Efficiency Estimates for the Agricultural Production in Vietnam: A Comparison of Parametric and on-parametric Approaches

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1 2009, Vol 0, o2 62 Effcency Estmates for the Agrcultural Producton n Vetnam: A Comparson of Parametrc and on-parametrc Approaches guyen Khac Mnh and Gang Thanh Long * Abstract Ths paper uses both parametrc and non-parametrc approaches to estmate techncal, allocatve, and economc effcences for the agrculture producton n sxty provnces of Vetnam n the perod Under dfferent technology specfcatons, both approaches show that the average techncal, allocatve, and economc effcency estmates were not hgh, and there would be a large room for the studed provnces to mprove ther agrcultural producton effcency. To examne consstency of the estmates from two approaches under dfferent specfcatons of returns to scale, we use Spearman rank test, and the results ndcate that parametrc and non-parametrc approaches provde dfferent estmates. Keywords: data envelopment analyss (DEA), stochastc fronter producton functon (SFPF), Spearman rank JEL Classfcaton: C4, N5 Introducton Snce the Do mo (renovaton) n the late 980s to transform the country from a centrally planned economy nto a market economy, Vetnam has notched mpressve achevements n both socal and economc aspects. The economy recorded an average growth of 8 percent over the past decade. Although the agrcultural sector has been reduced n terms of both share n gross domestc product (GDP) and number of labors over the past decade, t s stll playng an mportant role n the country, as more than 70 percent of the Vetnamese populaton are lvng n rural areas, where agrcultural producton actvtes are predomnant. In addton, the agrcultural sector also recorded remarkable achevements n changng Vetnam from a country wth a lot of people lvng n hunger to a country ranked as one of the bggest exporters of rce n the world snce md-990s. However, the agrcultural sector n Vetnam s also facng a number of constrants and challenges. For nstance, the structure of the agrcultural sector has been changed * Nguyen Khac Mnh (Correspondng author): Center for Development Economcs and Publc Polcy, Natonal Economcs Unversty, 207 Ga Phong Street, Ha Ba Trung Dstrct, Hano 0000, VIET- NAM. Telephone (Offce): , Fax: , Emal: mnhnk@neu.edu.vn Gang Thanh Long: Faculty of Economcs, Natonal Economcs Unversty, 207 Ga Phong Street, Ha Ba Trung Dstrct, Hano 0000, VIETNAM Telephone (Offce): , Fax: , Emal: longgt@neu.edu.vn

2 63 AGRICULTURAL ECO OMICS REVIEW very slowly, and agrcultural producton has been reled substantally on labor-ntensve and low-technology producton processes under relatvely small producton sze (MO- FA, 2007). Under such constrants and potental challenges from the accesson to the World Trade Organzaton (WTO) n early 2007, varous polcy ssues need to be consdered for Vetnam as a whole, and the agrcultural sector n partcular, because competton wll be fercer n an equal playng feld. Therefore, lookng for approprate development strateges for the agrcultural producton, ncludng productvty growth and effcency mprovement, s a must. Comprehensve studes on effcency estmates for the sector are thus requred. At the best of our knowledge, there have been no studes to estmate techncal, allocatve, and economc effcences for the agrcultural producton n Vetnam. Therefore, ths paper wll be the frst attempt to do such an mportant analyss. We wll use both parametrc and non-parametrc approaches to estmate these effcency measures for agrcultural producton n sxty provnces of Vetnam n the perod We then provde a comparson of results obtaned from these approaches n order to provde more concrete comments on the effcency performance of the sector. The remander of the paper s organzed as follows. Secton 2 provdes analytcal framework for measurng effcency, n whch both parametrc and non-parametrc approaches are presented. Descrptons of data and varables are provded n Secton 3. We wll present emprcal results and analyss n Secton 4, and concludng remarks n Secton 5. Analytcal Framework Ths paper wll use both parametrc and non-parametrc approaches to estmate effcency of agrcultural producton n sxty provnces of Vetnam durng The former s based on stochastc fronter producton functon (SFPF) technque, whle the latter s based on data envelopment analyss (DEA) technque. Parametrc Approach Stochastc Fronter Producton Functon (SFPF) The parametrc approach n ths paper s adopted from Kopp and Dewert (982) s cost decomposton procedure to estmate techncal, allocatve, and economc effcency measures. In general, the technology of a decson-makng unt (DMU) (e.g., a frm, a sector, or a provnce) represented by a stochastc producton fronter can be expressed as follows. ( ; ) Y = f X β + ε, (=, 2,, ) () = s a vector of functons of actual nput quanttes used by the th DMU; β s a vector of parameters to be estmated; ε s the composte error term; and s the number of DMUs. In Agner et al. (977) and Meeusen and Van den Broeck (977), ε s defned as follows. where Y denotes the outputs of the th DMU; Χ ( x, x 2,..., xp )

