Meta-Regression Estimates for CGE Models: A Case Study for Input Substitution Elasticities in Production Agriculture

Transcription

1 Meta-Regresson Estmates for CGE Models: A Case Study for Input Substtuton Elastctes n Producton Agrculture Kathryn A. Boys 1 and Raymond J.G.M. Florax 1,2 1 Dept. of Agrcultural Economcs, Purdue Unversty 403 W. State Street, West Lafayette, IN , USA Phone: +1 (765) , Fax: +1 (765) E-mal: kboys@purdue.edu, rflorax@purdue.edu 2 Dept. of Spatal Economcs, Vrje Unverstet De Boelelaan 1105, 1081 HV Amsterdam, The Netherlands May 2007, Prelmnary Verson Selected Paper prepared for presentaton at the Amercan Agrcultural Economcs Assocaton Annual Meetng, Portland, OR, July 29 August 1, 2007 Abstract: The selecton of approprate parameters for computable general equlbrum (CGE) models crtcally affects the results of appled economc modelng exercses. Vald and relable parameter selecton models are needed, and typcally comprse drect estmaton, expert opnon, or copycattng of results from semnal studes. The purpose of ths study s to use meta-analyss to summarze and more accurately estmate elastctes of nput substtuton, specfcally between labor and other nputs n agrcultural producton. We construct a comprehensve database of elastcty estmates through an extensve lterature revew, and perform a meta-regresson analyss to dentfy structural sources of varaton n elastcty estmates sampled from prmary studes. The use of meta-analyss contrbutes to mproved baselne analyss n CGE smulatons because t allows for the computaton of nput parameters talored to a specfc CGE model setup. We correct for varatons n research desgn, whch are typcally constant wthn studes, and account for bas assocated wth undue selecton effects assocated wth edtoral publcaton decson processes. Improved accuracy and knowledge of the dstrbuton of mputed nput parameters derved from a meta-analyss contrbutes to mproved performance of CGE senstvty analyses. Keywords: meta-analyss, cross-prce elastcty, nput substtuton, agrcultural producton, CGE parameters JEL Classfcaton: C13, C68, Q13 Copyrght 2007 by K.A. Boys and R.J.G.M. Florax. All rghts reserved. Readers may make verbatm copes of ths document for non-commercal purposes by any means, provded that ths copyrght notce appears on all such copes.

2 1. Introducton Despte ts general acceptance and wdespread use, computable general equlbrum (CGE) models contnue to suffer from crtcsm concernng fundamental aspects underlyng the use and performance of general equlbrum prncples. Much of ths crtcsm stems from the weak econometrc foundatons upon whch CGE models are typcally based (Jorgenson 1984; Shoven and Whalley 1992; McKtrck 1998). The selecton of approprate parameters for CGE models mpacts, and n some cases even drves, the results of appled economc modelng exercses (Arndt et al. 2002; McDanel and Balstrer 2002). Despte the mportance of judcously chosen mputed values for nput parameters, CGE modelers typcally obtan behavoral parameters from external sources based upon data and models that may not be consstent wth the CGE model for whch they are used. Snce the selected behavoral parameters provde the bass for calbrated outcomes and subsequent senstvty analyses, the selecton of approprate baselne parameters s key to mprovng the valdty of CGE model results. Several alternatve parameter selecton methods are avalable. Drect estmaton of nput parameters, although obvously the preferred method because t s ste specfc and precse, s challengng and costly. Due to data lmtatons, and econometrc challenges (msspecfcaton bas, dentfcaton problems, and multcollnearty) as well as the consderable cost nvolved, researchers do not frequently pursue ths approach. Instead, researchers typcally draw estmated nput parameters from secondary sources. These parameter estmates are usually derved usng drect estmaton or expert opnon, and requre thoughtful consderaton of both the source of the estmate and the purpose for whch t wll be appled. The calculaton of specfc nput parameters, such as elastctes, s affected by condtons and assumptons specfc to each estmaton process (Blackorby and Russell 1989). Wthn the context of agrcultural producton, for example, estmates are dependent on the atttude, outlook, and producton possbltes for producers (Masters et al. 1996). Tme horzon, level of aggregaton, sze and relatve openness of the market under consderaton are among several other factors that should be consdered when selectng nput parameters. Multplyng these consderatons by the large number of parameters that s typcally needed and the large number of regons and extensve tme perods potentally under consderaton n any sngle model, t s easy to understand why the ssues presented by the econometrc crtque (McKtrck 1998), reman largely unaddressed. Due to the challenge of selectng approprate nput parameters and to the lack of estmates avalable for some regons and applcatons, values for well-examned settngs are often broadly appled. To evaluate and offset the mpact that elastcty assumptons have on a smulaton outcome, researchers frequently perform a senstvty analyss n whch the assumed elastcty s systematcally vared around the mputed value. Ths process, whle useful for ndcatng the senstvty of results to elastcty assumptons, provdes no gudance as to the approprateness of the baselne assumpton. As an alternatve to these approaches, one mght chose to survey the exstng lterature and to combne publshed elastcty estmates n some manner. Among the most rgorous of such methods s meta-analyss. Meta-analyss can be used to mprove the estmaton of these crucal economc parameters by combnng relevant estmates, nvestgatng the senstvty of estmates to varatons n underlyng assumptons, dentfyng and flterng out publcaton bas, and explanng varaton n reported estmates through meta-regresson analyss (Rose and Stanley, 2

