A Comparison of Panel Data Models in Estimating Technical Efficiency

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1 DISCUSSION PAPER SERIES IZA DP No A Comparson of Panel Data Models n Estmatng Techncal Effcency Masoomeh Rashdghalam Almas Heshmat Ghader Dasht Esmal Pshbahar March 2016 Forschungsnstut zur Zukunft der Arbe Instute for the Study of Labor

2 A Comparson of Panel Data Models n Estmatng Techncal Effcency Masoomeh Rashdghalam Unversy of Tabrz Almas Heshmat Sogang Unversy and IZA Ghader Dasht Unversy of Tabrz Esmal Pshbahar Unversy of Tabrz Dscusson Paper No March 2016 IZA P.O. Box Bonn Germany Phone: Fax: E-mal: za@za.org Any opnons expressed here are those of the author(s) and not those of IZA. Research publshed n ths seres may nclude vews on polcy, but the nstute self takes no nstutonal polcy posons. The IZA research network s commted to the IZA Gudng Prncples of Research Integry. The Instute for the Study of Labor (IZA) n Bonn s a local and vrtual nternatonal research center and a place of communcaton between scence, polcs and busness. IZA s an ndependent nonprof organzaton supported by Deutsche Post Foundaton. The center s assocated wh the Unversy of Bonn and offers a stmulatng research envronment through s nternatonal network, workshops and conferences, data servce, project support, research vss and doctoral program. IZA engages n () orgnal and nternatonally competve research n all felds of labor economcs, () development of polcy concepts, and () dssemnaton of research results and concepts to the nterested publc. IZA Dscusson Papers often represent prelmnary work and are crculated to encourage dscusson. Caton of such a paper should account for s provsonal character. A revsed verson may be avalable drectly from the author.

3 IZA Dscusson Paper No March 2016 ABSTRACT A Comparson of Panel Data Models n Estmatng Techncal Effcency The purpose of ths paper s two-fold. Frst, compares the performance of varous panel data models n estmatng techncal effcency n producton. Second, apples varous stochastc fronter panel data models to estmate the techncal effcency of Iran s cotton producton and to provde emprcal evdence on the sources of techncal neffcency of cotton producng provnces. The results ndcate that labor and seeds are determnants of cotton producton and norganc fertlzers result n reducng techncal effcency. The mean techncal effcency of the models s around 80 percent. Varatons n the dstrbuton of estmated effcency amongst the dfferent models s large. JEL Classfcaton: C23, D24, Q12 Keywords: techncal effcency, labor use, panel data modelng, tme-varant, persstent neffcency, ndvdual heterogeney, model comparson, cotton producton, Iran Correspondng author: Almas Heshmat Department of Economcs Sogang Unversy Baekbeom-ro (Snsu-dong #1), Mapo-gu Seoul Republc of Korea E-mal: heshmat@sogang.ac.kr

4 1. Introducton Stochastc fronter models are consstent wh the objectve of output maxmzaton or nput mnmzaton n producton. In recent decades there has been ncreased avalably of panel data whch has led to a surge n stochastc fronter panel data methodologes amed at estmatng techncal effcency n producton. These models dffer n the way n whch they account for varous aspects of producton to generate consstent and unbased estmates. Lerature has developed enough to account for tme-varance, heteroscedastc, persstent techncal effcency effects, separaton of neffcency and ndvdual effects and dentfcaton of determnants of neffcency and estmatons of ther effects. A few studes also compare the performance of panel data models usng the same panel dataset (Kumbhakar and Heshmat, 1995; Greene, 2015a, 2005b; Emvalomats, 2009; Wang and Ho, 2010; Kumbhakar et al., 2014). Ths study contrbutes to the exstng lerature by comparng all exstng stochastc fronter panel data models usng same panel dataset. Iran s the second largest economy n the Mddle East and North Afrcan regon after Saud Araba, wh an estmated gross domestc product of $406.3 bllon n Unlke Saud Araba, Iran s economy s dversfed wh agrculture and ndustry sectors havng large shares. It also has the second largest populaton (78.5 mllon people n 2014) n the regon after Egypt. Iran s economy s composed of a large hydrocarbon sector, small scale agrculture and servces sectors and a notceable state presence n manufacturng and fnancal servces. It ranks second and fourth n natural gas and proven crude ol reserves n the world respectvely. 1 Influenced by recent decades of frequent economc and technologcal sanctons aganst the country and the Iran-Iraq war n the 1980s, food secury s a top natonal prory n the country. Ths mples pursung: () relance on natonal resources through hgher domestc productvy and selfsuffcency n staple crops and anmal products, and () mprovng food consumpton patterns through an ncreasng share of anmal proten ntake. Food avalably shows sgns of mprovement due to ncreased productve capacy n the man food crops along a ten-year reform perod ( ). However, the producton s not suffcent to meet domestc demand whch s met only through complementary mports. Lnked to the goal of food secury s enhancng the productvy of Iran s agrculture. Ths objectve may be nterpreted both n terms of ncreasng total agrcultural producton and n terms of ncreasng productvy of factors so that productvy gans may account for at least 2.6 per cent of the country s economc growth. Productvy gans should be expressed both n terms of enhancng per hectare productvy due to hgher effcency of agrcultural land and enhancng water use productvy n the agrculture sector (FAO, 2012). Cotton s one of the most mportant fber producng plants n the world. Ths crop not only provdes fber for the textle ndustry, but also plays an mportant role n the feed and ol ndustres wh s 1 For an overvew of the Iran s economy see 2