3 2009, Vol 0, o2 64 e = v - u, (=, 2,, ) (2) where v s are assumed to be ndependently and dentcally dstrbuted (..d) random 2 errors under dstrbuton ( 0, v ) σ, and they are ndependent of the u s; and u s are nonnegatve random errors, whch are assocated wth techncal neffcency n producton, and assumed to be..d and truncated (at zero) under normal dstrbuton wth mean µ, ( ) 2 2 and varance u (, u ) σ µ σ. The maxmum lkelhood estmaton for equaton () provdes estmators for β and v u 2 2 u varance parameters, σ = σ + σ, as well as γ = σ / σ. Replacng equaton (2) nto equaton (), and then subtractng v from both sdes of equaton () to yeld: Y = Y - v = f X ; β - u, (3) ( ) where Y s the observed output of the th DMU, and t s adjusted for the stochastc nose captured by v. Equaton (3) s the bass for dervng the techncally effcent nput vector and the dual cost fronter of the producton functon represented by equaton (). For a gven level of output Y, the techncally effcent nput vector for the th t DMU ( X ) s derved by smultaneously solvng equaton (3). Assumng that the producton functon n equaton () s self dual (such as Cobb- Douglas form), the dual cost fronter can be derved algebracally. The cost functon for the th DMU facng the fxed factor prce W >0 s defned as the mnmum-value functon of the cost mnmzaton. Solvng the problem, we can get: (,, ) C = h W Y ψ, (4) where ψ s a vector of parameters, and Ws are nput prces. The economcally effcent nput vector for the th e DMU s derved by usng Shephard s lemma, denotng X. The observed techncally effcent and economcally effcent costs of producton of P P the th DMU are equal to x t w j j and x e w j j, respectvely. These cost measures are used to compute techncal effcency (TE) and economc effcency (EE) ndces for the th DMU as follows. TE EE P = P P = P w x t j j w x j j j w x e j j j. (5). (6) w x

4 65 AGRICULTURAL ECO OMICS REVIEW Followng Farrell (957), the allocatve effcency (AE) ndex can be derved from equatons (5) and (6) as follows. AE P = P w x e j j w x t j j. (7) Therefore, the total cost or economc neffcency of the th DMU,.e. e t ( W. X- W. X ), can be decomposed nto techncal neffcency,.e. ( W. X W. X ) and allocatve neffcency,.e. (. t e W X - W. X ). -, Emprcal Models Model : Producton functon and cost fronter Under the parametrc approach, we wll use the Cobb-Douglas stochastc producton fronter to estmate effcency levels for the agrcultural producton actvtes n the sample provnces of Vetnam. The producton functon s generally specfed as follows. lny = β + β ln x + β ln x + β ln x + ε, (8) o where Y s output and x s are nputs for the agrcultural producton actvtes n the th provnce. Specfcally, these varables are defned as follows. Y (Output) s the gross value-added (GVA) of the th provnce s agrcultural producton actvtes. It s calculated as the sum of the value-added of the man agrcultural producton actvtes n the th provnce, ncludng farmng, forestry, anmal husbandry, fshng, and sdelne actvtes. It s measured n bllons of Vetnamese Dong (VND); x (Labor) s the number of labors used n these agrcultural producton actvtes n the th provnce. It s measured n thousand persons. x 2 (Fertlzers): s total amount of fertlzers used n these agrcultural producton actvtes n the th provnce. It s measured n thousand tons; x 3 (Land): s the total area used for these agrcultural producton actvtes n the th provnce. It s measured n thousand hectares; βs are parameters to be estmated; and ε s the composte error term, whch was defned prevously. Note that, the producton fronter n equaton (8) represents the varable returns to scale (VRS) technology. In order to obtan the producton fronter under the constant returns to scale () technology, we mpose a restrcton that the sum of the output elastctes of nputs 3 equals to one,.e., = β =. It means that, under technology, we wll estmate a k k producton functon as follows.