3 2005). Further, through the use of meta-analyss, confdence ntervals used n senstvty analyss can be emprcally derved and thus be a gude to mprovng the relablty of CGE-based applcatons. Ths paper ams to analyze the sources of varaton n emprcally derved elastcty estmates and to determne reasonable estmates for nput substtuton elastctes n producton agrculture. We performed a comprehensve revew of the agrcultural producton lterature, ncludng both publshed and non-publshed sources, to attan the nput needed for the meta-analyss. We used a random selecton process to dentfy studes to be ncluded n ths analyss, and constructed a database of elastcty estmates. Subsequently, we utlzed meta-regresson analyss to summarze emprcal elastcty estmates, and to explore varaton n the outcomes across studes. In partcular, elastcty varaton due to model characterstcs, data characterstcs, and characterstcs of the economy under nvestgaton are examned (Koetse et al. 2006). The metaanalyss consders substtuton elastctes regardng the substtutablty between labor and other nputs n agrcultural producton. As t s developng country analyses that are most frequently forced to adopt elastctes from secondary sources, we also nvestgate the extent to whch estmates vary sgnfcantly across regons. We organze the remander of ths paper as follows. Secton 2 provdes a bref ntroducton to meta-analyss, and lays out the potental value of meta-analyss n terms of provdng better nputs for CGE modelng. In Secton 3, we dscuss several sources of varaton related to data, model characterstcs, and sectoral dfferences that are potentally relevant n explanng structural varaton among estmates reported n the lterature. Secton 4 dscusses the samplng desgn employed n the current applcaton and provdes an exploratory account of the estmates sampled from the lterature as well as the results of the meta-regresson analyss. Secton 5 concludes and provdes suggestons for areas of future research. 2. Meta-analyss and CGE modelng Econometrc estmates from a more or less talored prmary study or an authortatve semnal contrbuton to the lterature, lterature revews, nternatonal comparsons, expert opnon, or arbtrarly assgnng values to free parameters all consttute standard approaches to solvng the parameter mputaton problem (Harrson et al., 1993; Abdelkhalek and Dufour, 2004). Among those, the use of econometrc estmates s the most frequently employed. There are two sources of complcatons and concerns dependng on whether the specfc settng n terms of, for nstance, regon, ndustry and tme perod for whch an estmate s desred, has been thoroughly studed or not. Consder a well-studed settng for whch a seres of emprcal estmates s avalable from dfferent prmary studes. Even f all estmates represent the same underlyng fxed populaton value, we would statstcally expect samplng varaton to result n estmates of dfferent magntude, and even of opposte sgns across the dfferent prmary studes. For nstance, Koetse et al. (2006) show that cross-prce elastctes for captal-energy substtuton range from 3

4 approxmately 0.4 to +0.8, wth 35 percent of the estmates beng negatve. 1 In addton, there may be msmatches n terms of the specfcaton or the assumptons mantaned n the prmary study as compared to the CGE polcy experment (Hertel et al., 2006). Dfferences n the examned tme-perod are lkely relevant, because many econometrc studes use annual data, whle CGE analyses typcally assume sgnfcantly longer adjustment perods. Moreover, the ecologcal fallacy or mcro-macro problem assocated wth applyng results of mcroeconomc studes to the household representatons and sector aggregatons usually explored by CGE models, s unavodable (Arndt et al. 2002). Fnally, even f the lterature would provde a clear ndcaton of a reasonable value for the nput parameter needed for CGE polcy smulatons, t would be dffcult to come up wth a confdence nterval for that parameter. Typcally confdence ntervals vary wdely (agan, see Koetse et al. 2006, for an example), they are to a consderable dependent on the sample sze of the prmary study, and they may have played a role n the decson whether a specfc study wll be publshed or not. 2 For less well examned settngs, the challenge of obtanng free parameter values s even greater. Lack of emprcal evdence encourages relance upon expert or the modeler s sound judgment. Alternatvely, practtoners apply parameter values for specfc studed regons, ndustres and tme perods to unexamned cases. In both nstances, there s obvously great potental for, and lkelhood of, sgnfcant dfference between the employed and true parameter values. In fact, the prncple of usng values for studed stes and applyng those to unstuded stes s qute common n envronmental economcs, and s referred to as value or beneft transfer. A growng number of studes shows that extreme cauton s needed n applyng transferred values, because the valdty may be questoned (Brouwer 2000), and the performance and relablty s rather dsappontng, even for values based on meta-analyss (Brouwer and Spannks 1999; Engel 2002; Jang et al. 2004; Brander and Florax 2006). Recognzng the lmtatons of parameterzng appled general equlbrum models n ths way, several alternatve approaches have been proposed. Some authors have advocated an econometrc approach n whch parameters are estmated usng the actual model data (Jorgenson 1984; McKtrck 1998). Whle ntutvely appealng, the emprcal applcaton of ths methodology s lmted. Data demands, conceptual and computatonal challenges n estmaton, and uncertanty concernng the valdty of resultng estmates have lmted the mplementaton of ths approach (Arndt et al. 2002). Buldng upon ths, and n an effort to address several of the lmtatons of ths technque, Arndt et al. (2002) ntroduced a maxmum entropy approach to parameter estmaton. Other authors have adopted a mult-perod valdaton/calbraton approach n whch, after runnng the model over a number of perods, nfluental free parameters are adjusted to permt the model to better replcate hstorcal data (Kehoe et al. 1995). In the sequel we nvestgate the extent to whch meta-analyss can be used to crcumvent some of the abovementoned problems. 1 Ths s not meant to mply that the authors mantan that these elastctes represent one underlyng populaton value. They show that a Q-test rejects the null hypothess of homogenety of the estmates (see Koetse et al. 2006, for detals). 2 In comparng 46 dstnct emprcal economc lteratures, Doucoulagos and Stanley (2007) fnd that publcaton selecton dstorts nferences and s generally wdespread, except for areas where there s substantal competton and debate over rval theores. 4

