ESTIMATING SUPPLY RESPONSE IN THE PRESENCE OF TECHNICAL. INEFFICIENCY USING THE PROFIT FUNCTION: An Application to. Ethiopian Agriculture

Transcription

1 ESTIMATING SUPPLY RESPONSE IN THE PRESENCE OF TECHNICAL INEFFICIENCY USING THE PROFIT FUNCTION: An Applcaton to Ethopan Agrculture by Suleman Abrar * Department of Economcs, Unversty of Lecester Unversty Road, Lecester, LE1 7RH, The UK Emal: as210@lecester.ac.uk Abstract: Studes of supply response usng the proft functon have typcally mantaned the neo-classcal assumpton of effcency. Usng farm-level data from Northern Ethopa, ths study examnes the mpact of techncal neffcency on the response of small holder farmers. Two systems of output supply and nput demand functons are estmated and compared: one the standard model n whch techncal effcency s assumed and another n whch techncal neffcency s explctly ncorporated nto the proft functon. Whle the results from non-nested hypotheses tests are nconclusve, the model wth techncal neffcency s preferred to the other model for theoretcal consstency. Incorporaton of neffcency has generally ncreased the magntudes and the statstcal sgnfcance of own prce elastctes, substantally so n the case of teff and fertlzer. The results ndcate that farmers n Ethopa do respond postvely and sgnfcantly to prce ncentves. The results also underscore the need to mprove farmer s access to better qualty land, farm nputs and credt, and publc nvestment n roads and rrgaton. JEL: O13, Q11, Q12. Keywords: Supply Response, Techncal Ineffcency, Elastctes, Proft functons * We thank the European Unon for fnancal support and the Department of Economcs, Adds Ababa Unversty for allowng unlmted access to the data set. Very helpful comments were obtaned from Dr. Carlos Arnade, Dr. Olver Morrssey, Professor Tony Rayner and Dr. Mchael Trueblood. All remanng errors are mne.

2 Techncal Ineffcency and Supply Response n Ethopa 2 1 Introducton Agrculture domnates the Ethopan economy, accountng for the bulk of exports and employment, and s almost totally a small holder sector. As n many other developng countres, economc polces have not favored agrculture, and per capta agrcultural producton declned steadly snce the 1970s, but reforms have been mplemented snce the early 1990s. Market lberalzaton polces, n partcular prce ncentves, were mplemented n the 1990s, wth some mprovement n the overall performance of the economy (Abrar, 2000). Nevertheless, how much of ths recovery s due to prce ncentves and how much due to non-prce factors s not clear. Nor s clear whether small holder farmers are more responsve to prces of some outputs and nputs than others. Partly ths s attrbutable to a lack of farm-level analyss of the effects of polces (especally relatng to prces) on the supply response of peasant farmers. Nearly all studes of supply response n Ethopa use aggregate tme seres data, and estmate export supply response for coffee (Dercon and Lulseged 1994, 1995; Alem 1996) or supply response of food grans (Abebe, 1998; Zerhun, 1996). Several studes have shown that there s mpressve potental for ncreasng the effcency and productvty of peasant agrculture n Ethopa (e.g., Seyoum et al, 1998; Croppenstedt and Mulat, 1997). Nearly all of these studes only estmated the level of techncal effcency, gnorng the role of prces on the producton and nput allocaton decsons of farmers. However, ths s rather the general trend and not unque to Ethopa. On the other hand, most mcro-economc studes of supply response to prces have mantaned the neo-classcal assumpton of effcency. Only a few studes n the lterature have combned these two ssues and estmated farm responses to prces n the presence of neffcency (e.g., Kumbahakar, 1996). One of the most comprehensve works n the area has shown that elastctes estmated based on a model wthout neffcency are ncorrect (Kumbahakar, 2001). Ths study addresses supply response and neffcency smultaneously wthn the framework of proft functons, so does t augment prevous work whch gnores neffcency (Abrar, 2002), but used the same data set to estmate supply response. The current study also

3 Techncal Ineffcency and Supply Response n Ethopa 3 adds to the small lterature on supply response n Sub-Saharan Afrca usng farm-level data (e.g. Savadogo, et al, 1995; Hattnk, et al, 1998). Based on the establshed theory of dualty, Arnade and Trueblood (2002) recently ntroduced a method to ncorporate techncal neffcency nto the proft functons, and the resultng system of output supply and nput demand equatons. We follow ths approach to explore whether the standard proft functon s ms-specfed by not takng techncal neffcency nto account, and f so, how that nfluences parameter estmates and elastctes. Arnade and Trueblood (2002) llustrated ths novel approach usng state level data from Russan agrculture, focussng mostly on the prce elastctes. Apart from servng the man goal of demonstratng the theoretcal approach, the emprcal results provde some useful nsghts nto Russan agrculture. However, the emprcal applcaton suffers from the well-known problems of nconsstency assocated wth applyng farm-level theory to aggregate data. In calculatng neffcency and elastctes, they have assumed, wthout testng, that corporate farms n each state have smlar technology. Snce the underlyng producer theory behnd these estmates s based on a proft maxmzng ndvdual producer, t cannot be readly appled at hgher levels of aggregaton wthout a pror testng. Further, they have not provded tests of the consstency of the results wth the curvature and symmetry restrctons mpled by the underlyng dualty theory. To conduct a crtcal test of these assumptons requres farm-level data (Shumway, 1995). We use farm-level survey data from Northern Ethopa coverng 630 rural households n to estmate two systems of output supply and nput demand (wth and wthout ncorporatng techncal neffcency). We compare the two models based on non-nested hypotheses tests as well as conformty to neo-classcal assumptons of producton theory. We also nclude a full range of non-prce factors that are beleved to be mportant n affectng agrcultural producton n Ethopa. Whle the results from non-nested hypotheses tests are nconclusve, the model wth techncal neffcency s found to be more approprate for theoretcal consstency. A comparson of parameter estmates and elastctes from the two models shows that the presence of techncal