5 2009, Vol 0, o2 66 ln( Y / x ) = α + α ln( x / x ) + α ln( x / x ) + ε, (9) 3 o where (Y /x 3 ) s per-hectare gross value-added of agrculture producton actvtes n the th provnce durng the study perod; (x /x 3 ) s per-hectare number of labors. Ths varable mples the level of labor ntensty n agrculture producton actvtes n the th provnce durng the study perod; and (x 2 /x 3 ) s per-hectare tons of fertlzers. Ths varable shows how much fertlzers were used n agrculture producton actvtes n the th provnce durng the study perod. The cost functon can be obtaned from producton functon n equaton (8) by solvng the cost-mnmzng problem. The dual cost fronter of the producton functon n equaton (8) s then expressed as follows. ln( C / W ) = α + α ln( W / W ) + α ln( W / W ) + α lny, (0) where C s the mnmum cost for agrcultural producton actvtes n the th provnce; and Y s the output of the provnce. Model 2: Ineffcency effects model Wth regard to the techncal neffcency effect model, the component of techncal neffcency effects n the fronter producton functon s defned to rely on provncespecfc factors, ncludng captal-labor rato (whch s approxmated by the rato of number of tractors and number of labors) and geographc locaton (or economc regons). The followng s the specfcaton for the model 2: ut = δ0 + δkl Ln( tractor / labor) + δ x + δ2x2 + δ4x4 + δ5x5 + δ6x6 + δ7 x7 + δ8 x8 + δ9t + wt, () where: Ln(tractor/labor) s the natural logarthm of number of tractors per labor. x s dummy varable = f provnce s n the regon, 2 and = 0 otherwse. x 2 s dummy varable = f provnce s n the regon 2, and = 0 otherwse. x 4 s dummy varable = f provnce s n the regon 4, and = 0 otherwse. x 5 s dummy varable = f provnce s n the regon 5, and = 0 otherwse. x 6 s dummy varable = f provnce s n the regon 6, and = 0 otherwse. x 7 s dummy varable = f provnce s n the regon 7, and = 0 otherwse. x 8 s dummy varable = f provnce s n the regon 8, and = 0 otherwse. t s tme; and w t s errors terms whch are assumed to be ndependently and dentcally dstrbuted followed by the truncaton of the normal dstrbuton wth zero mean and unknown varance σ. 2 w

6 67 AGRICULTURAL ECO OMICS REVIEW on-parametrc Approach The non-parametrc approach n ths paper s based on the data envelopment analyss (DEA) technque (Charnes et al., 978; and Färe et al., 985, 994) n order to estmate techncal, scale, allocatve, and economc effcency measures for agrcultural producton actvtes n the sampled provnces. Suppose that we have provnces ( =60), each producng one output by usng k=, 2,, P nputs. Let Y be the output the th provnce (=,2,, ), and x k be the k th nput of the th provnce (=,2,, ; k=,2,, P). Also, let λ j (, 2,, ) be a weght. The nput-orented measure of techncal effcency (TE) for the th provnce s calculated as the soluton to the followng programmng problem. subject to: Y j θ = mn θ (2) j θ, λ λ Y, where =, 2,, (3) λ j jk x θ x k, where =, 2,, ; k=, 2,, P (4) λ 0, (5) where θ s the techncal effcency (TE) measure of the th provnce under technology. If θ =, the th provnce s agrculture producton s on the fronter and s techncally effcent under. If θ <, the th provnce s agrculture producton s below the fronter and s techncally neffcent under. Under DEA, the techncally effcent cost of producton of the th provnce s gven by.( ) W θ X. In order to derve a measure of the total or overall economc effcency (CE) ndex, we solve the cost mnmzng DEA model (Färe et al., 985, 994) as follows. subject to: Y mn w x k j * xj λ j P k= * k, (6) λ Y, where =, 2,, (7) λ x x, where =, 2,, ; k=, 2,, P (8) j jk * k λ 0, (9) * where x s the cost mnmzng or economcally effcent nput vector for the th provnce, gven ts nput prce vector and output level. The CE ndex for the th provnce s

