; fax: E-mal addresses: tom_vukna@ncsu.edu (T. Vukna), xzheng@ncsu.edu (X. Zheng), mchele_marra@ncsu.edu (M. Marra), Armando.Levy@brattle.com (A. Levy). measure the potental envronmental benefts of dlng the offered parcel. The score s the sum of sx separate categores each expressng dfferent envronmental attrbutes such as wldlfe habtat, water qualty or sol eroson reducton. Ths score s then combned wth the farmer's bd va a formula establshed by USDA at the end of the bddng perod to obtan an ndex whch provdes the rankng used to decde program partcpants. The man objectve of ths paper s to understand how farmers formulate optmal bddng strateges when competng n the CRP auctons. Snce ndvdual envronmental scores measure dfferent potental envronmental benefts, some of whch could affect long term farm proftablty and land values whereas others are more of a publc goods nature, exactly how farmers condton ther bds on those ndvdual categores should reveal nformaton about farmers' preferences towards conservaton and protecton of the envronment /$ - see front matter 2008 Elsever B.V. All rghts reserved. do: /j.jndorg

2 1324 T. Vukna et al. / Int. J. Ind. Organ. 26 (2008) There are several papers that examne CRP aucton data n the lterature. For example, Shoemaker (1989) examned the results of early bddng behavor on land values and argued that asymmetrc nformaton about farmer rsk averson and farmers learnng the bd cap (the maxmum acceptable bd, whch was not revealed n the early sgn-up perods) caused bds to approach the bd cap. Smlarly, Rechelderfer and Boggess (1988) found that when conservaton contracts are sold n sequental auctons, farmers can analyze the results of the precedng rounds and ncrease ther bds. Mranda (1992) used bd data from the frst CRP sgn-up to test f landowners consder n ther bddng behavor the sol productvty gans from placng land n the CRP. She found a strong postve relatonshp between the opportunty cost of placng land n the CRP and the bd, but a much weaker relatonshp between the bd and future on-farm productvty gans. Fnally, Krwan, Lubowsk and Roberts (2005) estmated the premum receved by CRP partcpants above ther reservaton rents and found that n sgn-ups 20 and 26 those premums amounted to 10 40% of the CRP total payments. Ths paper dffers from the earler CRP lterature n that by modelng a new generaton of CRP auctons n whch envronmental scores and bds are jontly used to determne the wnners, we accomplsh two thngs: frst, explan how bdders formulate bds gven dfferences n the envronmental characterstcs of ther land, and second uncover farmers' preferences towards dfferent categores of envronmental benefts. The CRP auctons are sgnfcantly dfferent from the nsttutons typcally studed n the aucton lterature. Frst, n the CRP auctons wnners are determned by a combnaton of low bds and hgh envronmental scores rather than the bds only. Second, the wnner determnaton rule and the number of unts offered n the aucton (number of parcels that wll be accepted nto the program) are not revealed to the bdders when they bd. Fnally, the number of potental bdders n each of the CRP auctons are n the thousands, whle typcal auctons deal wth no more than a few dozen potental bdders. These mportant dfferences prevent us from usng a structural approach based on the game theoretc aucton models (e.g. Guerre et al., 2000) to emprcally analyze the aucton data. 1 1 Promnent examples of emprcal research on auctons that nvolve government agences as auctoneers such as the CRP nclude the seres of papers examnng the auctons for outer contnental shelf (OCS) ol exploraton tracts (e.g., Hendrcks and Porter, 1988; Leland, 1978), U.S. Forest Servce tmber auctons (e.g., Athey and Levn, 2001; Hale, 2001), Federal Communcatons Commsson spectrum auctons (Ausubel et al., 1997), and government procurement auctons (e.g. Thel, 1988; Levn and Smth, 1990). Instead, we model farmers' optmal bddng strategy usng decson theoretc approach remnscent of the early emprcal works on auctons (e.g., Fredman, 1956; Capen et al., 1971). 2 Our model provdes the unque soluton to the optmal bd whch separates the measurement of the farmer's agrcultural producton values and envronmental benefts from the strategc effect resultng from the program scorng rules. An ncrease n an ndvdual envronmental score has two effects on the optmal bd: t rases a farmer's total score whch ncreases the probablty a bd s accepted (a postve-strategc effect) and t rases a farmer's long run proft/utlty thereby lowerng the opportunty cost of CRP partcpaton (a negatve-envronmental effect). The model dentfes these two effects even when the trade-off between envronmental scores and bds s unknown. The emprcal analyss s carred out usng the ndvdual contract data for the 15th sgn-up CRP aucton from North Carolna. Ths s the frst aucton followng the major changes n the program structure where bdders were frst made aware of the envronmental scorng rules before the sgn-up perod. The results show that farmers do n fact condton bds on the strength of ther envronmental scores and that they consstently value envronmental mprovements, especally the long-term benefts of enhanced sol productvty beyond the contract perod. The rest of the paper s organzed as follows: the next secton descrbes the nsttutonal detals of the CRP and the aucton data. The thrd secton presents the decson theoretc model of the farmers' bddng behavor when they hold heterogenous belefs, whle the fourth secton bulds on the theory to formulate an econometrc model. The ffth secton presents and dscusses the emprcal results emphaszng the dual effect of the scorng rules on the equlbrum bd. The sxth secton concludes wth a dscusson of the polcy mplcatons of the emprcal results. 2. Program descrpton and data The US Conservaton Reserve Program was ntroduced n the Food Securty Act of 1985 (the 1985 Farm Bll). Accordng to the program, a farmer can bd qualfed land nto the program and, f the bd s accepted, contract to receve annual rental payments equal to the value of the submtted bd n exchange for removng the land from agrcultural producton and puttng t to a conservaton use. In addton to an annual per-acre rental payment, the farmer may request a one- 2 For an excellent survey of ths lterature see Laffont (1997).