5 2.1 Overvew meta-analyss Tradtonally, we use qualtatve lterature revews to summarze the nformaton avalable n a specfc lterature, and to present an overvew of ssues relevant to a partcular topc. Incdentally, the narratve s complemented by quanttatve nformaton, but ths does usually not extend beyond smple cross-tabulatons and graphs. In performng lterature revews, however, authors often make subjectve choces about whch studes are ncluded, the relatve attenton (weght) pad to the results of those studes, and whch factors are deemed to be responsble for study fndngs (Stanley and Jarrell 2005). Further, beyond smple comparson, the lterature revew approach does not permt for a quanttatve assessment of study results, and t s mperatve that a sample selecton correcton strategy s employed n order to avod the wtherng nfluence of publcaton bas. Although lterature revews are valuable n ther own rght, there are a number of dsadvantages n solely relyng on surveys of the lterature. Most lterature revews are mplctly based on technque known as vote-countng, whch essentally bols down to countng the number of sgnfcantly postve, sgnfcantly negatve, and nsgnfcant results (or n the case where unty s the reference case, elastc versus nelastc results). The results are smply talled, and the category wth the pluralty of cases s usually taken to reveal the true characterstcs of the underlyng populaton. However, Hedges and Olkn (1985) pont out that ths procedure contans a fatal flaw, because paradoxcally t tends to lead to makng the wrong nference when the number of underlyng studes ncreases. 3 Qualtatve approaches to the revew of prmary studes have, however, long been used n evaluatng both nputs and outcomes of CGE smulatons. As an example, n ther revew of Armngton trade substtuton elastctes, McDanel and Balstrer (2002), summarzed and dentfed qualtatve trends n studes whch econometrcally estmated these elastctes for US mports. Several of the prmary fndngs of ths revew conform to what one would expect for any seres of elastcty estmates: long-run estmates are hgher than short-run estmates, and more dsaggregate analyses fnd hgher elastctes. Although useful for offerng comment concernng the drecton and possbly a qualtatve assessment of the magntudes of mpact of varous estmaton characterstcs, potentally ths type of approach suffers from the votecountng flaw, the dffculty of dentfyng and remedyng publcaton bas, and the general dffculty of assessng research results n a stuaton where a multtude of underlyng factors (e.g., sector, specfcaton, type data, tme perod) change smultaneously. By comparson, meta-regresson analyss offers a rgorous approach to both surveyng and summarzng the lterature. Descrbed as the analyss of analyses (Hunter and Schmdt 1990), meta-analyss s the statstcal analyss of results collected from ndvdual studes for the purpose of ntegratng the research fndngs (Glass 1976). Wth ths approach, the process of prmary study selecton s made explct, and statstcal tests can be employed to test for the occurrence and severty of publcaton bas (Macaskll et al. 2001; Florax 2002; Stanley 2005; Roberts and Stanley 2005). Further, as meta-regresson analyss nvolves an analytcal method to examne results and ther varance across studes, subjectvty s effectvely excluded from 3 The statstcal cause for ths rather counterntutve result s that the Type-II errors of each of the underlyng studes do not cancel out. 5

6 nfluencng revew fndngs. In short, meta-regresson analyss offers a means of objectvely explanng why, and quantfyng how, estmates dffer from a range of emprcal studes (Roberts 2005). Several revews exst whch offer good ntroductons to meta-analyss n general and assocated statstcal methods (Hedges and Olkn 1985; Cooper and Hedges 1994), and to economc applcatons n partcular (Stanley and Jarrell 1989; Stanley 2001), so we wll only provde background nformaton n bref. The objectve of meta-analyss s to combne research results from prevous studes, usually referred to as effect sze assumng that the underlyng populaton effect sze s fxed or random. Typcally the fxed and random effects models n meta-analyss employ the nverse (estmated) varance of the effect szes as weghts n order to correct for the precson wth whch the effect szes have been estmated. The seres of estmated effect szes and ther assocated standard errors are attaned through a comprehensve revew of the relevant lterature, and they are ncluded n a database of prmary study results whch also contans observable dfferences between studes such as data type, specfcaton detals, geographcal locaton and tme perod to whch the effect sze pertans, and type of estmator used to estmate the effect sze. Subsequently, nstead of smply combnng effect szes nto an overall effect sze usng a fxed or random effects model, one can also explot the varaton n effect szes by allowng for dfferences n the underlyng populaton effect szes usng a meta-regresson approach. Meta-regressons n economcs have been mplemented usng a varety of dfferent estmators rangng from ordnary least squares (eventually usng the sandwhch procedure to attan standard errors allowng for heteroskedastcty and clusterng), to mxed effects models and herarchcal modelng approaches. These estmators have ther own respectve pros and cons (see also Abreu et al. 2005). OLS s obvously neffcent, because t dscards the nformaton on the estmated standard errors that can be taken from the prmary studes, and dsregards the autocorrelaton that may result from samplng multple estmates from the same prmary study. Heteroskedastcty caused by unequal varances s taken nto account n the fxed effects estmator, whch s essentally weghted least squares usng the nverse standard errors of the prmary studes as weghts. The fxed effect model s rather restrctve n the sense that t assumes the populaton effect sze to be a fxed unknown constant that can be fully explaned by observable dfferences between studes. 4 Ths s a rather heroc assumpton f the underlyng studes are heterogeneous and dfferences across studes are only partly observable. Instead of assumng a fxed populaton effect sze, the mxed effect estmator rests on the assumpton that the populaton effect sze s drawn from a normal dstrbuton centered on the true populaton effect sze, wth an unknown varance to be determned from the data. The heterogenety n effect szes s partly observable and can be specfed as so-called moderator or condtonng varables n the meta-regresson, and to the extent that t s not observable, t s accounted for n 4 In meta-analyss the fxed effect estmator typcally pertans to the stuaton where the varaton n estmated effect szes s fully attrbutable to a lmted number of observable dfferences between studes. In that case the estmator s equvalent to the mean of the nverse-varance weghted estmated effect szes. Ths s equvalent to usng weghted least squares (WLS) wth approprately defned weghts. Snce a typcal (economc) model would not assume that dfferences are perfectly explanable by the observable factors, the varance reported for WLS and the fxed effect estmator are not dentcal. The WLS-estmated standard errors need to be rescaled by the square root of the resdual varance (see Abreu et al. 2005, for more detals). 6