7 2009, Vol 0, o2 68 then computed as follows. CE P k= = P k= x x * k k w w k k, (20) whch s the rato of the mnmum cost to the observed cost. The allocatve effcency (AE) ndex, derved from equatons (2) and (20), s expressed as follows. CE AE =. (2) θ It should be noted that equaton (7) also accounts for the nput slacks, whch are not captured by equaton (5). Followng Ferrer and Lovell (990), ths procedure attrbutes any nput slacks to allocatve neffcency on the ground that slack reflects an napproprate nput mx. The overall techncal effcency under (TE ) can be decomposed nto two components,.e., purely techncal effcency and scale effcency, by solvng a VRS DEA model, whch s n turn obtaned by mposng the addtonal constrant = λ = VRS on equaton (5) (Banker et al., 984). Let θ denote the TE ndex of the th provnce under VRS (TE VRS ), then the techncally effcent costs of producton of the th provnce * under VRS s equal to wk x k θ P k= VRS. Because the VRS analyss s more flexble and envelops the data n a tghter way VRS than the analyss, we usually have VRS TE measure ( θ ) to be equal or greater than the TE measure ( θ ). Ths relatonshp s used to obtan a measure of scale effcency (SE) of the th provnce as follows. VRS j θ SE =, (22) θ where SE = ndcates scale effcency, and SE < ndcates scale neffcency. Scale neffcency s due to the presence of ether ncreasng or decreasng returns to scale, whch can be determned through a non-ncreasng returns to scale (NIRS) DEA IRS model by substtutng the VRS constrant = λ = wth = λ. Let θ represent the techncal effcency measure under NIRS specfcaton. If θ = θ, there IRS are ncreasng returns to scale, and f θ < θ there are decreasng returns to scale (Färe et al., 994). j j j j IRS j Descrptons of Data and Varables In ths paper, we wll use panel data of nputs and output for agrcultural producton

8 69 AGRICULTURAL ECO OMICS REVIEW actvtes n sxty provnces of Vetnam n the perod The data were collected by the General Statstcs Offce of Vetnam (GSO) through the years. Table provdes statstcal summary for output (gross value-added or GVA) and nputs (labor, machnery, fertlzers, and land). Table. Summary of Inputs and Output Year Obs. GVA (V D Mllon) Labor (,000 persons) Tractor (unt) Fertlzers (,000 tons) Land (,000 hectares) ,650 7,674 25, , ,248 8,270 35,42,452 6, ,003 2,854 37,278,426 7, ,499 22,647 45,026,449 7, ,479 23,276 87,88 2,253 7, ,54 23,90 95,527 2,398 7, ,774 23,978 08,397 3,038 7, ,272 24,60 3,7 3,80 7, ,767 24,869 20,605 3,297 7, ,58 25,082 43,360 3,462 8, ,395 25,22 62,246 3,553 9, ,47 25,426 6,492 3,53 9, ,89 25,876 67,322 3,437 9, ,384 26,620 79,670 3,79 9, ,960 26,550 93,504 3,776 9, ,928 26,74 20,490 3,79 9,75 Source: Authors estmates. As mentoned earler, the output s the sum of the value-added of producton from farmng, forestry, anmal husbandry, fshng, and sdelne actvtes. All the values of GVA reported n Table are adjusted by the Vetnam s GDP deflator, n whch the year 994 s the base year. As can be seen, the GVA of the agrcultural producton has ncreased sgnfcantly over the past decade. The number of labors used n the emprcal models excludes labor force workng for the rural ndustres, constructon, transportaton, commerce, and other mscellaneous occupatons. Only labors workng for farmng, forestry, anmal husbandry, fshery, and sdelne producton actvtes are ncluded. Machnery s consdered as captal nput for the agrcultural producton actvtes n ths paper, and t s measure by the number of tractors used for farmng, forestry, anmal husbandry, fshery, and sdelne producton actvtes, such as plowng, rrgatng, dranng, harvestng, farm product processng, transportaton, plant protecton, and stock breedng. Fertlzers refer to the sum of pure weght of ntrogen, phosphate, potash, and complex fertlzers, whle land refers to total cultvated areas at the end of each year.

9 2009, Vol 0, o2 70 Emprcal Results and Analyss Estmated Results from Parametrc Approach We frst conduct some hypotheses tests wth the maxmum lkelhood estmates of parameters n the Cobb-Douglas stochastc fronter producton functon, defned n equatons (8) and (9), whch are obtaned for the total sample. Table 2a presents the test results of varous null hypotheses on the sample. The null hypotheses are tested by usng lkelhood rato test. The lkelhood rato test statstc s λ = -2 L( H ) - L( H ), where L(H 0 ) and L(H ) are the values of the log-lkelhood [ 0 ] functon under the specfcatons of the null and alternatve hypotheses, H 0 and H, respectvely. If the null hypothess s true, then λ has approxmately a Ch-square (or mxed Ch-square) dstrbuton wth degrees of freedom equal to the number of restrctons. Table 2a. Statstcs for Tests of Hypotheses ull Hypothess Log-lkelhood Functon Test Crtcal Value Statstcs (λ) % 0.5% Decson Under the assumptons of H 0 : µ = 0, η= H : µ π 0, η= H 0 : µ = 0, η= H : µ = 0, η π H 0 : µ = 0, η= H : µ π 0, η = Reject Reject Reject H 0 : µ = γ = η = Reject Under the assumptons of VRS H 0 : µ = 0, η= H : µ π 0,η= H 0 : µ = 0, η= H : µ = 0, η π H 0 : µ = 0, η= H : µ π 0, η π Reject Reject Reject H 0 : µ = γ = η = Reject ote: The crtcal value for ths test nvolvng γ=0 s obtaned from Kodde and Palm (986). Every null hypothess s rejected at the percent sgnfcance level. Source: Authors estmates

