Efficiency Analysis of DevelopingCountry Agriculture: A Review of theFrontier Function Literature

Boris E. Bravo-Ureta and Antonio E. Pinheiro

This article reviews and critiques the frontier literature dealing with farm level efficiency indeveloping countries. A total of 30 studies from 14 different countries are examined. Thecountry that has received most attention is India, while rice has been the most studiedagricultural product. The average technical efficiency (TE) index from all the studies reviewedis 7270. The few studies reporting allocative and economic efficiency show an average of68% and 43%, respectively. These results suggest that there is considerable room to increaseagricultural output without additional inputs and given existing technology. Several of thestudies reviewed have sought to explain farm level variation in TE. The variables mostfrequently used for this purpose have been farmer education and experience, contacts withextension, access to credit, and farm size. With the exception of farm size, the results revealthat these variables tend to have a positive and statistically significant impact on TE. Thispaper shows that considerable effort has been devoted to measuring efficiency in developingcountry agriculture using a wide range of frontier models, Despite all this work, the extent towhich efficiency measures are sensitive to the choice of methodology remains uncertain.

The role that agriculture should play on economicdevelopment has been recognized for years, 1 Theadoption of new technologies designed to enhancefarm output and income has received particular at-tention as a means to accelerate economic devel-opment (Schultz; Kuznets; and Hayami and Rut-tan). However, output growth is not only deter-mined by technological innovations but also by theefficiency with which available technologies areused (Nishimizu and Page). The potential impor-tance of efficiency as a means of fostering produc-tion has yielded a substantial number of studiesfocusing on agriculture.

In the 1960s the ‘poor but efficient hypothesis’,advanced by T,W. Schultz, generated a great dealof empirical work designed to test the allocative orprice efficiency of peasant farmers (e.g., Hopper;Chennareddy; and Sahota). In the early 1970s, Lauand Yotopoulos published two important papers

Associate Professor and Research Assistant respectively, in the Depart-ment of Agricultural and Resource Economics, at the University ofConnecticut, Storrs, CT. The authors gratefully acknowledge the com-ments made by Munir Ahmad, Horatio Cocchi, and two anonymousreviewers on earfier drafts, and the secretarial support of Dorine Nagy.

Scientific Contribution No. 1471 of the Storrs Experiment Station.‘ For an earlier analysis of the role of agriculture in economic devel-

opment see Johnston and Mellor, and Nicholls. For a more recent dis-cussion see Hayami and Ruttan (pp. 11-40).

where they developed a dual profit function modelto measure both allocative and technical effi-ciency. 2 Meanwhile, a separate body of efficiencyliterature evolved based on a seminal paper writtenby Farrell in 1957, Farrell’s original work hasgiven rise to a host of related models known col-lectively as frontier methodology.

A major improvement of the frontier modelsover the Lau and Yotopoulos formulation is theability of the former to provide firm specific effi-ciency measures while the latter yields efficiencymeasures only for groups of firms. In addition, thefact that the frontier is consistent with the textbookdefinition of a production, profit and cost function(i.e., with the notion of maximality or minimal-ity), has made this tool very popular in appliedproduction analysis (Forsund, Lovell andSchmidt), This popularity is evidenced by the pro-liferation of methodological and empirical frontierstudies over the last two decades.

The purpose of this article is to take stock ofwhat we have learned from some of these frontierstudies by reviewing the literature dealing withfarm level efficiency in developing countries. The

2 This profit function model has been applied by several researchersincluding Sidbu, Junankar, Khan and Maki, and Trosper. An extensionof this model has been developed by Toda (1976 and 1977).

Bravo- Ureta and Pinheiro .7,-,” .,, .,. -,.- ... --

plan of the paper is to first present a summary ofthe frontier function methodology to provide aframe of reference for readers not familiar with thistopic. Next we review efficiency measures re-ported in the literature for a wide range of devel-oping countries along with analyses that havesought to explain efficiency variation across farms,We then discuss some key methodological issuesthat arise in the empirical analysis of efficiencyusing frontiers. Finally, a summary is presentedalong with some policy implications stemmingfrom the studies reviewed and suggestions for fur-ther research.

Frontier Function Methodology

The original frontier function model introduced byFarrell uses the efficient unit isoquant to measureeconomic efficiency, and to decompose this mea-sure into technical and allocative efficiency. In thismodel, technical efficiency (TE) is defined as thefirm’s ability to produce maximum output given aset of inputs and technology. Stated differently,technical inefficiency reflects the failure of attain-ing the highest possible level of output given in-puts and technology. It is important to distinguishTE from technological change, where the latterreflects an upward shift of the production functionor a downward shift of the unit isoquant. Alloca-tive (or price) efficiency (AE) measures the firm’ssuccess in choosing the optimal input proportions,i.e., where the ratio of marginal products for eachpair of inputs is equal to the ratio of their marketprices. In Farrell’s framework, economic effi-ciency is a measure of overall performance and isequal to TE times AE (i.e., EE = TE X AE).

The large number of frontier models that havebeen developed based on Farrell’s work can beclassified into two basic types: parametric and non-parametric. Parametric frontiers rely on a specificfunctional form while non-parametric frontiers donot. 3 Another important distinction is between de-terministic and stochastic frontiers. The determin-istic model assumes that any deviation from thefrontier is due to inefficiency, while the stochasticapproach allows for statistical noise.

The deterministic parametric approach was ini-tiated by Aigner and Chu, who estimated a Cobb-Douglas production frontier through linear andquadratic programming techniques. This proce-

3 Readers interested on detailed reviews of frontier function methodsam referred to Fot’sund,Lovell,and Schmidt;Schmidt;Battese;Bauer;andSeifordandThrall.