7 the addtonal random effect. Ths well-known estmator that s wdely used n medcal applcatons of meta-analyss (Sutton et al. 2000) s based on the followng model: T = θ + ε, θ = α + x β + μ, 2 where ε ~ N( 0, σ ) 2 where μ ~ N( 0, τ ), (1) where T s the estmate of the underlyng populaton effect sze θ of study, α s a common factor, and x contans a set of desgn and data characterstcs. Devatons of the estmated effect sze T from the true effect sze θ are random, and the true effect sze and the precson of the 2 2 estmated effect sze σ vary across studes. The term σ s known as the wthn-varance, and s taken from the prmary studes. Any remanng heterogenety between estmates s ether explanable by observable dfferences modeled through moderator varables contaned n x, or t s random and normally dstrbuted wth mean zero and varanceτ 2, the so-called betweenvarance. The unknown varance can be estmated by an teratve (restrcted) maxmum lkelhood process or, alternatvely, usng the emprcal Bayes method, or a non-teratve moment-estmator (see Thompson and Sharp 1999, for detals). We use the teratve restrcted 2 2 maxmum lkelhood estmator wth weghts ϖ ˆ 1/( ˆ ˆ = σ + τ ) to obtan estmates for the 2 regresson coeffcents and ˆ τ. Meta-analyss s not wthout ts lmtatons ether. Some practcal degree of subjectvty relates to the operatonalzaton of the moderator varables and the specfcaton and estmator choce for the meta-regresson equaton. From a fundamental perspectve, the consderaton of all avalable estmates regardless of ther qualty has been used as an objecton to the technque. Some opponents have mantaned that meta-analyss amounts to comparng apples and oranges, and others have advocated usng the estmates from the best or bggest study n terms of sample sze (Wachter 1988). 2.2 Meta-analyss contrbutons to CGE modelng Ths general crtque notwthstandng meta-analyss has now found a home n appled economcs, and the technque prolferated from envronmental economcs, n whch the early contrbutons were made, to economc felds such as ndustral organzaton, and labor, transportaton and nternatonal economcs (see Florax et al. 2002; and Abreu et al. 2005, for varous examples). In spte of ts prevalent use, however, the tools of meta-analyss have not yet been explctly appled n the context of CGE analyses. 5 There are several routes through whch the tools of meta-regresson analyss could potentally contrbute to CGE modelng. The most obvous of these applcatons nclude meta-regresson use n the selecton of baselne parameter estmates, and n the provson of sutably small standard error results to mprove CGE senstvty analyss. Less drectly, parameters derved through CGE model calbraton and the standard errors of those parameters would also beneft due to potental mprovements n the accuracy of free parameters. Followng a bref revew of CGE model structure, these contrbutons are further explored. 5 At present, lterature searches on the topc offer, at best, examples of meta-analyses n whch CGE smulaton results were ncluded together wth econometrc results. 7

8 The general form of a statc CGE model may be represented as ( ) F Y, X, βδ, = 0, where Y s a vector of endogenous varables, X a vector of exogenous varables, β a vector of k free parameters, and δ a vector of p calbraton parameters. Whle both β and δ are categores of parameters, they are derved n dfferent ways by the CGE analyss process. The free parameters nclude behavoral parameters such as elastctes, and are (most often) obtaned from external sources or estmated n analyses exogenous to the CGE soluton process. In contrast, the calbrated parameters are usually share or scale parameters; values for these are determned wthn the model soluton process and are dependent upon the functonal form F, free parameter values specfed n β, and the smulaton base year data. Through calbraton, gven values of β, (unque) values of δ are determned, whch permts the model to exactly reproduce base or reference year data. Meta-regresson analyss could assst n provdng estmates and assocated standard errors for the free parameters β, and hence ndrectly affect the magntude and varance of the calbrated parameters δ. Meta-analyss we beleve, can contrbute to CGE modelng n at least two dfferent ways. Frst, by mprovng the accuracy of free parameters. Meta-analyss permts the ncorporaton of all avalable emprcal nformaton concernng an economc relatonshp of nterest nto a CGE models (Florax et al. 2002). As meta-analyss by nature ncreases the power of hypothess testng n the process of combnng research results, the combned effect sze has a comfortably smaller varance. In addton, meta-regresson analyss can be used to assess and model potental heterogenety across effect sze estmates by systematcally accountng for characterstcs of the data, the research desgn of the prmary studes, and characterstcs n terms of sectors, geographcal coverage and the tme-perod to whch the estmates pertan. Secondly, the use of meta-analyss can contrbute towards mproved senstvty testng. Much attenton has been pad thus far to the potental contrbutons of meta-analyss to mprovng the estmaton of free parameters. Equally mportant, though, s the potental contrbuton of metaanalyss to assessng the CGE model robustness. To evaluate and offset the mpact that elastcty assumptons have on a smulaton outcome, many authors frequently perform a senstvty analyss n whch the assumed elastcty s systematcally vared around the mputed value. Somewhat surprsngly, however, although confdence n CGE model conclusons depend crtcally on the sze of the confdence nterval around parameter estmates, standard robustness analyss s usually local and often nvolves only ncreasng or decreasng the values of key parameters. Ths approach, however, does not consder potentally avalable nformaton about the precson of the orgnal estmates (Hertel et al. 2007). 6 6 A thrd way n whch meta-regresson could contrbute to CGE modelng was already mentoned above, and pertans to the stuaton n whch value transfer s used to obtan relable estmates for regons or sectors for whch there s lmted avalable data (Florax et al. 2002). To date, outsde of envronmental applcatons, meta-analyss has not been wdely used for ths purpose (see Mller 2000, for an nterestng applcaton to value of lfe estmates for dfferent countres). 8