3 T. Vukna et al. / Int. J. Ind. Organ. 26 (2008) tme cost share payment to partally offset the cost of conservaton practces she promsed to nstall on her land. Ths contract s generally for 10 or 15 years. USDA perodcally announces sgn-up perods when farmers can offer bds to place land nto the program. The 1996 Federal Agrcultural Improvement and Reform Act (the 1996 Farm Bll) made some fundamental changes to the CRP. It placed addtonal restrctons on qualfyng land and the total acreage that could be accepted nto the program (36.4 mllon acres natonally, 10% of each state's total cropland and 25% of the county's total cropland). It also requred for the frst tme an upper lmt on acceptable bds. The maxmum acceptable bd (cap) was now equal to the average land rental rate for each sol type n the county where the proposed CRP land s located, plus a $5 per acre mantenance allowance (USDA, 1997a). The Bll also provded for contnuous sgn-up perods for partcular partal-feld practces, such as rparan buffer strps, that nvolve a small amount of acreage, but provde a dsproportonately large envronmental beneft. 3 Thrty-three sgn-up perods have been held snce the CRP's ncepton. Bds n sgn-up perods 1 9 were not ranked accordng to the potental envronmental benefts the parcel would provde. Begnnng wth the 10th sgnup perod an Envronmental Benefts Index (EBI) was calculated for each parcel offered but ths nformaton was not shared wth farmers pror to the submsson of bds. Fnally, begnnng wth the 15th sgn-up perod producers were made aware of most of the scorng rules makng up the EBI before the sgn-up perod. The data used n ths study comes from the 15th sgn-up perod n North Carolna, whch was held n The defntons of ndvdual envronmental scores are presented n Table 1. A more detaled summary of the scorng rules s presented n Table 2. In order to rank bdders, the EBI combned the envronmental scores (N1 N6) that measure the potental envronmental benefts of an offered parcel wth the cost factor (N7). 4 Of the sx envronmental scores, N3 (on-farm benefts from reduced wnd and water eroson) and N4 (long term benefts of cover beyond the contract perod) measure benefts that are largely concentrated on the farm n the form of ncreased future productvty of 3 In a contnuous sgn-up, f the land s elgble and the bd s at or below the bd cap, plus an ncentve payment of up to 25% of the cap, the land s accepted automatcally nto the CRP. As such, contnuous sgn-ups are not nterestng for the types of questons we address n ths paper. 4 The EBI has changed snce. For nstance, carbon sequestraton has been added as an envronmental category; see e.g., Krwan, Lubowsk and Roberts (2005). Table 1 Components of the envronmental benefts ndex 15th sgn-up EBI components Max. ponts N1: Wldlfe habtat 100 N2: Water qualty benefts from reduced 100 water eroson, run-off and leachng N3: On-farm benefts from reduced wnd 100 and water eroson N4: Long-term benefts of cover beyond 50 the contract perod N5: Ar qualty benefts from reduced wnd eroson 25 N6: Benefts from enrollment n conservaton 25 prorty areas N7: Cost factor 200 Total: 600 Source: USDA (1997b). land once the retred land comes back nto agrcultural servce. In addton, the CRP provdes envronmental benefts that are spread across a larger area beyond the farm borders such as wldlfe habtat (N1), water qualty (N2) and ar qualty benefts (N5). Fnally, score N6 (benefts from enrollment n conservaton prorty area) does not correspond to any plot-specfc envronmental potental. All parcels located n a gven geographcal area, n our case the long leaf pne prorty area, automatcally earn 25 ponts regardless of ther envronmental characterstcs. N6 s most easly nterpreted as a geographc control for some unmeasured envronmental potental. The cost factor (N7) s obtaned by convertng a farmer's dollar bd (rental rate offered) nto EBI ponts usng a partcular transformaton scheme (see formulae n the bottom two rows of Table 2). For example, f n the 15th sgn-up a farmer submtted a bd of $40/acre and requested no cost-share money, N7 ¼ 190 ð Þþ ¼ 153:94. If she submtted a bd of $30, her N7 would ncrease to Envronmental scores are computed by the personnel of two USDA agences n each county: the Farm Servce Agency (FSA) and the Natural Resource Conservaton Servce (NRCS). Ponts are assgned n each envronmental category for each offered parcel as prescrbed by the handbook whch lsts specfc detals on how ponts are to be assgned for each conservaton practce and land characterstc (USDA, 1997b). The bddng process has become much more transparent snce the 1996 Farm Bll was enacted. There has been a concerted effort to see that all bdders have the same nformaton about how ther EBI s determned. Each bdder s gven a fact sheet about the scorng rules for each envronmental category, and FSA and NRCS personnel revew the sheet wth the applcant. Before submttng a bd, each bdder knows