.rsfllclency .wuaysls OJuevelopmg L ounny ,4grwun4re w

dure was further developed by Timmer, who in-troduced the probabilistic frontier productionmodel. Timmer estimated a series of frontier pro-duction functions dropping at each stage the ex-treme observations. This process continues untilthe rate of change of the parameter estimates sta-bilizes. All these deterministic programming ap-proaches yield estimators with undefined statisticalproperties.

Another class of deterministic parametric mod-els is the statistical production frontier proposed byAfriat, in which technical efficiency is measuredby a one-sided disturbance term. When explicitassumptions for the distribution of the disturbanceterm are introduced, the frontier is estimated by themaximum likelihood method. If no assumptionsare made concerning the distribution of the errorterm, the frontier can be estimated by the correctedordinary least squares method (COLS) which con-sists of neutrally (i,e., the intercept only) shiftingthe frontier upwards until no positive error termremains.

The stochastic frontier production model incor-porates a composed error structure with a two-sided symmetric and a one-sided component(Aigner, Lovell, and Schmidt; and Meeusen andvan den Broeck). The one sided component re-flects inefficiency, while the two-sided error cap-tures the random effects outside the control of theproduction unit including measurement errors andother statistical noise typical of empirical relation-ships.

The estimation of a stochastic frontier functioncan be accomplished in two ways. First, if no ex-plicit distribution for the el%ciency component ismade, then the production frontier can be esti-mated by a stochastic version of COLS. On theother hand, if an explicit distribution is assumed,such as exponential, half-normal or gamma, thenthe frontier is estimated by maximum likelihoodmethods. According to Greene (1980), the maxi-mum likelihood estimates (MLE) make use of thespecific distributions of the disturbance term and,thus, are more efficient than COLS. The initialinability of calculating individual firm efficiencymeasures from the stochastic frontier model wasovercome by the work of Jondrow, Lovell,Materov and Schmidt.

More recent developments in frontier methodol-ogy include multi-equation models based on pro-duction, cost or profit function specifications(Bauer; Schmidt and Lovell; and Kumbhakar).Other recent extensions of the stochastic frontierapproach are models that take advantage of paneldata structures (Pitt and Lee; Battese, Coelli andColby; and Cornwell, Schmidt and Sickles). A ma-

90 April 1993 ARER

jor advantage of panel data models is that there isno longer need to assume that inefficiency is inde-pendent of the regressors. In addition, these mod-els do not restrict the efficiency term to follow aspecific distribution for the inefficiency term whilemaking these restrictions testable propositions(Bauer),

Frontier Function Studies of DevelopingCountry Agriculture

For expository purposes, the studies reviewed inthis section are divided, according to the type ofmethodology used, into two major groups: I) De-terministic Production Frontiers; and H) StochasticProduction Frontiers. In turn, the studies using de-terministic models are subdivided into a) paramet-ric and b) non-parametric frontiers, while thosebased on stochastic models are subdivided into a)cross-sectional, b) panel data, and c) dual fron-tiers. An important point to keep in mind is that allstochastic frontiers are of the parametric type.Some key characteristics of the studies reviewedare presented in Table 1.

In addition to focusing on some methodologicalaspects and on the reported efficiency levels, wealso summarize the findings concerning the rela-tionship between efficiency and various socioeco-nomic variables. Two approaches are commonlyused to examine these relationships. One approachis to compute correlation coefficients or to conductsimple non-parametric analyses. The other route,usually referred to as a second step analysis, is tofirst measure farm level efficiency and then to es-timate a regression model where efficiency is ex-pressed as a function of socioeconomic attributes.Table 2 presents the most salient features of thestudies that have examined efficiency variationacross farms.

I. Deterministic Production Frontiers

a) Parametric Frontiers: Shapiro and Muller mea-sured technical efficiency through a deterministicCobb-Douglas production frontier obtained by lin-ear programming. A major objective of this studywas to analyze the roles of information and mod-ernization in the production process of 40 cottonfarms in Tanzania. Using correlation analysis,Shapiro and Muller found that technical efficiencyhad a high positive association with both generalmodernization and information.

Shapiro investigated technical efficiency for asample of 37 Tanzanian cotton farmers. A Cobb-Douglas production frontier, derived by linear pro-

gramming, yielded a 66% average level of techni-cal efficiency. These results led the author to con-clude that, ii contrast with the ‘poor but efficient’hypothesis advanced by T.W. Schultz, productionin traditional agriculture suffered significant inef-ficiencies.

Belbase and Grabowski used the COLS proce-dure to estimate a deterministic Cobb-Douglas pro-duction frontier model to investigate efficiency inNepalese agriculture. A model where the depen-dent variable was the total value of rice, maize,millet and wheat production yielded an averagetechnical efficiency level of 80%. Separate fron-tiers were estimated for rice and maize which re-vealed average efficiency levels of 84% and 67%,respectively. Based on the efficiency measures ob-tained from the equation for all crops, correlationanalysis showed that nutritional levels, income,and education were significantly related to TE,while no relationship was found for farming expe-rience. The study suggested that technical effi-ciency gains could be attained through extensionand education, and that the introduction of newtechnologies has been a key element in raising pro-ductivity in Nepalese agriculture.

Ali and Chaudry examined the technical, allo-cative and economic efficiency for a sample of 220farmers located in four irrigated cropping districtsof the Pakistani Punjab. Separate Cobb-Douglasprobabilistic production frontiers were estimatedfor each district. The average TE, EE and AE mea-sures reported were 84?io, 5170 and 61YO, respec-tively. Based on these measures the authors con-cluded that technical inefficiency caused from 40to 50% loss in farm profits, while the loss in profitsdue to allocative inefficiency was only around 2%.

