Agri-environment Policy Design With Hidden Information and Hidden Action: Input Quotas vs Input Charges

Transcription

1 Agr-enronment Polcy Desgn Wth Hdden Informaton and Hdden Acton: Input Quotas s Input Charges Adam Ozanne* School of Economc Studes, Unersty of Manchester, Manchester M3 9PL, UK. Ben Whte School of Agrcultural and Resource Economcs, Unersty of Western Australa, 35 Strlng Hghway, Crawley, Perth, Western Australa AARES Annual Conference Fremantle, -5 February 003 * Adam Ozanne s currently stng the School of Agrcultural and Resource Economcs at the Unersty of Western Australa. Please emal comments to Adam.Ozanne@man.ac.uk

2 Abstract Moxey, Whte and Ozanne (999 hae shown how transfer payments coupled wth nput quotas can be used to desgn optmal truth-tellng mechansms for oluntary agr-enronmental schemes under hdden nformaton about complance costs. Ozanne, Hogan and Colman (00 adapted the Moxey et al. model to analyze hdden acton n such schemes, analyzng the relatonshps between nput abatement, the cost of montorng complance and farmers rsk preferences. Whte (00 extended the Moxey et al. model to analyze the desgn of contracts under both hdden acton and hdden nformaton, but used an nput charge/transfer payment approach rather than the orgnal nput quota/transfer payment one. In addton, he assumed that farmers caught cheatng face a arable fne, related to the amount of nput they apply n excess of the amount agreed n the contract, rather than a fxed fne as assumed by Ozanne et al. Whte argues that hs results show that an nput charge/transfer payment polcy s more effcent than a quota when the regulator cannot obsere complance costs of nddual farmers. Ths paper ntegrates the preous work, deelopng a model of both hdden acton and hdden nformaton n agr-enronmental schemes based on the nput quota/transfer payment approach of Moxey et al. (999 and Ozanne et al. (00, rather than the nput charge/transfer payment approach of Whte (00, but the arable fne of the latter rather than the fxed fne assumed by Ozanne et al. Ths ntegrated model shows that, contrary to Whte (00, the nput quota and nput charges approaches lead to dentcal outcomes n terms of abatement leels, compensaton payments, montorng costs, probabltes and socal welfare.

3 3. Introducton Moxey, Whte and Ozanne (999 use a prncpal-agent model to show how transfer payments coupled wth nput quotas can be used to desgn optmal truth-tellng mechansms for oluntary agr-enronmental schemes such as Countrysde Stewardshp, Ntrate Senste Area Scheme and Enronmental Senste Area Scheme. The soluton results n a menu of contracts specfed n terms of transfer payments and nput quotas. Producers choose the contract for ther type: hgh complance cost producers choose a hgh nput quota and low transfer payment contract whle low complance cost producers choose a low quota and hgh transfer payment contract. Moxey et al. only consdered the hdden nformaton (or aderse selecton aspect of asymmetrc nformaton problem facng a regulator. Howeer, f the regulator cannot obsere post-contractual nput use and therefore has to ncur montorng costs to ensure that farmers comply wth contracts, there s a hdden acton problem as well. Ozanne, Hogan and Colman (00 adapted the Moxey et al. model to analyze hdden acton n such schemes, showng that, because of the trade-off between ncreased enronmental beneft and ncreased cost of montorng complance, only a second-best soluton can be obtaned. Taken together these two papers prode a theoretcal framework that coers both types of nformaton asymmetry n agrenronmental polcy, but treatng them separately. Whte (00 extended the Moxey et al. model to analyze the desgn of contracts under both hdden acton and hdden nformaton, but used an nput charge/transfer payment approach rather than the orgnal nput quota/transfer payment one. In addton, he assumed that farmers caught cheatng face a arable fne, related to the amount of nput they apply n excess of the amount agreed n the contract, rather than a fxed fne as assumed by Ozanne et al. Whte argues that hs results show that an nput charge/transfer payment polcy s more effcent than a quota when the regulator cannot obsere complance costs of nddual farmers. Ths paper ntegrates the preous work, deelopng a model of both hdden acton and hdden nformaton n agr-enronmental schemes. The model s based on the nput quota/transfer payment approach of Moxey et al. (999 and Ozanne et al. (00, rather than the nput charge/transfer payment approach of Whte (00, but the arable fne of the latter rather