5 seeds, whch are rch n ol (18-24 per cent) and proten (20-40 per cent). An estmated 350 mllon people around the world are engaged n cotton producton eher on-farm or n transportaton, gnnng, balng and storage. Annually 25 mllon tons of cotton s produced n the world, around 80 per cent of whch s n Chna, the Uned States of Amerca, Pakstan, Inda and Uzbekstan (FAO, 2010). The total area under cotton producton n Iran n 2012 was about 123,000 hectares. Most cultvated areas devoted to cotton producton are located n the Khorasan (31 per cent) and Golestan (15.3 per cent) provnces. Total cotton producton was about 337,000 tons, of whch 86,837 tons were produced n Khorasan and 61,742 tons were produced n Fars provnces. The producton per hectare n Fars provnce s hgher than n Golestan. Snce ndustres n Iran need double the amount of present producton levels, most of whch s provded through mports. Consderng the urgent need for ncreasng cotton producton and due to lmed supply of arable land, ths study uses the stochastc producton functon methodology to study the techncal effcency of Iran s cotton producton usng panel data for provnces. Ths study also provdes emprcal evdence on the sources of techncal neffcences and gves polcy recommendatons for ncreasng cotton producton. The fronter functon methodology has been gven partcular attenton for measurng and comparng the performance of ndvdual producton uns whn a geographc locaton, an ndustry or a servce sector. Extensve research n ths feld has resulted n the rapd development of econometrc technques concernng specfcatons, estmatons and testng ssues. These technques have been rapdly developed and mplemented n a large number of areas usng mostly cross-sectonal mcro data. Methods have also been developed to estmate frm effcency usng panel data. Some of the problems related to dstrbutonal assumptons encountered n the crosssecton approach are avoded n panel data models. Panels also gve a large number of data ponts and have the advantage of separatng ndvdual and tme-specfc effects from the combned effect (Heshmat et al., 1995). Another advantage of panel data s that f neffcency s tme-nvarant one can estmate neffcency consstently whout dstrbutonal assumptons (Schmdt and Sckles, 1984). The assumpton that neffcency s tme-nvarant s que strong, although the model s relatvely smple to estmate f effcency s specfed as a fxed parameter nstead of as a random varable (Battese and Coell, 1988; Kumbhakar, 1987; Pt and Lee, 1981). The other extreme s assumng that both neffcency and nose terms are ndependently and dentcally dstrbuted (..d.). Ths assumpton makes the panel nature of the data rrelevant. There are also models that fall between these extreme (Kumbhakar et al., 2014). Ths paper does two man thngs: Frst, compares the performance of varous panel data models for estmatng techncal effcency n producton. Second, apples varous stochastc fronter panel data models to estmate the techncal effcency of cotton producton n Iran and provdes 3

6 evdence on the sources of techncal neffcences n s producton. The emprcal analyss uses panel data from Iran s cotton producng provnces for The results ndcate that labor and seeds are the man determnants of cotton producton and that norganc fertlzers result n reducng techncal effcency. The mean techncal effcency n most models was found to be around 80 per cent, but varatons n dstrbuton and across provnces were large. These can be attrbuted to the mpact that geography and management have on techncal effcency. The result provdes researchers a pcture of the performance of dfferent models; also provdes polcymakers an estmate of effcency n cotton producton n each provnce. The remander of ths paper s organzed nto fve sectons. Frst, we present the methodologcal framework adopted n ths study whch s followed by a descrpton of the data and emprcal model specfcatons. Next we present the results and polcy recommendatons. The last secton gves the conclusons. 2. Methodology The stochastc fronter approach for estmatng techncal effcency s based on the dea that an economc un may operate below s producton fronter due to errors and some uncontrollable factors. A study of the fronter started wh Farrell (1957) who suggested that effcency could be measured by comparng realzed output wh the maxmum attanable output. Later, based on Farrell s effcency noton Agner et al. (1977) and Meeusen and van den Broeck (1977) ndependently proposed stochastc fronter models (Emvalomats, 2009). Estmatng neffcency n these models requres dstrbutonal assumpton unless one uses the corrected ordnary least squares (COLS) and makes the assumpton that there s no nose. Schmdt and Sckles (1984) dscuss three problems wh cross-sectonal models that are used to measure neffcency. Frst, the maxmum lkelhood (ML) estmaton method whch s used for estmatng parameters and neffcency estmates usng the Jondrow, Lovell, Materov and Schmdt (1982) formula depends on the dstrbutonal assumpton of nose and neffcency components. Second, the techncal neffcency component has to be ndependent of the regressors (at least n the sngle equaton models) an assumpton that s unlkely to be true f a frm maxmzes profs and also knows s level of neffcency. Thrd, the Jondrow et al. (1982) estmator s not consstent. If panel data are avalable, that s, each un s observed at several dfferent ponts of tme some of these lmatons can be removed. However, to overcome some of these lmatons, the panel models requre other assumptons, some of whch may or may not be realstc (Kumbhakar et al., 2015). Thus, both costs and benefs are assocated wh the use of panel data for measurng performance. A key advantage of panel data s that enables the modeler to take nto account some heterogeney that may exst beyond what s possble to control usng a cross-sectonal approach whch lumps 4

