Xiaobing Wang*, Heinrich Hockmann**

Transcription

1 TECHNICAL EFFICIENCY UNDER PRODUCER S INDIVIDUAL TECHNOLOGY: A METAFRONTIER ANALYSIS Xaobng Wang, Henrch Hockmann Center for Chnese Agrcultural Polcy, Instute for Geographcal Scences and Natural Resources Research, Chnese Academy of Scences Tel / Fax Emal: xbwang.ccap@gsnrr.ac.cn; Instute of Agrcultural Development n Central and Eastern Europe (IAMO), Germany. Tel: , Fax: , Emal: Hockmann@amo.de Selected Paper prepared for presentaton at the Internatonal Assocaton of Agrcultural Economsts (IAAE) Trennal Conference, Foz do Iguaçu, Brazl, 18 4 August, 01. Copyrght 01 by Xaobng Wang and Henrch Hockmann. 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. 1

2 ABSTRACT Dfferences n resource endowment between regons nfluence the technologes appled n agrculture and cause locaton-specfc effects on producton and techncal change. Access to technologes may also dffer whn regons because producers may apply dfferent technologes n producton due to dfferent characterstcs. Whn ths settng, we extend the exstng lerature by consderng that producers face regon- and farm-specfc producton fronters. The treatment of essentally heterogeneous techncal effcency (TE) s performed followng a two-step procedure. Frst, a random coeffcent specfcaton of the producton technology s used to measure the nteractons of technology adopton wh tme, nput factors and output. Second, lnear programmng technques are employed to envelop the optmal level of technology. Ths procedure s appled to household-level data from eastern, central and western provnces n Chna. Our results provde evdence that techncal effcency s sgnfcantly affected by farm heterogeney. Ths factor nfluences TE drectly as a producerspecfc nput, and ndrectly through nteracton wh observable nputs such as land, labor, capal and ntermedate nputs. Our results also prove the assumpton that farmng technology exhbs regon-specfc characterstcs. Furthermore, there s a dspary of TE across provnces that narrows over the study perod and s drven by the shfts of producton to the metafronter. JEL classfcaton: D4, N55, O13 Keywords: techncal effcency, metafronter, random coeffcent model, Chnese agrculture 1 INTRODUCTION An ncreased level of effcency that better employs scarce resources n agrcultural producton s an mportant ndcator of a naton s transon process from an agrculturalbased, labor-ntensve economy to one ncreasngly based on ndustres and servces. Chna s agrculture s unque n that s characterzed by an extremely egalaran dstrbuton of cultvated land, whch means that there are more than 00 mllon rural households, each of whch cultvate less than 0.55 hectares (NSBC 005). There s ltle reason to beleve that Chna could expand the average household s holdng of land (through the rapdly-growng land rental markets) (Kung 00), and even f dd, the lerature suggests that there are small posve economes of scale n Asan agrculture (Trueblood and Coggns 003). In addon, the country s extenson system for expandng new technology n producton has collapsed (Hu et al 009). Concerned wh natonal food secury, Chna s polcal agenda has always placed a hgh prory on fndng methods to motvate small farmers to mprove ther effcent use of nput resources, and thus contrbute to the rse of productvy. Techncal procedures usng stochastc fronter (SFA) or data envelopment analyss (DEA) are generally famlar to studes that evaluate the contrbuton of techncal effcency (TE) change to total factor productvy (TFP) (e.g. Bonds and Hughes 007). Regardng the applcaton of SFA n Chna, several studes conclude that although TE has mproved greatly snce nstutonal reforms have been ntroduced, regonal TFP growth dffers largely due to regonal varatons of TE n both magnude and drecton (Fan 1991; Wu 1995; Kalrajan et al 1996). These conclusons have also been verfed by applyng the DEA approach (Mao and Koo 1997). However, all of these studes rely on provncal quantle producton data, whch restrcts the analyss to the provncal or regonal level and hdes the varaton of TE and