10 7 AGRICULTURAL ECO OMICS REVIEW The frst null hypothess test,.e. u s nonnegatve half normal dstrbuton wth µ=0. The results suggest that the techncal effcency component s followng the truncated normal dstrbuton. The second null hypothess,.e. there are no techncal neffcency effects or ( H 0 : γ = µ = η = 0 ), s rejected at % sgnfcance level for both cases. If the null hypothess s true, there are no fronter parameters n the regresson equaton, and the estmaton becomes an ordnary least square estmaton. The results suggest that the average producton functon s an nadequate representaton of the Vetnamese agrcultural sector, and t wll underestmate the actual fronter due to techncal neffcency effects. To estmate producton fronter for the agrcultural producton n the sampled provnces, both cases of Cobb-Douglass producton functon under the and VRS are employed n ths paper. We use the computer program FRONTIER Verson 4. (Coell, 996a) for our estmaton. The maxmum-lkelhood (ML) estmates of the parameters for the stochastc producton fronter obtaned from the program are presented n Table 2b. Table 2b. Maxmum Lkelhood Estmates for Parameters Models under the Assumpton of Constant Returns to Scale () Model Model 2 t-rato Parameter coeffcent Standarderror coeffcent standarderror t-rato Constant α Ln(labor/land) α Ln(fertlzer/land) α Constant δ Ln(tractor/labor) δ kl x δ x 2 δ x 4 δ x 5 δ x 6 δ x 7 δ x 8 δ t δ Sgma-squared σ Gama γ µ η Log Lkelhood ote: Source: u v 2 2 / u σ = σ + σ ; and γ = σ σ. Authors estmates.

11 2009, Vol 0, o2 72 As expected, the sgns of the slope coeffcents of the stochastc producton fronter are postve and hghly sgnfcant. The estmate of the varance parameter, γ, s also postve and sgnfcantly dfferent from zero, mplyng that the neffcency effects are sgnfcant n determnng the level and the varablty of output of the agrcultural producton actvtes n the sampled provnces. The estmaton of Cobb-Douglass producton functon under the VRS assumpton n Table 2b also shows that the output elastcty of labor (0.2737) s hgher than the output elastctes fertlzers (0.782). Thus, t s obvous that the agrcultural producton actvtes n the sampled provnces of Vetnam durng the study perod were heavly reled on labor. 2 As mentoned, the varance σ helps to know whether the sampled provnces had hgher producton effcency durng the study perod, as t represents the total varance of output. Ths varance contans a random error term ( σ ) and a techncal neffcency 2 u term ( σ ). Table 2c ndcates that 2 v 2 σ s small (only ), meanng that there were nsgnfcant changes n the agrcultural outputs of the sampled provnces over the past decade. Table 2c. Maxmum Lkelhood Estmates for Parameters of Ineffcency Model under the Assumpton of Varable Returns to Scale (VRS) Varables Model Model 2 t-rato coeffcent Parameter coeffcent Standarderror standarderror t-rato Constant β Ln(labor) β Ln(fertlzer) β Ln(land) β Constant δ Ln(tractor/labor) δ kl x δ x 2 δ x 4 δ x 5 δ x 6 δ x 7 δ x 8 δ t δ Sgma-squared σ Gama γ µ η Log Lkelhood ote: = + u v σ σ σ ; and Source: Authors estmates. 2 2 / u γ = σ σ.

