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DISCUSSION PAPER December 005 RFF DP Incentve Payment Programs for Envronmental Protecton A Framework for Elctng and Estmatng Landowners Wllngness to Partcpate Davd F. Layton and Juha Skamäk 1616

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DISCUSSION PAPER December 005 RFF DP Incentve Payment Programs for Envronmental Protecton A Framework for Elctng and Estmatng Landowners Wllngness to Partcpate Davd F. Layton and Juha Skamäk 1616 P St. NW Washngton, DC Incentve Payment Programs for Envronmental Protecton: A Framework for Elctng and Estmatng Landowners Wllngness to Partcpate Davd F. Layton and Juha Skamäk Abstract Ths paper consders the role of ncentve payment programs n elctng, estmatng, and predctng landowners conservaton enrollments. Usng both program partcpaton and the amount of land enrolled, we develop two econometrc approaches for predctng enrollments. The frst s a multvarate censored regresson model that handles zero enrollments and heterogenety n the opportunty cost of enrollments by combnng an nverse hyperbolc sne transformaton of enrollments wth alternatve-specfc correlaton and random parameters. The second s a beta-bnomal model, whch recognzes that n practce elcted enrollments are essentally nteger valued. We apply these approaches to Fnland, where the protecton of prvate nonndustral forests s an mportant envronmental polcy problem. We compare both econometrc approaches va cross-valdaton and fnd that the beta-bnomal model predcts as well as the multvarate censored model yet has fewer parameters. The beta-bnomal model also facltates polcy predctons and smulatons, whch we use to llustrate the framework. Key Words: protecton, endangered, voluntary, ncentve, tobt, beta-bnomal, stated preferences 005 Resources for the Future. All rghts reserved. No porton of ths paper may be reproduced wthout permsson of the authors. Dscusson papers are research materals crculated by ther authors for purposes of nformaton and dscusson. They have not necessarly undergone formal peer revew. Contents 1. Introducton Fnland s Forest-Conservaton Polcy Problem Modelng Partcpaton n Incentve-Payment Programs... 5 Multvarate Censored Regresson Model... 5 Beta-Bnomal Model The Stated-Preference Survey and Data Econometrc Model Results Multvarate Censored Regresson Model Beta-Bnomal Model Polcy Evaluaton Dscusson... 0 References... Tables and Fgures... 5 Incentve Payment Programs for Envronmental Protecton: A Framework for Elctng and Estmatng Landowners Wllngness to Partcpate Davd F. Layton and Juha Skamäk 1. Introducton Incentve payment programs are ncreasngly popular mechansms for achevng envronmental polcy goals. They are used, for example, n the Unted States, European Unon, and Australa to encourage sol and water conservaton and the adopton of envronmentally frendly agrcultural practces (OECD 003). The protecton of endangered speces and habtat on prvate lands, whch ths paper addresses, s another mportant envronmental polcy problem, one whch ncentve payment programs, f properly desgned, may help to resolve. The conceptual framework for usng ncentve payment programs and, more generally, voluntary approaches for achevng envronmental polcy goals have been nvestgated by Smth (1995), Wu and Babcock (1995, 1996, and 1999), Polasky and Doremus (1998), Segerson and Mcel (1998), Innes (000), and Smth and Shogren (00). 1 Emprcal research on landowners wllngness to partcpate n envronmental polcy programs has focused almost entrely on dscrete-choce econometrc models, whch explan landowners wllngness to partcpate n varous envronmental and agrcultural polcy programs. These studes nclude Cooper and Kem (1996), whch estmates farmers wllngness to adopt practces that mprove water qualty; Cooper and Osborne (1998), whch estmates a model for the partcpaton of farmers n the Conservaton Reserve Program; Lynch and Lovell (003), whch analyzes the wllngness of landowners to partcpate n a conservaton easement program by purchasng or transferrng development rghts; and Cooper (003), whch jontly estmates farmers partcpaton n multple envronmental stewardshp programs. All model ther program partcpaton as a bnary choce. Lohr and Park (1995) extend the standard bnary-choce model usng Roy s dentty, Davd F. Layton s Assocate Professor at the Danel J. Evans School of Publc Affars, Unversty of Washngton, Seattle. He may be contacted at Juha Skamäk s a Fellow at the Washngton-DC based thnk-tank Resources for the Future. He may be contacted at 1 Albern and Segerson (00) revew economc ssues related to voluntary programs. dervng a dscrete-contnuous model of partcpaton and ts ntensty. Ther focus s on modelng partcpaton. Although t s natural to begn wth a pure dscrete-choce partcpaton problem, polcymakers are not nterested solely n the number of partcpants n a gven program, but also n how much land wll be protected under varyng polcy confguratons. It s partcularly mportant, when desgnng a large-scale program that may have tens or hundreds of thousands of partcpants, to know