4 1326 T. Vukna et al. / Int. J. Ind. Organ. 26 (2008) Table 2 Scorng rules for the CRP 15th sgn-up Man Categ. Sub-category (allocated ponts) N1 Cover factor (50) Proxmty to wetland (10) N2 Prorty Ground water area (30) qualty (20) N3 Erodblty ndex (100) N4 Long-term tree, shrub, and wetland retenton (50) N5 Wnd eroson (25) N6 N.E. cape fear for wldlfe habtat (25) N7 N7=190 (bd/165) 190 a (200) Source: USDA (1997b). a Addtonal 10 ponts contngent on declnng a cost share. Proxmty to prot. area (10) Surface water qualty (40) Upland-wetland rato (10) Cropped wetland converson (10) Endang. spec. area (15) Contract area (5) 5 To conform to prvacy rules, the NRCS strpped each ndvdual bd of any nformaton that could possbly dentfy a farmer, whch effectvely precludes any economc analyss that would requre bdders soco-economc characterstcs. On the other hand ths data set s unque n that t contans the records on all submtted bds,.e. those accepted as well as the rejected bds. the number of ponts earned n each envronmental category, the total envronmental score and the applcable bd cap for the parcel under consderaton, but not the value of the cost factor N7. Ths nformaton (N1 N6) s entered on the Conservaton Reserve Program Worksheet whch s sgned by the bdder (USDA, 1997b). The formula for convertng monetary bds nto the cost factor (N7) ponts as well as the weght of N7 n the total EBI were not known to farmers pror to the submsson of bds. Bdders n the 15th sgn-up were told only that a lower bd would mprove ther chances of acceptance, but were not told exactly how lowerng ther bd would affect ther cost factor (N7). Addtonally, requestng a cost share would lower the EBI by 10 ponts. The N7 formula and ts weght n the total EBI were then determned by the Secretary of Agrculture after all the bds had been receved n Washngton. Ths fnal decson was made on a natonal bass, takng total EBI scores, total program cost and the county, state, and natonal acreage caps nto account and communcated to growers through the FSA county offces. All bdders knew ther respectve bd caps. The emprcal analyss n ths paper s performed wth the ndvdual CRP contracts data that contan the followng varables: acres offered, rental rate offered (bd), maxmum pay rate (cap), total cost share, envronmental scores (N1 N6), cost factor (N7) and 7 the total EBI (Σ k=1 Nk). 5 Summary statstcs for the entre data set are gven n Table 3. Note the small values of envronmental scores for ar qualty (N5) and conservaton prorty areas (N6) relatve to ther maxmal levels. Accordng to the EBI, ar qualty s not an envronmental concern n rural North Carolna. The average sze of N5 s 0.003, whereas the maxmum number of ponts that could have been earned n ths category was 25. The number of plots elgble for recevng N6 ponts was also very small. Notce that the number of North Carolna farmers nterested n partcpatng n the program was The mnmum EBI score needed to wn acceptance nto the program was 259, and the percentage of successful bdders was 68%. 3. A smple optmal bddng model The most common approach n the aucton lterature s to specfy bdders' belefs accordng to a game theoretc soluton concept such as a Bayesan Nash equlbrum n whch each bdder correctly accounts for the effects of ther own bds on the bds of others. That s, one farmer's belef about the bds of others s a functon of her own bd (see, for example, Laffont, 1997). In ths paper, we do not pursue a game theoretc Table 3 Summary statstcs for all observatons n 15th sgn-up Varable Mean S.D. Number of bds 2915 Bd ($) Bd cap ($) EBI EBI cut-off 259 Accepted bds 68.2% N N N N N N