7 ndvdual effects wh random errors. Ths can be acheved by ntroducng an ndvdual (unobservable) effect, say,, that s tme-nvarant and ndvdual-specfc, and whch has not nteracted wh other varables. Havng nformaton on uns over tme also enables one to examne whether neffcency has been persstent over tme or whether the neffcency of uns s tme-varyng. There may be a component of neffcency that has been persstent over tme and another that s vared over tme. Related to ths, and a key queston that needs to be consdered wh regard to tme-nvarant ndvdual effects, s whether an ndvdual effect represents (persstent) neffcency, or whether the effects are ndependent of neffcency and capture (persstent) unobserved heterogeney. A second queston related to ths s whether ndvdual effects are fxed parameters or are realzatons of a random varable (Kumbhakar et al., 2015). Thus, nformaton about persstence and tme-varance of neffcency effects and ther separaton from unobserved heterogeney effects s mportant n polcymakng for promotng effcency n the producton of scarce resources. In ths study we outlne 12 panel data models grouped nto four groups n terms of the assumptons made on the temporal behavor of neffcency. A common ssue among all the models s that neffcency s ndvdual-specfc. Ths s consstent wh the noton of measurng effcency of decson-makng uns. Models 1 to 3 assume the neffcency effects to be tme-nvarant and ndvdual-specfc. Models 4 to 7 allow neffcency to be ndvdual-specfc but tme-varyng. Models 8 to 10 separate neffcency effects from unobserved ndvdual effects. Fnally, models 11 and 12 separate persstent neffcency and tme-varyng neffcency from unobservable ndvdual effects. In general, all performance measurement methods are expected to generate ndvdual-specfc effects. Thus, n contnuaton we focus on the tme-varance of neffcency effects and ther separaton from non-neffcency heterogeney effects. 2.1 Models wh tme-nvarant neffcency effects Model 1: We frst consder the case n whch neffcency s assumed to be ndvdual-specfc but tmenvarant. In ths case the model can be estmated assumng that eher the neffcency component (u ) s a fxed parameter (the fxed-effects model) or a random varable (the random-effects model). The fxed-effects model can be wrten as (Schmdt and Sckles, 1984): (1) y x u ( 0 0 u ) x (2) x where s the log of output for provnce at tme t; β s a common ntercept; x s the vector of nputs (n logs); β s the assocated vector of technology parameters to be estmated; v s a random 5

8 two-sded nose term that can ncrease or decrease output (ceters parbus); and u 0 s the nonnegatve one-sded neffcency term. The model n (2) looks smlar to a standard fxed-effects (FE) panel data model. Once are avalable, the followng transformaton s used to obtan an estmated value of (Schmdt and Sckles, 1984): ˆ (3) u max 0, ˆ ˆ 1,..., N Ths formulaton mplcly assumes that the most effcent un n the sample s 100 per cent effcent. If one s nterested n estmatng frm-specfc effcency, can be obtaned from the relaton: (4) TEˆ exp( ˆ ), 1,..., N u The weakness of ths model s s strong assumpton of tme-nvarant neffcency and nably to separate neffcency and ndvdual heterogeney. Model 2: Instead of assumng α (and thus u ) n (2) as fxed parameters, s also possble to assume that α s random and uncorrelated wh the regressors. If the assumpton of no correlaton s ndeed correct, then the random-effect (RE) model provdes more effcent estmates than the FE model. The RE model can be estmated by two dfferent methods: One, by estmatng by the generalzed least squares (GLS) technque commonly used for a standard RE panel data model. Lke the FE estmator, RE s modfed and re-nterpreted to obtan estmates of neffcency. Now assume u s a random varable and let E u μ and u u μ. We rewre the model as: y 0 x u (5) * ) x u ( 0 * * x u, where β μ. The advantage of ths model compared wh Model 1 s that allows for testng the assumpton of fxed or random neffcency and provdes a possbly for estmatng the model effcently. Model 3: 6

9 An alternatve to the GLS method s mposng dstrbutonal assumptons on the random components of the model, and estmatng the parameters by the maxmum lkelhood (ML) method (Pt and Lee, 1981). For ML, the model s wrten as: (6) y u v f ( x ~ N u,, ) 2 ~ N(0, ), v 2 (0, ). u, Through the eraton procedure, the ML estmaton method generates hgher effcency n estmaton but at the cost of strong assumptons of normaly of the random error term. 2.2 Models wh tme-varant neffcency effects Model 4: The models ntroduced earler assume techncal neffcency to be ndvdual-specfc and tmenvarant. That s, neffcency levels may be dfferent for dfferent ndvduals, but they do not change over tme. In other words, these models suggest that an neffcent un (for example, a provnce) never learns or s able to reduce s neffcency over tme. Ths mght be the case n some suatons where neffcency s, for example, assocated wh manageral ables and there s no change n management for any of the frms durng the perod of the study. Also f the tme perod of the panel s partcularly short neffcency may persst. Even ths s, at tmes, unrealstc, partcularly when market competon s taken nto account. To accommodate the noton of productvy and effcency mprovement, we need to consder models that allow neffcency to change over tme. Then we ntroduce models n whch the neffcency effects are tme varyng. Recall the Schmdt-Sckles (1984) model n (2), where α representng a mxture term of neffcency and ndvdual effects s tme-nvarant. To make tme-varyng, Cornwell et al., (1990) suggest replacng α by α where: 2 (7). t Note that the parameters α, α and α are farm-specfc and t s the tme trend varable (hereafter, we denote ths model as the CSS model). More generally, f we represent the model as: (8) y x, 0 t t 1 2 2, then the form of the model looks lke a standard panel data model. Lke the Schmdt and Schles s (1984) model, we may apply a whhn estmator n (8) to obtan consstent estmates of β, and 7