Taylor, Drummond and Gomes formulated aCobb-Douglas deterministic frontier productionfunction to analyze the impact of a World Banksponsored credit program (PRODEMATA) on al-locative and technical efficiencies for a sample ofBrazilian farmers. The production frontier was es-timated using both COLS and maximum likelihood(statistical frontier) assuming that, in the lattercase, the non-negative farm effects had a gammadistribution. Estimates of technical efficiency forfarms participating in the credit program versusnon-participants revealed no major differences be-tween the two groups, Moreover, participants ex-hibited allocative efficiencies slightly lower thanthe rest. Hence, these results imply that this creditprogram was not successful in improving farmlevel efficiency.

b) Non-Parametric Frontiers: The only applica-tion we found of a non-parametric frontier meth-odology to farm data from a developing country is

Table 1. Empirical Estimates of Technical Efficiency

Sample TE AE EEAuthor(s) Country Product Size % % %

I. Deterministic Production Frontiersa) Parametric Frontiers

Shapiro and Muller Tanzania Cotton 40 —aShapiro Tanzania Cotton 37Belbase & Grabowski

66 ❑ ~Nepal Whole Farm 537 80 — —

Rice — 84Maize

Ali & Chaudry— 67

Pakistan Crops 220 84 61 51Taylor, Drummond & Gomes Brazil Whole Farm 433 17 74 13Ekanayake & Jayasuriya Sri Lanka

Head Rice 63 53 — —Tail Rice 61 50 — —

Average 63 68 32

b) Non-Parametric Frontiers

Ray India Whole Farm 63 — — —Average — — —

II. Stochastic Production Frontiersa) Cross-Sectional Frontiers

Kalirajan (1981) IndiaHuang & Bagi IndiaKalirajan & Shand (1985) IndiaBagi IndiaKalirajan (1984) PhilippinesKalirajan & Flinn PhilippinesEkanayake Sri Lanka

HeadTail

Ekanayake & Jayasuriya Sri LankaHeadTail

Taylor & Shonkwiler BrazilRawlins JamaicaPhillips & Marble GuatemalaKalirajan (1990) PhilippinesSquires & Tabor Indonesia

IndonesiaIndonesiaIndonesiaIndonesia

Bravo-Ureta & Evenson Paraguay

Plnheiro Dominican RepublicAverage

b) Panel Data Frontier

Kalirajan & Shand (1986)Battese, Coelli & ColbyBattese & Coelli (1992)Dawson, Lingard & WoodfordKalirajan (1991)Battese & Tessema

*(Indian villages)

FanAverage

c) Dual Frontiers

Ali & FlinnBailey, Biswas,

Kumbhakar & SchulthiesAverage

IndiaIndiaIndiaPhilippinesIndiaAurepalle*ShirapurKanzaraChina

PakistanEcuador

RiceWhole FarmRiceFive CropsRiceRice

RiceRice

RiceRiceWhole FarmCropsMaizeRiceJava Riceoff-Java RiceCassavaPeanutsMung BeansCottonCassavaCrops

7015191588179

6361

6361

433152

13841034293231611776987

10160

6789

—916350

10050

1005071737579697057685558597070

——

——

— —— —

— —— —

——

—— —— —

— —— —— —— —70 4189 5244 3168 41

RiceWhole FarmWhole FarmRiceRiceWhole FarmWhole FarmWhole FarmAggregate

RiceMilk

3438152230

353829

12068

70 — —8485 — —89 — —69 — —

100 — —84 —76 — —77 — —82 — —

— — 6988 — —

88 — 69

“Figure not reported in the study.

92 April 1993 ARER

Table 2. Socio-Economic Factors Related to Technical Etllciency in Third World Agriculture

AverageTechnicalEfficiency Socio*

Author Country Product % Economic Factors

L Deterministic Production Frontiersa) Parametric Frontiers

Shapiro & Muller Tanzania Cotton — Information (+)Modernization (+)

Belbase & Grabowski Nepal Whole Farm 80 Income ( + )Rice 84 Education (+)Maize 67 Nutrition (+)

[Experience]Ali & Chaudry Pakistan Mixed Crops 84 Irrigation ( + )Taylor, Dmmmond & Gomes Brazil Whole Farm 17 [Credit]

b) Non-Parametric Frontiers

Ray India Mixed Crops — Information (+)[Farm Size]

II. Stochastic Production Frontiersa) Cross-Sectional Frontiers

Kalirajan (1981) India Rice 67 Management Policies (+)Experience (+)Ext, Visits ( + )[Education, Tenure]

Huang & Bagi India Whole Farm 89 [Farm Size]

Kalirajsm& Shand (1985) India Rice

Bagi India Mixed Crops

Kalirajan (1984) Philippines Rice

Kalirajan & Flinn Philippines Rice

Ekanayake

Taylor & ShonkwilerRawlinsPhillips & Marble

Kalirajan (1990)

Squires & Tabor

Bravo-Ureta & Evenson

Plnbeiro

Sri-Lanka

BrazilJamaicaGuatemala

Philippines

Indonesia

RiceHeadTailWhole FarmMixed CropsMaize

Rice

Java Riceoff-Java RiceCassavaPeanutsMung Beans

Paraguay CottonCassava

Dominican Republic Mixed Crops

—

91

63

50

10050717375

79

69705768555859

70

Non-formal Educ (+)[Schooling]Irrigation (+)Larger Farms ( + )Education ( + )Fertilizer (+)Extension (+)Experience (+)[Tenure, Age, Edu]Transplanting (+)Experience (+)Extension ( + )Fertilizer (+)Literacy (+)Experience (+)Credit (+)[Credit]Rural Development (+)School Yrs >4 (+)[School Yrs <4]Crop Establish. (+)Non-Farm Income (+)[Years of Educ., Time of

Establish., Tenure][Farm Size, Farm Region][Farm Size, Farm Region][Farm Size, Farm Region][Farm Size, Farm Region][Farm Size, Farm Region]Credit (+)Extension Hrs. (+)[Size, Age, Educ.]Education (+)Age <25 (+)Experience (+)[Contract, Credit, Agr. Ref,

Farm Size, People per Houshld.]

