Efficiency of Rice Farming Households in Vietnam: A DEA with Bootstrap and Stochastic Frontier Application Linh Hoang Vu 1

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1 1 Abstract Effcency of Rce Farmng Households n Vetnam: A DEA wth Bootstrap and Stochastc Fronter Applcaton Lnh Hoang Vu 1 Ths study estmates techncal effcency obtaned from both Data Envelopment Analyss (DEA) and stochastc fronter approach usng household survey data for rce farmng households n Vetnam. A bootstrap method s used to provde statstcal precson of DEA estmator. Bootstrap has not commonly used n emprcal analyss despte beng an mportant statstcal tool for mprovng the estmaton precson. Techncal effcency s modeled as a functon of household and producton factors. The results from the determnstc, semparametrc and parametrc approaches ndcate that among other thngs, techncal effcency s sgnfcantly nfluenced by prmary educaton and regonal factors. In addton, scale effcency analyss shows that many farms n Vetnam are operatng wth less than optmal scale of operaton, especally n the Central regon. Keywords: Data Envelopment Analyss (DEA), stochastc fronter, effcency, rce, bootstrap, Vetnam. 1. INTRODUCTION Agrculture n Vetnam s the most mportant sector as t contrbutes about 21.8 percent to gross domestc product (World Bank 2006) and supports obs for 67.3 percent of the populaton 2. In agrculture, rce s the most mportant crop n Vetnam. It s planted on 84 percent of cultvated area and consttutes more than 85 percent of Vetnam s total gran output. It also provdes about 85 percent of the total daly calore ntake for the Vetnamese people (Nghem and Coell 2002). Snce the reformng Do Mo polcy launched n December, 1986, the government has lberalzed the rce market as well as the markets for agrcultural nputs. The government has also promoted the cultvaton of hghyeldng rce varetes. As a result, rce producton and export have ncreased steadly. Rce producton ncreased from 15.1 mllon tons n 1987 to 32.6 mllon tons n 2000, a growth of 6.1% per year, whle rce yelds ncreased from 2.70 tons/ha n 1987 to 4.25 tons/ha n 2000, a growth of 3.3% per year (IRRI 2006). Snce the launch of Do Mo polcy, rce producton, rce area and rce yeld have ncreased sgnfcantly although recently, the growth of rce area has slowed down and even become slghtly negatve. 1 Department of Appled Economcs, Unversty of Mnnesota, Mnnesota, USA. Emal: vuxx0090@umn.edu 2 Author calculated based on IRRI (2005).

2 2 Vetnam has been a maor rce exporter snce 1989, currently the second largest rce exporter, exportng 5.2 mllon tons n 2005, equvalent to 18.2 percent of total world rce trade (FAO 2006). Recently, modern rce technology has been wdely appled. The adopton rate of fertlzer-responsve, hgh-yeldng modern rce varetes ncreased from 17% n 1980 to nearly 90% n 2000 (Tran and Kasa 2006). Fgure 1: Rce Producton, Yeld and Area n Vetnam (1975=100) Index Year Yeld Producton Rce area (Source: Author calculated from IRRI 2006) Despte the mportance of rce producton n Vetnam as well as n the world market, there have been very few studes on the effcency of Vetnamese rce farms. Ths paper s the frst attempt to estmate farm-level techncal and scale effcency and determne the factors nfluencng techncal effcency for rce producton n Vetnam. Ths paper would be useful for those nterested n Vetnam s rce producton as well as a contrbuton to the emprcal work on effcency, notably the applcaton of a bootstrap procedure to establsh the statstcal propertes of DEA techncal effcency. Effcency can be estmated by ether parametrc or nonparametrc methods. Parametrc measurement ncludes specfyng and estmatng a stochastc producton fronter or stochastc cost fronter. In ths method, the output (or cost) s assumed to be functon of nputs, neffcency and random error. The man strength of the stochastc fronter functon approach (SFA) s ts ncorporaton of stochastc error, and therefore permttng hypothetcal testng. The dsadvantage of ths approach s the mposton of an explct functonal form and dstrbuton assumpton of the error term. On the other hand, the non-