10 then the estmated resduals of the model ( x β ). A dsadvantage of ths model s that the tme-varant s a functon of a tme trend and as such s unable to capture possble (non-trend) fluctuatons n neffcency over longer perods. Model 5: In Model 5 we use the followng generc formulaton to dscuss the varous models n a unfyng network: (9) y u u v f ( x G( t) u, ~ N u, ) 2 ~ N(0, ),, v 2 (, ). u, where 0 s a functon of tme (t). In ths model, neffcency (u ) s not fxed for a gven ndvdual; nstead, changes over tme and also across ndvduals. Ineffcency n ths model s composed of two dstnct components: the non-stochastc tme component, G(t), and a stochastc ndvdual component, u. s the stochastc component, u, that utlzes the panel structure of the data n ths model. The u component s ndvdual-specfc and the G(t) component s tme-varyng and s common for all the ndvduals. Gven u 0, u 0 s ensured by havng a non-negatve G(t). Now we consder some specfc forms of G(t) that are used n lerature. For example Kumbhakar s (1990) model assumes: 2 (10) G( t) 1 exp t t So that G(t) can be monotoncally ncreasng (decreasng) or concave (convex) dependng on the sgns and magnudes of and. Agan lke Model 4, change neffcency n Model 5 s tme drven and a non-lnear exponental functon tme. However, the trend pattern s smlar for all ndvduals and the dfference n performance among ndvduals s due to u. The random and nonlnear nature of the model requres eratve estmaton by the ML estmaton method. Model 6: Battese and Coell (1992) have proposed an alternatve formulaton n whch G(t) s specfed as: exp, (11) G( t) t T where T s the termnal perod of the sample. Agan as n Model 5, n Model 6 the neffcency s tme-drven and the smpler one-parameter functon must be estmated by the ML estmaton method. 8

11 Model 7: Kumbhakar and Wang (2005) use the followng specfcaton to specfy a model of tme-varant effcency drven by tme: exp, (12) G( t) t t where s the begnnng perod of the sample. Ths s the oppose of Model 6 where T represents the last perod of observaton. The reference ponts n these two models are the nal and fnal perods. Analytcally (11) and (12) are the same, but they are nterpreted dfferently. In Battese and Coell (1992) and the reformulated specfcaton by Kumbhakar (1990), u ~N μ, σ specfes the dstrbuton of neffcency at the termnal pont, that s, u u when. Wh (12), u ~N μ, σ specfes the nal dstrbuton of neffcency. The strength of Model 6 s n accountng for market entry, whle accounts for market ex n formulatng the reference pont n Model 7. A mxture model formulaton of the two nal and termnal reference ponts mght be superor to the two models ndvdually. 2.3 Models separatng neffcency and unobserved ndvdual effects Models 8 and 9: The model as specfed n (1) and (2) s a standard panel data model where α s an unobservable ndvdual effect. Standard panel data fxed and random-effects estmators are appled to estmate the model parameters ncludng α. The only dfference s that we transform the estmated value of α to obtan the estmated value of u, namely u by usng the hghest α as a reference for the fronter. A notable drawback of ths approach s that ndvdual heterogeney cannot be dstngushed from neffcency. In other words, all tme-nvarant heterogeney such as sol qualy that s not necessarly neffcent s ncluded as neffcency, and therefore u mght be pckng up heterogeney n addon to or even nstead of neffcency (Greene, 2005b; Kumbhakar and Heshmat, 1995). Outlers servng as a reference and confounded neffcency can overestmate or bas performance estmates. Another potental ssue wh the models (1) and (2) s the tme-nvarant assumpton of neffcency. If T s large, seems mplausble that the neffcency of a frm may stay constant for an extended perod of tme and that a frm wh persstent neffcency wll survve n the market. So should one vew the tme-nvarant component as persstent neffcency or as ndvdual heterogeney that captures the effects of tme-nvarant covarates and has nothng to do wh neffcency? If the latter s true, then the results from the tme-nvarant neffcency models are wrong. Perhaps the truth les somewhere n between. That s, a part of the neffcency mght be 9