3 technology whn provnces. Thus, polcy mplcatons based on provncal- or regonal-level studes may not necessarly be approprate at lower admnstratve levels (Pender et al 1999). Usng household-level data, Brümmer et al (00) found that the dfference n productvy pror to and after the 1990s resulted from dfferences n TE n the two perods, whch was brought about by land polcy and the frequent adjustment of market polces. Because ths study s lmed to households n the Zhejang provnce, s dffcult to generalze s fndngs to households across dfferent economc, socal and geographc locatons. Parallel theoretcal and methodologcal developments on effcency analyss concentrate on the dentfcaton of determnants of neffcency such as locaton-specfc factors of producton and the behavour of producers. Usng household-level data, Wang et al (1996) and Lu and Zhuang (000) found that under the constrant of market dstortons, TE could manly be explaned by farm-specfc effects. Based on crop-specfc producton functons, Huang and Kalrajan (1997) and Tan and Wan (000) presented evdence that TE s responsve to crop varetes and plantng systems, whch are under the nfluence of technologcal mprovement. Zhang et al (011) concluded that techncal effcency and s varaton across provnces are nfluenced by local land reallocaton polces and nstutonal settngs. The basc assumpton of the abovementoned studes s that all producers operate under a gven technology, and thus face the same producton effcency fronter. Dfferences n resource endowment among regons nfluence the adopton of technology and the varaton of TE. Ths dea has been nlayed nto a meta-fronter functon to allow measurng TE for each group of producers under group-specfc producton fronters (Hayam 1969; Hayam and Ruttan 1970, 1971; Battese and Rao 00; Stewart et al 009). Ths has nspred a number of studes on agrcultural producton across regons whn a country as well as across countres (Battese et al 004; Bravo-Ureta et al 007; Chen and Song 008). However, s observed that dstnct producers even whn a local regon may have access to dfferent technologes due to dfferent farm and household characterstcs. Metafronter analyss generally aggregates the producer-specfc technologes nto several compose measures, and fals to capture the mpact of heterogeneous technologes avalable to each producer n a certan regon. To account for farm-specfc factors, random parameter models (RPM) can be used. Ths class of models was ntroduced by Tsonas (00) and extended by Alvarez et al (003, 004). In these models, heterogeney s captured by an unobservable varable that s smulated by suable estmaton procedures. The goal of our paper s to extend the exstng lerature n two dmensons. Frst, we use a random coeffcent model to analyze the magnude and drecton of TE change under farm heterogeney and regon-specfc fronters. Ths approach also allows us to assess whether regonal varaton of output s due to farm neffcences or s caused by the varous sources of nput heterogeney such as capal vntages, land qualy and human capal, etc. Second, we rely on a metafronter approach to nvestgate the sgnfcance of regonal sources of techncal effcency. The rest of ths paper s organzed as follows. Secton specfes the random parameter model and the metafronter functon. Secton 3 presents the data source and descrptve statstcs of varables used n the estmatons. Emprcal results are presented and dscussed n Secton 4. The ffth secton concludes the paper wh a summary and a dscusson of polcy mplcatons. THEORETICAL BACKGROUND The theoretcal framework s developed whn a panel data methodology, wh = 1,,N farms and t = 1,..,T observatons per farm. The frst step concerns the estmaton of regon- 3