Bravo- Ureta and Pinheiro Eficiency Analysis of Developing Country Agricuhure 93

Table 2. Socio-Economic Factors Related to Technical Efficiency in Third WorldAgriculture (continued)

AverageTechnical

AuthorEfficiency Socio*

Country Product % Economic Factors

b) Panel Data Frontiers

Kalirajan & Shand (1986) India Rice 70 Experience (+)Education ( + )Credit (+)Extension ( + )

Kalirajan (1991) India Rice 69 Access to Ext. (+)Confidence in Tech. (+)[School Years, Farm sizel

c) Dual Frontiers

Ali & Flinn Pahtan Rice 69* Education (+)Off-Farm Employment (–)Credit (+)

*The signs inside the parenthesis reflect the direction of statistically significant associations between technical efficiency and thevarious socioeconomic variables. The variables shown inside brackets had no statistically significant association with technicalefficiency.*This is a measure of profit efficiency rather than technical efficiency.

the study by Ray, who used linear programming tomeasure efficiency for a sample of 63 West Bengalfarms. The efficiency measures were decomposedinto output or technical efficiency, and into infor-mational efficiency. The latter was defined as theratio between optimal output given the existingtechnology and optimal output when additionaltechnology information is available. Univariateand multivariate statistical tests were conducted tocompare the performance of three farm groupsclassified according to size. The results revealedthat, although there was no significant differencein output efficiency across farm size groups, infor-mational efficiency was very low for the smallfarms. The author suggested that marked improve-ments could be attained by the diffusion of infor-mation about the standard crop production technol-ogy.

To summarize, a total of seven deterministicstudies were reviewed in this section, six paramet-ric and one non-parametric. The parametric stud-ies, five of which relied on the Cobb-Douglasfunctional form, reported efficiency measuresranging from 17% to 84910with an average of 63910.The average allocative and economic efficiency forthe two studies in this group reporting these mea-sures are 68?10and 32%, respectively. The onlynon-parametric study included did not report aver-age efficiency.

II. Stochastic Production Frontiers

a) Cross-Sectional Frontiers: Several of the effi-ciency studies performed using stochastic method-

ology have focused on Indian agriculture, a subjectthat has captured the attention of economists for along time (Bhagwati and Chakravarty). The earli-est stochastic frontier function study using Indiandata appears to be the one by Kalirajan (1981).This author explored TE in paddy production for arandom sample of farms located in the State ofTamil Nadu by estimating, using maximum likeli-hood, a Cobb-Douglas production frontier. A sec-ond step analysis showed that management prac-tices and contacts with local extension agents hada significant positive impact on technical effi-ciency.

Huang and Bagi examined the TE of a sample of151 farms in the Punjab and Haryana states ofIndia, based on a translog production frontier es-timated via maximum likelihood. The studyshowed an average TE level close to 90%, whilethe performance of small vis-il-vis large farms wasalmost equal.

Kalirajan and Shand estimated a Cobb-Douglasproduction frontier by maximum likelihood for arandom sample of 91 paddy farmers from theCoimbatore district in the Indian state of TamilNadu. In a second step analysis, where farm levelTE was the dependent variable, these authorsfound that the level of schooling was not statisti-cally significant in explaining differences betweenmaximum and actual yields. However, the farm-ers’ non-formal education, defined as their under-standing of current technology, had a significantpositive role on productivity.

Bagi examined farm-level technical et%cienciesfor individual crops based on data from a sample of

94 April 1993 ARER

58 multi-crop farms in the Indian State of UttarPradesh. The analysis proceeded with the estima-tion, by maximum likelihood, of separate Cobb-Douglas stochastic production frontiers for fivecrops (wheat, gram, gram/barley, paddy, and jwar/arhar). The results suggested that the partial elas-ticities of production varied from crop to crop, thatTE levels were different for each crop as well asacross farms, and that average TE was higher forirrigated crops (paddy and wheat). Bagi’s analysisindicated that consolidation of individual plots intofarm units could increase output as well as techni-cal efficiency for all crops. Significant positive ef-fects in output and technical efficiency were alsoreported for education, fertilizer use, and inputquality.

Kalirajan (1984) examined how the efficient useof new technology affected production levels in 81Philippine rice farmers, using a translog stochasticproduction frontier. The results revealed a widevariation in technical efficiencies across farmsranging from 42% to 91?ZO,with only 30% of thefarmers operating close to the frontier. The resultsof a second step model, showed that the number offarm visits by extension agents was significant inexplaining the wide variation in the observed lev-els of technical efficiency. Kalirajan concludedthat the new technology was not fully understoodby the farmers in the sample.

Kalirajan and Flinn estimated a translog stochas-tic production frontier by maximum likelihood tomeasure TE for a sample of 79 farmers in the Phil-ippines. These authors regressed TE on severalfarm specific biological and socio-economic vari-ables. The results indicated that crop establishmentby transplanting rice seedlings, fertilizer applica-tion, years of farming, and extension contacts hada significant influence in the level of technical ef-ficiency among sample farmers,

Ekanayake examined efficiency for a sample of123 Sri-Lankan rice farmers. The sample was di-vided into head and tail, according to whether thefarm had good (head) or poor (tail) water access,Separate stochastic Cobb-Douglas productionfrontiers were estimated for each group via maxi-mum likelihood. The results suggested that therewas no significant technical inefficiency for farm-ers with better water access (head). However, forthe poorly situated group (tail) there was signifi-cant technical inefficiency (5070). In a second stepanalysis, Ekanayake found that literacy, experi-ence, and credit availability had a significant pos-itive impact on the technical efficiency level of thetail farmers. This was also true when analyzing thetail farmers’ “apparent” allocative efficiency(AAE), defined as the ratio of profit at predicted

output to maximum profit, In addition, technicalefficiency was found to be significantly related toAAE.