3 3 parametrc approach or the data envelopment analyss (DEA) has the advantage of no pror parametrc restrctons on the technology, hence less senstve to model msspecfcaton. However, because DEA s a determnstc approach, all devatons from the fronter are consders as neffcences, makng t senstve to measurement errors and data noses. There have been many studes on effcency n agrculture n developng countres, most of whch apply stochastc fronter approach. Tham et al (2001) summarzes 51 observatons of TE n developng countres from 32 studes publshed before In Vetnam, there are only a few papers that calculate effcency and determne the factors affectng effcency of Vetnam s agrculture. Past studes on effcency of rce producton n Vetnam only use smple measures of productvty such as yeld per hectare. To our knowledge, Kompas (2004) s the only attempt to calculate average techncal effcency for rce sector n Vetnam, usng a stochastc producton fronter based on a regonlevel panel data. In hs study, average techncal effcency for the whole country s 0.65 n 1999 and 0.78 for the prncpal rce areas (Red Rver Delta and Mekong Rver Delta). However, Kompas (2004) uses aggregate regonal data, whch may not gve useful nformaton on the effcency at farm level. Gven the advantages and dsadvantages of both DEA and SFA method, t maybe helpful to use both methods and compare them on the same data set. In addton, establshng the statstcal propertes of DEA estmator s useful for overcomng the dsadvantage of the nonparametrc method and mprovng the result robustness. Recent advances n DEA lterature nclude usng bootstrap to establsh the confdence nterval of techncal effcency (see Smar and Wlson 2000). The bootstrap method n Smar and Wlson (2000) has been appled emprcally n several studes of farm effcency n developed countres (e.g. Brümmer 2001, Latruffe et al 2003, Ortner et al 2006 and Olson and Vu 2007). The obectves of ths paper are twofold. Frstly, t uses both bootstrapped DEA method to estmate techncal and scale effcency of rce farmng households n Vetnam. Secondly, t uses estmates from both DEA and SFA n the second stage to determne the factors nfluencng these estmates. Ths paper contrbutes to the effcency lterature by usng weghted Tobt regressons to estmate the effects of factors on farm techncal effcency. Whle most of the studes on effcency lmt n the pont estmates, ths paper adds to the few papers (Brümmer 2001, Fraser et al 2006) that cover both pont estmates and confdence ntervals by DEA and SFA method. It s also the frst paper studyng rce farmng effcency n Vetnam usng household data. 2. EFFICIENCY MEASUREMENT Followng the semnal work by Farrell (1957) and others, economc effcency s typcally decomposed nto three types: techncal, allocatve and scale

4 4 effcency 3. Techncal effcency (TE) measures the frm s ablty to use the avalable technology n the most effectve way. Allocatve effcency (AE) s dependent on prces and measures the frm s ablty to make optmal decsons on product mx and resource allocaton. Combnng measures of techncal and allocatve effcency yelds a measure of economc effcency. Scale effcency measures the optmalty of the frm s sze. 2.1 Data Envelopment Analyss As a nonparametrc approach, DEA (Charnes et al 1978, Färe et al 1994) s used to derve techncal and scale effcency. DEA method can be appled usng ether output-based or nput-based approach dependng on whether they use nput dstance functon or output dstance functon. In ths paper, we use DEA method to estmate nput-based techncal and scale effcency as well as outputbased techncal effcency. Estmates were made usng lnear programmng n the software GAMS/OSL. The nput-based techncal effcency under VRS s the focus of our study. Based on a smoothed bootstrap procedure for DEA estmators proposed by Smar and Wlson (1998, 2000), the paper estmates the bas and the confdence nterval of the nput-based techncal effcency wth VRS, usng the package FEAR developed by Wlson (2005). Techncal and Scale Effcency For the th farm out of n farms, the nput-based techncal effcency (TE) under constant return to scale (CRS) s obtaned by solvng the followng problem TE = Mnθ CRS θ,λ CRS CRS subect to Y Yλ; θ X Xλ; λ 0 (1) CRS where X and Y are the nput and output vector respectvely, θ s techncal effcency of farm under CRS and λ s an n 1 vector of weghts. In general, 0 CRS CRS θ 1, where θ = 1 f the farm s producng on the producton fronter CRS and hence, techncally effcent. When θ <1, the farm s techncally neffcent. In the case of varable returns to scale, one can fnd techncal VRS effcency θ under varable return to scale (VRS) by addng the convexty n constrant λ = 1 to (1). Because the varable return to scale s more flexble = 1 VRS so the convex hull envelops the data more tghtly than under CRS, θ equal or greater thanθ CRS 4. s always Scale effcency (SE) s measured by the formula: SE CRS θ = (2) θ VRS 3 Farrell (1957) used the term prce neffcency nstead of allocatve effcency 4 Some authors call θ total or overall techncal effcency and VRS CRS θ pure techncal effcency.