9 In many nstances, the dstrbuton of the free parameter s unknown. 7 As a result, dstrbutons are often drawn from lterature sources and t s generally assumed that all parameters of a smlar type share the same dstrbuton. Further, even when normalty s assumed and standard errors are avalable the factors drvng the magntude and varance of the free parameters are unknown. Thus, the lkely changes n the values of these parameters n response to exogenous shocks cannot be antcpated. Through meta-analyss, standard errors of parameters can be determned and the relatve magntude of sources contrbutng to varaton n sze and varance can be dentfed. Usng ths nformaton rather than assumed dstrbutons of free parameters can be evaluated through the usual systematc senstvty analyss methods. 3. Sources of elastcty estmate varaton Pror to provdng a practcal example of the meta-regresson technque and the ways n whch t can contrbute to CGE modelng, we frst consder potental sources causng varaton across effect sze estmates. Although the dstncton between free and calbrated parameters s largely arbtrary (Abdelkhalek and Dufour 2004), we focus our dscusson on elastcty estmates, whch are usually treated as free parameters. Analyses n whch the heterogenety of elastcty estmates s explored, typcally consder a wde array of potental explanatory varables relevant to that partcular lterature. In dentfyng possble common sources of varance, ths study draws from numerous recent applcatons of meta-analyss as well as the theoretcal lterature regardng the nature of producton process estmaton. Sources of varaton are dvded nto three broad categores: model characterstcs, data characterstcs, and characterstcs of the sector under consderaton. 3.1 Model characterstcs Several features of the model used to derve elastctes are expected to mpact the obtaned estmates, among whch the most mportant are the choce of the estmatng functon and functonal form, the sample sze and tme horzon under consderaton, and the excluson of relevant varables. These potental sources of elastcty estmate varaton are examned below. Functon, functonal form, and estmaton procedure. A frst ssues concerns the choce between the use of a cost, proft, or producton functon. Whle, theoretcally these alternatve approaches should yeld consstent estmates, n practce ths s not always the case. In consderng the dual cost and proft functons, for example, Hameresh and Grant (1979) found that estmates of ther stochastc forms are not necessarly dual to one another. Further, the choce of functonal form also vares between studes and has mportant mplcatons for the magntude of elastcty estmates. By way of example, use of a constant elastcty of substtuton functon (CES) provdes for relatvely easy estmaton, but t requres substtuton elastctes between all pars of 7 The most common excepton to ths s n cases where a sngle, emprcally derved estmate s used. Recently, Hertel et al. (2007) proposed a method by whch elastctes of substtuton among mports from dfferent countres were calculated by usng delvered good prces to trace out commodty demand curves. Usng the econometrcally estmated standard errors, the dstrbuton of trade elastcty estmates was constructed; these values were then used to repeatedly solve the model to determne the confdence ntervals for results of nterest (.e., welfare effects). Ths nnovatve approach s successful and, through ts results, does hghlght the mportance ncorporatng emprcally based confdence ntervals nto systematc senstvty analyses. The extensve data requrements of ths approach, however, may make the approach less appealng n vew of wdespread mplementaton n CGE modelng. 9

10 factors to be equal. As wll be descrbed below, ths study wll also consder the tme perod among possble explanatory varables. It s worth notng that, due to theoretcal and computatonal advancements over tme, the choce of functonal form s n many cases lkely to be correlated wth the perod of study. Further, as the selecton of estmaton procedure s frequently drven by the choce of estmaton technque, the technque chosen s smlarly lkely to be correlated wth both the perod of study and the functonal form. Omtted varables. Dfferences n model specfcaton and excluson of relevant varables from some (but not all) prmary studes wll affect the estmates generated by both prmary studes as well as the meta-analyss. To account for these dfferences n model specfcaton, all varables ncluded n prmary elastcty estmaton are recorded and treated as exogenous factors for the meta-regresson. Other characterstcs of the model specfcaton, such as assumptons concernng returns to scale, and the relatve neutralty of technologcal change, are consdered n a smlar manner. Sample sze. As wth other types of estmates, the sze of the orgnal sample affects the precson of the estmated elastctes. Sample sze of prmary studes s ncluded n the meta-analyss ether through drect ncluson n the estmatng equaton, or through usng the sample sze as a tool to assgn weghts to observatons n the regresson analyss (studes wth hgher number of observatons receve greater weght). Standard errors of the orgnal elastcty estmates may alternatvely be used n ether of these ways. For the present analyss we have collected nformaton concernng both the number of observatons and standard errors. Although standard errors are the preferred measure, n many nstances these values are not provded n the prmary studes. Koetse (2006) provdes an outlne for estmatng the standard errors of dfferent substtuton elastcty measures usng auxlary nformaton provded n the prmary studes. However, even when employng these technques, t s not always feasble to attan standard errors. Eventually, estmates for whch standard errors are not avalable wll be excluded from the analyss. Tme horzon. The Le Chateler-Samuelson prncple mples that, n absolute terms, uncondtonal elastctes are larger than condtonal elastctes. In accordance wth ths prncple long-run elastctes are expected to be greater than short-run elastctes. Further, and due to the mplct dfferences underlyng these measures, ths prncpal mples that short-, medum- and long-run elastctes should be examned separately. Where not explctly defned by the prmary study, dfferentaton among the horzon of estmated elastctes s determned usng general characterstcs of each type of elastcty. Specfcally, short-run elastctes are assumed to nclude non-neutral technologcal change and use tme seres data. It wll be assumed that medum-run elastctes are those that use panel data, and long-run elastctes use cross-secton data. Gven these assumptons, t s antcpated that there wll be a hgh correlaton between the tme horzon of elastcty estmates and varous data type detals descrbed below. 3.2 Data characterstcs Two sources of heterogenety may be attrbutable to characterstcs of the data. Both the frequency of data collecton (.e., monthly, quarterly, annual) and characterstcs of the data such 10