4 4 than the fxed fne assumed by Ozanne et al.. Ths ntegrated model shows that, contrary to Whte (00, the nput quota and nput charges approaches lead to dentcal outcomes n terms of optmal abatement leels, compensaton payments, montorng costs and probabltes of detecton, and socal welfare.. The model Agr-enronmental polcy s modeled as a socal welfare maxmzaton problem that recognzes the constrants facng polcy-makers due to nformaton asymmetry and the costs of montorng contracts wth farmers. The followng sectons use prncpal-agent theory to model agrenronmental contracts between a regulator and farmers, progressng from a stuaton where the regulator has perfect nformaton, through separate models for hdden nformaton and hdden acton, to an ntegrated model whch ncludes hdden nformaton, hdden acton and the cost of montorng complance.. Perfect nformaton Adoptng the approach and notaton used by Moxey et al. (999, t s assumed that the regulator ams to maxmze a socal welfare functon wth three terms: z = ( x * - x + (b - c (x - (+ eb =, ( where farmer s assumed to be more effcent than farmer. The frst term on the rght hand sde of equaton ( represents the beneft of nput abatement, where x * s the optmal nput leel used by farmer f he or she does not partcpate n the scheme, x s the agreed nput quota f she partcpates, and measures the enronmental beneft per unt of nput abatement. The second term, (b c (x, ges the th farmer's monetary Note that, n amalgamatng the models, t has been necessary, for the sake of consstency, to make mnor notatonal adjustments when summarzng the models presented n Ozanne et al. and Whte. These adjustments are not always ponted out, but hae no sgnfcant mpact on the results and should not present any dffculty to the careful reader.

5 5 utlty (or rent as the dfference between the transfer payment, b, offered to nduce partcpaton and the cost of complance, c (x, where the latter functon s defned as the proft forgone, c (x = π (x * - π (x ( wth c (x<0, c (x>0, c (x>c (x and c (x>c (x by defnton (see Moxey et al., 999, for a more detaled dscusson of the propertes of the complance cost functon. The fnal term on the rght-hand sde s the net socal cost of the transfer payment, where e represents the shadow costs of publc funds n terms of the dstortonary effects of general taxaton. Ths specfcaton of objecte functon assumes that the scheme apples to a small area relate to the total agrcultural area, so that prce effects are zero. It also assumes that the benefts from contractng wth one farm do not depend on any other farms jonng the scheme; ths enables us to use a lnear benefts of abatement functon. If the regulator has perfect nformaton about the farmer s complance cost functon and the farmer s actons ex post, the objecte functon ( s maxmzed subject to the nddual ratonalty (IR constrants, b - c (x 0 =, (3 and non-negatty constrants, x 0 and b 0. The nternal soluton s gen by, ( = (4 + e where s the optmal nput quota for the th farmer when the regulator has perfect nformaton ˆ * and the correspondng transfer payment s b = c ( = π π (. Together, the contracts (, bˆ represent the frst-best soluton to the problem facng the regulator. Equaton (4 ndcates that these contracts ensure that the margnal cost of complance s equal to the margnal beneft of abatement to socety. These contracts, arred at usng the nput quota/transfer payment