5 5 In general, 0 SE 1, wth SE=1 representng effcent economy of scale. SE< 1 mples that the nputs are not scale effcent, whch can be ether ncreasng returns to scale (IRS) or decreasng returns to scale (DRS). 2.2 Bootstrappng the DEA estmator Whle DEA methods have been wdely appled, most researchers have largely gnored the statstcal propertes n the estmators. Ignorng the statstcal nose n the estmaton can lead to based DEA estmates and msleadng result because all the devatons from the fronter are consdered as neffcency. Smar and Wlson (1998, 2000) argue that bootstrap s the most currently feasble method to establsh the statstcal property for DEA estmators. Ths paper apples Smar and Wlson (1998, 2000) smoothed bootstrap procedure to correct the bas n DEA estmators and establsh ther confdence nterval. The procedure for ths paper s descrbed n more detals n the Appendx. 2.3 Stochastc Fronter Method The producton functon under VRS s specfed as (see Agner et al 1977, Battese and Coell 1992): lny = f ( ; β ) + ε X wth X s the nput and Y the output vector for farm ; f (X ; ) s normally assumed ether Cobb-Douglass producton technology or translog technology. Both functonal forms are used extensvely n lterature 5. In ths paper, we choose Cobb-Douglass functonal form. We choose the Cobb-Douglass functonal form for convenence because we have a relatvely large number of nputs n the producton fronter functon. Furthermore, the Cobb-Douglass functonal form s also more convenent n testng the return to scale hypothess. The Cobb-Douglass producton functon under VRS s: lny = β 0 + β k ln X The error term n equaton (3) s composed of two components (Agner et al 1977): ε = v u T k = 1 2 where v s are assumed to be ndependently and dentcally N(0, σ v ) representng the random errors. The term u represents techncal neffcency of farm but unlke v, t s only a one-sded varable takng non-negatve values. In ths paper, we assume u to be half-normal dstrbuton, stated by Greene (1997) 2 as the most useful formulaton. In other words, u = U where U ~ N(0, σ u ). The techncal effcency of farm s TE = exp(-u ), whch s greater than zero k + ε (4) 5 In Tham et al (2001) s meta-analyss, among 33 studes used stochastc fronter methods, 19 used the Cobb- Douglass functonal form aganst 14 that used a translog functonal form.