5 T. Vukna et al. / Int. J. Ind. Organ. 26 (2008) approach because we don't beleve farmers consder the strategc effect of ther bds on the bds of others due to the fact that the number of potental bdders s large and they are geographcally dspersed. As seen from Table 3, there are 2,915 bdders for one CRP aucton n our data set and they are spread across the entre state. Moreover, the acceptance nto the program s based on the natonally determned EBI cut-off score so n effect an ndvdual farmer-bdder s competng aganst farmers from the entre country. Based on these nsttutonal features, we propose a smple decson theoretc model where economc agents (farmers) maxmze proft/utlty n a perfectly compettve framework. We assume that farmers are rsk neutral and each of them s endowed wth a pece of land of a gven sze and fxed characterstcs whch can be ether farmed or enrolled n the CRP n ts entrety. By assumng exogenous, fxed characterstcs and land endowments, we avod the problems of dealng wth the farmer's decson of whch parcel of land to enroll and whether to nstall certan conservaton practces that may ncrease the EBI score and for whch cost-share money s avalable. 6 Partcpaton n the CRP generates a stream of conservaton payments from the government, mposes certan costs caused by an mmedate loss of farmng ncome and creates non-stochastc envronmental benefts. When placng a bd, farmer holds prvate expectatons about the stream of dscounted future profts from farmng y and envronmental benefts caused by dlng the land under the CRP contract e. Both y and e are measured relatve to the status quo of leavng the land n agrcultural producton. The dscounted future stream of government payments to program partcpants s denoted by b. From a farmer's pont of vew, the cost of program partcpaton can be defned as the net agrcultural cost of retred land (ncludng both current costs and future benefts) C =y e 0. The net benefts of enrollng the land nto the program are smply b C. Consder the problem of the farmer decdng on the bd b that she s gong to submt to the program for a 6 parcel wth envronmental score s = Σ k =1 Nk. 7 A 6 These smplfcatons are not overly restrctve because a) the choce of parcel s somewhat restrcted by the elgblty rules (USDA 1997b), and b) the cost share requests are not very common, accountng for only 11% of the total submtted bds n the 15th sgn-up. 7 Ths s a smplfcaton because the actual bds submtted by farmers are per acre annual rental rates B whereas b =Σ T t =0 δ t B s the present value of the stream of submtted bds (annual CRP payments) over the length of the contract perod T. sgnfcant feature of the CRP auctons s that farmers do not know the trade-off between bds and the cost factor (N7). Ex post, the trade-offs have been lnear (see the bottom row n Table 2), but ex ante, they are (and contnue to be) unknown. Farmers are only told that lower bds and hence hgher scores mprove ther chances of acceptance. Therefore, we assume that P (b ), the farmer's belef about the probablty of beng accepted nto the program when he bds b, s contnuous and decreasng on the support [0,β ] where β s the maxmum allowable bd (cap), that s, AP ðb Þ Ab b0. Ths captures the fact that the hgher the bd, the lower the acceptance probablty wll be. It s also assumed that P (β )N0 as there s also a probablty that a bd at the cap β wll be accepted. In our settng, farmer 's belefs P are affected by two factors: her belefs about the unknown CRP scorng rules and her belefs about the strength of her envronmental score s. In the rest of the paper, we assume that farmers share common belefs about CRP scorng rules but dffer systematcally condtonal on ther own envronmental scores, that s, the heterogenous belefs across farmers stem from ther envronmental scores. Therefore, the probablty P s condtoned on s, that s P(b s ). To solve the model, we need to consder three possble scenaros. Frst, a bdder wth C N β would not bother to partcpate, so n our data we only observe bdders wth 0 C β. Second, a bdder wth C = β should be ndfferent between partcpatng and not partcpatng and f she chooses to partcpate, she would bd b = β. Fnally, a bdder wth 0 C b β, would surely partcpate and would determne her optmal bd by solvng the expected proft maxmzaton problem 8 max 0bb V P b ðb C ÞPb ð js Þ: ð1þ The Kuhn Tucker soluton s C ¼ b T þ PbT js PVðb T js Þ b bp ð2þ b T þ PbT js P V ðb T js Þ b b P f b T ¼ b P ð3þ wth the second order condton 2PVðb js ÞþPWðb js Þðb C Þb0: ð4þ 8 Snce we do not observe any bd wth b =0, when solvng the model we gnore the possble corner soluton of b =0. 9 PVðb js Þ ¼ APbjs ð Þ and PWðb js Þ ¼ A2 Pbjs ð Þ. Ab 9 Ab 2