the number of hectares that may be enrolled under a specfc program confguraton. Our goal n ths paper s to provde a methodology for elctng enrollments n ncentve payment programs; flexble econometrc models for analyzng the resultng data; and an approach for generatng expected enrollments for dfferent combnatons of program attrbutes. Our results estmate potental enrollment n an ncentve payment program for protectng certan small-scale, speces-rch forest areas n Fnland. Our model focuses on estmatng partcpaton as a functon of two key attrbutes of the program: payment amount and contract length. Fnnsh forests are an especally nterestng and compellng settng for our applcaton. In stu speces conservaton on prvate lands s a partcular problem n Fnland s conservaton polcy, as forests cover about three-quarters of the country s total land area, and most forests are nonndustral, prvate holdngs. Such holdngs make up about 60 percent of the forestland and provde approxmately three-quarters of the ndustral tmber supply n Fnland. Forest ownershp s wdespread, as approxmately 10 percent of Fnland s populaton owns at least some forest area. Fnland already has an actve, f small, ncentve payment program n place for the protecton of forests that have partcular ecologcal mportance. Fnland s currently consderng employng ths program n a large expanson of conservaton efforts. 3 We use a stated-preference (SP) survey of nonndustral, prvate forest owners to collect data on the expected enrollment n alternatvely confgured ncentve payment programs. Instead of smply posng bnary partcpaton questons, the survey asks forest owners also for the number of hectares they would enroll n dfferent ncentve payment programs. Consequently, Parks and Kramer (1995) estmate partcpaton n the Wetlands Reserve Program, but they use county-level, not ndvdual-level, data on partcpaton. 3 To enroll a suffcently large amount of land, many landowners wll need to be convnced to set asde all or a porton of ther lands. Voluntary partcpaton s consdered to be a key element of the new conservaton program as non-voluntary approaches usng command-and-control mechansms would be poltcally dffcult. The potental for conflct s easly understood when one consders that one n ten Fnns mght expect to be drectly affected. our data are a combnaton of dscrete partcpaton decsons enrched by contnuous data on enrolled hectares. Snce data on enrollment n ncentve payment programs are often censored, we start by developng a censored regresson model of enrollment. To facltate modelng multple program responses for each landowner, we use a panel-type multvarate censored regresson model. Usng ths as our base model, we then specfy a rch correlaton structure based on alternatvespecfc correlaton components and random coeffcents. As an alternatve to the censored regresson model, we develop a beta-bnomal model for enrollments. The beta-bnomal model treats enrollments of dfferent stands n a forest holdng as separate choce occasons. Total enrollment by a landowner s then determned by the sum of stand-specfc enrollment decsons over all avalable stands. Consequently, the structure of the beta-bnomal model constrans total enrollment to a range between zero and the total hectares n the holdng. To our knowledge, the beta-bnomal model has not been appled n ths context before. It has been appled n marketng research snce Chatfeld and Goodhardt (1970), but n envronmental economcs, the econometrc model most closely related to the beta-bnomal model seems to be the Drchlet model of recreatonal trp demand, whch has been developed and estmated recently by Shonkwler and Hanley (003) and Moeltner and Shonkwler (005). Comparng the beta-bnomal model wth the censored regresson model usng crossvaldaton and a mean square error (MSE) crteron, we fnd that although the beta-bnomal model has fewer parameters to estmate, t performs ether equally well or better than the censored regresson model. Other propertes of the beta-bnomal model are also useful for polcy desgn and analyss: the model provdes closed-form predcted enrollments, and predcted enrollments are a smooth functon of program attrbutes. Snce the analyst s choce between the two models may vary dependng on the applcaton, we descrbe both econometrc models n some detal. Methods developed n ths study are not lmted to SP applcatons and forestry but may apply to a broader set of applcatons assocated wth predctng land-use decsons. Incentve payment programs are ncreasng n popularty, and methods for analyzng them are therefore mportant. The methods developed and analyzed n ths study can also accommodate the analyses of agrcultural and envronmental polcy programs, of whch a vast range s n place around the world. Understandng and predctng landowners decsons are ndspensable when assessng such polcy programs. 