4 Techncal Ineffcency and Supply Response n Ethopa 4 neffcency has restrcted responses of farmers to changes n prce and non-prce ncentves. The rest of the paper s organsed as follows. Secton 2 outlnes the procedure for ncorporatng techncal neffcency nto the proft functon framework. The data and econometrc approach are set out n Secton 3. Secton 4 presents and dscusses the results. The conclusons are n Secton 5. 2 Modellng Framework One method for addressng neffcency and supply response nvolves a smultaneous estmaton of effcency and proft functon parameters n a sngle step (Kumbhakar, 1996, 2001). Whle ths approach has many advantages, such as estmatng neffcency scores and the parameters jontly and allowng standard statstcal testng procedures to establsh a level of confdence n the neffcency scores, t reles on computatonally demandng estmaton technques, and mposes restrctons on the dstrbuton of model errors. Furthermore, t s not always possble to overcome the dffcult task of dstngushng between techncal and allocatve neffcency. Arnade and Trueblood (2002) develop an alternatve approach for ncorporatng techncal neffcency nto a system of output supply and nput demand equatons. Ther approach reles on less restrctve assumptons and sorts out the effects of techncal and allocatve neffcency, but must be mplemented n two steps. Usng the exstng dual relatonshps among cost functons, dstance functons and techncal neffcency, they show how techncal neffcency s ncorporated nto the proft functon as an exogenous varable through output prces. Suppose that the producton technology s homogeneous of degree k, and that outputs are separable from nputs. Fare and Prmont (1995) have shown that the nput dstance functon s homogeneous of degree -1/k n outputs f the technology s homogeneous of degree k,.e., (1) 1/k D I ( y, x) = DI (y, x),

5 Techncal Ineffcency and Supply Response n Ethopa 5 where D I (.) s the nput dstance functon; y represents a vector of m outputs; x represents a vector of n nputs; and s a parameter. Assumng effcency, the dualty between the nput dstance functon and the cost functon can be expressed as: (2) C( y, w) = mn w'x, s.t. ( y, x) = 1, x D I where w represents a vector of nput prces; and C(.) s the cost functon. Fare et al (1990) establshed that the dstance functon s equal to the recprocal of techncal neffcency, denoted by. Thus, the cost mnmzaton problem (bearng n mnd the assumpton of homogenety and the propertes of the correspondng cost functon) can be expressed as follows: (3) (4) (5) (6) mn w'x, x = mn w'x, = mn w'x, = C( -k s.t. D y, w) = 1 s.t. DI ( y, x) = s.t. D ( y, x) = 1 1 I I ( -k C( y, w). y, x) = 1 The proft maxmzaton problem s therefore gven by: (7) max y p'y - -1 C( y, w), where p s a vector of output prces. The frst order condton for each y s: (8) (9) p p 1 = C, y C =, y or = 1,..., m. The proft functon at the optmal output level s: (10) π (p, w) = max p'y - -1 C( y,w),

6 Techncal Ineffcency and Supply Response n Ethopa 6 where y denotes the optmal output levels. Usng Hotellng's Lemma, the proft maxmzng levels of output supply and nput demand equatons are, respectvely, derved from (10) as: (11) y ( p, w) = π( p, w)/ p, = 1,,m, and (12) -x r ( p, w)/ = π( p, w)/ w r, r = 1,, n. where and r ndex the outputs and nputs respectvely. In ths model, therefore, techncal neffcency nteracts wth output prces multplcatvely. To mplement ths model, techncal neffcency scores need to be calculated frst usng the non-stochastc programmng approach. Then, the neffcency scores are specfed as an explanatory varable n a proft functon and the correspondng system of output supply and nput demand equatons. The most wdely used approaches for measurng techncal effcency are the Stochastc Fronter Approach and Data Envelopment Analyss (see for e.g., Coell, Rao, and Battese, 1998; Coell, 1995). Techncal effcency scores calculated from the non-stochastc programmng approaches can be used as explanatory varables wthout resortng to sequental econometrc estmaton (Arnade and Trueblood, 2002). For ths reason, we compute techncal effcency scores usng the DEA approach. 3 Data and Estmaton Procedures The data we use s the Ethopan Rural Household Survey (ERHS), a naton-wde survey of rural households conducted durng The survey was undertaken n 18 vllages across the country from whch nearly 1500 households were selected randomly 1. For ths study, we consder only 630 farmers from nne vllages of Northern Ethopa. The consderable geographc dsperson of the sampled vllages represents the dversty of farmng systems n the country and, gven large dfferences n accessblty to nput and output markets, means that there are large varatons n prces faced by dfferent households. 1 The sample conssts of nne peasant assocatons (PAs) namely, Haresaw Taba, Geblen Taba, Dnk, Shumshaha, Yetmen, and four PAs n the vcnty of Debre Brhan town. All the study vllages are found n regon 3, wth the excepton of Geblen and Harasaw, for whch a dummy s ncluded (du12). The fnal sample conssts of only 514 as farmers wth ether cultvated land less than 0.1 hectares, or zero labour or zero output or zero and negatve proft are excluded.