6 6 and lesser than 1. The estmaton of stochastc fronter model s done by maxmum lkelhood method n STATA verson 9.0 software. The confdence ntervals of TE n ths paper are establshed followng Horrace and Schmdt (1996). 3. DATA The data s taken from Vetnam Household Lvng Standard Survey (VHLSS 2004). The survey s mplemented by General Statstcs Offce of Vetnam wth techncal support from World Bank. In the VHLSS 2004 survey, there are 8813 households lvng n both rural and urban areas surveyed, ncludng about 4300 households producng rce. From that sample, we chose randomly a sub-sample of 600 households. After calculatng the effcency, we dropped 5 extreme observatons to reduce the possblty of DEA s senstvty to outlers. Effcency scores are recalculated usng the fnal sample of 595 farm households 6. The measure for output s the harvested rce quantty durng the last year. The nputs nclude nne categores: Fertlzers, pestcdes, seed, famly labor, hred labor, owned fxed asset and equpment value, asset hre (ncludng cattle hre) and mantenance, small tool and energy, and other farmng expendture and rce land. Snce besde rce growng, household are also engaged n other actvtes, famly labor s measured by the total famly hours allocated n farmng adusted by the percentage of rce producton over total farm producton. Rce land s measured by the land area allocated for rce producton. Other nputs are measured by the expendtures n current money value. In our sample, on average, rce occupes for 46% of agrcultural household outputs. Ths number s close to the macro percentage- the percentage of rce producton value n total agrcultural producton value for the whole country s 41.5% n Summary statstcs for these households are lsted n Table 1. Table 1. Summary statstcs for rce farmng farms Varable Mean Std. Dev. Mn Max Input and output vectors Rce quantty (kgs) Rce value Seed expendtures Fertlzer expendtures Pestcde expendtures We choose a sample of 595 farms nstead of 4300 farms to enable calculatng the effcences by the DEA and bootstrap method. For example, to run a bootstrap of 2000 replcatons for a sample of 4300 farms wll requre smultaneously solvng 4300 ( ) 17.2 mllons lnear equatons, an overburdened task for an average PC (see Smar and Wlson 2000 for the calculaton of number of equatons). In our analyss, the number of lnear equatons to be solved n the bootstrap step s 595 ( ) 2.4 mllons lnear equatons.

7 7 Famly hours for farmng Percent of rce (percent) Estmated famly hours for rce producton (hours) Rce land area (square meters) Fxed asset and equpment value Hred-n labor expendture Asset hre and mantenance Small tool and energy Other expendture In thousand VND at current value. 4. EMPIRICAL RESULTS 4.1 Techncal Effcency The estmated DEA and SFA effcences are presented n Table 2. The average techncal effcency estmated by DEA method s hgher than by SFA method. Smlar results have been reached n Kalatzandonakes and Dunn (1995) for corn farms n Guatemala and Wadud and Whte (2000) for rce farmers n Bangladesh. The nput-based TE s slghtly hgher than the output-based TE. Wth a gven bundle of nputs, an average household can ncrease ts output by 30.7% (=1/TE VRS-OUT -1). On the other hand, that household can reduce ts nputs by 27.4% (=1/TE VRS-IN -1) wthout changng the level of ts output. Estmates from determnstc DEA model have downward bases n effcency scores because n the model, the true producton fronter s unknown, and the ponts on the observed producton fronter may be neffcent n the presence of the true producton fronter. Usng bootstrap method as n Smar and Wlson (2000), we estmate bas-corrected TE scores and fnd them sgnfcantly lower than the ntal TE scores. Table 2: DEA and SFA estmates TE CRS OUT TE VRS -IN TE VRS- Bascorrected TE Lower bound Hgher bound TE by SFA Lower bound Hgher bound Average Medan Std. Dev Mn Max Fgure 2 shows the dstrbuton of ntal DEA estmates, bas-corrected DEA estmates and the 95-percent confdence nterval for the nput-based methods. If

8 8 we only know the ntal DEA estmates, t appears that on averages, rce farms n Vetnam can reduce ther nputs by 27.4% and stll can produce the same outputs. Yet, after correctng for the bas, the amount of nput savng s 47.5% (=1/ ). In the same way, an average farm can reduce ther nputs n the range from 29.7% to 68.6% wth 95% confdence nterval. By stochastc fronter method, the correspondng values 57.8% (=1/ ) for Cobb- Douglass specfcaton. It s clear that the amount of nput savng s consderable. To compare the estmates from nonparametrc and parametrc approaches, we use the pared t-tests and Spearman rank correlaton. The results are presented n Table 3. Based on pared t-test, on average, the techncal effcency scores n nonparametrc, both before and after correctng for bas, are hgher than n parametrc method although the dfference s smaller for bas-corrected estmates. The Spearman correlaton coeffcents between the effcency rankngs of the sample farms are postve and sgnfcant, mplyng that the effcency scores calculated n both methods are not ndependent. In other words, the effcency rankngs of farms n Vetnam are consstent n both methods. Fgure 2: Intal and Bas-Corrected Input-Based Techncal Effcency Under VRS Effcency score TE-n Bas-corrected TE-n Lower bound Hgher bound Percent of farms Table 3: Pared t- tests and Spearman rank correlaton tests