6 1328 T. Vukna et al. / Int. J. Ind. Organ. 26 (2008) The formula for the nteror soluton optmal bd (2) ndcates that bdders mark-up ther bds above the cost of program partcpaton C by P ð b4 js Þ P Vðb 4 js Þ z0.10 It s also apparent that gven fxed belefs P, the potental for envronmental mprovement (ether through ncreased future productvty of land or a more pleasant envronment) reduces the cost of program partcpaton and hence the bd Comparatve statcs results Applyng the mplct functon theorem to the frst order condton (2) holdng C constant, we can show that the optmal bd vares wth s as follows: db 4 APðb 4 js Þ As ¼ þ AP V ð b4 js Þ As b 4 C ds 2PVðb 4 js ÞþPWðb 4 js Þðb 4 C Þ ð5þ The sgn of (5) s theoretcally ambguous. Snce the denomnator s negatve by the second order condton, db 4 ds s gong to be postve as long as the numerator s postve. Ths would mean that the optmal bd ncreases wth an ncrease n the envronmental score of the plot, an ntutvely plausble result. The optmal bds would always ncrease n envronmental scores as long as: AP b 4 js As N APV b4 js b 4 C : ð6þ As Intutvely, (6) restrcts the farmers' belefs about the probablty of beng accepted from changng too slowly as s changes. In order for db4 to be postve, the ds probablty a bd s accepted must change at least at some bounded rate. 11 Applyng the mplct functon theorem to (2) holdng s constant, we obtan another comparatve statcs 10 The magntude of the mark-up can thought of as the nformaton rent earned by the farmers due to ther prvate nformaton about the opportunty cost of ther land. In fact, the asymmetry of nformaton between the farmers and the CRP admnstrators s the prncpal reason for desgnng such an elaborate aucton scheme. In the absence of such asymmetrc nformaton problem, the CRP could smply pay the farmers ther true reservaton prce for the respectve plots and the entre auctonng mechansm would be superfluous. 11 We acknowledge that f the second order condton for proft maxmzaton does not hold, then multple optma or no optmum n the bddng strategy are possble. As shown later when estmatng the model, we choose a specfcaton for P(b) such that (4) s automatcally satsfed. On the other hand, the condton that db4 N0 ds from (6) wll be checked emprcally after estmaton. result descrbng how the optmal bd vares wth net agrcultural costs of retred land: db 4 PV b 4 ¼ js dc 2PVðb 4 js ÞþPWðb 4 js Þ b 4 ð7þ ð C Þ Snce the denomnator s negatve by the second order condton and the numerator s negatve by our prevous assumpton, the optmal bd s always ncreasng n the net agrcultural costs C. Snce C =y e s decreasng n envronmental benefts, t follows that the optmal bd must be decreasng n envronmental benefts. 4. The Econometrc Model Although the theoretcal model above does not provde a closed form soluton for the optmal bd, t does establsh a behavoral relatonshp between bds and measures n our data. The Kuhn Tucker condtons (2) and (3), together wth the fact that a bdder wth C =β would bd b =β f she chooses to partcpate, yeld estmatng equatons b 4 ¼ C Pb4 js PVðb 4 js Þ f b4 b bp s observed ð8þ b P þ P bp js PV b P js V C V P b f b 4 ¼ b P s observed ð9þ that can be estmated wth the avalable data. A sutable estmaton technque for the problem at hand s the nonlnear least squares (NLLS) method that uses (8) as the moment condton. The NLLS method s chosen because a closer examnaton of the estmatng equatons reveals that wth C 0, the lower support of b equals P ð b4 js Þ, whch clearly ndcates ts dependence on the parameters to be estmated through P( s ) P Vðb 4 js Þ and P ( s ). 12 Ths volates the regularty condtons of the classcal maxmum lkelhood estmaton (Donald and Paarsch, 1993, 1996; Chernozhukov and Hong, 2004; Hrano and Porter, 2003) and hence prevents us from usng a standard tobt type estmator that would accommodate both the nteror soluton (8) and the corner soluton (9) of the aucton model. The NLLS method s easy to mplement and does not suffer from such a problem. Its drawback s that the estmaton uses only the porton of the data set where the submtted bds are less than the bd cap. As a result, the estmaton 12 The upper support for b s β.