7 Techncal Ineffcency and Supply Response n Ethopa 7 Sx outputs, two varable nputs (chemcal fertlzer and labour) and three fxed nputs (land adjusted for qualty, anmal power and farm captal) are used n the fnal estmaton. We nclude four exogenous controls -extenson servces, land access, market access, and ranfall. We consder fve major cereals - teff 2, wheat, barley, maze, and sorghum. A sxth output varable s formed as other crops. Ths s an aggregate of three mnor cash crops categores - legumes, root crops and vegetables. Detals of measurement of varables and summary statstcs on producton, nput use and prces are gven n Appendx A. The Emprcal Model We use the quadratc functonal form, whch has the advantageous feature of selfdualty (Abrar, 2001 provdes a detaled analyss of the choce of functonal form based on ths survey data). The quadratc normalsed restrcted proft functon s gven by: (13) * π = α r α p + * * r 2 * γ p w + r r α w * r r k 8 β z * φ p z + k k k k k r k 6 6 φ w z rk j γ * r k + ε. p p + 2 * * j j * * γ rqwr wq + r q k h δ khzk zh where * s the normalsed restrcted proft, p * s the normalsed prce of output, w r * s the normalsed prce of nput r, z k s the quantty of fxed nput or other exogenous varable k, and s techncal neffcency. The α 0, α, α r, β k, γ j, γ rq, γ r, δ kh, φ k and φ rk are parameters to be estmated and ε s an error term wth the usual propertes. The correspondng output supply and nput demand equatons are derved from (13), respectvely, as: (14) y = α + 6 j γ j 2 p * j + 2 r γ w r * r + 8 k φ z k k + ν, = 1,...6, and (15) x r = α τ + r 6 γ r 2 p * j + 2 q γ rq τw * q + 8 k φ τz rk k + ν, r r = 1,..2. where y and x r denote the quanttes of outputs and varable nputs, respectvely, and ν s the error term. Note that, n the absence of techncal neffcency, = 1, the model reduces to the tradtonal output supply and nput demand system. Homogenety s 2 s a cereal unque to Ethopa, a non-exportable cash crop that s an mportant staple food n Northern and Central Ethopa.

8 Techncal Ineffcency and Supply Response n Ethopa 8 mposed by dvdng proft and all prces by the wage rate, so the labour demand equaton s excluded. The fnal estmaton s for the system of sx output supply equatons and one nput demand equaton (fertlzer) usng teratve Seemngly Unrelated Regresson (SUR). Not all farmers n the sample use fertlzer. In countres lke Ethopa, where there s low level of market ntegraton and other forms of nput market mperfectons preval, low use of fertlzer could be the result of these external factors rather than a ratonal decson based on prces. To correct for selectvty bas (to ensure zero expectaton of the error terms) we estmated the fertlzer demand equaton usng the two-stage Heckman procedure. Frst, the probablty of usng fertlzer s estmated by probt maxmum lkelhood usng the followng bnary choce model: (16) F* = H + u where F* s an unobserved latent varable determnng the farmers decson to buy fertlzer, and may be thought of as the expected beneft (known only to the farmer) of buyng fertlzer, H s a set of household characterstcs hypothessed to affect fertlzer use, and u s error term. The observed bnary varable F wll be: (17) F = 1 (F* > 0,.e., users) F = 0 otherwse (.e., F* 0, non-users) The resultng values of the vector are used to compute the vectors of nverse Mlls ratos, M 1 = (/) and M 2 = (- /1- ), respectvely, for sub-samples of users and non-users ( and are respectvely the standard normal densty and cumulatve dstrbuton evaluated at the pont H). In the second stage, the adjusted demand functon for fertlzer for each sub-sample s estmated along wth the other equatons n the system by ncludng M 1 and M 2 as regressors for user and non-user sub-samples respectvely. Once ths correcton s made all observatons, ncludng zero observatons, can be used to estmate the fertlzer demand equaton.

9 Techncal Ineffcency and Supply Response n Ethopa 9 4 Results and Dscusson In what we beleve s the only attempt to apply DEA to Ethopan data, Abrar (1995b) used the same data set used here and estmated dfferent varants of output-orented DEA techncal effcency scores for a sample of Central Ethopan farmers, and found that a large proporton of the farmers are operatng under CRS. Hence, we calculated techncal neffcency measures usng the output orented CRS DEA approach from the DEAP software (Coell, 1996), and the results are reported n Table A3. The mean techncal effcency s 0.55, confrmng the establshed fact that there s a sgnfcant potental to mprove the effcency of Ethopan small holders (see for e.g., Abrar, 1996; Croppenstedt and Mulat, 1997; Battesse and Senat, 1998). 3 Ths fgure s slghtly hgher compared to the (CRS) mean effcency calculated by Abrar (1995b), whch s n the range of We can see from Table A3 that about 45 percent of the farmers have techncal effcency scores less than Two dfferent models of output supply and nput demand systems are estmated. Model 1 s the standard model where techncal effcency s assumed, and Model 2 s the model that allows for techncal neffcency. Estmated parameters from the sevenequaton systems of output supply and fertlzer demand equatons for Models 1 and 2, wth symmetry mposed, are gven n Appendx Tables B1 and B2 respectvely. The sgns and magntudes of the parameters are generally consstent wth theory. All own prce coeffcents have expected sgns except for barley n Model 1, whch s statstcally nsgnfcant. There are a few unexpected sgns as well for non-prce varables, all of whch are nsgnfcant wth the excepton of ranfall for sorghum, agan n Model 1. Nearly half of the parameters are sgnfcant at fve percent. We lmt our dscusson to the estmated elastctes at data mean ponts derved from the two models. 3 For a comparson of techncal effcency estmates from the DEA and the Stochastc approaches usng the same data set, see Abrar (1995a).