4 specfc producton functons. We model producton n an nput augmentaton framework,.e., we defne effectve nputs (x e ) as: e τ xt x e t μ x x e. (1) Here, x s a vector 1 of observable nputs and t accounts for technology change (TC). The symbols t and represent parameter vectors, whle represents a non-observable farmspecfc factor. It can be expected that ths nput s a surrogate for several determnants of farm producton usually not observable, lke nput qualy, farm structure and organzaton, as well as socoeconomc characterstcs of the farm households. The unobservable component s used n an attempt to measure the level and the complex nteracton of these determnants. In ths general representaton, the unobservable nput can have two specfcatons. Frst, = m ndcate that farms operate at the optmal level of the specfc factor. Second, however, farmers may not fully explo the productve capables of the unobserved factor, n ths case = m < m. Under ths assumpton, the dfference m - m can be regarded as a generc component of techncal effcency (please see equaton 6 below). y The maxmum level of producton (y) s gven when = m : e ; m f x. () Actual producton s: y f x ; m e, or e x ; m TE y f, wh TE e f x ; m. (3) e f x ; m In the emprcal applcaton we assume a translog producton functon: e e e e x ; m I α x 'ln x 1 ln x ' A xx ln x ln f 0. (4) Rearrangng terms provdes: ln f m mm t tt tm e x m m 1 ; m 1 0 t m α x α xtt α xmm 'ln x 1 ln x ' A xx ln x t. (5) A smlar relatonshp holds for = m. The varous parameters assocated wh t and m are functons of x, xx as well as xt, and x. Gven ths specfcaton of the producton functon, TE s gven by: 1 In ths paper vectors and matrces are represented by bold small and capal letters, respectvely. 4

5 lnte 0 t γ ' ln x, wh 0 ( m m ) 1 t x ( m m ) γ t x m α tm xm ' ( m m ) mm m m. (6) Accordng to (6), TE conssts of four components. The frst represents a tme-nvarant frmspecfc effect, whereas the other terms reflect the nteracton of m and m wh tme and nputs. An nterestng term n the expresson s t, snce provdes nformaton about the change of neffcency over tme, and thus, reveals whether there are catchng up or fallng behnd processes. Equatons (3) and (6) constute a system that cannot be estmated drectly, snce neher m nor m are known. However, the estmaton can be conducted when the system s transformed nto a standard fronter model: ln y e ;m u v f x (7) e where u s defned by (6) and ; m f x s gven by (5). Equaton (7) can be estmated usng maxmum smulated lkelhood (Greene 005) by makng the conventonal assumpton regardng v and u. Thus, v represents a random error term wh v ~ N 0, v, and u s the techncal neffcency wh u ~ N 0, u. Moreover, m s assumed to obey a standard normal dstrbuton, e.g. m ~ N 0, 1. When estmatng the RPM, the parameters assocated wh m are dentfed up to ther sgn. Moreover, gven the dstrbutonal assumpton about m they must be regarded as nput-specfc standard devatons (Greene 005). Thus, the mpact of m on producton s not unquely dentfed. Alvarez et al (003, 004) extended the standard approach by assumng that producton reacts posvely to an ncrease of the unobservable component, e. g.: e f x ;m m 0. (8) Ths restrcton dentfes the sgns of the correspondng parameters; n addon, farm-specfc values of unobserved heterogeney can be estmated by (Alvarez et al 004): R 1 k m, r f y t, m, r, X, δˆ R r Eˆ 1 m X, δ (9) R 1 k f y t, m ˆ, r, X, δ R r1 where m,r s a draw from the populaton of m, R s the number of the draw, and f denotes the porton of the lkelhood functon for frm, evaluated at the parameter estmates and the current value of m. The vector δ ˆ represents a vector of estmated parameters. The capal,r The reason s that m and the assocated parameters enter the model multplcatvely. 5