7 T. Vukna et al. / Int. J. Ind. Organ. 26 (2008) yelds consstent but less effcent estmates relatve to the case where the entre data set were used. The next problem stems from the fact that the ndvdual opportunty costs of program partcpaton C are not drectly observable. To address ths problem we rely on the fact that the maxmum bd cap s determned by the auctoneer for each submtted plot as the average rental rate for the county and sol type n whch the submtted plot belongs. Therefore, the ndvdual opportunty cost of the CRP partcpaton can be approxmated wth some lnear combnaton of the maxmum bd cap β and the measurements of the parcel's potental envronmental benefts gven by ts ndvdual categores of the EBI score N1 through N6: C ¼ a 0 þ ab P þ X6 g k N k : ð10þ In addton, as our model requres P ( s )b0, P(β s ) N 0, and 0 P(b s ) 1, for b (0, β ] (the last relatonshp s due to the fact that P s defned as probablty), we specfy the probablty P(b s )as " # Pb ð js Þ ¼ M ðh 0 þ h 1 s Þ 2 exp b ðh 0 þ h 1 s Þ 2 ð11þ where M N0 s a normalzng constant that guarantees P (b s ) 1forb (0, β ]. Ths specfcaton satsfes all the restrctons mposed by the propertes of P( s ) and some other requrements of the theoretcal model. In partcular, ths specfcaton guarantees that the second order condton (4) holds and hence the optmal bd represents the unque maxmum of the farmers' objectve functon. 13 Fnally, we also assume that the optmal bd b n (8) s observed wth error u wth the property E(u )=0. Wth these assumptons, (8) and (10) yeld the moment condton expressed n terms of the observed bds b Eb ð Þ ¼ a 0 þ ab P þ X6 g k N k þ ðh 0 þ h 1 s Þ 2 ð12þ wth the restrcton 0VC ¼ a 0 þab P þ X6 g k N k b P b ðh 0 þ h 1 s Þ 2 : ð13þ 13 Note that M s not dentfed as t drops out of the frst order condton. But ths does not affect any of our emprcal results. Collectng all the unknown parameters n φ, the NLLS estmator bφ s defned as ub¼arg mn u 1 N X N ¼1 " # 2 b a 0 ab P X6 g k N k ðh 0 þ h 1 s Þ 2 ð14þ where N s the sample sze. 14 Followng Wooldrdge (2002), the asymptotc varance of the NLLS estmator can be obtaned as follows A c var ðubþ ¼ T T XN ¼1 XN ¼1 XN ¼1 j u mb V j u mb! 1 ub 2 j u mb V j u mb! j u mb 0 j u bm! 1 ð15þ where mb ¼ ab 0 þ abb P þ P6 bg k N k þ hb 0 þ hb 1 s Þ 2 ; ub ¼ b mb ; andj u mb ¼ A m b Au. After estmaton, we can decompose the bd nto the program partcpaton cost Cb ¼ ab 0 þ abb P þ X6 gb k N k ð16þ where AC ANk ¼ gb k, and the strategc component Pb ð js Þ P 0 ðb js Þ ¼ h bþ hb 1 s Þ 2 : ð17þ Therefore, an ncrease n an ndvdual envronmental score N k has two effects on the optmal bd. Frst, t rases farmer's long run benefts ether through ncreased future sol productvty or a more pleasant envronment thus lowerng the optmal bd (the drect envronmental effect). Second, t rases a farmer's envronmental score s whch ncreases the probablty that a bd wll be accepted, whch n turn (f (6) s satsfed) ncreases the optmal bd (the ndrect strategc effect). Hence, the margnal effect of an ncrease n any component of the envronmental score on the equlbrum bd, that s, 4 AN k Ab can be dsentangled nto two effects: a) the effect on future farmer's proft/utlty gven by the ncreased future sol productvty and better envronment, and b) the ncrease n payments accrung 14 In practce, we estmate the NLLS model wthout constrant (13) and then check whether (13) holds usng parameter estmates for each observaton. Estmatng the NLLS model wth constrant (13), whch s nonlnear, s extremely dffcult.

8 1330 T. Vukna et al. / Int. J. Ind. Organ. 26 (2008) to the bdder as a result of her land beng perceved by the CRP as envronmentally more valuable thereby commandng a hgher envronmental score. The former component (16) represents the farmer's valuaton of envronmental benefts at the margn, whereas the latter component (17) can be nterpreted as the margnal nformaton rent. 5. Estmaton results Pror to estmaton, the data (bds and scores) have been scaled (dvded) by 100 for numercal reasons. Therefore, the estmate of a 0 s scaled down by 100, θ 0 s scaled down by 10, θ 1 s scaled up by 10, whereas other parameters are not affected. The estmaton ncludes only envronmental scores N1 N4. Ths s because n North Carolna, very few farmers obtaned nonzero values for the remanng two scores and even f the scores are nonzero, there s very lttle varaton n the data. For N5 (ar qualty benefts) only 1 out of 1738 observatons wth nteror bds have a nonzero score. For N6 (conservaton prorty areas), only 10 out of 1738 observatons wth nteror bds have a nonzero score and the score s the same for all of these observatons (Table 4). The estmaton results are presented n Table 5.Before lookng and the statstcal and economc sgnfcance of the estmated parameters, we frst checked whether the condton β (θ 0 +θ 1 s ) 2 N C 0 s satsfed for the nteror bds as requred by our model (8). Ths s satsfed for 1731 out of 1738 observatons. To assess how well the model fts the data, we compare the observed bds wth ther model predctons. As seen from Table 6, the forecasted bds ft the actual bds pretty closely for all percentles of the bd dstrbuton ndcatng that our model fts the data very