Ekanayake and Jayasuriya, using the same dataset as Ekanayake, compared the effects of estimat-ing TE using a stochastic frontier versus a deter-ministic COLS model. The authors found that, forthe ‘head’ farmers, COLS yielded an average TEof 5370 while the stochastic method gave an aver-age of 100%. By contrast, both procedures reveala 50% mean TE level for the ‘tail’ farmers,

In another comparative study, Taylor andShonkwiler used the same data set as Taylor,Drummond and Gomes to evaluate the perfor-mance of a deterministic frontier with that of astochastic frontier assuming a Cobb-Douglas pro-duction model. The frontier parameters were esti-mated by maximum likelihood methods, assuminga gamma distribution for the former and a half-normal for the latter. The results showed that forboth groups, participants and non-participants, av-erage technical efficiency estimates for the sto-chastic frontier (71YOand 70%) were much higherthan those obtained from the deterministic frontierspecification (17% and 5.990). Given the large dif-ference between the two models and the extremelylow technical efficiency estimates obtained by thedeterministic specification, the authors concludedthat the latter produced misleading results, An im-portant similarity, however, was that the creditprogram was found to have no impact on improv-ing technical efficiency under both models.

Rawlins evaluated the effects of the JamaicanSecond Integrated Rural Development Project(IRDPII) on the level of technical efficiency for asample of peasant farmers. This evaluation wasbased on data for 80 farmers participating in theIRDPII and for 72 non-participants. A Cobb-Douglas stochastic production frontier was esti-mated for each of the two groups. The results re-vealed that there was relatively less variation of thefrontier across IRDPII farms. However, technicalefficiency for the non-participants (7570) washigher than that of the participants (7 l%). Despitethese results, the author concluded that the pro-gram succeeded in shifting outward the productionfrontier of the participant farmers.

Phillips and Marble examined the influence ofeducation on technical efficiency for a sample of1348 Guatemala maize producers. In their anal-ysis, a Cobb-Douglas stochastic production fron-tier was fitted via COLS. The analysis revealedthat education, measured either in terms of literacyor years of schooling, had a positive but statisti-cally insignificant effect on productivity. The au-thors went on to conclude that four or more years

Bravo- Ureta and Pinheiro E@ciency Analysis of Developing Country Agriculture 95

of formal education were required before increasesin productivity could be observed.

Kalirajan (1990) set out to obtain consistent andefficient estimates of economic efficiency—firmspecific TE and input specific AE-for a sample of103 Philippine rice farmers. Using a translog sto-chastic production frontier, the mean technical ef-ficiency was estimated to be 79%, with a low of64% and a high of 92%, Input specific AE indi-cated that farmers were inefficient with respect toall inputs. The results of a second step analysis,also based on maximum likelihood methods,showed that non-farm income and method of cropestablishment were the major factors affectingtechnical efficiency.

Squires and Tabor used a translog stochasticproduction frontier, estimated by maximum likeli-hood procedures, to measure crop-specific techni-cal efficiency in Indonesian agriculture. The re-sults suggest that technical efficiency estimates arehigher for the production of irrigated rice com-pared to the other three crops, The mean TE esti-mates for Java rice, off-Java rice, cassava, pea-nuts, and mung beans were 69’70,70?i0,57%, 68%and 55%, respectively, A second step analysisshowed that TE is not significantly related to farmsize.

Bravo-Ureta and Evenson, using the decompo-sition methodology developed by Kopp andDiewert, as modified by Bravo-Ureta and Rieger(1991), examined the technical, allocative andeconomic efficiency for a sample of peasant farm-ers from Eastern Paraguay. Separate Cobb-Douglas production frontiers were estimated for 87cotton and 101 cassava producers. The averageEE, TE and AE levels for the cotton farmers were41%, 58% and 70%, respectively. The corre-sponding figures for the cassava producers were52%, 59% and 89%. F-tests were used to examinethe association between TE, AE and EE, and farmsize, operator age, education, extension contactsand credit. Surprisingly, the results revealed a veryweak connection between efficiency and socioeco-nomic characteristics.

Using the same methodology as Bravo-Uretaand Evenson, Pinheiro recently estimated a Cobb-Douglas total value product frontier to analyze EE,TE and AE for a sample of 60 peasant farmerslocated in the Dajabon region of the DominicanRepublic. He found that the average EE, TE andAE for the sample were 31%, 7090 and 44%, re-spectively. In a second step analysis, Pinheirofound that education and farmer experience had apositive impact on TE. He also found that contractfarming, being an agrarian reform beneficiary, andfarm size were positively associated with EE and

AE, while household size exhibited a negative im-pact on both of these measures of performance.

b) Panel Data Frontiers: An emerging andpromising area in efficiency analysis concerns theuse of panel data. The first detailed discussion offrontier function methodology for panel data is thepaper by Schmidt and Sickles. More recent contri-butions to this methodology have been made byBattese and Coelli (1988 and 1992), Kalirajan(1991), Cornwell, Schmidt and Sickles, and Kum-bhakar. In this section we review seven studies thathave relied on agricultural panel data to estimatestochastic frontier functions for developing coun-tries.