10 Techncal Ineffcency and Supply Response n Ethopa 10 For ease of comparson between the two models, own prce, cross-prce, non-prce and fertlzer demand elastctes are separately reported n Tables 1 through 4 respectvely. Table 1 Own-Prce Elastctes of Output Supply Model 1 Model 2 Crop Elastcty Crop Elastcty 0.21*** 0.20** 0.09* *** 0.16*** 0.17*** Notes: * sgnfcant at 10%; ** sgnfcant at 5%; *** sgnfcant at 1%. Table 2 Demand Elastctes Model 1 Model 2 Wth Res. To: Varable Elastcty Varable Elastcty Prces Non-Prces Ran Infrastructure -0.18** 0.13*** 0.10* *** 0.22*** 0.22** 0.16*** 0.15*** ** 0.03 Ran Infrastructure -0.28* 0.57*** 0.12* -0.38*** *** 0.40*** 0.33*** 0.25*** 0.26*** * 0.60*** Notes: * sgnfcant at 10%; ** sgnfcant at 5%; *** sgnfcant at 1%. Own Prce Elastctes Own prce elastctes are all less than unty, often consderably so n Model 1. Magntudes of these elastctes range from for barley to 0.21 for wheat n Model 1. Further, only wheat and sorghum have own prce elastctes that are sgnfcant at 5 percent. Such a response of farmers to prces of wheat and sorghum

11 Techncal Ineffcency and Supply Response n Ethopa 11 could be drven by subsstence needs (.e. hgher prces encourage hgher producton for own-consumpton so as to avod the need to purchase these foods) as shares of marketed surplus are much hgher for other crops and teff than for wheat and sorghum (see Table A1).

12 Techncal Ineffcency and Supply Response n Ethopa 12 Table 3 Cross-Prce Elastctes Model 1 Model 2 Crop/Prces Elastcty Crop/Prces Elastcty -0.20** 0.11** * *** 0.14** -0.06*** *** -0.11** 0.03** *** -0.21*** * ** ** *** * ** -0.19** 0.05* ** -0.24** * * * Notes: *sgnfcant at 10%; ** sgnfcant at 5%; *** sgnfcant at 1%.

13 Techncal Ineffcency and Supply Response n Ethopa 13 Table 4 Non-Prce Elastctes of Output Supply Model 1 Model 2 Non-Prce Varable Elastcty Non-Prce Varable Elastcty Ran Market Access Ran Market Access Ran Market Access Market Access Ran Ran Market Access Ran Market Access 1.56*** 0.76*** 0.19*** 0.18*** 0.11*** *** 0.42*** 0.30*** ** *** 0.82*** 0.13*** 0.10* 0.08** * *** 0.20*** 0.19*** 0.19** 0.14*** 0.12* 0.03** *** 0.43*** 0.32*** 0.18*** 0.08*** * *** 0.27*** 0.20*** 0.19*** 0.15*** ** Ran Market Access Ran Market Access Ran Market Access Market Access Ran Ran Market Access Ran Market Access Notes: * sgnfcant at 10%; ** sgnfcant at 5%; *** sgnfcant at 1%. 2.48*** 1.02*** 0.38*** * ** 3.56*** 0.33*** 0.32*** *** 0.93*** *** 0.16*** 0.17** *** 0.24*** *** 0.46*** 0.39*** 0.25** ** *** 0.22* 0.36*** ** * 0.26** 0.44** 0.46***