12 73 AGRICULTURAL ECO OMICS REVIEW In both Table 2b and 2c, the estmates for varables representng regons show a postve and statstcally sgnfcant coeffcent for the Regon 4, whle negatve and statstcally sgnfcant coeffcents for other seven regons. In other words, locaton had sgnfcant mpacts on the effcency of the studed agrcultural producton actvtes. Also, n both Tables 2b and 2c, the coeffcents for the varable representng captal-labor rato,.e. Ln(tractor/labor), are both negatve and statstcally sgnfcant, meanng that techncal neffcency would have been reduced f agrcultural labors had been more techncally equpped. Table 2d. Maxmum Lkelhood Estmates for Parameters for Cost Fronter under the Assumptons of Constant Returns to Scale () Varables / Parameters Coeffcent Standard-error t-rato LnA Ln(W /W 3 ) Ln(W 2 /W 3 ) LnY σ γ µ η Log lkelhood A Source: Authors estmates. The dual cost fronter model, derved from the stochastc producton functon, s presented n Table 2d. In the form of Cobb-Douglas cost functon, we have: C( W, Y ) = 0.387W W W Y Agan, sgnfcant dfferences between the coeffcents for labor (0.43), land (0.494), and fertlzers (0.0076) show that the costs of the agrcultural producton actvtes n the sampled provnces were heavly depended on the costs of labor and land. Table 3 shows the frequency dstrbuton of the estmated techncal effcency measures for the agrcultural producton of the sampled provnces under and VRS assumptons and cost effcency estmated from cost functon under the assumpton of. The estmated mean techncal effcency was percent under the assumpton, and percent under VRS assumpton. These estmates mply that there were consderable neffcences n the agrcultural producton actvtes of the sampled provnces. In other words, there would be a substantal room for these provnces to mprove ther agrcultural producton effcency. More than 90 percent of the sampled provnces had techncal effcency at less than 60 percent, whle only about 5 percent of these provnce had techncal effcency of more than 80 percent. The estmated results also show that there was a wde range of techncal effcency of agrcultural producton between the sampled provnces, as the hghest effcency was about 82.68, whle the lowest effcency was only 3.38 percent.

13 2009, Vol 0, o2 74 Table 3. Frequency Dstrbuton of Producton Effcency under, VRS, and Cost Effcency (CE) Effcency Range Varable Returns to Scale (TEVRS) Constant Returns to Scale (TE) Cost Effcency (CE) Mean Std. Dev. Obs. Mean Std. Dev. Obs. Mean Std. Dev. Obs. [0, 0.2) n.a [0.2, 0.4) [0.4, 0.6) [0.6, 0.8) [0.8, ) n.a n.a All Mean Medan Maxmum Mnmum Std. Dev Obs Source: Authors estmates. Estmated Results from on-parametrc Approach The DEA models are estmated by usng the computer program DEAP Verson 2.0 (Coell, 996b). Table 4 presents the techncal, allocatve, and economc effcency measures estmated from the DEA, as well as ther frequency dstrbutons. The estmated mean techncal effcency was 66.3 percent for the DEA model (crste), and 72.6 percent for the VRS DEA model (vrste). Only 2.7 percent of the sampled provnces (or 3 out of 60) were n nterval of [80 %, 00%) effcent under the DEA model, whle 35.6 percent of the sample (or 22 out of 60) were nterval of [80 %, 00%) effcent under VRS DEA model. The scale effcency vared from 60 percent to 00 percent, wth a mean of 90.9 percent. The estmated allocatve effcency ndces under assumptons are presented n Table 5. The mean allocatve effcency (AE) and cost effcency (CE) ndces under the assumptons estmated from the cost-mnmzng DEA model were percent and percent, respectvely. Therefore, under DEA models, especally wth assumpton, t s shown that there were substantal neffcences n the agrcultural producton actvtes n the sampled provnces durng the past decade. The dstrbuton of the estmated economc effcency ndces n Table 5 shows that there was a wde range of economc effcency dfferences. The mnmum economc effcency level was only 24 percent, whle the maxmum level was as hgh as percent. About 6.7 percent of the sampled provnces (or 37 out of 60) had economc effcency level between 20 percent and 60 percent, meanng that there was a large room for these economcally neffcent provnces to mprove ther economc effcency of the agrcultural producton actvtes. The number of provnces wth economc effcency

14 75 AGRICULTURAL ECO OMICS REVIEW ranged from 80 percent to 00 percent was extremely low, only about 5 percent (3 out of 60) under DEA model. Table 4. Frequency Dstrbuton of Producton Effcency Range Mean crste (DEA model) Std. Dev. Obs. Range vrste (DEA model) Mean Std. Dev. Obs Range Mean Scale Std. Dev. [0.2, 0.4) [0.4, 0.6) [0.6, 0.7) [0.4, 0.6) [0.6, 0.8) [0.7, 0.8) [0.6, 0.8) [0.8, ) [0.8, 0.9) [0.8, ) [,.2) [0.9, ) All All All Mean Medan Maxmum Mnmum Std. Dev Obs Source: Authors estmates. Obs. Table 5. Frequency Dstrbutons of Producton Effcency under and VRS, estmated from the cost-mnmzng DEA model AE Range Mean Std. Dev. Obs. Range Mean Std. Dev. Obs. [0.6, 0.7) [0.2, 0.4) [0.7, 0.8) [0.4, 0.6) [0.8, 0.9) [0.6, 0.8) [0.9, ) [0.8, ) All All Mean Medan Maxmum Mnmum Std. Dev Obs Source: Authors estmates. A Comparson of Parametrc and on-parametrc Estmates In ths paper we appled two approaches to estmate techncal, allocatve, and eco- CE