9 9 Sample Mean Effcency DEA SFA t- rato Spearman rank correlaton Intal TE Bas-corrected TE Sgnfcant at the 1% level Table 4 shows the dstrbuton of techncally effcent farm n the dataset accordng to DEA method. Farms n Southern Regon- the man producton regon n Vetnam - are most effcent. Farms n Central Regon are least techncally effcent. In addton, average techncal effcency and percentage of techncal effcent farms are hgher for large farms than for small farms and for dversfed farms than for manly rce farms. Large farms are defned as farms wth total farm output value hgher than 15 mllon VND (about $1000) 7. Manly rce farms are farms wth rce output equvalent more than 70% of total farm output value. About 70% of farms n our sample are manly rce farms and 37% of farms are large farms. Table 4: Dstrbuton of average techncal effcency Regon Average TE Bas-corrected TE Number of farms wth TE=1 All farms Red Rver Delta North East North West North Central Coast South Central Coast Central Hghlands South East Mekong Rver Delta North Center South Large farm Small farm Dversfed farm Manly rce farm Scale effcency % of farms wth TE=1 7 That number s chosen arbtrarly based on the dstrbuton of farm output value.

10 10 Farm household scale effcency scores are presented n Table 5. The farm households n the South are more scale effcent than farms n the North and the Center and large farms are more scale effcent than small farms. However, manly rce farms are more scale effcent than dversfed farms. About 23.4% of total farms are workng wth optmal scale operaton and a maorty of farms (59%) are operatng wth ncreasng return to scale. That suggests that a large number of Vetnamese rce farms should ncrease ther scale of operatons to gan scale effcency. For the stochastc functonal form, the sum of coeffcents from the Cobb- Douglass producton fronter s mplyng ncreasng return to scale. We reect the hypothess of constant return to scale (sum of coeffcent equal to one) at one-percent level of sgnfcance. Table 5: Dstrbuton of average scale effcency Number of farms wth % wth SE SE=1 DRS IRS SE=1 All farms Red Rver Delta North East North West North Central Coast South Central Coast Central Hghlands South East Mekong Rver Delta North Center South Large farm Small farm Dversfed farm Manly rce farm Factors assocated wth effcency Total farm output (ml. VND) A relevant queston s what factors can nfluence the farm techncal effcency. The factors ncluded for close examnaton n ths study nclude household characterstcs, producton structure, land characterstcs and regonal varables. Household characterstcs varables nclude total number of household members (household sze), adult rato n the household, household head s age and

11 11 household head s schoolng. Household head s schoolng s dvded nto four categores: no formal educaton, wth prmary schoolng (from 1 to 5 years), wth secondary schoolng (from 6 to 9 years) and wth hgh schoolng or hgher (10 years and up). In our data, 32% of household heads have prmary schoolng, 45% have some secondary schoolng, 14% have more than 9 years of schoolng and only 7% never go to school. Other varables that mght affect farm techncal effcency nclude farm sze (representng by total farm output value), captal to labor rato (mllon VND/hour), land to labor rato (square meter/hour), non-farm ncome rato and number of extenson vsts. Total farm output value ncludes both rce and other crop/lvestock ncome. Captal s measured as total fxed asset value. Bnary varables nclude dummes for land characterstcs (rented land, hgh qualty land), educaton level (prmary, secondary, hgh school), borrow money, modern rrgaton, and regonal bnary varables whch are grouped nto two sets- one set nclude dummes for Center and South regon wth North beng the reference regon. Most of the lterature on the effects of factors to effcency use Tobt analyss for DEA estmates. Ths model s employed n most of papers usng DEA method to estmate the factors assocated wth techncal effcency. However, standard Tobt model has a dsadvantage because t does not account for the bas and confdence nterval n the DEA ntal scores. We develop a weghted Tobt model wth the nformaton obtaned from the bootstrap procedure to overcome ths lmtaton. The dependent varable n ths model s the ntal TE calculated by DEA but wth the weghts equal to the recprocals of the wdth between hgher bounds and lower bounds for the bas-corrected TE. The dea s that, the hgher the wdth s, the larger the measurement error can occur. Therefore, weghted Tobt analyss reduces estmaton error by punshng the observatons wth larger wdth- or hgher possblty of measurement error. Fnally, model 5 s maxmum lkelhood estmaton for stochastc fronter TEs. The result n table 6 shows that farmer s age has a negatve effect to TE although the effect s only sgnfcant for Model 1 and Model 2. Ths s consstent wth the fndngs of Coell and Battese (1996), Seyoum et al. (1998), and Dhungana et al (2004). Table 6: Factors nfluencng techncal effcency Standard Tobt Weghted Tobt Stochastc fronter Dependent varable TE by DEA TE by DEA TE by SPF Number of obs LR ch2(18) = Prob > ch