12 persstent, whle another part may be transory. Unless the parts are separated from tme-nvarant ndvdual effects, one has to choose eher the model n whch α represents persstent neffcency or the model n whch α represents an ndvdual-specfc effect (heterogeney). In ths paper, followng Kumbhakar and Heshmat (1995) we consder both specfcatons. Thus, the models we examne can be wrten as: (13) y x u If we treat α as fxed parameters whch are not part of neffcency, then the model becomes the true fxed-effects panel stochastc fronter model (Greene, 2005a), whch we consder as Model 8 n our study. The model s labeled the true random-effects panel stochastc fronter model when α s treated as a random varable and s mentoned as Model 9 n ths research. Kumbhakar and Heshmat (1995) treated α as persstent and u as transory components of overall neffcency. Model 10: Usng a dfferent approach, Wang and Ho (2010) solved the problem n Greene (2005a) by proposng a stochastc fronter model n whch the whn and frst-dfference transformaton on the model can be carred out and yet a closed-form lkelhood functon s stll obtaned usng the standard practce used n lerature. The Wang and Ho (2010) model s wrten as: y u h x v h u u 2 ~ N (0, ),, v f ( z ), 2 u ~ N (, u ), The key feature that allows the model s transformaton s the multplcatve form of neffcency effects, u, n whch the ndvdual-specfc effects, u, appear n multplcatve forms wh ndvdual and tme-specfc effects, h. As u does not change wh tme, the whn and frstdfference transformatons leave ths stochastc term ntact. (14) 2.4 Models separatng persstent neffcency from unobservable ndvdual effects Model 11: So far we have dscussed two types of tme-varyng panel data models. In the frst group of models, neffcency s a product of a tme-varyng functon drven by a tme trend and s squares, whle n the second s a devaton from the nal and termnal tme reference ponts. The advantage of ths specfcaton of neffcency s that the lkelhood functon s easy to derve. The second class 10

13 of models examned controlled for frm-effects and allowed neffcency to be tme-varyng. Unfortunately, these two classes of models are not nested and, therefore, the data cannot help one n testng to choose whch formulaton s approprate. However, both these classes of models vew frm effects (fxed or random) as somethng dfferent from neffcency. That s, neffcency n these models s always tme-varyng and can eher be..d. or a functon of exogenous varables. Thus, these models fal to capture persstent neffcency, whch s hdden whn frm effects. Consequently, these models are ms-specfed and tend to produce a downward bas n the estmate of overall neffcency, especally f persstent neffcency exsts and s magnude s sgnfcant. Models 11 and 12 separate persstent and tmevaryng neffcency components. Identfyng the magnude of persstent neffcency s mportant, especally n short panels, because reflects the effects of nputs lke management (Mundlak, 1961) and other unobserved nputs whch vary across frms but not over tme. The resdual component of neffcency mght change over tme whout any change n a frm s operatons. Therefore, a dstncton between the persstent and resdual components of neffcency s mportant and thus they have dfferent polcy mplcatons. Thus, our Model 11 s the Kumbhakar and Heshmat (1995) model that s specfed as: (15) y u u x 0 u The techncal neffcency part s decomposed as u u τ where u s the persstent component (for example, tme-nvarant management effects) and τ s the resdual (tme-varyng) component of techncal neffcency, both of whch are non-negatve. The former s only frmspecfc, whle the latter s both frm and tme-specfc. To estmate the model we rewre (15) as: (16) y x 0 A u ( E( ) and E( )) The error components,ω, have zero mean and constant varance. The model can be estmated eher by the least squares dummy varable approach or by the generalzed least squares (GLS) method. Followng Kumbhakar and Heshmat (1995) we use a mult-step procedure to estmate the model. In step 1, we estmate (16) usng the standard fxed-effects panel data model to obtan consstent estmates of β. In step 2, we estmate persstent techncal neffcency, u. In step 3, we estmate β and the parameters assocated wh the random components, v and τ. Fnally, n step 4, the tme-varyng (resdual) component of neffcency,τ, s estmated. The mult-step procedure s cumbersome, but has the advantage of avodng strong dstrbutonal assumpton by estmatng the model usng the ML estmaton method. 11

14 Model 12: Because the assumptons made n prevous models are not fully satsfactory, we ntroduce a fnal model by Kumbhakar et al. (2014) and Colomb et al. (2014) that overcomes some of the lmatons of the earler models. In ths model the error term s spl nto four components whch gven the nputs take nto account dfferent factors affectng output. The frst component captures frms latent heterogeney (Greene, 2005a, 2005b), whch has to be dsentangled from neffcency effects; the second component captures short-run (tme-varyng) neffcency. The thrd component captures persstent or tme-nvarant neffcency as n Kumbhakar and Hjalmarsson (1993, 1995) and Kumbhakar and Heshmat (1995), whle the last component captures random shocks. Then, our fnal model s the Kumbhakar et al. (2014) model whch s specfed as: (17) y f ( x ; ) u 0 Estmaton of the model n (16) can be undertaken n a sngle stage ML method based on the dstrbutonal assumpton of the four components (Colomb et al., 2011). However, here we consder a smpler mult-step procedure. For ths, we rewre model (17) as: (18) y 0 f ( x ; ) where α α E η E u ; η E η ; and v u E u. Ths model can be estmated n three steps. In the frst step, the standard random-effect panel regresson s used to estmate. Ths procedure also gves predcted values of and, whch we denote by and. The tme-varyng techncal neffcency, u, s estmated n the second step and n the fnal step, we can estmate η followng a procedure smlar to that n step 2. Presstent techncal effcency can then be estmated from η. The overal techncal effcency, OTE, s then obtaned from the product of PTE and RTE, that s, (Kumbhakar et al., 2015). In order to provde an overvew of the models structures and dfferences, Table 1 gves a summary of the models based on ther common characterstcs related to the error component structure, treatment of frm-specfc and tme-specfc effects, techncal effcency and s temporal structure and the estmaton method and s underlyng assumptons. Insert Table 1 about here 3. Data Ths research used panel data for Iran's 13 cotton producng provnces whch s an unbalanced panel data wh 151 observatons. Data summary related to research varables as gven n Table 2. The measurement of output Y s the mean of provncal cotton producton n tons per hectare. Fertlzer represents the quanty of anmal manure fertlzers used for producton per 12