6 6 approach, are effectely dentcal to perfect nformaton contracts obtaned by Whte (00, equaton (7 usng the nput charge/transfer payment contract approach: t = (5 + e where t s the nput charge, snce socal welfare s maxmzed when t = - c (x.. Hdden nformaton wth frst-best contracts If the regulator offers the frst-best contracts (, bˆ but cannot obsere farmer type, there s an ncente for the less effcent farmer, type, to be declare that he or she s a more effcent farmer, snce obtanng contract ( ˆx, ˆb by ths decepton earns rent: ˆb c ( ˆx > 0 snce IR s bndng and therefore c ( ˆx < c ( ˆx = ˆb Note, howeer, that a smlar ncente to be economcal wth the truth does not exst for the more effcent farmer, who would be worse of f he or she obtaned contract ( ˆx, ˆb : ˆb c ( ˆx < 0 snce IR s bndng and therefore ˆb = c ( ˆx < c ( ˆx Thus, offerng the frst-best menu of contracts when there s hdden nformaton s costly to the regulator snce total transfer payments ncrease whle oerall abatement decreases. The regulator may reduce the cost of the scheme by only offerng contract ( ˆx, ˆb. Howeer, ths wll only attract the less effcent farmers and abatement wll be lower than desred..3 Hdden nformaton: second-best contracts The Moxey et al., 999, model was based on the assumpton that, although the regulator s unable to obsere whether nddual farmers are more or less effcent, t does hae subjecte pror probabltes, γ, for the two types as well as beng able to obsere farmer's actons ex post. The regulator s am s therefore to maxmze expected socal welfare,

7 7 * z = γ [ ( x x + ( b c ( x ( + e b ] (6 = subject to the nddual ratonalty constrants (3 and hdden nformaton ncente compatblty (HIIC constrants, b - c (x b j - c (x j, j =,; j. (7 whch ensure that there s no ncente for ether producer to choose the wrong contract. Moxey et al. show that IR and HIIC are bndng, and that the second-best contracts, (, bˆ, are gen by: c ( = (8 + e γ e = + e γ ( + e [ ( ( ] > + e ( (9 bˆ c ( = bˆ c ( ˆ (0 x b ˆ c ( 0 ( = From equaton (8 t can be seen that the nput quota offered to the less effcent farmer s the same as under perfect nformaton,.e. ˆx = ˆx. Howeer, equaton (9 shows that, snce c (x>c (x by defnton, the quota offered to the more effcent farmer s hgher than n the frst-best soluton;.e. abatement s reduced, ˆx > ˆx. Furthermore, although equaton ( shows that the transfer payment offered the more effcent farmer equals hs or her cost of complance, equaton (0 shows that the less effcent retans some rent.

8 8 The correspondng hdden nformaton contracts obtaned by Whte, 00, equatons (0 and ( usng the nput charge/transfer payment contract approach are defned by the followng: t = ( + λ t = γ e x + + λ γ ( + e ( t x ( t x ( t ( Whte does not pont ths out, but, as n the perfect nformaton case, these second-best contracts under hdden nformaton - usng the nput quota/transfer payment approach and nput quota/transfer payment approaches respectely - are effectely dentcal. For the less effcent farmer, ths s obous from equatons (8 and (. It s less obous, from comparson of equatons (9 and (, for the more effcent farmer, but neertheless true, snce t s smple to show that as c (t j = x (t j, x ( t x( t ( x ( x = (3 ' x ( t Thus, when hdden nformaton alone s consdered, the nput abatement leels, compensaton payments, socal welfare and nformatonal effcency losses are exactly the same whether agrenronmental contracts are desgned usng an nput charge or nput quota approach..4 Hdden acton If the regulator obseres the farm type but not the farm s nput use wthout montorng, there s an ncente for both types of farmers to accept the approprate contract, but exceed the nput quota stpulated n the contract (or mpled by the nput charge, whlst clamng the full transfer payment. Ozanne et al., 00, and Whte, 00, both show montorng can reduce ths hdden acton problem, but that, because there s a trade-off between nput abatement and the montorng