well. Lookng at the estmated coeffcents one can see that they all have meanngful magntudes and some of them are statstcally sgnfcant. For example, the estmate of α ndcate that an ncrease n a bd cap by $1 would ncrease the bd by roughly 76 cents. The coeffcents on Table 4 Summary statstcs for observatons wth nteror bds Varable Mean Stand. Dev. Number of bds 1738 Bd ($) Bd cap ($) N N N N N N Table 5 Estmaton results Parameter Estmate t-statstc a α γ γ γ γ θ θ N1 N4 scores are small relatve to α, and all except N2 are negatve ndcatng that farmers value envronmental benefts and are wllng to decrease ther bds n the antcpaton of envronmental benefts that the program wll produce. For example, an ncrease n N4 score (long term benefts of cover beyond the contract perod) by 1 pont, wll decrease the average optmal bd by about 5 cents per acre per year. The magntudes of the remanng two negatve coeffcents (N1 wldlfe habtat, and N3 on-farm benefts from reduced wnd and water eroson) are tny and the parameters are not statstcally sgnfcant. The coeffcent on the remanng envronmental score, N2 (water qualty benefts), s actually postve and sgnfcant. A 1-pont ncrease n N2 would ncrease the equlbrum bd by 2 cents, ndcatng that n ths case farmers demand compensaton for the provson of envronmental benefts. The hghlghted results provde evdence that farmers tend to value more the envronmental benefts whch drectly affect future productvty of ther land than those benefts whch focus on larger geographcal areas or enhance the envronment n a publc good sense. Gven the fact that N4 bascally reflects the ncreased sol productvty caused by dlng the land durng the contract perod that farmers can approprate through ncreased future yelds, the estmated margnal effects seem to ndcate that farmers are wllng to shade ther Table 6 Model ft: comparson of observed and predcted bds Percentles Observed bds ($) Predcted bds ($) mean

9 T. Vukna et al. / Int. J. Ind. Organ. 26 (2008) There s a subtle dfference n the way the margnal effects have been estmated. The margnal envronmental effects are the estmated parameters of the model so there s one parameter estmate for the entre sample. On the other hand, the strategc effect s calculated for each ndvdual farmer n the sample, so the result presented n Table 7 s the average over all farmers. Table 7 Average quanttes of economc nterest Item 15th sgn-up Bd $42.70 Cost component C $42.27 Strategc component Pðb4 jsþ P V ð b 4 jsþ $0.43 Effect of 1 pont ncrease n s on Pðb4 jsþ P V ð b 4 jsþ $0.73 bds more f they antcpate future sol productvty gans. Ths result dffers from Mranda (1992) who found dfferences n the relatonshp between the bd and future on-farm productvty gans across regons. Wth the excepton of the Corn Belt and Lake States, farmers n that study ether dd not understand or were falng to act on the on-farm productvty effects caused by sol eroson. Wth mnor exceptons, n all other areas (ncludng Southeast) landowners dd not systematcally take the sol productvty effects nto consderaton when formulatng ther land management strateges. To the extent that dynamc neffcences assocated wth sol degradaton come from farmers' dsregard for future sol productvty, our results show that farmers n fact behave non-myopcally. In addton to the relatonshp between the opportunty cost of program partcpaton and the optmal bd, our econometrc model also enables the quantfcaton of the strategc component of the optmal bd. The decomposton of the bd nto the cost component (16) and strategc component (17) has been done n Table 7. As seen from the results, the cost component amounts to $42.27 per acre per year, or 99% of the total bd, and the strategc component on average amounts to $0.43 or 1%. Ths ndcates that the CRP auctons are pretty compettve as the mark-up only accounts for a very small part of the bd. The obtaned results show that farmers condton ther bds on ther total envronmental scores. As ndcated n the fnal row of Table 7, for each pont ncrease n ther total score s farmers ncreased the strategc component of ther bd by an average of 73 cents. Ths margnal effect of a 1-pont ncrease n s on the strategc component of the bd would amount to the same margnal ncrease n the optmal bd provded that C s held constant. However, nterestngly enough, when emprcally checkng condton (6) that guarantees that the optmal bd s ncreasng n the envronmental score s, t turns out that t s satsfed for only 732 out of 1738 observatons. The envronmental effect and the strategc effect can be added together to obtan the total effect of a 1-pont ncrease n any of the envronmental scores on the equlbrum bd. For example, a 1-pont ncrease n N4 would have a drect negatve envronmental benefts effect on equlbrum bd of 4.81 cents and an average postve margnal strategc effect of 73 cents. 15 Therefore the total effect s cents, meanng that a 1-pont ncrease n N4 score would cause the farmer to ncrease her bd by cents. 