6 letter n case of nputs ndcates that the lkelhood functon s evaluated for all observatons of frm. Gven the estmated level of m, effcency scores can be computed by (Jondrow et al 198; Alvarez et al 004): m m lnte j E u, m 1 (10) m wh u, u v and v u. 3 v The second step nvolves estmatng the metafronter functon. By defnon, the metafronter functon cannot fall below the determnstc porton of the group-specfc stochastc fronter models. Moreover, must be ensured that the estmated metafronter best envelops the determnstc components for dfferent groups. Battese et al (004) proposed a method called the mnmum sum of absolute devatons to dentfy the envelope. Followng ths approach, the metafronter functon s estmated by solvng the followng LP problem: I T I T ln f ; δ ln f x ; m ˆ k k f,, δ ln x ; δ Mn 1 t1 x (11) subject to ln f x ; δ ln f x ;m,ˆ δ,k k 1 t1 where ln f s the logarhm form of the producton functon n (), estmates obtaned from the stochastc group-specfc fronter, and of the metafronter functon to be estmated. δˆ k δ s a vector of parameter contans the parameters Once the values of δ are estmated, the technology gap rato (TGR) can be estmated. TGR for the -th producer n the k-th group at the t-th tme perod can be obtaned by: TGR ( X,Y ) k f x ;m, δ,k k f x ; δ (1) Then, a measure of the total output-orented techncal effcency TE ( X,Y ) TGR TE (13) o k k TE o ( X,Y ) s obtaned by: Fgure 1 asssts n provdng an ntuve nterpretaton of our procedure. We bascally dstngush three levels of producton: farm, regonal, and natonal. The farm-specfc technologes are consdered by m, the ndcator of farm heterogeney. Both the farm level and the regonal level are estmated by equaton (7). The next step conssts of determnng the 4 3 The model can be estmated usng Lmdep 9.0 or NLog 4.0. The routne also provdes the values of the unobserved components and effcency. 4 k Here denotes group-specfc (k) techncal effcency provded by the frst step for ndvdual producers () TE and tme (t). 6

7 metafronter functon as an envelope of regonal producton functons. Ths s done by usng equaton (11). Fgure 1: Illustraton of Meta-fronter, regonal and ndvdual fronter functons y metafronter functon regonal producton functons farm producton functon x 3 DATA SOURCES and DESCRIPTIVE STATISTICS The database used n ths study was drawn from a fxed-pont survey across Zhejang, Hube, and Yunnan provnces that s conducted annually by the Chnese Mnstry of Agrculture. These three provnces were chosen to reflect the dversy of Chnese agrcultural producton. Zhejang provnce s one of the rchest provnces n the East, Hube provnce represents the central mddle-ncome regon, and Yunnan provnce belongs to West Chna and s one of the poorest regons n the country. 5 The sample collecton proceeded n a stratfed manner. Inally, every county was stratfed by annual net ncome per capa nto upper, mddle, and lower groups. Representatve vllages n each group were chosen accordng to geography (plan, hlly, or mountanous area), locaton (cy, suburb, or rural), and economc characterstcs defned as manly agrculture, forestry, anmal husbandry, fshery or others. Household data from the respectve vllages were then randomly selected. To mantan longudnal household nformaton, the same households were ntervewed each tme the survey was conducted. If the household was dropped from the survey and was not recorded on the household lst n the vllage, a new sample household was recrued from the same vllage wh another ID and remaned n the survey for the followng years. 6 These characterstcs allowed us to establsh a balanced panel data from 1995 to 00, n whch 133 households were attaned from Zhejang, 160 households from Hube and 15 households from Yunnan. The household data contaned detaled nformaton on agrcultural producton operatons. Table 1. Descrptve statstcs of varables by provnces, Varable Symbol Un No. of Mean Observaton Zhejang Standard Devaton Mnmum Maxmum 5 Per capa gross regonal product n Zhejang, Hube and Yunnan n 004 amounts to 3,94 RMB, 10,500 RMB and 6,733 RMB, respectvely (NSBC, 006). 6 Households dropped from the survey due to the emgraton of the whole famly from the vllage to the urban area or other towns or vllages, or the famly members ded after several years of beng n the survey. 7