11 as the level of aggregaton, or the temporal and/or spatal range that s captured by the data may have an mpact on the elastcty estmates. Concernng the data perodcty, studes have found that there s substantal varaton n estmated elastctes n terms of the type of data used n prmary studes. For example, n ther study of prce and ncome elastctes of resdental water demand, Dalhusen et al. (2003) found that the use of annual data yelded sgnfcantly lower absolute values of the prce elastctes as compared to daly data. Dfferences n the type of data can smlarly mpact the magntude of the estmates. Dalhusen et al. (2003) report that the use of cross secton data s assocated wth sgnfcantly lower prce elastctes (n absolute value) as compared to tme seres data, whle panel data caused the absolute value of prce elastctes to be sgnfcantly greater than for tme seres data. Although these examples consdered prce and/or ncome elastctes rather than the nput substtuton elastctes, t s antcpated that smlar trends n reported elastctes wll be observed n ths analyss. 3.3 Sectoral characterstcs Characterstcs and local economc condtons of the producton sector under consderaton wll ntroduce some systematc varaton nto the elastcty estmates. Ths study wll nclude varaton due to these exogenous sources due to the geographc regon, the tme perod under consderaton, and the relatve tradablty of the sector(s) consdered n the prmary studes. Regon and tme perod. Substtuton between nputs wll depend upon both characterstcs of the producton process and the relatve cost of nputs. As both technology and prces vary across space, t s antcpated that some of the heterogenety across estmates wll be correlated wth the regon to whch the estmate pertans. Due to technologcal advancement, nduced nnovaton, and other exogenous condtons, elastctes of nput substtuton change over tme. These relatve changed n the trade-off over tme has long been recognzed as an mportant estmaton consderaton, and has been the focus of numerous studes. It s expected that a majorty of the research whch may make use of the results of ths study wll focus upon relatvely current data, and as such would only requre elastcty estmates drawn from recent lterature. However, n the case where researchers may wsh to use hstorcal data for baselne analyss or other purposes, elastcty estmates from all avalable tme perods wll be consdered. Tradablty. The relatve openness of an economy wth respect to both the nputs and the outputs of a partcular sector has mportant mplcatons for the elastctes of substtuton between goods. From the nput sde, both the tradablty and the relatve ntensty of use of an nput wll affect that nput s relatve prce, and as such also ts relatve substtutablty. Smlarly, on the output sde, the opportuntes for a sector to access and be affected by nternatonal markets wll shape the demand for that sector, and as such t wll also shape the demand for nputs by that sector. 4. Input substtuton elastctes n agrculture As an llustraton of how meta-regresson analyss can contrbute to CGE modelng, we explore the case of captal-labor nput substtuton n agrcultural producton. The followng dscusson presents the samplng desgn for the meta-analyss as well as exploratory results and the results from the meta-regresson analyss. 11

12 4.1 Samplng desgn and exploratory results For topcs as mportant and well studed as nput substtutablty n the agrcultural sector, the number of potentally relevant prmary studes s qute large. When conductng a meta-analyss on smaller lteratures t s possble to nclude all relevant studes. In nstances wth large populatons, however, ths s not reasonable (or, arguably, needed), and a samplng process s used nstead. To obtan an estmate of the populaton of studes avalable, a comprehensve revew of the agrcultural producton lterature was conducted. As a startng pont, ths revew tapped both databases of academc journals (Agrcola, Econolt) and workng papers (AgEcon Search). 8 As ths study seeks to examne temporal, sectoral and spatal varaton n elastcty estmates, a large number of vared search terms were used, such as agrculture nput substtuton, labor (and labour) elastcty, and captal nput. No restrctons concernng the year of publcaton or release were mposed; however, only manuscrpts avalable n Englsh or French were ncluded. Lterature surveys on ths topc were also dentfed (Salhofer 2000; Uchda 2005; Keeney and Hertel 2006), and ther reference lsts were added to the lst of relevant prmary studes. Fnally, an Internet search engne (Google Scholar) was used to dentfy studes whch may not (yet) be publshed n academc journals, and whch were not dentfed through prevous searches. Whle many meta-analyses only nclude artcles that are publshed n (leadng) academc journals (e.g., Knell and Stx 2005), ths last search s partcularly mportant to ensurng nclusveness of the meta-database, because much research concernng the agrcultural sector of developng countres s completed by natonal government organzatons and NGOs. We dentfed 496 unque studes through ths search process. 9 Once the populaton of potentally relevant studes was dentfed, a random selecton process was used to dentfy studes to be ncluded n ths analyss. Once selected, a copy of the artcle was obtaned and revewed for ts relevance to ths study. Papers that were not drectly relevant to the research problem (.e., presented only theoretcal dscusson, focused on analytcal technques, or derved elastcty estmates other than those of nterest to ths analyss) were excluded. 10 Further, a number of studes, whch contaned elastcty estmates of nterest, had to be elmnated, because they dd not present suffcent nformaton for ncluson n the metaregresson analyss. Through ths process a total of 225 studes were revewed, of whch 35 were judged sutable for ncluson n the meta-regresson analyss. 8 Workng papers were ncluded to help offset potental publcaton bas, or what s often called the fle-drawer problem. The fle drawer phenomenon refers to the fact that the odds of emprcal studes wth statstcally nsgnfcant or counterntutve theoretcal results to get publshed are smaller (Rosenthal 1979). However, assumng a normal dstrbuton of study results, such aberratons are to be expected and should not be excluded from publcaton. It s therefore desrable to nclude workng papers and other unpublshed reports n the meta-sample. 9 As mght be magned, the use of repeated and smlar keyword searches resulted n the same studes beng dentfed repeatedly. Obvously, duplcaton was avoded n constructng the database. The total populaton of 496 studes was drawn largely from the database searches (n = 468), whereas examnng the references of lterature revews dentfed another 28 unque studes. For ths analyss, the Internet search process dd not yeld any studes that were not prevously dentfed, ft the language crtera, and could be obtaned drectly or through academc loans. 10 These excluded papers, however, dd prove valuable n provdng valuable leads to other studes, whch were consdered for ncluson n ths analyss. 12