15 2009, Vol 0, o2 76 nomc effcency measures for the agrcultural producton actvtes, n whch the parametrc approach s based on SFPF technque, whle the non-parametrc s based on DEA technque. It mght not be expected that effcency estmates obtaned from one technque would be more (or less) than those obtaned from the other technque. However, n ths paper, we can see that the estmated average effcency levels based on SFPF model under and VRS (37.32 percent and percent, respectvely) are much lower than those obtaned from DEA model (66.3 percent and 72.6 percent, respectvely). The queston s why these approaches provded dfferent estmated results under the same assumptons on returns to scale, and the same set of data? To examne ths queston, we compute the Spearman rank correlatons between effcency rankngs of the sampled provnces. The results are presented n Table 6. Table 6. Spearman Rank Correlatons Effcency SFPF DEA Spearman rank correlaton (p) Probablty TE TE VRS CE Source: Authors estmates. The results show that, on average, the estmated techncal effcency levels under and VRS assumptons from SFPF model are sgnfcantly smaller than those from DEA model. Therefore, under the same set of data, the assumpton on returns to scale s found to be crtcal n explanng the dfferences n effcency measures obtaned from these approaches. However, t s not really surprsed to have such dfferent estmates from two approaches, as these estmates are consstent wth the expectaton that effcency scores obtaned from the non-parametrc approach would be hgher than those from the parametrc approach. Ths comment has been ndcated n a number of exstng studes. For nstance, Drake and Weyman-Jones (996), explorng the UK buldng frms, produced nsgnfcant rank correlaton coeffcents between the estmated effcency levels from both approaches. Ferrer and Lovell (990) found hgher techncal effcency, but lower economc effcency for the parametrc method n comparson wth the non-parametrc method, and nsgnfcant rank correlatons between the estmated effcences from two approaches. Usng the data for the Guatemalan farmers, Kalatzandonakes and Dunn (995) reported a sgnfcantly hgher level of mean techncal effcency under DEA than under the stochastc fronter. The dfferences n the estmated results from two approaches could be manly attrbuted to the dfferent characterstcs of the data, the choce of nput and output varables, measurement and specfcaton errors, as well as estmaton procedures. Concludng Remarks Ths paper uses and compares both parametrc and non-parametrc approaches n es-

16 77 AGRICULTURAL ECO OMICS REVIEW tmatng techncal, allocatve, and economc effcency measures for the agrcultural producton actvtes n sxty provnces of Vetnam durng The parametrc approach s based on Kopp and Dewert (982) s cost decomposton to estmate effcency measures for a Cobb-Douglas stochastc producton functon and dual cost fronter, whle the non-parametrc approach s based on varous nput-orented DEA models. Under the specfcaton, the average techncal, allocatve, and economc effcency estmates were 66.3 percent, percent, and percent, respectvely, n parametrc approach, and percent, percent, and 42.8 percent, respectvely, n non-parametrc approach. Under the VRS specfcaton, techncal effcency estmated from parametrc approach was percent, n non-parametrc approach, whle t was 72.6 percent. On average, the estmated techncal and economc effcences were sgnfcantly hgher n the non-parametrc approach than n parametrc approach. However, the effcency rankngs of the sampled provnces based on these two approaches are postvely and sgnfcantly correlated. By operatng at full economc effcency levels, the sampled provnces would be able to reduce ther costs of agrcultural producton actvtes about 46 to 76 percent, dependng upon the estmaton approach and the assumpton on returns to scale. In other words, there would be a large room for the studed provnces to mprove ther agrcultural producton effcency. The comparson of the estmated results from two approaches shows that they were dfferent, n whch DEA provded hgher estmates than those from SFPF. The dfferences could be attrbuted to varous reasons, such as the choce of nput and output varables, and measurements and specfcaton errors. otes 2 X.Y denotng dot product (or scalar product) for two vectors X = ( x, x2,..., x n ) and Y y y2 y n = (,,..., ). Thus, X. Y = x y. n = In Vetnam, there are eght economc regons: Northeast (Regon ), Northwest (Regon 2), Red Rver Delta (Regon 3), North Central Coast (Regon 4), South Central Coast (Regon 5), Central Hghlands (Regon 6), Southeast (Regon 7), and Mekong Rver Delta (Regon 8). References Agner, D. J.; Lovell, C. A. K; Schmdt, P Formulaton and Estmaton of Stochastc Fronter Producton Models, Journal of Econometrcs, 6, Banker, R. D.; Charnes, A.; Cooper, W. W Some Models for Estmatng Techncal and Scale Ineffcences n Data Envelopment Analyss. Management Scence 30, No. 9, Battese, G.E.; Coell, T. J Fronter Producton Functons, Techncal Effcency, and Panel Data: Wth Applcaton to Paddy Farmers n Inda. Journal of Productvty Analyss, 3, Charnes, A.; Cooper, W. W; Rhodes, E Measurng the Effcency of Decson Makng Unts. European Journal of Operatonal Research 2,