8 Output Y Yuan Labor A Day Land L Mu Capal K Yuan Intermedate V Yuan Hube Output Y Yuan Labor A Day Land L Mu Capal K Yuan Intermedate V Yuan Yunnan Output Y Yuan Labor A Day Land L Mu Capal K Yuan Intermedate V Yuan Output Y Yuan Labor A Day Land L Mu Capal K Yuan Intermedate V Yuan Source: Fxed-pont household level data, Mnstry of Agrculture (MOA), Chna. The dependent varable used n the fronter producton functons s the value of output, whch aggregates the value of physcal products from crops, lvestock and other agrcultural products. Labor nput s defned as total annual workng days allocated to agrcultural producton, forestry, anmal husbandry and fshery actves. Land nput ncludes cultvated land, husbandry land and woodland. Capal s taken as the monetary value of farm machnes. Intermedate nputs sum up expendure on chemcal fertlzer, pestcdes, plastc flm and other expendures nvolved n producton. All value varables n the un of RMB are normalzed at constant 1995 prces. Descrptve statstcs of the varables presented n Table 1 reveal sgnfcant varatons of output and nputs across provnces. Rural households n Zhejang, on average, earn more agrcultural ncome usng less land and labor, but more capal and ntermedate nputs compared to households n Hube and Yunnan. Ths mght be caused by dfferent resource endowment and farm structures across provnces, ndcatng that technology adopted by rural households s to a large extent regon-specfc. Ths suggests that metafronter does exst n Chna s agrcultural producton. Thus, prevous studes that do not account for regon-specfc technology are perhaps nadequate for modelng Chnese agrcultural producton. All 8

9 4 EMPIRICAL RESULTS The data descrbed n the prevous secton were used to estmate the stochastc provncespecfc and pooled producton functons shown n equaton (7). The stochastc provncespecfc producton functons are estmated usng the household data separately for each provnce, whereas n the pooled estmaton, the data from all provnces are consdered. The varables used n the model estmaton were normalzed by ther respectve geometrc means to avod numercal dffcultes n the maxmum lkelhood estmatons, and to faclate the nterpretaton of the parameter estmates. 7 The estmated coeffcents for each model are presented n Table. Standard varatons of compose error terms ( v + u ) are approxmately 0.0 n Hube, 0.8 n Yunnan and 0.35 n Zhejang, mplyng that a large part of output varaton s explaned by the model. However, not only the sze but also the structures of the two error terms vary among the provnces. The mportance of neffcency compared to the random effects on output varably s expressed n term whch s equal to the relaton of the u and v. Thus, values larger than 1 mply that neffcency s more pronounced than random nfluences. Ths holds for Zhejang and Hube, whle n Yunnan both sources have approxmately the same value. Further dfferences among the provnces exst wh respect to the mpact of TC. Whle agrculture n Zhejang and Yunnan benefed from techncal progress, producton n Hube s characterzed by accelerated technologcal progress (a t and a tt < 0). On average, Yunnan benefed more from TC than Zhejang. However, n the latter we observed an acceleratng growth of producton possbly whle the growth rate n Yunnan was decreasng. In all provnces techncal change was capal savng ( kt < 0), and ntermedate nputs and labor usng ( at > 0, vt >0). Land savng TC was estmated for Yunnan and Hube, whle n Zhejang was land usng. The estmates of #, wh # = A, L, K, V are the producton elastces at the sample mean. Our results ndcate that there s no jont pattern of average elastces of physcal nputs among regons. The two most mportant factors are labor and ntermedate nputs, the latter of whch accounted for approxmately 40% of producton. The producton elastces of labor are approxmately 0.4 n Zhejang and Hube, but n Yunnan s sgnfcantly smaller at approxmately Ths structure of the elastces s consstent wh the level of regonal development. Snce Yunnan s less developed than the other regons, can be expected that the opportuny costs of labor are relatvely low n ths regon, whch mples that farms allocate comparatvely more labor to agrcultural producton than farms n other regons. The lowest producton elastcy s observed for capal, wh values at about 0.0. Ths holds for all regons. However, contrary to labor ths s not an ndcator that capal s abundant, but rather scarce. Snce an elastcy s the rato of margnal and average product, a small elastcy can also be attrbuted to a hgh average factor productvy. Ths wll be the case when the factor s scarce, for example capal n Chnese agrculture. The producton elastcy of land also dffers sgnfcantly across regons and ranged from about 0.18 n Hube to 0.08 n Zhejang and.1 n Yunnan. The sum of the ndvdual producton elastces provdes the elastcy of scale. Ths ndcator ranges from about 0.9 n Zhejang and Hube to about Due to ths procedure, the parameter estmates for x cannot be drectly nterpreted as average producton elastces n the group-specfc estmatons. However, the dfference between the estmates and the average producton elastcy was rather low. Thus, n order to faclate comparson between the group-specfc and the pooled models, s approprate to regard the parameter estmates as far approxmatons for the producton elastces. 9