14 Techncal Ineffcency and Supply Response n Ethopa 14 In Model 2, all but two own prce elastctes have ncreased. In percentage terms, the hghest ncrease n own prce elastcty s for fertlzer followed by teff and wheat. Magntudes of these elastctes range from 0.02 for maze and barley to 0.52 for wheat. Own prce elastcty of wheat has more than doubled, and s stll the hghest. The own prce elastcty of teff has ncreased substantally from 0.06 to 0.30, and has now become the second hghest. The most dramatc ncrease has occurred for fertlzer, whch has ncreased from to What s more, t has now become sgnfcant at one percent. Other crops has also become sgnfcant at one percent. The only change n sgn occurred for the own prce elastcty of barley, whch now has the approprate (postve) sgn, but s stll statstcally nsgnfcant. On the other hand, own prce elastctes of maze and sorghum have decreased. In general, therefore, takng effcency nto account has ncreased the magntudes and sgnfcance of own prce elastctes, substantally so n the case of fertlzer and teff. Cross-Prce Elastctes In Model 1, ten of the thrty (excludng fertlzer) cross-prce elastctes are statstcally sgnfcant, most nvolvng wheat and sorghum (the only two crops wth sgnfcant own-prce elastctes). s a strong complement to wheat, a weak substtute wth other crops and a strong substtute wth barley. s a strong substtute wth sorghum. On the other hand, barley and sorghum are strong complements to each other (wth the hghest cross-prce elastcty of 0.35). All but two crops have the expected negatve output elastcty wth respect to fertlzer prce. The elastcty for maze and barley wth respect to fertlzer s postve (and statstcally sgnfcant for the latter). Ths could be due to the lower use of fertlzer for barley and opportunstc plantng of fertlzer-ntensve crops lke teff (a substtute for barley). Lower barley prces could result n more land for, and hgher producton of, teff and hence hgher demand for fertlzer. In Model 2, most of the cross-prce elastctes have ncreased n absolute terms. Elastctes of all crops wth respect to prce of barley have now become substantally hgher. So s the elastcty of fertlzer demand to the prce of wheat, whch has

15 Techncal Ineffcency and Supply Response n Ethopa 15 ncreased from 0.13 to 0.57, becomng the hghest prce elastcty. However, there are only few nstances of changes n the relatonshps of the crops, mostly for sorghum., whch was complementary to teff and other crops, has now become a substtute. The only other change n sgn s between wheat and maze, whch have now become substtutes. In terms of sgnfcance, a major shft has occurred n the complementarty of wheat and teff, whch has changed from beng sgnfcant at fve percent to nsgnfcant. Also, the relatonshp between fertlzer and barley has now become statstcally nsgnfcant. In general, the pattern that emerges s complementary teff and wheat competng wth (beng substtutes for) complementary barley and sorghum. Note that teff and wheat are opportunty crops that are produced n large quanttes only when there s good ran and when fertlzer s avalable. They are usually produced by shftng land away from the regular crops (barley, sorghum and other crops) to whch a dsproportonately larger share of the land (just over 80 percent) s allocated. The complementarty of teff and wheat may have to do wth the fact that they are often grown on share cropped land, whch means that they share access to land nputs. Ths may explan why teff s not found to respond sgnfcantly to fertlzer prce although wheat has the expected negatve and sgnfcant response. Non-Prce Elastctes In Model 1, land sze, ran and land qualty, seem to be most mportant factors. Output responses to the sze of land holdng and land qualty are postve and statstcally sgnfcant for all crops, and response to land access s postve and sgnfcant for most crops. The elastcty of output wth respect to ran s sgnfcant n all cases and postve for all crops except sorghum. The result for sorghum s not entrely unexpected: t s customary for Ethopan farmers to shft from sorghum towards hghyeldng, short-cycle and less drought tolerant crops such as teff (a substtute and the crop most responsve to ran) n seasons of abundant and regular rans. The results confrm that nothng s as crucal for agrculture n ths drought-prone regon as ran and better qualty land. In most cases, ncorporaton of techncal neffcency has ncreased the magntudes and statstcal sgnfcance of elastctes of non-prce factors. Once agan, land sze,

16 Techncal Ineffcency and Supply Response n Ethopa 16 ran and land qualty are the most mportant factors. Interestngly, the ncorporaton of neffcency has dramatcally ncreased both the magntude and the statstcal sgnfcance of agrcultural extenson. For example, elastcty of teff wth respect to extenson has ncreased from 0.01 to Ths varable has ncreased fve-fold n the sorghum equaton, and at least two-fold n all the others. In addton, n the model wthout neffcency, ths varable was statstcally sgnfcant only n the fertlzer demand equaton, but now t s sgnfcant n all equatons except other crops and maze. Therefore, the mpact of extenson on output supply s lkely to be serously hampered by the presence of techncal neffcency. On the other hand, the magntude and sgnfcance of farm captal have mostly worsened, havng wrong sgns n some cases. Ths may have to do wth the fact that t s measured n value terms. Specfcaton Tests To determne the mpact of techncal neffcency on the supply response of the farmers, we compared the two models based on non-nested hypotheses tests and conformty to regularty condtons of symmetry, monotoncty and convexty. The two models are non-nested n that one cannot be expressed as a specal case of the other by parametrc restrctons. The tradtonal hypothess tests cannot be appled n ths case. To choose between the two models, we conducted two regresson-based tests, known as J and JA, along the lnes of Doran (1993). Ths nvolves re-estmatng the proft functon and testng the relatve performance of ftted values from each model n a composte model. The test statstcs and assocated t-values are reported n Table 5. The J-test does not dscrmnate between the two models. The JA-test however accepts Model 2 aganst Model 1 at 5%. Unfortunately, lack of conclusve evdence from tests of non-nested hypotheses s qute common (e.g., Frank et al, 1990; Doran, 1993; Arnade and Trueblood, 2002).