12 12 Log lkelhood Adult rato (0.14) (-0.27) 0.02 (0.44) Household sze (-0.85) (-0.96) (1.06) Captal/Labor (0.07) (-0.15) (-0.68) Land/Labor (5.83) a (5.66) a (0.4) Head's age (-2.75) a (-1.81) c (-0.38) Prmary (1.64) c (1.66) c (2.1) b Secondary (-0.63) (-0.05) (2.49) b Hgh educaton (-0.68) (-0.73) 0.06 (1.76) c Farm output (2.67) a (2.13) b (1.4) Land qualty (0.51) (1.51) (5.47) a Non-farm rato (0.03) (-0.18) (-1.45) Irrgaton (0.07) (0.12) (3.81) a Extenson vst (0.29) (0.9) (0.49) Rented land rato (-0.27) 0.03 (0.31) (0.12) Borrow (-2.7) a (-1.74) c (-0.91) Exclusve rce (-2.99) a (-3.58) a (3.05) a Center (-3.22) a (-4.18) a (-3.83) a South (-1.22) (-2.25) b (-5.42) a Constant 1.02 (11.63) a (9.33) a (9.41) a Note: t-statstcs n parentheses. a Sgnfcant at 1%. b Sgnfcant at 5%. c Sgnfcant at 10% Prmary educaton of the household heads s postvely related to the farmer techncal effcency n all models but the mpact s more sgnfcant for the stochastc fronter estmates. The mpacts of secondary and hgher educaton to techncal effcency are more ambguous. Whle secondary and hgher educaton are assocated wth hgher techncal effcency ndces as calculated by stochastc fronter, they are nsgnfcant for those calculated by the standard and weghted Tobt. Ths mght ndcates a more consstent role of prmary educaton rather than secondary or hgher educaton for mprovng farmers effcency. One ustfcaton for the possble lmted effects of hgher educaton to techncal effcency s that the farmers wth hgher educaton tend to shft to non-farm actvtes, therefore ther educaton do not contrbute for mprovng farm techncal effcency. A smple OLS regresson ndcates that non-farm rato s postvely assocated wth the household head s year of schoolng at 5% sgnfcant level.

13 13 To test the hypothess that household decsons are collectve and nfluenced by the household member wth hghest educaton level rather than the household head s educaton, we also use the maxmal educaton level of the households as a regressor nstead of head s educaton level. We don t fnd any sgnfcant relatonshp between the household s hghest educaton level and ts techncal effcency. The fndng suggests that the head s educaton may be a more mportant factor n decdng the household techncal effcency. The land/labor rato has a sgnfcant postve mpact on techncal effcency for both DEA models but not for the SFA model. Ths means that ncreasng rce land s generally assocated wth better techncal effcency. Gven the shortage and fragmentaton of land n a populated economy as n Vetnam, ths fndng s reasonable. Based on World Rce Statstcs of Internatonal Rce Research Insttute (IRRI 2005), we estmated that nearly 90 percent of farms n Vetnam have farm area less than 1 ha n 1994 whle the correspondng rato for Phlppnes n 1991, Pakstan n 1990 and Thaland n 1988 are 37, 36 and 11 percent respectvely. On the other hand, the captal/labor rato effect on techncal effcency s nsgnfcant n all models. Farm sze has sgnfcant postve effect on techncal effcency n DEA models but not n SFA model, where the effect s postve but nsgnfcant. It ndcates that farm operatons n Vetnam are n general not optmal for techncal effcency. Modern rrgaton also has postve effect but the effect s only strongly sgnfcant for stochastc fronter model. Among the bnary varables, land qualty effect s postve n all models but only sgnfcant for the SFA model. Farms wth loans seem have lower techncal effcency scores than farms wthout loans although the effect s only sgnfcant for DEA models. Ths fndng s as expected snce farms wth loans may be more constraned wth the debt burden than those wthout loans. Regonal dummes show that both the Center and the South dummes are negatve, ndcatng that other thng beng equal, a farm n the North s more techncally effectve than n the Southern or n the Central regon. The mpact of Center dummy s strongly sgnfcant at 1% level n all models whle South dummy s only nsgnfcant n the standard Tobt model. Yet, n Table 4, we see that average techncal effcency score s hgher n the South than n the North. Ths hgher effcency scores can be explaned by the nfluences of other factors, such as farm sze- an average farm n the South s almost as bg as 2.5 tmes an average farm n the North (see Table 5). Other factors such as household sze, household adult rato, extenson vsts and rented land rato are nsgnfcant to techncal effcency n all models.