15 hectare. Measurement for labor nput L s the total number of employees per hectare n dfferent provnces. Seed represent klograms of seeds and seedlngs per hectare. The data used for ths paper came from Iran s Mnstry of Agrculture Jhad, where the data are collected regonally through an annual survey that uses a common questonnare across all provnces. The summary statstcs of the data s provded n Table 1. The table shows that cotton producton vared between a mnmum of 1,092 kg to a maxmum of 3,895 kg per hectare n the dfferent provnces, and mean cotton producton was about 2,513 kg per hectare. Seed consumpton ranged between 20 to 205 kg per hectare wh a standard devaton of among provnces. The number of labor per hectare was about 77, whch may reflect the fact that cotton producton s labor ntensve n Iran. Organc fertlzer usage decreased over tme. Ths reflects the trend that young farmers are more lkely to use chemcal fertlzers and overlook the mportance of organc manure. Insert Table 2 about here 4. Analyss of the Results 4.1 Specfcaton and estmaton testng and model selecton For the purposes of ths study, we analyzed a Cobb Douglas producton functon for Models A smple functonal form was chosen for a number of reasons. Frst, the man objectve was to nvestgate the sensvy of effcency results across dfferent specfcatons and decomposon of techncal effcency. Ths can be acheved more easly wh a smple functonal form. Second, the mplcatons of assumptons regardng effcency and s decomposon were easer to nvestgate whn the frame of a smple functonal form. Thrd, we were nterested n average elastces whch are obtaned whout employng a flexble functon form. The estmaton results are gven n Table 3. Insert Table 3 about here For comparng some nested models we used a generalzed lkelhood rato (LR) test. Based on the results of ths test n Table 4, Model 5 was rejected n favor of the tme-nvarant model (Model 3). Gven the results of the statstcal tests ths table suggests that the tme-nvarant model was preferred to the tme decay model (Model 6) and Model 7. The results dscussed earler mply that techncal effcency measures do not appear to be affected by tme. Insert Table 4 about here 4.2 Analyss of results from selected models For all models the estmated output elastcy wh respect to labor was negatve and statstcally sgnfcant, ndcatng that producton decreased wh such nputs. The negatve sgn mples that by ncreasng nputs by k-tmes, provnces wll get less output than current levels. In other words 13

16 provnces wll pay more to get less. Ths may be due to labor applcaton n the thrd stage of producton when should already be decreased. Increase n seed use wll lead to an ncrease n cotton output whch s statstcally sgnfcant n all models except Models 4, 5 and 8. Ths ndcates the mportance of seeds n cotton producton. The elastcy of output wh respect to fertlzers s negatve but nsgnfcant. The negatve elastces for labor and fertlzers reported n ths paper are consstent wh other studes. Mohammed and Saghaan (2014) found negatve elastcy for these two nputs n rce producton n Korea and Chakraborty et al., (2002) concluded that fertlzers and machnery had negatve effects on cotton producton n rrgated farms n Texas. Wan and Cheng (2001) and Chen et al. (2003) found excessve labor usage n Chnese agrculture. Ther study focused on an analyss of effcency n producton rather than output responsveness to nput utlzaton. In terms of polcy mplcatons s more mportant to determne whch varables lead to neffcency. The varables consdered n current study to dentfy possble nfluences on techncal effcency are chemcal fertlzers versus anmal fertlzers, pressurzed rrgaton versus classcal rrgaton and machne use for seed and fertlzer spreadng to ndcate the extent to whch farms use modern producton technologes. The posve sgn of the parameters of these varables n Table 4 means the assocated varables have a negatve effect on techncal effcency. Accordng to ths table use of more norganc fertlzers than organc ones leads to a sgnfcant decrease n techncal effcency. Unpressurzed rrgaton versus classcal rrgaton was used n order to nvestgate whether techncal effcency ncreased when more machnery was used n rrgaton of cotton farms. The result shows that led to an nsgnfcant ncrease n techncal effcency n cotton producton. Probably the reason for ths s that there s not much dfference between provnces when comes to usng rrgaton technology. The results also suggest that the current extenson program should be reorented to gve more emphass to the applcaton of nputs and producton practces. Descrptve statstcs for techncal effcency accordng to dfferent models are presented n Table 5. Accordng to ths table, varous models clearly produced dfferent results. Mean techncal effcency of Model 10 was the hghest, whle was the least for Model 9. The average techncal effcency for Models 1 and 2 was about 0.80 wh a maxmum of 1, whle the mnmum for Model 1 was 0.65 and for Model 2 was Therefore, the gap between the most effcent and neffcent provnces was about Ths gap states the dfference between provnces n nput allocatons for cotton producton. The mean value of techncal effcency accordng to most of the models was more than The average effcency ndces reported n ths study are whn the bounds of those found n other studes on effcency of cotton farms. Usng farm-level data from four countes n west Texas, Chakraborty et al., (2002) estmated average effcency as 80 per cent. Another study of cotton producton found average techncal effcency of 79 per cent for farms n Çukurova regon n Turkey (Gul et al., 2009). 14