17 Techncal Ineffcency and Supply Response n Ethopa 17 Table 5 Non-nested Hypotheses Tests Null Hypothess Alternatve Hypothess Model 1 Model 2 Model Model ** Notes: The upper number s J-statstc and the lower number s JA-statstcs (both of whch are t-values). No astersks, two astersks and sngle astersks ndcate sgnfcance at 1%, 5% and 10% respectvely. The proft functon needs to be compatble wth the theoretcal requrements of homogenety, symmetry, monotoncty and convexty. Homogenety s mantaned n all estmaton by normalzng by the wage rate, and hence cannot be tested. We frst conducted a test for symmetry globally, subject to homogenety. A Wald test s carred out for ths purpose, and t s asymptotcally dstrbuted as ch-square wth the number of degrees of freedom equal to the number of restrctons mposed by the null hypothess. The followng symmetry restrctons are tested and mposed n the fnal estmaton: (18) (19) γ γ j r = γ (, j = 1,...6, j) j = γ ( = 1,...6; r = 1, and stands for fertlzer) r A jont test of these symmetry restrctons cannot be accepted for both models. But when tested ndvdually, t was accepted n 82 percent of the cases for Model 2 whle t was accepted n only 64 percent of the cases for Model 1. It needs to be stressed that symmetry s not a behavoural assumpton, rather t s a mechancal consequence of applyng Young s theorem, and as such asymmetrc responses are not contradctory wth the hypothess of proft maxmzaton (Savadogo et al, 1995). However, snce symmetry s a necessary condton for dervng the nput demand equatons from the proft functon, we mpose t n our estmaton.

18 Techncal Ineffcency and Supply Response n Ethopa 18 Then we checked for monotoncty and convexty after estmaton. Monotoncty requres that the ftted values of the output supply (nput demand equatons) are postve (negatve). The necessary condton for convexty s that all terms on the leadng dagonal of the Hessan of the normalzed proft functon must be postve, or alternatvely the own-prce elastctes should have the expected sgns. The suffcent condton s that ths Hessan must be postve defnte. Monotoncty (at data mean ponts) cannot be rejected for both models. We can see from Tables 1 and 2 that Model 2 satsfes the necessary condton for convexty, but not Model 1 because of the wrong sgn for the own prce of barley. Falure to satsfy convexty casts a serous doubt on the valdty of the assumpton of proft maxmazaton, although there mght be other reasons for ts rejecton (see Shumway, 1983; and Hggns, 1986 for detals). In general, therefore, based on theoretcal consstency, Model 2 s clearly preferred to Model 1. Further, the coeffcent on the one stand alone techncal neffcency varable,, s statstcally sgnfcant n all the equatons except n wheat and sorghum, mplyng that techncal neffcency does really matter. 5 Conclusons and Polcy Implcatons Increasng the effcency and productvty of smallholder agrculture has been an mportant objectve of the Ethopan government n the 1990s. Market lberalsaton, n partcular prce ncentves, and encouragng fertlzer use have been the major polcy nstruments. There has been lmted research on how farmers respond to these ncentves. The purpose of ths study s to assess the supply response of Ethopan farmers n the presence of techncal neffcency. Two systems of output supply and nput demand functons are estmated: one ncorporatng neffcency and another wthout neffcency. We compared the two models based on non-nested hypotheses tests and conformty to neo-classcal assumptons of producton theory. A number of mportant conclusons emerge. Frst, whle non-nested hypotheses tests provde no conclusve evdence, the model wth techncal neffcency s clearly preferred to the other model based on theoretcal consstency. Second, the results ndcate that techncal neffcency restrcts the parameter estmates of the tradtonal model. The effect of neffcency may have been compounded nto the parameter estmates of the standard model due to the excluson of the neffcency varable from

19 Techncal Ineffcency and Supply Response n Ethopa 19 the model; thus resultng n smaller elastcty estmates. Incorporaton of neffcency has generally ncreased the magntudes and the statstcal sgnfcance of own prce elastctes, substantally so n the case of teff and fertlzer. In most cases, ncorporaton of techncal neffcency has ncreased the magntudes and statstcal sgnfcance of elastctes of non-prce factors, partcularly agrcultural extenson. Thrd, peasant farmers n Ethopa respond postvely and sgnfcantly to prce ncentves. Forth, fertlzer usage appears to be more responsve to output prces, partcularly of teff, barley and wheat, than to ts own prce. Polces drected at mprovng output prces may be the most effectve way to encourage ncreased fertlzer use. Nevertheless, the response of output, especally that of teff, to fertlzer prce s neglgble. It s evdent that educaton and extenson servces are requred to ensure that fertlzer s used effectvely. Fnally, gven the features of peasant farmng n Ethopa, gettng prces rght s not n tself an adequate polcy to ncrease output and productvty n agrculture. Output prces are clearly an mportant part of the ncentve structure, but non-prce factors are the bndng constrants. Therefore, n addton to prce ncentves, effectve polces that mprove farmer s access to land, credt and nputs, and publc nvestment n roads and rrgaton, are requred. Such polces are lkely to have a drect effect on output, facltatng ncreased proftablty, but equally mportant are the ndrect effects by encouragng ncreased usage of fertlzer.