Kalirajan and Shand estimated a translog pro-duction frontier for paddy using a balanced paneldata for 34 farm households from the Tinnevelydistrict in South India.4 The period covered goesfrom the second crop in 1981 to the second crop in1983 which yields five observations per farm giventhat each year had two crops. Assuming that effi-ciency is time invariant, the results gave an aver-age level of TE of 70.2% with a low of 64% and ahigh of 9 lYo. In order to test the notion that TE istime invariant, separate stochastic frontiers wereestimated for each cross section. A chi-square sta-tistic was then used to test the null hypothesis thatthe parameters for each pair of frontiers, one pairat a time, were the same. These pairwise compar-isons supported the notion that TE was time invari-ant for this sample. In a second step analysis, Kal-ijaran and Shand formulated a linear model to ex-amine the relationship between TE and foursocioeconomic variables. These results showed apositive relationship between TE and farming ex-perience, education, access to credit, and exten-sion services.

Battese, Coelli and Colby, based on earlier workby Battese and Coelli (1988), introduced a modelallowing for unbalanced panel data while main-taining the assumption that efficiency for a givenfirm remained constant over time. Using the Cobb-Douglas functional form, Battese, Coelli andColby estimated a production frontier for a sampleof farmers from Aurepalle, a village located in thestate of Andhra Pradesh in India. The sample con-sisted of 289 observations encompassing 38 farmhouseholds that provided data for at least one yearover the period 1975–76 to 1984-85. The analysisreveals TE measures ranging from 66.2% to91.490 with a mean of 83.7%.

In a more recent paper, Battese and Coelli

4 A balanced panel data set is one in which each firm in the sample isobserved in every time period covered by tbe data.

96 April 1993 ARER

(1992) introduced a stochastic production frontiermodel which permits individual firm level effi-ciency levels to vary over time while allowing thedata set to be unbalanced. The authors employed asubset of the data used by Battese, Coelli andColby consisting of 15 paddy farmers for the pe-riod of 1975-76 through 1984-85. For nine farms,data were available for all ten years while in somecases data were available for only four years. Fivealternative Cobb-Douglas models were estimatedand various tests supported the notion that individ-ual firm technical efficiency levels were time vari-ant. The results showed that farm level TE rangedfrom 67.6% to 88.6% in 1975–76, and from88.8% to 96.2% in 1984-85.

Dawson, Lingard and Woodford estimated aCobb-Douglas stochastic production frontier bymaximum likelihood procedures, using panel datafor a sample of 22 rice farmers for the years 1970,1974, 1979, 1982 and 1984 from Central Luzon inthe Philippines. These authors assumed technicalefficiency to be invariant over time. The resultsrevealed a fairly narrow range of technical effi-ciency going from 84~o to 9570 with a mean of89. 3f?10.The authors compared the frontier resultswith those obtained from covariance analysis. Al-though the latter methodology yielded a mean ef-ficiency level of only 58 .6~o, the Spearman corre-lation coefficient between the two sets of effi-ciency vectors was 0.95, Given the relatively highefficiency levels obtained with the frontier ap-proach the authors concluded that, in their studyarea, there was little room for increasing output bybetter use of existing resources and that futuregains in rice output would have to come from ad-ditional technological progress.

Kalirajan (1991) used panel data for the period1983–86 for a sample of 30 Indian rice farmersfrom the Coimbatore district to estimate, via max-imum likelihood, a translog stochastic productionfrontier. His analysis revealed that technical effi-ciency across the sample farms ranged from 53%to 95% with a mean of 69.3%. Additional analysesshowed that TE measures for a given firm did notchange significantly over time. The results of asecond step analysis, indicated that access to ex-tension services and confidence in the technology(technical advice) were the major determinants oftechnical efficiency at the farm level.

Battese and Tessema estimated, by maximumlikelihood, Cobb-Douglas stochastic productionfrontiers based on unbalanced panel data from arandom sample of three Indian villages for theyears 1975–76 to 1984-85. In this study, statisticaltests were performed to discriminate between mod-els in which both input elasticities and technical

inefficiency were allowed to vary over time fromtime-invariant models. The hypothesis that the in-put elasticities were time-invariant was rejected fortwo of the three villages. The results also indicatethat inefficiency was significant in two of the vil-lages, and that in one case, inefficiency was sig-nificantly different over time while in the other itwas time-invariant.

The last study to be reviewed in this section wasrecently published by Fan who, based on earlierwork by Nishimizu and Page, decomposed outputgrowth in Chinese agriculture into increases in in-puts, technological change, and institutional re-form. Fan assumes that improvements in technicalefficiency over time are a reflection of the institu-tional reforms enacted in Chinese agriculture overthe period analyzed. He estimated a simplifiedtranslog production frontier using aggregate datafrom 29 provinces, municipalities, and autono-mous regions for the years 1965, 1970, 1975, and1976 through 1986. The results showed that, forthe whole country, the total growth in agriculturalproduction from 1965 to 1985 was 5.04% per year.Of this total growth, 57.7% was attributed to totalinput growth and the remaining 42.3~o to growthin total factor productivity. In turn, about 63% ofthe growth in total factor productivity was found tostem from improvements in technical efficiencywith the remaining 37?Z0from technologicalchange.

c) Dual Frontiers: As is the case with panel datafrontiers, dual based frontier methodologies arerelatively recent. We have found only two appli-cations of dual frontiers to developing country sit-uations. In one of these applications, Ali and Flinnused a single equation dual profit frontier model toexamine farm-specific profit efficiency ‘‘, . , de-fined as the ability of a firm to achieve the highestpossible profit, given the prices and levels of fixedfactors of that firm” (p. 304). A translog stochas-tic profit frontier was estimated via maximum like-lihood for a random sample of 120 rice producersfrom the Pakistani Punjab. The computed range inprofit inefficiency went from a low of 5% to a highof 879iowith a mean of 3170. In other words, theaverage farmer realized 31Yo less in profits thanwhat would be possible given efficient resourceuse. In a second step model, where loss of profitwas regressed on several household characteris-tics, the authors found that education had a signif-icant role in reducing profit inefficiency. In addi-tion, farmers reporting off-farm employment anddifficulties in securing credit to purchase fertilizerexhibited higher levels of profit inefficiency.