14 14 5. SUMMARY AND CONCLUSION Ths paper analyses techncal effcency for a sample of rce producers n Vetnam usng the parametrc, non-parametrc and sem-parametrc fronter approaches compares the effcency estmates obtaned from these approaches and dscuss the effects nfluencng techncal effcency estmates. The mean techncal effcency s under CRS, under VRS for outputorented DEA and under VRS for nput-orented DEA. A bootstrap procedure correctng for the bas, yelds a mean estmate of for nputorented DEA. Confdental nterval s also establshed for the bas-corrected estmates. Stochastc fronter estmaton yelds a mean estmate of The varances of estmates from DEA and SFA methods are smlar but the varances of bas-corrected TEs after bootstrappng are sgnfcantly lower than the parametrc approach, whch s a further advantage of the bootstrap method for DEA over the parametrc approach. The Spearman correlaton test confrms that our effcency scores calculated from dfferent approaches are postvely and sgnfcantly correlated. The results reveal substantal producton neffcency for sample rce farmers n Vetnam and hence sgnfcant potental for farmers to reduce ther costs by ncreasng effcency. On average, a farm can reduce ts cost by 30-69% dependng upon the method employed. A further 12 percent cost reducton can be obtaned by operatng wth optmal scale. A maorty of farms, partcularly n the Central regon, are operatng wth ncreasng return to scale. Gven the mportance of rce producton for ncome, food securty, employment and export n Vetnam, the benefts from ncreasng farm effcency are very substantal. Results from stochastc, non-parametrc as well as new sem-parametrc approaches suggest that techncal effcency n producton s nfluenced by educaton, especally prmary educaton. The mpacts of secondary and hgher educaton are less robust to model specfcaton. Secondary schoolng s hghly postve for stochastc model but not for the other models. The analyss also ndcates that ncreasng land holdng and farm sze has substantal benefts for effcency mprovement. Besdes, regonal factors are mportant n nfluencng techncal effcency. The Red Rver Delta, whch s very densely populated and has very small landholdngs, hghly lowland rrgated and hghly labor ntensve rce cultvaton methods, s most techncal effcent. The Mekong Rver Delta, whch produces more than a haft of the whole country rce producton, has more potental for mprovng techncal effcency. The land n ths regon s one of the best rce growng regons of the world and there s stll capablty for ncreasng rce area. Whle almost all arable land s under ntensve cultvaton n the North, only 67% of the arable land s under cultvaton n the Mekong Delta. On the other hand, factor such as non-farm rato or extenson support do not