17 Insert Table 5 about here Fgure 1 presents kernel densy dstrbuton of techncal effcency estmates for Models As an example, consder Models 5 and 6, n whch the dstrbuton of techncal effcency scores range from 0.59 to 0.94 and 0.64 to 0.95 respectvely. Fgure 2 llustrates the lower quartle, medan and upper quartle effcences over tme across 12 models, n whch the spread of the effcency can be seen. Accordng to ths fgure Model 4 had the wdest effcency and Model 8 had the narrowest spread, slghtly narrower than Model 9. As Fgure 2 shows, the tme-seres pattern for most of the models s smlar. Due to unbalanced panel data, mean of effcency n tme-nvarant models (Models 1-3) was not constant. Insert Fgure 1 about here Insert Fgure 2 about here For an nvestgaton of the performance of dfferent sample provnces and ther poson compared wh the provnce wh the best practced technology, we would rank the provnces. Descrptve statstcs for techncal effcency measured by provnces are presented n Table 6. Estmated effcency measures for dfferent models reveal that there are dfferences between provnces n terms of effcency. For example, estmated techncal effcency accordng to Model 1 n East Azerbajan and Kerman provnces was 100 and 65 per cent respectvely. On the other hand, techncal effcency was estmated to be the hghest for East Azerbajan, Esfahan, Ardebl and Tehran and the lowest for Kerman, Mazandaran, Golestan and Khorasan. So we conclude that there s the possbly of ncreasng cotton producton n dfferent provnces through better nput and extenson practces. Insert Table 6 about here The results show that dfferent ranks for provnces determned by the 12 models. All the models except Models 8, 9 and 10 showed consstent rankngs among provnces. The yearly mean of provncal techncal effcency for the 12 models s presented n Table 7. There were some varatons n techncal effcency over tme. Accordng to most of the models, techncal effcency decreased durng the perod; 2007 was the most effcent year and 2012 the most neffcent year durng the study perod. The value of techncal effcency accordng to all models, except Model 10, for the entre perod was que hgh and was mostly concentrated n an nterval of per cent. Insert Table 7 about here Parwse rank order correlatons of Models 1 to12 are reported n Table 8. There s a perfect match between Models 11 and 12. The correlaton between Models 6 and 7, and also between Models 1, 2 and 3 was hgh. These models seem to be the most consstent n generatng smlar results, whle the results of techncal effcency estmates between Model 10 and Models 1-9 and also between Model 8 and Models 1-7 are to a large extent ndependent, wh a rank-order correlaton of less 15

18 than In Fgure 3 scatter plot matrces for Models 1-12 graphcally llustrate the dfferences between the models n the rankng of the provnces. The straght lnes n the graph ndcate a perfect match between two compared models. These results prove the fndngs as gven n Table 8. Insert Table 8 about here Insert Fgure 3 about here Table 9 shows Kendall s rank-order correlaton for the persstent techncal effcency measure between Models 11 and 12. Accordng to ths table, assessments of resdual techncal effcency for these two models are to a large extent posvely correlated, wh a rank-order correlaton of The results based on persstent and resdual techncal effcency are ndependent, wh a rankorder correlaton of Insert Table 9 about here 4.3 Polcy recommendatons The results of our research are mportant as they provde detaled nformaton to polcymakers. Our recommendatons for polcymakers nclude: There s a need to use effcent machnery to reduce the labor s contrbuton n cotton producton n Iran n order to enhance productvy. Rate of use of norganc fertlzers as compared to organc fertlzers was negatvely related to effcency, mplyng that mplementng polces wll reduce norganc fertlzer usage. Such a decson wll help remove the subsdy gven to chemcal fertlzers. Emphass should be placed on strengthenng the capacy of cotton farmers through farmer tranng workshops geared towards manageral and resource use effcency. Ths should be done n a collaboratve manner nvolvng the government, dstrct assembles and NGOs. Large dfferences between regons show provncal dspares, whch n turn ndcate that locaton has a sgnfcant mpact on the effcency of cotton producton n Iran. One reason for ths could be the envronmental condons that exst n dfferent parts of the country. Ths mples further research whch consders geographcal condons n measurng techncal effcency n dfferent zones. 5. Concluson Ths paper nvestgated the techncal effcency of cotton producton and s determnants n Iran s man cotton producng provnces. Twelve stochastc producton fronter models were estmated. The models dffered n ther underlyng assumptons of tme-varant/nvarant techncal effcency and s decomposon as well as separaton of techncal neffcency and provnce heterogeney effects. The models ncorporated almost all prevously used model specfcatons. Estmatng the 16