20 Techncal Ineffcency and Supply Response n Ethopa 20 References Abrar, S. (1995), Effcency of Farmers n Ethopa, Ethopan Journal of Economcs, Vol. IV, No. 2. Abrar, S. (1996), `Techncal Effcency of Fertlzed Farms n Ethopa: An Applcaton of Stochastc Fronter Approach`, Ethopan Journal of Development Research 18 (2), Abrar, S. (2000), The State of the Ethopan Economy: the Legacy, Recent Trends and the Road Ahead, Austran Journal of Development Studes, specal ssue 3, Abrar, S. (2001), Dualty, Choce of Functonal Form and Peasant Supply Response n Ethopa, CREDIT Research Paper No. 01/20, School of Economcs, The Unversty of Nottngham. Abrar, S. (2002), Peasant Supply Response n Ethopa: A Farm-level Proft Functon Analyss, CREDIT Research Paper No. 02/16, School of Economcs, The Unversty of Nottngham. Arnade, C. and Trueblood, M.A., (2002), Estmatng a Proft Functon n the Presence of Ineffcency: An Applcaton to Russan Agrculture, Journal of Agrcultural and Resource Economcs 27(1), Coell, T.J., (1995), 'Recent Developments n Fronter Modelng and Effcency Measurement', Australan Journal of Agrcultural Economcs, 39(3), Coell, T.J., (1996), 'A Gude to DEAP Verson 2.1: A Data Envelopment Analyss (Computer) Program', CEPA Workng Papers No. 8/96, Department of Econometrcs, Unversty of New England. Coell, T., D. Rao, and Battese, G.E., (1998) 'An Introducton to Effcency and Productvty Analyss', Boston MA, Kluwer Academc Publshers. Croppenstedt, A. and D. Mulat (1997), An Emprcal Study of Cereal Crop Producton and Techncal Effcency of Prvate Farmers n Ethopa: A Mxed Fxed-random Coeffcents Approach, Appled Economcs, 29, Doran, H. (1993), Testng Non-nested Models, Amercan Journal of Agrcultural Economcs 75 (February), Fare, R., S.Grosskopf, and H.Lee, (1990), A Non-Parametrc Approach to Expendture-Constraned Proft Maxmzaton, Amercan Journal of Agrcultural Economcs 72, Fare, R., and D.Prmont, (1995) Mult-output Producton and Dualty: Theory and Applcatons, Boston MA. Kluwer Academc Publshers. Farroq, U., T. Young, N. Russell and M. Iqbal (2001), The Supply Response of Basmat Rce Growers n Punjab, Pakstan: Prce and Non-prce Determnants, Journal of Internatonal Development, 13(2), Frank, M.D., Beatte, B.R. and Embelton, M.E. (1990), A Comparson of Alternatve Crop Response Models, Amercan Journal of Agrcultural Economcs 72 (August), Kumbhakar, S. (1996), 'Effcency Measurement wth Multple Outputs and Multple Inputs', Journal of Productvty Analyss 7, Savadogo, K., T. Reardon and K. Petola (1995), Mechanzaton and Agrcutural Supply Response n the Sahel: A Farm-Level Proft Functon Analyss, Journal of Afrcan Economes, 4(3), Seyoum, E., Battese, G.E., and Flemng, E.M., (1998), 'Techncal Effcency and Productvty of Producers n Eastern Ethopa: a Study of Farmers Wthn and Outsde the Sasakawa-Global 2000 Project', Agrcultural Economcs 19,

21 Techncal Ineffcency and Supply Response n Ethopa 21 Appendx A Defnton of Varables The output varables for ndvdual crops are measured as total output produced, n klograms. We used the actual market prces collected n each vllage by an ndependent prce survey. In a very few cases where the prce of a crop s not reported, we used unt values. For "other crops", a Laspeyer's quantty and prce ndex was calculated by takng the share of the value of the output as a weght. s measured as total amount appled n klograms. The prce of fertlzer s calculated by dvdng total expendture by the amount appled. For those farmers who do not report use of purchased fertlzer, the mean of those who appled (n the same vllage) s used (to mpute the cost of non-purchased fertlzer usage). Labour s defned as the number of person-days of tradtonal (share) and hred labour used n ploughng and harvestng. Famly labour s not ncluded as t s treated as fxed. Also, share labour s adjusted for qualty usng average product as a weght. The wage rate per person-day s calculated from the wage bll of hred labour. For those farmers (vllages) wth no hred labour, we mputed the wage rate from the off-farm ncome of farm-related employment. Land s total area of land cultvated n hectares. Land qualty s defned as an ndex of the qualty of cultvated land (1 beng worst, 2 medocre and 3 best). We combned the two ndces of land qualty gven n the data (one for fertlty and another for steepness) nto one ndex usng total area cultvated as a weght. Anmal power s defned as the total number of oxen owned (and may capture access to natural fertlzer n addton to wealth effects). Farm captal s measured by the value of hoes and ploughs owned. A proxy for access to land s measured by the share of the harvest pad n the form of rent for land. Infrastructure (and/or market access) s measured by dvdng the total populaton of the nearest town (or bg market) to the road dstance between the town and the vllage. 4 The ranfall varable s measured by multplyng the amount of ran n mllmetres by the dummy for ran ncluded n the questonnare, n whch the farmer s asked f ran was enough or on tme. Ths way of measurng ranfall captures the seasonal and/or temporal varaton of ran, as well as the amount, whch s typcally mportant n the case of Ethopa. s measured by the number of hours of extenson servces obtaned. 4 We thank Bereket Kebede for brngng ths varable to our attenton.