13 Dependent upon the research objectves, data avalablty, and characterstcs of the producton sector under consderaton, authors of prmary studes may choose to use one or more alternatve elastcty measures. Input substtuton elastctes most commonly fall wthn one of three categores: one-nput one-prce elastctes (e.g., cross-prce elastcty, Allen-Uzawa elastcty), two-nput one-prce elastctes (.e., Morshma elastctes), and two-nput two-prce elastctes (.e., shadow prce elastctes). Dfferences between these measures are well documented and wll not be dscussed here (see, e.g., Koetse et al. 2006). In constructng the database, observatons of each of these types of elastctes were ncluded. For the present analyss however, wth the desre to focus upon potental contrbutons of metaregresson analyss to CGE modelng, only the elastcty most commonly used n the GTAP CGE model s ncluded. We therefore select the Allen elastctes of substtuton between captal and labor. As ths measure s symmetrc, prmary study observatons of labor-captal substtuton are also ncluded. Secton 3 presented a dscusson of the factors that may contrbute to the heterogenety that s observable n the elastcty estmates. Each of these was ncluded n the current analyss and, together wth detals of the specfc types of heterogenety captured by each, they are summarzed n Table 1. The table should be self-explanatory. Fgure 1 shows that approxmately 80 percent of the estmated elastctes are postve, wth an average value of The range s substantal, manly due to a negatve outler, and ranges from 46 to +6. The 95 percent confdence ntervals are generally qute small. < Table 1 and Fgure 1 about here > For meta-regresson analyss the standard errors of the prmary estmates are requred; surprsngly often, however, these are not provded n the studes. In order to ncrease the number of observatons n the dataset, where suffcent nformaton s provded n the prmary study, standard errors for observatons are calculated followng the procedure outlned by Koetse (2006). Fnally, we would lke to comment on the treatment of multple tme perods used n some of the prmary studes. Frequently, especally among older artcles, authors chose to estmate elastctes over several overlappng tme perods. 11 In such nstances, to reduce collnearty among observatons, only one of the avalable tme perods was ncluded. The choce of perod was based upon the prmary study authors descrpton of the adherence of each estmated model to the assumptons of producton theory (.e., symmetry, concavty), and the relatve sze of standard errors for each estmate. By these crtera, most often the longer of the avalable tme seres were selected. For the purpose of estmaton, unless otherwse ndcated, reported estmates were attrbuted to the year that marks the md-pont of the selected tme seres. In addton to sources of varance attrbutable to the selecton of the model, data, and sector, explanatory and dependant varables ncluded n the prmary study regressons also must be consdered. The broad categores of captal and labor explored n ths analyss reflect aggregated 11 By way of example, Boyle (1981) estmated nput substtuton n Irsh agrculture for the perods , and

14 categores of several types of captal and labor whch were ncluded n the prmary study estmatons. The underlyng studes revewed for ths analyss also frequently ncorporated measures of land, government polces, and characterstcs of the producton envronment (e.g. weather) nto ther estmatons. Smlarly, nputs used to produce specfc agrcultural outputs. Due to the numerous and extremely dverse collecton of varables whch were ncluded among the prmary study estmatons, t s not possble to drectly reflect each of these measures n the meta-regresson. Instead, types of varables were aggregated and a dummy varable used to ndcate the ncluson of one or more members of each aggregate n the prmary analyss. Descrptons of the nputs and outputs aggregated nto each of these categores are presented n Table 2. < Table 2 about here > The current analyss ncludes only observatons whch reflect captal-labor substtuton and whch are measured usng Allen partal elastctes. Wthn ths restrcted sample, several of the varables presented n Table 1 are ether poorly represented or are entrely absent. Table 3 presents a lst and descrptve statstcs for varables whch were suffcently represented as to be retaned n the meta-regresson. As may be noted, wthn each varable category, n many nstances poorly represented varables were aggregated nto an Other varable. < Table 3 about here > 4.2 Meta-regresson results The general form of the meta-regresson model was prevously presented n equaton (1), and the fxed effects ncluded n the specfcaton reflect dfferences n model characterstcs, data characterstcs, and sector characterstcs. Further, although t should theoretcally be rrelevant, we nclude a dummy varable capturng the use of labor-captal rather than captal-labor elastctes. An overvew of the varables ncluded n the analyss s provded n Table 3, and the results of the mxed effects model are presented n Table 4. < Tables 4 about here > Interpretaton of these results s the same as that for other forms of regresson. In ths analyss, the constant provdes a measure of captal-labour substaton under the baselne condtons of a translog cost functon wth an teratve estmator used to calculate a short-run elastcty. The value obtaned for ths constant (4.08) was found to be precse and t s magntude reasonable when consdered relatve to other estmaton results. Results presented n Table 4 suggest that sgnfcant dfferences n estmated elastcty values are observed and attrbutable to several sources of varance. Of characterstcs under control of study authors, the choce of functon and estmator were found to have a sgnfcant mpact on the derved elastcty. Several characterstcs related to the expermental desgn were also found to be mportant. In partcular, use of regonally or natonally aggregated data, and the moderatng varables ncluded n the prmary analyss were statstcally sgnfcant. 14