The second dual based study is by Bailey, Bis-was, Kumbhakar and Schuhhies who analyzed the

Bravo- Ureta and Pinheiro Eficiency Analysis of Developing Country Agriculture 97

technical, allocative and size inefficiency for asample of 68 Ecuadorian dairy farms. Size ineffi-ciency occurs when a firm fails to produce at thepoint where marginal cost equals output price. Theanalysis was accomplished by estimating a systemof equations consisting of the production frontierand the first order conditions for profit maximiza-tion assuming a Cobb-Douglas technology. Theresults indicate that the average loss in profits dueto technical inefficiency ranged from 24.4% forsmall farms to 22.790 for the large operations, Theaverage increase in cost due to allocative ineffi-ciency ranged from 8.4% for small farms to 5.670for large farms. Size inefficiency measures re-vealed that in most cases milk price exceeded mar-ginal cost, implying that the production level wasless than optimal. The average loss in profits dueto size inefficiency goes from 12.8% for smallfarms to 11.8% for large farms, Based on the re-sults reported in the paper we calculated an aver-age technical efficiency level of around 88’%0.

To sum up, in this section we reviewed 24 sto-chastic frontier studies, 17 of which used theCobb-Douglas functional form while the remain-ing seven employed translog models. The averageTE for the 15 studies using cross-sectional datawas 70%, with a low of 50% and a high of 100Yo.The average AE and EE estimates reported were68% and 41%, respectively. Panel data frontierswere estimated in seven studies which yielded anaverage TE of 82%, and a range going from 69%to 1009o. Finally, only one of the two dual frontierstudies reviewed reported a TE measure (88’%0).

Some Methodological Considerations

As is the case with all empirical work in econom-ics, the frontier studies summarized in the preced-ing section are subject to criticism on a number offronts. The purpose of this section is to discusssome methodological considerations that should bekept in mind when interpreting the studies re-viewed. We make no attempt to determine howeach of the studies reviewed measures up to eachpotential criticism. Such a task would undulylengthen an already long paper.

The first factors to be included here are the sen-sitivity of efficiency measures to variations in in-put quality across farms that are explicitly ac-counted for, and to the choice of variables includedin the model. Despite the potential distortions thatthese two facto~s might have on efficiency, it is notpossible to determine their actual significancegiven that this type of information is not typicallydiscussed in the literature. We should indicate,

however, that Schmidt has argued that the decisionof which variables to include in the model mayhave a more important effect on efficiency than onother features of the technology, such as econo-mies of size,

The second important issue has to do with thechoice between a non-parametric and a parametricspecification, keeping in mind that the latter can bedeterministic or stochastic. Gong and Sickles con-cluded recently that, due to lack of empirical anal-ysis, little can be said about how non-parametricfrontiers perform in relation to parametric models.However, several papers have compared the per-formance of different parametric frontier models,using the same data set, for developing as well asdeveloped countries (e. g., Bravo-Ureta andRieger, 1990; Ekanayake and Jayasuriya; Koppand Smith; and Taylor and Shonkwiler). The stud-ies reviewed here, as can be gleaned from the datapresented in Table 1, show that stochastic modelsyield a somewhat higher average TE than theirdeterministic counterparts. In our opinion, it canbe argued with justification that stochastic modelsare more reliable than deterministic models be-cause the former account for statistical noise.

A third matter that arises, which is not unique tofrontier studies, concerns the choice of functionalform in parametric models. Despite its well knownlimitations, the Cobb-Douglas functional form hasbeen widely used in farm efficiency analysis forboth developing and developed countries. The per-tinent question when interpreting parametric stud-ies is the possible sensitivity of the efficiency mea-sures to the choice of functional form. In one of thefew studies examining the impact of functionalform on efficiency, Kopp and Smith concluded‘, . . . that functional specification has a discern-ible but rather small impact on estimated effi-ciency” (p. 1058). The extent to which the resultsof Kopp and Smith can be generalized is notknown. One can argue, however, that an integralpart of applied production analysis should be theevaluation of the impact of functional form on thekey results of the study. The methodological foun-dation for this type of evaluation stems from recentdevelopments in the econometric literature dealingwith specification tests (Greene, 1990a).

Another important issue that concerns the sto-chastic frontier models is the distributional as-sumptions made for the one-sided error. Much ofthe literature to date has followed the half normaldistribution, as originally proposed by Aigner,Lovell and Schmidt, despite the fact that moreflexible distributions are available. One of the fewpapers that have examined the sensitivity of theefficiency results to distributional assumptions was

98 April 1993 ARER

published recently by Greene (1990b), where heintroduced a stochastic frontier specification thatincomorates the ~amma distribution. After com-parin~ several s~ecifications, Greene concludedthat, for his data, efficiency levels were essentiallythe same for the half normal, truncated normal andexponential distributions while the gamma modelyielded higher efficiency. As Bauer concluded in arecent review of new developments in frontierfunction methodology, additional empirical as wellas theoretical work is needed to arrive at a betterunderstanding of the effects that alternative distri-butional assumptions might have on efficiency.

A fifth methodological concern has to do withthe use of the two step procedure to examine thedeterminants of efficiency. Critics of this approachcontend that the socioeconomic variables shouldbe incorporated directly in the production frontiermodel because such variables may have a directimpact on efficiency (Battese, Coelli and Colby).Kalirajan (1991) has recently defended the twostep procedure by stating that socioeconomic at-tributes have a round about effect on productionand, hence, should be incorporated into the anal-ysis indirectly, Ray has argued that this procedureis justifiable if one assumes that the productionfunction is multiplicatively separable in what hecalls discretiona~ and nondiscretionary inputs.The latter inputs are those commonly used to ex-plain variations in efficiency. One way out of thisproblem is to be found in a recent paper by Kum-bhakar, Ghosh and McGuckin, who presented amodel where the determinants of technical effi-ciency can be estimated together with the rest ofthe parameters of the frontier model.