10 n Yunnan. Ths result s also consstent wh labor-ntensve and capal-extensve producton, snce economes of scale usually can only be exploed through the adopton and ntensve use of new machnery. Table. Parameter estmates for the random coeffcent model across provnces and Metafronter functon, Random coeffcent model Zhejang Hube Yunnan All Metafronter (0.090) (0.0149) (0.0173) 0.91 (0.0101) Impact of techncal change T (0.0085) (0.0035) 0.0 (0.0034) (0.001) TT (0.0054) (0.005) (0.007) (0.000) 0.01 AT (0.009) (0.0066) (0.007) (0.0030) 0.00 LT (0.0118) (0.006) (0.0056) (0.0041) KT (0.004) (0.004) (0.005) (0.0017) VT (0.0075) (0.0041) (0.0043) ( Mean of the random process (average producton elastces) A (0.039) (0.006) (0.0185) (0.008) L (0.089) (0.0184) (0.016) (0.0070) K (0.0115) 0.07 (0.0084) (0.0098) (0.0035) V (0.000) (0.019) (0.0137) (0.005) Coeffcents of unobservable factor 0M (0.015) (0.0067) 0.69 (0.0087) (0.0044) TM (0.0050) (0.004) (0.008) (0.001) AM (0.0174) (0.0135) (0.0155) (0.0071) LM (0.019) (0.0110) (0.019) (0.0083) KM (0.0089) (0.0061) (0.0070) (0.0040) VM (0.0119) (0.0079) (0.0107) (0.0060) MM (0.0181) (0.0079) (0.0110) (0.0084) (Next) 10

11 Table. contnued Random coeffcent model Zhejang Hube Yunnan All Metafronter Pure second order effects AA (0.0399) (0.0349) (0.0394) (0.0134) LL (0.0354) (0.0156) (0.0373) (0.0083) KK (0.0078) (0.0085) (0.0105) (0.0034) VV (0.0149) (0.0137) (0.013) (0.0061) AL AK AV LK LV (0.056) (0.0334) (0.0117) (0.0131) (0.07) (0.0179) (0.0169) (0.0135) 0.03 (0.0165) (0.000) (0.0345) (0.0105) (0.016) (0.0045) (0.074) (0.0075) (0.0148) (0.0068) (0.03) (0.007) KV (0.0080) (0.0094) (0.017) (0.0039) Effcency dstrbuton v u (0.0133) (0.0133) (0.006) (0.009) (0.1470) (0.1470) (0.099) (0.0401) LogL Ob Source: Own estmates. Notes: Fgures n parentheses are standard devaton. Correspondng to restrcton (8), producton s ncreasng wh m n all provnces. Moreover, the vast majory of the coeffcents are hghly sgnfcant. Ths ndcates that agrcultural producton s strongly affected by determnants that are not contaned n the household data. Possble canddates nclude sol qualy and also socoeconomc characterstcs such as household sze, off-farm labor supply or hred labor nput. The combned effects of the unobserved components are rather complex and lead to dfferent mpacts on the producton elastces. Thus, the structure of the parameter estmates for #M, wh # = A, L, K, V are que heterogeneous across regons. However, s nterestng to note that more favore unobserved components do not necessarly lead to a better exploaton of techncal progress and producton possbles. Ths s only the case n Yunnan ( TM > 0), whle n the other two regons the oppose effect domnates. Ths mght ndcate that techncal progress whn the latter regons s drven by catchng up processors of farms lackng behnd, an nterpretaton that s supported by the low mpact of techncal change n Hube and Zhejang. 11