15 Among these results s one unexpected outcome. As was prevously noted, a dummy varable was ncluded n ths model to ndcate whether the observaton was drawn from an captal-labor or labor-captal APE measure. As, these values should be theoretcally symmetrc, t was antcpated that ths varable would not be sgnfcant. Surprsngly however, ths measure was found to be both relatvely large n magntude and precse. Further consderaton of ths result s requred. 5. Conclusons The purpose of ths study was to explore the means by whch CGE modelng could beneft through the use of tools offered by meta-regresson analyss. Through the use of an applcaton whch explored the substtutablty of captal and labor used n agrcultural producton, t was demonstrated that elastcty estmates drawn from lterature sources can vary sgnfcantly due to characterstcs of ther estmaton. As such, these results underscore the mportance of carefully consderng the constructon of free parameters whch are ncluded n CGE smulatons. Opportuntes for Future Research: Several opportuntes exst to mprove and extend ths research. Ths study used as an example applcaton nput-substtuton elastctes n agrculture. Ths methodology can, however, of course be usefully appled to the estmaton of several other behavoral parameters of nterest to CGE modelers. Among the most appealng canddates for such an analyss are the Armngton trade parameters whch are commonly used n many for CGE models. Several opportuntes for further research also exst wthn the context of the current study. As an obvous startng pont, the number of observatons used n ths analyss needs to be extended. In dong so, beyond smply ncreasng the degrees of freedom, attenton wll also need to be pad to expandng the varance of explanatory varables captured n the revewed studes. Further graphcal and statstcal exploraton of the data for heterogenety (.e. through the use of the Q- statc, normalzed Z-scores, and/or the Galbrath dagram) would also be useful. Fnally, and perhaps most mportantly, future work should consder publcaton bas. As the objectve of ths research s to demonstrated how meta-regresson can provde mproved estmates for regons and sectors whch are not partcularly well studed, ths last recommendaton s partcularly mportant to obtanng unbased estmates for these areas and ndustres. References Abreu, M., H.L.F. de Groot and R.J.G.M. Florax A Meta-Analyss of β-convergence: The Legendary 2%. Journal of Economc Surveys. 19(3): Allen, R.G. and J.R. Hcks A Reconsderaton of the Theory of Value, Pt. II. Economca 1: Alston, J. M. C. Marra, P.G. Pardey, and T.J. Wyatt Research returns redux: A metaanalyss of the returns to agrcultural R&D. Australan Journal of Agrcultural and Resource Economcs. 44(2): Arndt, C., S. Robnson, and F. Tarp Parameter estmaton for a computable general equlbrum model: a maxmum entropy approach. Economc Modellng 19: Bnswanger, H The Polcy Response of Agrculture. Proceedngs of the World Bank Annual Conferece on Development Economcs. 15

16 Blackorby C. and R.R. Russell The Partal Elastcty of Substtuton, Dscusson Paper, no Unversty of Calforna, Department of Economcs, San Dego. Blackorby, C. and R.R. Russell Wll the Real Elastcty of Substtuton Please Stand Up? A comparson of the Allen/Azawa and Morshma Elastctes. Amercan Economc Revew. 79: Brander, L. and R.J.G.M. Florax The Valuaton of Wetlands: Prmary Valuaton Versus Meta-Analyss Based Value Transfer, n: J.I. Carruthers and B. Mundy (eds.), Envronmental Valuaton: Interregonal and Intraregonal Perspectves, Aldershot: Ashgate, Brouwer, R. (2000) Envronmental Value Transfer: State of the Art and Future Prospects. Ecologcal Economcs 32, Brouwer, R. and Spannks, F.A. (1999) The Valdty of Envronmental Benefts Transfer: Further Emprcal Testng. Envronmental and Resource Economcs 14, Cooper, H. and L.V. Hedges (eds.), The Handbook of Research Synthess, Sage Foundaton, New York, Dalhusen, J., R.J.G.M. Florax, H.L.F.M de Groot and P. Njkamp Prce and Income Elastctes of Resdental Water Demand: A Meta-Analyss. Land Economcs. 79(2): DeVuyst, E. and P. Preckel Senstvty Analyss Revsted: A Quadrature-Based approach. Journal of Polcy Modelng. 19(2): Doucoulagos, H. and T.D. Stanley Theory Competton and Selectvty. Workng Paper, Burwood: School of Accountng, Economcs and Fnance. Engel, S Beneft Functon Transfer Versus Meta-Analyss as Polcy-Makng Tools: A Comparson. In: R.J.G.M. Florax, P. Njkamp and K.G. Wlls (eds.), Comparatve Envronmental Economc Assessment. Cheltenham, Edward Elgar, Florax, R.J.G.M, H.L.F. de Groot, and R.A de Mooj Meta-analyss: A tool for Upgradng Inputs of Macroeconomc Polcy Models. Tnbergen Insttute Dscusson Paper /3. Florax, R.J.G.M Methodologcal Ptfalls n Meta-Analyss: Publcaton Bas, n: R.J.G.M. Florax, P. Njkamp and K.G. Wlls (eds.), Comparatve Envronmental Economc Assessment, Cheltenham: Edward Elgar, Glass, G.V Prmary, Secondary, and Meta-analyss of Research. Educatonal Researcher 5(10):3-8. Hamermesh, Danel S., and James Grant Econometrc Studes of Labor-Labor Substtuton and Ther Implcatons for Polcy. Journal of Human Resources 14(4): Harrson, G. W., Jones, R., Kmbell, L. J. and Wgle, R How robust s appled general equlbrum analyss? Journal of Polcy Modelng 15, Hedges, L.V., and I. Olkn Statstcal Methods for Meta-Analyss. New York: Academc Press. Hertel, T., D. Hummels, M. Ivanc, R. Keeney How confdent can we be of CGE- based assessments of Free Trade Agreements? Economc Modellng. 24: Hogg, D.W A meta-analyss of cosmc star-formaton hstory. Pubs. Astron. Soc. Pac. 2. Jang, Y., Swallow, S.K., and McGonagle, M.P. (2004) An emprcal assessment of convergent valdty of beneft transfer n contngent choce: ntroductory applcatons wth new 16