3 Ths paper s organzed n seven sectons. The second secton (below) descrbes Fnland s forest-conservaton polcy problem. The thrd develops the censored regresson and betabnomal econometrc models for analyzng the survey responses. The fourth explans our SP survey desgn, mplementaton, and the resultng data. The ffth secton presents estmaton results and model comparsons usng cross-valdaton. The sxth demonstrates how our methodology can be used n polcy analyss. The seventh secton concludes the paper.. Fnland s Forest-Conservaton Polcy Problem Forests provde the prmary lvng envronment for more than half the endangered natve speces n Fnland. The endangerment of forest speces s assocated wth forest-management practces that have changed forest composton, caused the loss of old-growth forests, fragmented remanng old-growth forests, and decreased the number of decayng trees n the forests (Hansk and Hammond 1995). Old-growth forests and so-called key habtats, hereafter termed bodversty hotspots, are consdered the prmary targets of endangered-speces protecton. These areas, n partcular the bodversty hotspots, are typcally small holdngs often less than a hectare but they provde a habtat for many threatened speces. Overall, about 6 percent of Fnland s forests can be classfed as ether old-growth or bodversty hotspots. Fnland has more than 400,000 prvately owned, nonndustral forest holdngs, whch on average are approxmately 37 hectares (Fnnsh Forest Research Insttute 000). These are typcally small unts of managed forest stands often not more than a hectare or two, and usually fewer than 10 hectares. Management of a forest stand typcally follows a 60- to 10-year rotaton cycle, dependng on geographcal locaton, sol condtons, and tree speces. Begnnng n 1997 Fnland mplemented an ncentve payment program for landowners to promote the protecton of old-growth forests and bodversty hotspots. Currently, a landowner who enrolls qualfed forest habtat n the program for 10 to 30 years s elgble for an ncentve payment, a cost-sharng compensaton that s determned by the surface area and tmber stock of the protected forest. By enrollng n the program the landowner s precluded from harvestng or managng the enrolled forest, although the program allows for nondsruptve uses, such as hkng and wldlfe vewng. A partcpatng landowner receves the ncentve payment n full at the begnnng of the protecton perod. The program has only a few partcpants to date, but t wll nevertheless play a central role n Fnland s plans to expand ts protecton of prvately owned, nonndustral forests (Mnstry of Agrculture and Forestry 001). Fnland has already placed under protecton contguous areas that make up more than 10 percent of ts total land area; those areas are mostly n the north, where state ownershp s more common and land values are lower. The current program proposes to supplement exstng conservaton areas by establshng a 4 network of many smaller protected forest habtats dspersed n a mosac pattern throughout the country. 3. Modelng Partcpaton n Incentve-Payment Programs The landowner s decson about how much elgble land to enroll depends on several varables among them the forest owner s plannng horzon and motves for makng the bequest, the age of the forest, ts stand structure, nonforest ncome, nterest rates, other land uses, and possble lqudty constrants. The prvate valuaton of a forest stand under n stu landowner preferences s examned thoroughly by the multple-stand forest-rotaton model of Tahvonen and Salo (1999). Ther study llustrates that partcpaton decsons nvolvng multple stands (tens or hundreds per each forest holdng n our applcaton), substantal nonforest ncome, and n stu preferences are so complex that a rotaton-based structural model s nfeasble and not lkely to provde much gudance for emprcal decsons such as functonal form. For ths reason, we pursue estmatng a predctve model for enrollments as a functon of program attrbutes. We develop alternatve econometrc models a multvarate censored regresson model and a beta-bnomal model of landowners partcpaton and enrollment n ncentve payment programs. These models respond to and address dfferent aspects of the data. The multvarate censored regresson model focuses on the many zero enrollments one often fnds n the data and vews enrollments as an approxmately contnuous varable. The beta-bnomal model s applcable to nteger-valued enrollments, whch s what we observe n our actual data set. In prncple, enrollments are contnuous, but because n practce they are often nteger valued, both models may be useful n dfferent applcatons. Multvarate Censored Regresson Model We frst model enrollment y usng a multvarate censored regresson specfcaton (descrbed n more detal by Cornck et al. 1994, Feenberg and Sknner 1994, and Moeltner and Layton 00): y y * t t t t = f( x, β, ε ) = * max(0, yt ) (1) 5 where y * t denotes the latent dependent varable for landowner and program t, y t s the observed enrollment (hectares), x t represents the contract (program) attrbutes, β s a vector of coeffcents, and ε t s a random error term. 4 If the landowner enrolls any forest area n a certan program, we observe y * t as the hectares enrolled, otherwse, a zero enrollment s observed. The typcal approach s to assume that ε t are multvarate normal, perhaps after a transformaton. Here