A sixth consideration relates to the validity ofefficiency results that rely on cross-sectional data.According to Dawson, efficiency measures de-rived from data for a single production periodmight be distorted by period specific abnormalit-ies. If these distortions are significant, then theresulting efficiency measures might not be accu-rate. It is because of this potential problem that therecent developments in stochastic frontier modelsfor panel data have been received with much en-thusiasm in the profession.

The studies reviewed above relying on paneldata yield, in general, higher average technical ef-ficiency levels than those estimated using a singlecross-section. In addition, some of the panel stud-ies support the notion that efficiency varies overtime. Despite these findings, the analysis to date isnot sufficient to make a judgement concerning theimpact on efficiency measures of using one cross-section versus a richer panel data set. One clearadvantage of having panel data, as stated earlier, is

that efficiency measures can be derived withoutimposing an arbitrary assumption on the distribu-tion of the efficiency term, and without the need toassume that technical efficiency is uncorrelatedwith the inputs (Bauer).

The final methodological question we addresshere is the choice between estimating a singleequation model as opposed to a system of equa-tions. An a priori advantage of a system of equa-tions is a potential gain in asymptotic efficiency inthe estimates of the technology and efficiency.However, an important drawback lies on the dif-ficulty in estimating systems that incorporate flex-ible functional forms (Bauer). Using a simulationapproach, Gong and Sickles concluded that a sin-gle equation model performed much better than asystem estimator in measuring firm level ineffi-ciency. Although there is no basis for extrapolatingthese results to other settings, the simulation re-sults do suggest that more complex frontier modelsdo not necessarily yield a more desirable outcome.

Summary and Concluding Comments

A total of 30 frontier studies using farm level datafrom 14 different developing countries were re-viewed. By far, the country that has received mostattention from frontier researchers is India, ac-counting for 10 of the 30 studies. In addition, 13 ofthe studies reviewed focused specifically on rice,making this the most studied agricultural productby frontier researchers. These studies were dividedinto two groups and five subgroups based on thetype of frontier methodology used.

The farm level technical efficiency indexes fromall the studies reviewed range from 1770 to 100%with an average of 7270. The reported allocativeefficiency indexes range from a low of 43?40to ahigh of 89% with an average of 68%. By contrast,the economic efficiency indexes go from 13% to69%, with an average of 43%. A major conclusionstemming from these efficiency measures is thatthere is considerable room to increase agriculturaloutput in developing countries without increasinginput levels and without requiring the introductionof new technology.

It is interesting to note that most frontier studieshave focused only on technical efficiency, eventhough it is by improving overall economic effi-ciency that major gains in output could beachieved. The relative importance of each of thesetwo components has been the subject of a livelyexchange in the literature (Leibenstein, 1966 and1978; Comanor and Leibenstein; and Stigler). Thissuggests that additional efforts should be devoted

Bravo- Ureta and Pinheiro

to examining the impact of both allocative andtechnical efficiency on performance.

The question that logically emerges is what canbe done to increase efficiency, The evidence sum-marized in this paper reveals that several variableshave been introduced in models seeking to explainfarm level variation in efficiency. The variablesthat have been used most frequently in these mod-els are farmer education and experience, contactswith extension, access to credit, and farm size,With the exception of farm size, the results revealthat these variables tend to have a positive andstatistically significant impact on technical effi-ciency. Specifically, this pattern was found in nineout of 14 studies for education, six out of seven forexperience, six out of six for extension, and fiveout of eight for credit. In general, these results areconsistent with the findings reported in the non-frontier literature (e.g., Lockheed, Jamison andLau; and Birkhaeuser, Evenson and Feder).

The results of the efficiency literature based onfrontier methodology are generally consistent withthe notion that human capital plays an importantrole in farm productivity in developing countries,Consequently, public investments designed to en-hance human capital can be expected to generateadditional output even in the absence of new tech-nologies. The fact that significant increases in out-put could be obtained by making better use ofavailable inputs and technology does not mean thatresearch designed to generate new technologyshould be overlooked, Rather, those in the busi-ness of increasing the supply of agricultural prod-ucts should keep in mind that there is much thatcan be done while the scientists are hard at work indeveloping the new know-how.

A surprising fact that emerges from this reviewof the literature is the limited number of studiesreporting an analysis between farm size and effi-ciency. This is surprising given the importance thathas been given to this subject in the developmentliterature (e.g., Berry and Cline; Bardhan; andCarter). This subject is likely to continue to play animportant role in the public policy arena in manydeveloping countries and, hence, it seems to usthat the frontier literature might be able to make amore substantial contribution to better inform thisdebate,

It is clear from this review that considerable ef-fort has been devoted to measuring efficiency indeveloping country agriculture using a wide rangeof frontier models. Despite all this work, the extentto which efficiency measures are sensitive to thechoice of methodology remains uncertain. The im-plication that can be derived from this point is that,given the importance and complexity of efficiency

Ejiciency Analysis of Developing Country Agriculture 99

measurement, a more systematic effort is neededto evaluate the performance of various efficiencyestimators for a given data set.

Finally, more work is also needed to get a betterunderstanding of the major determinants of outputand productivity growth. Recent advances in paneldata methodologies, along with models that enablethe joint estimation of efficiency and its determi-nants, open an exciting area for further research.Moreover, these methodologies make it possible todecompose total output growth into input growth,technical efficiency, and technological change.However, to make these methodologies truly use-ful, we will need to find the way to assemble thenecessary data. In our judgement, this will proveto be a challenging undertaking.

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