Technical Efficiency Analysis of the Milkfish (Chanos chanos) Production in Taiwan - An Application of the Stochastic Frontier Production Function

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1 Techncal Effcency Analyss of the Mlkfsh (Chanos chanos) Producton n Tawan - An Applcaton of the Stochastc Fronter Producton Functon Abstract Chn-Hwa Sun 1, Fu-Sung Chang, and Jn-Mey Yu 3 Mlkfsh has been farmed n Tawan for over 300 years. Faced wth a lmted land resource, the ndustry s lookng at the problem of how to mantan a sustanable and effcent producton. Ths study specfed a stochastc producton fronter functon to estmate potental mlkfsh farm output and effcency by usng data from a survey of 443 aquaculture mlkfsh farms. Both Translog and Cobb-Douglas fronter producton models are estmated usng the maxmum lkelhood estmaton method. Hypothess testng results shows that the Translog stochastc producton functon model fts the data better and the mlkfsh farmng n Tawan already exhbts dmnshng return to scale. Especally, the manageral manager s ablty and the pond producton condtons, whch ndcated by the type of mono/mult-speces cultured, water source, locaton, educaton, and years of experence statstcally sgnfcant capture the neffcency effects whch represent about 90.5% of the producton varaton. A comparson of the estmated maxmum potental mlkfsh producton per hectare under varous pond condtons provde managers how to swtch n nput resources could boost effcency. Keywords: Mlkfsh, Techncal Effcency, Stochastc Fronter Producton Functon, Translog Producton Functon, Cobb-Douglas Producton Functon, Dmnshng Return to Scale 1. Introducton Mlkfsh (Chanos chanos) s Tawan s number two nland aquaculture speces. Producton has grown sgnfcantly over the years and n 001 reached a level of 59,356 M.T. or NT$.53 bllon (US$75 mllon). Ths represents 1% of total volume and 11% of total value of nland aquaculture producton (Tawan Fsheres Yearbook, 00). Mlkfsh n Tawan s produced on about 9,880 hectares scattered over 11 of the 3 countes. 17% of nland aquaculture land s n mlkfsh producton. Tawan has a long hstory of mlkfsh farmng and producton practces have advanced sgnfcantly over tme. Mlkfsh have been grown n Tawan for over 300 years. Through tral and error, farmng practces have evolved that mtgate the challenges mposed by typhoons n summer, severe temperature n wnter and water fluctuatons, and geographc lmtatons. In recent years, Tawanese government has funded much research and worked wth scholars and ndustry to mprove producton technques. In 1978 deep-water pond s culture was fully developed. Successful artfcal fertlzaton trpled productvty n Inventng an automated floatng feedng system n 1983 brought sgnfcant labor savngs and greater proftablty to the ndustry. In 1984, a major breakthrough n artfcally rasng fsh fry overcame a producton bottleneck. In fact ths technology enabled Tawan to become a surplus exporter of fsh fry by All these producton advances have propelled Tawan s mlkfsh aquaculture ndustry to a hghly developed level. However, challenges reman. Mlkfsh farmng n Tawan s easly affected by temperature drops. They cannot sustan temperatures below 10 0 C and wll de. To cope, mlkfsh farmers sometmes hedge ther rsk by growng multple types of fsh together. Water constrants also affect producton. In adaptng, farmers produce mlkfsh both under freshwater and bracksh water condtons. Growng season lmtatons have been addressed by some farmers specalzng n only rearng fsh fry, others focusng on growng out the fry, and others dong the entre producton cycle. Land avalablty constrants are severe n Tawan whch has a populaton of 619 people/sq km. The ndvdual mlkfsh farmer s management ablty also leads to dfferent producton effcences. All these constrants wll be consdered to evaluate where further effcency gans are possble. 1 Professor n the Insttute of Appled Economcs, Natonal Tawan Ocean Unversty, Tawan. Assocate Professor n the Insttute of Appled Economcs, Natonal Tawan Ocean Unversty, Tawan. 3 Specalst n the Fsheres Admnstraton, Councl of Agrculture, Executve Yuan, Tawan. * Correspondng author: Fu-Sung Chang, Insttute of Appled Economcs, Natonal Tawan Ocean Unversty, Pe-Nng Road, Keelung, Tawan 0, R.O.C., , (Fax), e-mal: frank@mal.ntou.edu.tw.