17 2009, Vol 0, o2 78 Coell, T. J. 996a. A Gude to Fronter Verson 4.: A Computer Program for Stochastc Fronter Producton and Cost Functon Estmaton. Center for Economc Productvty Analyss (CEPA) Workng Paper No. 7/96. Unversty of New England, Armdale. Coell, T. J. 996b. A Gude to DEAP Verson 2.: A Data Envelopment Analyss (Computer) Program. Center for Economc Productvty Analyss (CEPA) Workng Paper No. 8/96. Unversty of New England, Armdale. Drake, L. and Weyman-Jones, T.G Productve and Allocatve Ineffcences n UK Buldng Socetes: A Comparson of Non-Parametrc and Stochastc Fronter Technques. The Manchester School, 64, Färe, R.; Grosskopf, S; Lovell, C. A. K The Measurement of Effcency of Producton. Kluwer-Njhoff Publcaton, Boston. Färe, R.; Grosskopf, S; Lovell, C. A. K Producton Fronters. Cambrdge Unversty Press, New York. Farrell, M. J The Measurement of Productve Effcency. Journal of Statstcal Socety, Seres A (General) 20, no. 3, Ferrer, G. D.; Lovell, C. A. K Measurng Cost Effcency n Bankng: Econometrc and Lnear Programmng Evdence. Journal of Econometrcs, Vol. 46, Issues -2, Kalatzandonakes, N. G.; Dunn, E. G Techncal Effcency, Manageral Ablty, and Farmer Educaton n Guatemalan Corn Producton: A Latent Varable Analyss. Agrcultural Resource Economc Revew, 24, Kodde, D. A.; Palm, F. C Wald Crtera for Jontly Testng Equalty and Inequalty Restrctons, Econometrca, 54(5), Kopp, R. J.; Dewert, W. E The Decomposton of Fronter Cost Functon Devatons nto Measures of Techncal and Allocatve Effcency. Journal of Econometrcs, 9, Meeusen, W.; Van de Broeck, J Effcency Estmaton from Cobb-Douglas Producton Functon wth Composed Error. Internatonal Economc Revew, 8, Mnstry of Foregn Affars of Vetnam (MOFA) Nong nghep Vetnam nhung nam gan day (Vetnam s Agrculture n Recent Years). Retreved on February 3, 2007 from Nguyen, K. M.; and Vu, Q. D Non-parametrc Analyss of Techncal, Pure Techncal, and Scale Effcences for the Aquaculture-processng Frms n Vetnam. In Proceedngs of Internatonal Conference on Vetnam Thaland Economc and Development Cooperaton. Natonal Economcs Unversty, Hano. Nguyen K. M A Comparatve Study on Producton Effcency n Manufacturng Industres of Hano and Ho Ch Mnh Ctes. Vetnam Development Forum (VDF) Dscusson Paper, No.3(E). Vetnam Development Forum, Hano. Nguyen, K. M.; and Gang, T. L. (eds.) Techncal Effcency and Productvty Growth n Vetnam: Parametrc and on-parametrc Analyses. The Publshng House of Socal Labour, Hano. Sharma, K. R., P. Leung; and H. M. Zalesk Techncal, Allocatve, and Economc Effcences n Swne Producton n Hawa: A Comparson of Parametrc and Non-parametrc Approaches. Agrcultural Economcs 20(), Shephard, R. W The Theory of Cost and Producton Functons. Prnceton Unversty Press, New Jersey.