22 Techncal Ineffcency and Supply Response n Ethopa 22 Table A1 Average Output, Input use and Prces by Crop Varable Land: Sze (ha) Share (%) Qualty Output: Quantty(Kg) Kg/ha Share (%) Surplus (%) Quantty(Kg) Kg/ha Prces (Brr/Kg) Table A2 Average Use of Inputs and Other Varables Varable Mean Cultvated Land (ha) Quantty(Kg) Kg/ha Prces (Brr/Kg) Labour Man-days Man-days/ha Wage Rate (Brr/day) (numbers) 2.48 (Brr) (Brr) Market Access (Pop/Km) Ran (mm) (hours) 3.27

23 Techncal Ineffcency and Supply Response n Ethopa 23 Table A3 Summary Statstcs on Techncal Effcency Dstrbuton Descrbtve Statstcs Mean St. Devaton Mnmum Maxmum Percent of Farmers Value

24 Techncal Ineffcency and Supply Response n Ethopa 24 Appendx B Detaled Econometrc Results Table B1 Parameter Estmates: Model 1 (wthout techncal neffcency) Varables Prce (0.58) (2.02)** (2.43)** (1.19) (1.35) (1.81)* (0.26) Prce (2.02)** (2.66)*** (1.39) (0.08) (3.38)*** (1.08) (2.58)*** Prce (2.43)** (1.39) (0.36) (1.50) (4.28)*** (0.97) (2.39)** Prce (1.19) (0.08) (1.50) (1.20) (0.80) (0.64) (0.22) Prce (1.35) (3.38)*** (4.28)*** (0.80) (2.27)** (0.53) (1.86)* Prce Other (1.81)* (1.08) (0.97) (0.64) (0.53) (1.72)* (0.29) Prce (0.26) (2.58)*** (2.39)** (0.22) (1.86)* (0.29) (0.54) (6.61)*** (10.45)*** (5.57)*** (5.81)*** (5.13)*** (5.48)*** (2.90)*** (0.17) (2.62)*** (5.67)*** (0.86) (0.66) (3.83)*** (4.28)*** (7.02)*** (5.74)*** (0.22) (2.46)** (1.97)** (1.85)* (2.24)** (3.37)*** (1.72)* (2.61)*** (4.18)*** (2.65)*** (3.02)*** (1.11) (6.04)*** (1.71)* (2.07)** (0.48) (4.67)*** (0.66) (1.41)

25 Techncal Ineffcency and Supply Response n Ethopa 25 Table B1 (contd.) Varables Market Access (1.07) (0.04) (15.36)*** (0.66) (14.33)*** (5.84)*** (3.31)*** Ranfall (16.70)*** (9.77)*** (2.21)** (5.27)*** (6.43)*** (4.39)*** (8.82)*** (0.14) (0.94) (1.68)* (0.44) (0.74) (0.50) (2.16)** DU (0.19) (0.81) (0.50) (0.13) (6.39)*** (0.80) (0.58) Mll's Rato (1.26) Constant (2.17)** (2.28)** (7.15)*** (1.19) (2.01)** (2.37)** (0.83) Notes: Absolute value of z-statstcs n parentheses. *Sgnfcant at 10%; ** sgnfcant at 5%; *** sgnfcant at 1%.

26 Techncal Ineffcency and Supply Response n Ethopa 26 Table B2 Parameter Estmates: Model 2 (Wth techncal neffcency) Varables Ineffcency ( ) (3.67)*** (1.43) (6.42)*** (2.90)*** (0.55) (3.78)*** (4.09)*** Prce (1.40) (1.46) (2.52)** (0.48) (0.74) (0.75) (0.98) Prce (1.46) (2.83)*** (1.03) (0.58) (2.02)** (1.86)* (3.28)*** Prce (2.52)** (1.03) (1.04) (0.36) (1.98)** (0.99) (1.66)* Prce (0.48) (0.58) (0.36) (1.09) (0.17) (0.29) (0.78) Prce (0.74) (2.02)** (1.98)** (0.17) (3.13)*** (1.26) (1.94)* Prce Other (0.75) (1.86)* (0.99) (0.29) (1.26) (5.74)*** (0.03) Prce (0.98) (3.28)*** (1.66)* (0.78) (1.94)* (0.03) (2.74)*** (8.16)*** (10.58)*** (7.35)*** (6.17)*** (10.76)*** (4.55)*** (5.53)*** (1.77)* (5.64)*** (0.79) (0.35) (1.69)* (1.30) (4.15)*** (0.53) (0.78) (2.09)** (0.16) (1.32) (0.97) (1.72)* (6.45)*** (2.68)*** (7.94)*** (4.66)*** (1.87)* (2.27)** (0.78) (1.80)* (1.62) (0.93) (0.05) (0.40) (0.47) (2.76)***

27 Techncal Ineffcency and Supply Response n Ethopa 27 Table B2 (contd.) Varables Market Access (0.16) (3.35)*** (4.41)*** (0.93) (6.39)*** (1.03) (4.19)*** Ranfall (5.84)*** (2.98)*** (4.82)*** (4.74)*** (0.86) (2.23)** (3.62)*** (1.98)** (2.06)** (2.45)** (0.91) (1.99)** (1.62) (2.79)*** DU (2.55)** (0.18) (0.30) (2.50)** (1.36) (1.89)* (1.36) Mll's Rato (1.66)* Notes: Absolute value of z-statstcs n parentheses. *Sgnfcant at 10%; ** sgnfcant at 5%; *** sgnfcant at 1%.