12 Based on the results n Table, a lkelhood rato (LR) test was conducted for the null hypothess that the provnce-specfc fronters are dentcal. The test statstcs rejected the null hypothess wh a p-value less than 0.001, mplyng that the provnce-specfc fronters are not the same. Moreover, conclusons regardng the effcency of agrcultural producton would also be based f all observaton were evaluated wh regard to the wrong reference technology. Therefore, the metafronter functon presented n equaton (11) must be estmated. The producton elastces of the metafronter functon are gven n the last column of Table. The structures of the elastces are bascally the same as those at the regonal level, though smaller n sze. Ths s consstent wh the presumpton that the metafronter functon s the envelope of the regonal producton functons. Moreover, the producton elastces provded by the metafronter functon vary from the estmates of a pooled estmaton (Table, Column 7). Ths holds especally for ntermedate nputs whose mportance s overestmated by the pooled estmaton. Table 3 presents average TE scores relatve to the stochastc regon-specfc fronter and metafronter technologes, as well as TGR scores for each provnce and all the samples by year. TE scores relatve to the regon-specfc technology average 0.84 both n Hube and Yunnan, and 0.75 n Zhejang. The dfferences between average TE scores ndcate that farms n Zhejang are consderably more heterogeneous wh respect to explong the regonal producton possbles than are farms n the other regons. Ths concluson s supported by the hgher standard varatons n TE relatve to the regon-specfc technology, whch are relatvely small n Hube and Yunnan but large n Zhejang, especally durng the late 1990s. Ths suggests that though the farmng management n Chna s smple due to the constrant of nputs endowment, s comparatvely more flexble on farmng management practce n Zhejang than n Yunnan and Hube. The hgh varaton of TE n Zhejang mples the exstence of more technologcally advanced farms n that regon, whch n turn are lkely to defne the nterregonal producton fronter. Ths conjecture s confrmed by the results of the metafronter analyss. Table 4 ndcates that the TGR of regon-specfc technology to the metafronter technology s relatvely small n Zhejang. Ths reflects the fact that farm households n comparatvely rch provnces lke Zhejang adopt more advanced technology for managng farms. Moreover, has been shown that n Zhejang, households are more lkely to use capal and other ntermedate nputs such as fertlzer and pestcde, rather than tradonal labor-ntensve technology (see Tables 1 and ). o Turnng to TE, we found that the relatve neffcency of producton s drven by TGR (Equaton 10), e.g. the neffcences among regons are more pronounced than those whn the regons. Average TE scores mply that all of the households n ths study were, on average, producng 8% of the outputs that could be potentally produced from the gven nputs by usng a regon-specfc technology as a reference; however, only half of them used the metafronter technology as a reference. TGR s at about 50%, ndcatng that producton could be doubled f farms were able to access the technology gven by the nterregonal o fronter. Moreover, lookng at the nterregonal dfference of TE, the results ndcate that Yunnan s n the process of catchng up wh Zhejang, e.g. adoptng the best regonal o producton technology. In sum, the developments of TE and TGR ndcate that Chnese agrcultural TFP growth can be further promoted through technology and knowledge transfer o whch wll fnd ther expresson n the mprovement of TE. 1