we frst transform the dependent varable usng the standard nverse 1/ hyperbolc sne (IHS) transformaton IHS( y) = ln( y + ( y + 1) ) of y. The IHS s smlar to the log transformaton, wth two man dfferences: t s well defned at zero wth IHS(0) = 0 and does not constran the dependent varable to be postve before transformaton. When potental enrollment s elcted usng SP surveys wth multple enrollment questons nvolvng alternatve program confguratons, or when actual enrollments n more than one program are modeled jontly, the analyst can beneft from applyng a multvarate approach, perhaps wth random coeffcents. Defne * Y as a T-dmensonal vector of enrollments to T program confguratons by landowner, and X as the T by k matrx of explanatory varables, such as program attrbutes and landowner and parcel characterstcs. 5 can be modeled as multvarate normal and as a functon of random coeffcents and correlated alternatve specfc errors: * Y IHS * ( Y ) = X β + ε () where ε s a functon of normally dstrbuted random coeffcents ~ β nteracted wth ndependent varables and normally dstrbuted alternatve specfc errors ν, so that ~ ε = X β + ν, where β ~ MVN ( 0, ) and ν ~ MVN ( 0, Σ), β and ν are ndependent. Consequently, the fnal multvarate censored regresson specfcaton for enrollments s: 4 One could also ncorporate upper censorng of enrollments. Gven the nature of our data wth a preponderance of zeros enrollments but nearly all enrollments below the upper lmt, upper censorng s not crucal for ths analyss. 5 Moeltner and Layton (00) assume multvarate normalty after takng the natural logarthm of the dependent varable whch treats the non-negatvty of enrollments ncely but creates some dffculty n managng zero enrollments as the log of zero s undefned. Burbdge et al. (1988) used the IHS transformaton as an alternatve to the Box and Cox (1964) for handlng extreme values of the dependent varable. It has been prevously used n the double-hurdle demand model by Yen and Jones (1997) and as a functonal form for SP data by Layton (001). 6 * ( Y ) ~ MVN(, Ω) whereω = X X + Σ IHS β, (3) The vector β s k by 1 and s a w by w dmensonal covarance matrx of random coeffcents, where w k covarance matrx for the alternatve specfc errors. so that not all coeffcents need be random. Σ s a T-dmensonal The T enrollments by each landowner can consst of up to T censored enrollments, or T uncensored enrollments, or any combnaton n between. The lkelhood of the model as defned by (1) and (3) s easest to wrte by notng that the multvarate normal densty can be wrtten as a censored component condtoned on the uncensored component, where ether the censored or uncensored components mght be null vectors for any gven landowner. The censorng of * Y nduces censorng on the ε. Denotng the normal densty by f( ), ts cdf by F( ), the uc c uncensored components of ε as ε, and the censored components as ε, the ndvdual lkelhood s: c uc uc ( ε ε ) f ( ε ) = F (4) The log lkelhood s c uc uc ( ) = ln( F( ε ε ) ln( f ( ε ) ln + (5) The model as defned by (3) allows for a very rch correlaton structure. We are aware of only one applcaton where both random coeffcents and correlated alternatve specfc errors are used a multvarate probt model by McCulloch and Ross (1994). It s mportant to note that n the multvarate censored regresson model scale s fully recoverable as a result of havng at least some uncensored observatons. Thus gven the cardnallevel nformaton on enrollments, one need not worry about the dentfcaton of Σ n prncple. However, some restrctons are necessary n practce as the number of potental terms n the covarance matrx for the alternatve-specfc errors for t alternatves s t(t+1)/, whch can become prohbtvely large very quckly, especally wth the addton of random parameters. To address ths problem, we consder specfcatons of the covarance matrx of alternatve-specfc errors that employ some natural restrctons and are easly generalzed to hgher dmensons. 7 Snce our emprcal applcaton wll consder enrollment n three dfferent program confguratons, our frst specfcaton s: σ 11 Σ = 0 0 σ σ 33 (6) Σ s the covarance matrx for an ndependent trvarate censored regresson model. We extend Σ to handle at least some correlaton by ncludng a common off-dagonal component n Σ : σ 11 Σ' = σ cov σ cov σ σ σ cov cov σ σ σ cov cov 33 (7) The covarance matrx n (7) mposes restrctons on the covarance structure, n that t has four free parameters nstead of the maxmum possble of sx. Snce Σ nests Σ, lkelhood rato tests can be employed n determnng model structure. 6 Gven the IHS-transformaton of the dependent varable, the expected hectare enrollment by landowner can be drectly derved as: 6 The covarance matrx n (7) can also be vewed as a generalzaton of the Butler and Mofftt (198) equcorrelaton structure for the panel probt model. Ther covarance matrx s based on assumng that the alternatve specfc errors ν are generated by a permanent component τ dstrbuted normally as N(0, σ τ ), and a transtory component γ t dstrbuted ndependent N(0, σ γ ), and γ

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