19 models by usng the same data allows sheddng lght on each model s strengths and weaknesses. Ths analyss was appled to 13 cotton producng provnces whch were observed over a perod of 13 years ( ). Ths study came to the concluson that labor and seeds are sgnfcant determnants of output n cotton producton, and only seeds posvely nfluence producton. The negatve sgnfcance of labor ndcates labor-hoardng behavor whch makes the provnces use more labor durng the producton season for whch they get less returns. Emprcal results of an nvestgaton of the sources of techncal neffcency showed that the rate of use of chemcal fertlzers equvalent to per un use of anmal fertlzers was a determnng factor n techncal neffcency n producton. Inorganc fertlzers result n reducng techncal effcency. Therefore, s possble to ncrease techncal effcency f more organc fertlzers rather than norganc fertlzers are used. The results also emphasze that accordng to most of the models mean techncal effcency was about than 80 per cent of the best practced technology. Average techncal effcency measures suggest that cotton producng provnces n Iran could ncrease ther producton by about 20 per cent through more effcent use of nputs, n partcular by usng organc fertlzers. Ths paper also dscussed the dfferent levels of techncal effcency among varous provnces n the country. The emprcal results show evdence of large dfferences n techncal effcency levels between provnces, whch shows that the mpact of geography and management on techncal effcency s que heterogeneous n dfferent provnces. Accordng to most of the models, East Azerbajan, Esfahan and Ardebl were the most effcent provnces for cotton producton. Results also ndcate that techncal effcency decreased durng the study perod. REFRENCES Agner, D., Lovell, C.A.K., and P. Schmdt (1977). Formulaton and estmaton of stochastc fronter producton functons. Journal of Econometrcs, 6(1), Battese, G.E. and T.J. Coell (1988). Predcton of frm-level techncal effcences wh a generalzed fronter producton functon and panel data. Journal of Econometrcs, 38, Chakraborty, K., S. Mrsa and P. Johnson. (2002). Cotton farmers techncal effcency: stochastc and nonstochastc producton functon approaches. Agrcultural and Resource Economcs Revew, 31(2), Chen, A. Z., W. E., Huffman and S. Rozelle (2003). Techncal Effcency of Chnese Gran Producton: A Stochastc Producton Fronter Approach, Paper prepared for presentaton at 17

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22 Table 1. Man characterstcs of dfferent models Model1 Model2 Model3 Model4 Model5 Model6 Model7 Model8 Model9 Model10 Model11 Model12 General frm effects: No No No No No No No Fxed Random Fxed No Random Techncal neffcency components: Persstent No No No No No No No No No No Yes Yes Resdual No No No No No No No No No No Yes Yes Overall techncal neffcency: Mean Tmenvnvnvnvnv. trunc. trunc. trunc. trunc. trunc. Tme- Tme- Tme- Tme- Zero Zero Zero Zero Zero - - Varance - - Homo. Homo. Homo. Homo. Hetero. Homo. Homo. Homo. Homo. Symmetrc error term: Varance Homo. Homo. Homo. Homo. Homo. Homo. Homo. Homo. Homo. Homo. Homo. Homo. Estmaton Method: COLS GLS ML OLS ML ML ML ML ML ML ML ML Notes: Fxed effects (Fxed), Random effects (Random), Homoscedastc varance (Homo.), Tme nvarant effcency (Tme nv.), Zero truncated error term (Zero trunc.), Corrected ordnary least squares (COLS), Maxmum lkelhood (ML), Generalze least squares (GLS). 20

23 Table 2. Summary statstcs of nputs and output data, , 13 provnces and 13 years, 151 observatons. Varable Label Mean Std.Dev. Mn Max Producton functon varables Output (Klogramms per hektares) Seed (Klogramms per hektares) Labor (man-day) Fertlzer (Klogramms per hektares) Ineffcency determnant varables n neffcency functon Rate of chemcal fertlzer per anmal fertlzer Rate of pressurzed rrgaton per classcal rrgaton E Machne use for seed spreadng (percent) E Machne use for fertlzer spreadng (percent) E

24 Table 3. Estmated stochastc fronter models (Estmated standard errors n parentheses), N=151 observaton. β β β β Gamma Hleq Tme Tme2 TmeT Z1 Z2 Z3 Z4 Model1 Model2 Model3 Model4 Model5 Model6 Model7 Model8 Model9 Model10 Model11 Moddel (0.058) (0.022) (0.021) (0.464) (0.030) (0.022) (0.022) (0.161) (0.047) (0.058) (0.022) (0.003) (0.002) (0.001) (0.001) (0.001) (0.001) (0.003) (0.003) (0.002) (0.469) (0.357) (0.415) (0.969) (0.485) (0.428) (0.428) (0.074) (0.871) (0.083) (0.469) (0.357) (0.107) (0.063) cons Z1 Z2 Z3 Z (0.291) (0.325) (0.678) (0.272) (0.626) (0.251) (0.010) (0.347) (0.717) (0.960) (0.105) (0.046) (0.330) (0.158) (0.516) (0.710) (0.984) (0.466) (0.315) R-squared Log-lkelhood

25 Table 4. Specfcaton tests for alternatve producton models Log- lkelhood under H 0 Log- lkelhood under H 1 Test statstc Crcal value at 5% Decson Model 3 versus Model Model 3 s accepted Model 3 versus Model , Model 3 s accepted Model 3 versus Model Model 3 s accepted Table 5. Descrptve statstc for techncal effcency measures by dfferent models Techncal Effcency Mean Std.Dev. Mn Max Model Model Model Model Model Model Model Model Model Model Model Model Notes: Models 1-3: Models wh tme-nvarant neffcency effects Models 4-7: Models wh tme-varant neffcency effects Models 8-10: Models separatng neffcency and unobserved ndvdual effects Models 11-12: Models separatng persstent neffcency from unobservable ndvdual effects 23

26 Table 6. Descrptve statstc for techncal effcency measures by provnces Provnce Model1 Model2 Model3 Model4 Model5 Model6 Model7 Model8 Model9 Model10 Model11 Moddel12 Markaz Mazandaran East-Azerbajan Fars Kerman Esfahan Semnan Yazd Tehran Golestan Ardebl Ghom Khorasan Table 7. Descrptve statc for techncal effcency measures by years year Model 1 Model 2 Model 3 Model 4 Model 5 Model 6 Model 7 Model 8 Model 9 Model 10 Model 11 Model