13 Table 3. Techncal effcency and technology gap rato estmates, Zhejang TE (0.0888) (0.0751) (0.0785) (0.1335) (0.0905) (0.107) (0.1089) (0.1098) (0.104) TGR (0.1779) (0.164) (0.1951) (0.1910) (0.1661) (0.190) (0.08) (0.070) (0.1898) TE o (0.151) (0.165) (0.1730) (0.1673) (0.1356) (0.1570) (0.1699) (0.1598) (0.1587) Hube TE (0.0819) (0.0934) (0.0647) (0.0653) (0.0666) (0.068) (0.096) (0.075) (0.077) TGR (0.1369) (0.1318) (0.1300) (0.1308) (0.119) (0.118) (0.198) (0.1450) (0.133) TE o (0.163) (0.1193) (0.103) (0.1151) (0.1049) (0.1119) (0.1185) (0.185) (0.1193) Yunnan TE (0.0783) (0.058) (0.0451) (0.054) (0.0564) (0.0514) (0.0465) (0.0578) (0.0563) TGR (0.0888) (0.0881) (0.119) (0.161) (0.175) (0.1308) (0.1467) (0.1649) (0.1336) TE o (0.0817) (0.0790) (0.105) (0.1107) (0.1104) (0.1148) (0.133) (0.1458) (0.1167) All TE (0.0916) (0.0788) (0.0665) (0.1011) (0.0818) (0.0835) (0.0888) (0.088) (0.0859) TGR (0.1655) (0.1508) (0.1616) (0.148) (0.145) (0.1534) (0.1704) (0.1877) (0.1617) TE o (0.1365) (0.1193) (0.1384) (0.196) (0.1174) (0.17) (0.1395) (0.1496) (0.1335) Source: Own estmates. Notes: Fgures n parentheses are standard devaton. 5 CONCLUSION In ths study we extend the exstng lerature by evaluatng the mpact of farm heterogeney when the producers n regons may access farm-specfc and tme-varyng technology. Furthermore, producers n dfferent regons face regon-specfc producton fronters. The 13

14 consderaton of essentally heterogeneous techncal effcency s frst estmated n a two-step procedure, a random parameter model followed by a metafronter producton functon. Utlzng household-level data from three provnces n Chna, the appled approach provdes new nsghts nto effcency analyss n general, and effcency problems faced by Chnese farms n partcular. The emprcal results presented here hghlght three mportant mplcatons whch requre specal attenton when used for evaluatng effcences. Frst, the results from random parameter models provde evdence that techncal effcency s, n addon to the four man physcal nputs (labor, land, capal and ntermedate nputs), sgnfcantly nfluenced by unobserved farm-specfc varables. These varables nfluence producton and TE drectly as a producer-specfc nput, and ndrectly through nteracton wh other observable nputs. Snce the mpact of the unobservable component s sgnfcant, omtng household heterogeney would result n a based parameter and thus effcency estmates. Ths mples that prevous studes that do not account for the unobservable component factors mght be nadequate for evaluatng TE of Chna s agrcultural producton. Second, farmng technology was found to exhb a regon-specfc feature. Over tme, the nature of technology changes, as ndcated by the sgn of the tme varable beng dentfed as posve n Yunnan and Zhejang, but negatve n Hube. The regonal dfferences n terms of return to scale can be explaned by the dfferent applcaton of physcal nputs and nteracton of manageral ably through the observable factors. The evdence s as follows: the use of less labor-ntensve farmng technology n Zhejang and Hube than n Yunnan; the use of more land-ntensve farmng technology n Hube than n Zhejang and Yunnan. Thrd, our results suggest that there s a dspary n TE across the three provnces, where the narrowng dspary over the study perod s drven by shfts of the producton to the metafronter. To further fll the gap across the regons, the Chnese government has prompted the Western Regon Development Strategy to ncrease nvestment and speed up the development of western regons. Furthermore, from 00, the government began to subsdze gran producers nstead of collectng agrcultural taxes. Subsdes, although just begnnng, are mostly evaluated as beng decoupled (Sonntag et al 005; Huang et al 011). Ths s expected to motvate households to ncrease nvestment, adopt new technologes and use physcal nputs more effcently n producton. The effects of these polces on agrcultural producton s worthy of further emprcal evaluaton. 14

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