9 9 costs borne by the taxpayer, nput abatement s lower than under perfect nformaton. Howeer, there are dfferences n how they model the stuaton. Both assume that the regulator montors nput use and fnes any farmer found not be complyng wth the terms of the agreed contract. Montorng s assumed to be perfectly accurate n the sense that when a farm s montored the regulator obseres the nput leel wthout error. The fne leel s exogenous, but the regulator can determne the probablty of detecton by aryng the frequency of montorng. Howeer, Whte assumes farmers caught cheatng face a arable fne, whch s proportonal to the quantty of nput they apply n excess of the reported amount, whereas Ozanne et al. assume a fxed fne. In addton, Ozanne et al. assume the compensaton payment s confscated, whle Whte does not. Here, a mxture of the aboe approaches s followed. The nput quota/transfer payment approach s used, as n Moxey et al. and Ozanne et al. Howeer, transfer payments are not confscated and fnes are not fxed; rather, as n Whte s model, t s assumed, that the penalty for non-complance s a fne of η per unt of nput n excess of the agreed quota, where η s the same for both types of farmer. The regulator offers farmers a menu of contracts, comprsng of nput quotas, transfer payments and montorng regmes. The probablty of detectng non-complance for the th farmer, correspondng to the respecte montorng frequency, s set at p. In addton, for smplcty, montorng costs are assumed to be lnear, mp, where the parameter m representng the cost of montorng a farm wth certanty, p=, s the same for both farm types. Thus, the regulator s objecte functon s: 3 z = ( x * - x + (b - c (x - (+ e(b + mp =, (4 It s a standard result that regulators prefer hgh penaltes as ths reduces the frequency of montorng and thus montorng costs. Howeer, penaltes for non-complance hae tended to be low and the legslaton establshng agr-enronmental schemes has not allowed regulators to set ther own penaltes (Natonal Audt Offce, Whte s orgnal specfcaton does not allow for the net socal cost of montorng to the taxpayer by multplyng the fnal term n the socal welfare functon, mp, by (+e. Here we follow Ozanne et al., who do.

10 0 Whte demonstrates that, to ensure ncente compatblty, montorng must be set such that t = p η, that s the nput charge s equal to the expected fne per unt of nput, and replaces the last term n the objecte functon wth mt /η. For, f t > p η rsk neutral producers would hae an ncente to under report nput use. On the other hand, f t < p η montorng costs would be excesse, snce settng p such that t = p η s suffcent to ensure complance. Usng the nput quota/transfer payment approach, ths s equalent to ntroducng the explct hdden acton ncente compatblty (HAIC constrants, p η c (x (5 nto the model. These HAIC constrants state that, to deter cheatng, the expected fnes per unt of abatement must be at least as great as the margnal profts foregone (recallng equaton ( for the respecte farm types. They follow drectly from Whte s characterzaton of the montorng regme, snce t = - c (x. They may also be dered by notng that, n order to deter cheatng, the certan return from complance must not be less than the expected return from noncomplance: bˆ c ( ( p ( bˆ c ( x + p ( bˆ c ( x η( x bˆ c ( x p η( x p c ( x c ( η for all x x In the lmt. ( x the fracton n the last equaton becomes the margnal cost of complance, The hdden acton model can now be soled by maxmzng socal welfare (4 subject to the IR constrants (3, the HAIC constrants (5, the non-negatty constrants, x 0 and b 0, and the probablty of detecton constrants, 0 p. The nternal soluton for the

11 regulator, yeldng the optmal nput quotas, transfer payments and detecton probabltes respectely for the two types of farmer, s gen by the followng: m ( = + ( > + e η + e (6 b ˆ = c ( (7 pˆ ( ˆ x = (8 η Equaton (6 confrms that, snce c (x >0 by defnton, the quota offered to the more effcent farmer s hgher than n the frst-best soluton;.e. abatement s reduced, >, for both types of farmer. Once agan, takng account of mnor notatonal adjustments and the fact that here we hae allowed for the socal cost of montorng to the taxpayer, t can be seen that the aboe s dentcal to the soluton obtaned by Whte, 00, usng the nput charge/transfer payment approach, t = m + ' + e η x ( t dt d ( x snce socal welfare s maxmzed when t = - c (x and = = = ( x. x ( t dx dx The model presented aboe adopts the arable fne approach of Whte, 00, rather than the fxed fne approach of Ozanne et al., 00. For the sake of completeness, t can be readly shown that the aboe soluton s dentcal to that obtaned by Ozanne et al.. For, f nstead of specfyng a fne per unt nput, η, the regulator mposes fxed fnes, F, where, F ( ˆ x = η ( equaton (6 can be rewrtten as,