15 15 sgnfcantly affect farm household techncal effcency. For extenson support, the reason may be due to lmted access of farmers to extenson servce. Polces leadng to mprovement of farm educaton, land qualty and land holdng wll be benefcal for mprovng farmers techncal effcency. The dstrbuton of techncal effcency and scale effcency across regons also provdes useful nformaton for polcy makers n enhancng the farm effcency for each regon. ACKNOWLEDGEMENT We would lke to thank Kent Olson, Paul Glewwe, Phlp Pardey and Terrance Hurley for ther helpful comments and the World Bank for data permsson; however all errors and vews expressed are ours. REFERENCES Agner, D. J., Lovell, C. A. K., Schmdt, P. (1977). Formulaton and Estmaton of Stochastc Fronter Producton Functon Models. Journal of Econometrcs 6, no. 1: Fraser, I., Balcombe, K., Km, P. (2006) Estmatng techncal effcency of Australan dary farms usng alternatve fronter methodologes? Appled Economcs 38: Battese, G. E., Coell, T. (1992). Fronter Producton Functons, Techncal Effcency and Panel Data: Wth Applcaton to Paddy Farmers n Inda. The Journal of Productvty Analyss 3: Brümmer, B. (2001). Estmatng Confdence Intervals for Techncal Effcency: The Case of Prvate Farms n Slovena. European Revew of Agrcultural Economcs 28, no. 3: Charnes, A., Cooper, W.W., Rhodes, E. (1978). Measurng the Effcency of Decson Makng Unts. European Journal of Operatonal Research 2: Chavas, J-P., Petre, R., Roth, M. (2005). Farm Household Producton Effcency: Evdence from the Gamba. Amercan Journal of Agrcultural Economcs 87, no. 1: Coell, T., Battese, G.E. (1996). Identfcaton of Factors Whch Influence the Techncal Ineffcency of Indan Farmers. Australan Journal of Agrcultural Economcs 40: Dhungana, B.R.; Nuthall, P.L., Nartea, G.V. (2004). Measurng the Economc Ineffcency of Nepalese Rce Farms Usng Data Envelopment Analyss. The Australan Journal of Agrcultural and Resource Economcs 48, no. 2: FAO. (2006). Foot Outlook- Global Market Analyss no. 1, 2006: Food and Agrculture Organzaton of the Unted Natons.

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18 18 ~ θ β + hε = 2 β hε f β + hε otherwse where h s the bandwdth of a standard normal kernel densty and ε s a random devaton from the standard normal.. To correct the varance of the generated bootstrap sequence when kernel estmators are used, construct another sequence θ 1 ~ = β + ( θ h / ˆ σ θ 1 β ) where β =(1/n) β. Thus, the sequence θ s obtaned by the smoothed bootstrap. It has better propertes than the smple bootstrap sequence n the sense that the varance of θ s asymptotcally correct. v. For =1,..,N, a pseudo data set of ( x,b, y,b ) where x,b = ( θˆ / θ ) x and y,b = y wth x, y the orgnal nput and output vectors of the th farm, respectvely. v. Calculate the new DEA score ˆ θ for each farm by takng the pseudo data as reference. v. Repeat step () to (v) for B tmes to yeld B new DEA techncal effcency scores ˆ θ for =1,,N. v. Calculate the bootstrap bas estmate for the orgnal estmator θˆ as B 1 bas B ( ˆ θ ) = B ˆ θ ˆ θ. The bas-corrected estmator of θˆ can be computed as b= 1 θˆ = ˆ θ ( ˆ bas B θ ). v. The percentle method s nvolved n constructng confdence nterval. The confdence nterval for the true value of θˆ can be establshed by fndng value a α, b α such that Prob α ˆ ( b θ ˆ θ aα ) = 1 α. Snce we do not know the dstrbuton of ( ˆ θ ˆ θ ), we can use the bootstrap values to fnd a ˆ b ˆ α, such that α Prob ˆ α ˆ ( b θ ˆ θ ˆ aα ) = 1 α. It nvolves sortng the value of ( ˆ θ ˆ θ ) for b =1,,B n ncreasng order and deletng ( ( α / 2) 100 percent of the elements at ether end of ths sorted array and settng aˆ α and bˆ α at the two endponts, wth aˆ α bˆ α. In our emprcal work, we set B=2000 to ensure the low varablty of the bootstrap confdence ntervals. The value of bandwdth of the densty estmate h s found by Smar and Wlson (2000) s method of mnmzng an approxmaton to the mean weghted ntegrated square error. N = 1