6. Conclusons In ths paper, we examne the behavor of bdders n a CRP aucton where wnners are determned by the monetary bds and the envronmental scores reflectng the envronmental benefts that the submtted parcel of land can potentally generate. The framework s of a more general nterest for analyzng other smlar programs where the number of potental entrants s large enough to elmnate the need to cast the problem n a game-theoretc framework. Such auctons are beng used or contemplated for other conservaton programs such as the floodplan swne farms buy-out program n North Carolna and a water conservaton land buy-back along the Flnt Rver n Georga. Ths paper s a frst attempt to quantfy and test bddng behavor n such a settng. Modelng ths unque nsttuton allows us to explan how bdders formulate bddng strateges usng ther belefs about how valuable ther parcel s from the perspectve of the auctoneer and to elct farmers' preferences towards dfferent types of envronmental goods. Based on our theoretcal model we stpulate that farmers should condton ther bds postvely on hgher envronmental score and negatvely on the ndvdual components of the score. The emprcal fndngs, based on the 15th sgn-up CRP aucton n North Carolna where the EBI score was known to the bdders, are generally supportve of the theoretcal predctons of our model. In partcular, we found that: a) farmers condton bds on ther envronmental score and b) farmers care about the envronment, but seem to value more those envronmental benefts that drectly affect the productvty of ther land and less those benefts whch resemble publc goods. These results may have valuable publc polcy mplcatons. For example, f the goal of the program s to maxmze the enrolled acreage subject to the fxed budget constrant, our results ndcate that there may be room for mprovement. Farmers are seen to nternalze those benefts whch postvely affect future productvty of ther land (.e., reduced sol eroson) and hence

10 1332 T. Vukna et al. / Int. J. Ind. Organ. 26 (2008) ncludng these categores n an envronmental scorng procedure may dstort ncentves. Snce the strategc effect s on average shown to be postve, ncludng onfarm envronmental benefts nto the scorng formula compensates farmers for somethng they would have done anyway by smply nflatng the strategc component of ther bds. On the other hand, the aucton s shown to be rather compettve as ndcated by the fact that the bdder mark-up s very small. Hence, redesgnng the aucton rules along the suggested lnes may not save much money to the program. References Athey, S., Levn, J., Informaton and competton n U.S. forest servce tmber auctons. Journal of Poltcal Economy 109, Ausubel, L.M., Cramton, P.C., McAfee, R.P., McMllan, J., Synerges n wreless telephony: evdence from the broadband PCS auctons. Journal of Economcs and Management Strategy 6, Capen, E.C., Clapp, R.V., Campbell, W.M., Compettve bddng n hgh-rsk stuatons. Journal of Petroleum Technology 23, Chernozhukov, V., Hong, H., Lkelhood estmaton and nference n a class of nonregular econometrc models. Econometrca 72, Donald, S.G., Paarsch, H.J., Pecewse pseudo-maxmum lkelhood estmaton n emprcal models of auctons. Internatonal Economc Revew 34, Donald, S.G., Paarsch, H.J., Identfcaton, estmaton, and testng n parametrc emprcal models of auctons wthn the ndependent prvate values paradgm. Econometrc Theory 12, Fredman, L., A compettve bddng strategy. Operatons Research 4, Guerre, E., Perrgne, I., Vuong, Q., Optmal nonparametrc estmaton of frst prce auctons. Econometrca 68, Hale, P.A., Auctons wth resale markets: an applcaton to U.S. forest servce tmber sales. Amercan Economc Revew 91, Hendrcks, K., Porter, R., An emprcal study of an aucton wth asymmetrc nformaton. Amercan Economc Revew 78, Hrano, K., Porter, J.R., Asymptotc effcency n parametrc structural models wth parameter-dependent support. Econometrca 71, Krwan, B., Lubowsk, R.N., Roberts, R.N., How cost-effectve are land retrement auctons? estmatng the dfference between payments and wllngness to accept n the conservaton reserve program. Amercan Journal of Agrcultural Economcs 87, Laffont, J.-J., Game theory and emprcal economcs: the case of aucton data. European Economc Revew 41, Leland, H., Optmal rsk sharng and the leasng of natural resources, wth applcaton to ol and gas leasng on the OCS. Quarterly Journal of Economcs 92, Levn, D., Smth, J., Comment on: some evdence on the Wnner's curse. Amercan Economc Revew 80, Mranda, M.L., Landowner ncorporaton of onste sol eroson costs: an applcaton to the conservaton reserve program. Amercan Journal of Agrcultural Economcs 74, Rechelderfer, K., Boggess, W.G., Government decson makng and program performance: the case of the conservaton reserve program. Amercan Journal of Agrcultural Economcs 70, Shoemaker, R., Agrcultural land values and rents under the conservaton reserve program. Land Economcs 65, Thel, S., Some evdence on the Wnner's curse. Amercan Economc Revew 78, U.S. Department of Agrculture (1997a): Agrcultural Resources and Envronmental Indcators, Economc Research Servce, Natural Resources and Envronment Dvson. Agrcultural Handbook No. 712, Washngton D.C. U.S. Department of Agrculture, 1997b. FSA Handbook: Agrcultural Resource Conservaton Program, 2-CRP (Revson 3). Farm Servce Agency, Washngton D.C. Wooldrdge, J., Econometrc Analyss of Cross Secton and Panel Data. The MIT Press, Cambrdge, MA.