12 ( = ( + e ( + m F whch s the Ozanne et al. soluton for rsk neutral farmers and lnear montorng cost and enronmental beneft functons. It wll be noted that ths requres dfferng fnes for the two types of farmer, F F, whereas the arable fne approach assumes the two types of farmer face the same fne per unt of nput n excess of the quota, η, f they are found n breach of contract..5 Hdden nformaton and hdden acton If the regulator obseres nether the farm type nor ther actons there s potental for a combnaton of both hdden nformaton (aderse selecton and hdden acton (moral hazard problems to occur. Amalgamatng the models presented n sectons.3 and.4, the regulator's problem s then to maxmze the expected socal welfare functon: = = * z γ [ ( x x + ( b c ( x ( + e( b + mp ] (9 subject to the IR constrants (3, HIIC constrants (7, HAIC constrants (5, non-negatty, x 0 and b 0, and probablty of detecton (or montorng frequency constrants, 0 p. Assumng a separatng soluton holds, so that IR and HIIC and both the HAIC constrants are bndng, the second-best contracts, (, bˆ, pˆ, are gen by: m = + ( > + e η + e ( (0 m γ e = + ( + e η γ ( + e [ ( ( ] > + e ( ( bˆ c ( = bˆ c ( ˆ ( x

13 3 b ˆ c ( 0 (3 = pˆ ( ˆ x = =, (4 η Once adjustments hae been made for mnor changes n notaton and treatment of the socal cost of montorng, t can be seen that the aboe s dentcal to Whte s separatng soluton obtaned usng the nput charge/transfer payment approach, t = m + + e η x ( t t = + + e η m x t ( γ e ( x ( t x ( t + γ ( + e x ( t snce socal welfare s maxmzed when t = - c (x and, as shown n sectons.3 and.4, x ( t = ( ˆ x and ( x ( x x ( t x( t = x ( t 3. Concluson Usng prncpal-agent theory, agr-enronmental polcy has been modeled as a socal welfare maxmzaton problem that recognzes the constrants facng polcy-makers due to nformaton asymmetry and the socal costs of montorng contracts wth farmers. Preous work by Moxey et al. (999, Ozanne et al. (00 and Whte (00 has been combned to prode a model of both hdden acton and hdden nformaton n agr-enronmental schemes. The model utlzes the nput quota/transfer payment approach of Moxey et al. (999 and Ozanne et al. (00, rather than the nput charge/transfer payment approach of Whte (00, but the arable fne of the latter rather than the fxed fne assumed by Ozanne et al. It has been shown that, contrary to Whte (00, the nput quota and nput charges approaches lead to dentcal

14 4 outcomes n terms of optmal abatement leels, compensaton payments, montorng costs, detecton probabltes and socal welfare. It s ntended that further work wll extend the model to allow for farmer rsk aerson, as n Ozanne et al. (00, and use numercal smulatons - based on plausble representatons of producton technology, farmer s rsk preferences and montorng costs - to analyze the relate mportance of hdden nformaton and hdden acton n the desgn of agr-enronmental contracts. Other possble areas nclude the effects of ncome uncertanty (as n Fraser, 00 and repeated contracts (as n Hogan, 00, and extendng the two-producer type model to a contnuum of producer types (as n Whte and Ozanne, 997. References Hogan, T. (00. Asymmetrc nformaton and agr-enronmental polcy. Unpublshed Ph.D. thess, Unersty of Manchester. Fraser, R. (00. Moral hazard and rsk management n agr-enronmental polcy. Journal of Agrcultural Economcs 53: Moxey, A., Whte, B. and Ozanne, A. (999. Effcent Contract Desgn for Agrenronmental Polcy. Journal of Agrcultural Economcs 50:87-0. Ozanne, A., Hogan, T. and Colman, D. (00. Moral hazard, rsk aerson and complance montorng n agr-enronmental polcy. European Reew of Agrcultural Economcs 8: Natonal Audt Offce (997. Report by the Comptroller and Audtor General: Protectng Enronmentally Senste Areas. London: HMSO. Whte, B. (00. Desgnng oluntary agr-enronmental polcy wth hdden and hdden acton: a note. Journal of Agrcultural Economcs 53: Whte, B. and Ozanne, A. (997. Asymmetrc nformaton and agr-enronmental polcy. Dscusson paper presented at the annual conference of the Agrcultural Economcs Socety, -3 March, Ednburgh Unersty.