2 Ths study looks at the factors of mlkfsh producton n Tawan and estmates a stochastc fronter producton functon to estmate the maxmum potental mlkfsh output and effcency. Ths study uses aggregate producton nformaton from the Fsheres Yearbook, and a Feld Survey Database ( ) wth nformaton on ndvdual mlkfsh pond culture. We then compute techncal effcency estmates for each mlkfsh farm. Whether the areas of effcency gans that could boost ndustry output and ncrease proftablty to Tawanese mlkfsh farmers?. Research Methodology.1. The Farrell s Fronter Producton Model Accordng to the Neo-Classcal economc theory, all frms are assumed to be fully effcent n ther use of technology so that nput and output prces are the only factors that decde output level. Farrell (1957) proposed a provocatve dea to explan the varablty of frms output levels. He defned the output of the most effcent frm as the producton fronter for all frms. From ths reference pont, Farrell defned two types of effcences, an allocatve effcency whch represents prce effects and a techncal effcency whch represents management effects. The fronter producton functon (FPF) defnes the most effcent potental output level under a fxed amount of factors nput. Techncal effcency means usng gven producton methods at optmal or less than optmal levels. Ager and Chu (1968) used lnear programmng, Tmmer (1971) appled probablty programmng, and Greene (1980) utlzed a revsed least square method to defne a determnstc FPF. If one assumes that all frms have the same techncal nformaton, then they should exhbt a common FPF, whch mples that any dscrepancy n output level relatve to the most effcent frm represents a management neffcency by that frm. The assumpton under the determnstc FPF, that all frms should have the same output from the same amount of nputs s often crtczed as unreasonable. Frms may encounter varous uncontrollable exogenous factors, such as performance of varous machnes, weather condtons, uncertanty of nput supples, etc. To remedy ths, a stochastc fronter producton functon (SFPF) was ndependently proposed by Agner, Lovell and Schmdt (1977) and Meeusen and van den Broeck (1977). Ther specfcaton, whch s for cross-sectonal data, has an error term wth two components, one to account for random effects and another to account for manageral techncal neffcency... Manageral Techncal Ineffcency Model Specfcaton A number of emprcal studes (e.g. Ptt and Lee, 1981) have estmated stochastc fronters and predcted frmlevel effcences usng these estmated functons, and then regressed the predcted effcences upon frmspecfc varables (such as manageral experence, ownershp characterstcs, etc) n an attempt to dentfy some of the reasons for dfferences n predcted effcences between frms n an ndustry. Ths two-stage estmaton procedure has long been recognsed as a useful exercse. However, t s nconsstent n t s assumptons regardng the ndependence of the neffcency effects n the two estmaton stages. The two-stage estmaton procedure s unlkely to provde estmates, whch are as effcent as those that could be obtaned usng a snglestage estmaton procedure. Ths ssue was addressed by Kumbhakar, Ghosh, and McGuckn (1991) and Refschneder and Stevenson (1991) who propose stochastc fronter models n whch the neffcency effects (u ) are expressed as an explct functon of a vector of frm-specfc varables and a random error. Battese and Coell (1995) propose a model, whch s equvalent to the Kumbhakar, Ghosh, and McGuckn (1991) specfcaton, wth the exceptons that allocatve effcency s mposed, the frst-order proft maxmzng condtons removed, and panel data s permtted. The Battese and Coell (1995) model specfcaton may be expressed as: Y = exp(xβ + ε ) = exp(xβ + y u ) ε = v u, = 1,..., N (1) where Y s the producton (or the logarthm of producton 1 ) of the th frm; X s a k 1 vector of nput quanttes of the th frm; β( 1 k) s a vector of unknown parameters; the v s are assumed to be dentcal ndependently dstrbuted (..d.) random errors wth N(0, σ ) and are ndependently dstrbuted of the u s; the u s are assumed v to be non-negatve random varables, assocated wth techncal neffcency of producton, whch are often assumed to be ndependently dstrbuted so that u s are obtaned by truncatng (at zero) the normal or 1 For example, f Y s the log of output and x contans the logs of the nput quanttes, then the Cobb-Douglas producton functon s obtaned. Techncal Effcency Analyss of the Mlkfsh (Chanos chanos) Producton n Tawan - An Applcaton of the Stochastc Fronter Producton Functon PAGE 1

3 exponental dstrbuton wth mean, m, and varance, σ u. The manageral techncal neffcency effect n the stochastc fronter model (1) can be specfed as follows, u = zδ + w () where z s a p 1 vector of varables whch may nfluence the effcency of the th frm; andδ s an 1 p vector of parameters to be estmated. Note that the dstrbuton range of the random errors v s [, + ], the dstrbuton range of the random neffcency factor u s [ 0, + ], and w s a truncated random error ( z δ ). Ths orgnal specfcaton has been used n a vast number of emprcal applcatons over the past two decades. The specfcaton has also been altered and extended n a number of ways. These extensons nclude the specfcaton of more general dstrbutonal assumptons for u, such as the one-sded dstrbuted truncated normal dstrbuton. Agner, Lovell, and Schmdt (1977) expressed the lkelhood functon n terms of two varance parameters, σ σu + σ v and λ σ u / σ v. Ifλ s greater than 1, the varance of the specfed frm neffcency effect (u ) s greater than the stochastc error. We utlze the parameterzaton of Battese and Corra (1977) who replaced σ v and σu wth σ = σ v + σ u and γ = σu /( σ v + σ u ), becauseγ must le between zero and one, whereas the λ -parameter could be any non-negatve value. γ values of zero ndcate that the devatons from the fronter are due entrely to nose, whle γ values of one would ndcate that all devatons are due to techncal neffcences. The parameter values for γ must le between 0 and 1; thus searchng ths range can provde a good startng value for an teratve maxmzaton process such as the Davdon-Fletcher-Powell (DFP) algorthm. The log-lkelhood functon of ths model s presented n the appendx n Battese and Coell (199). The probablty densty functon of v and u under v 0 and u 0 are as follows, 1 1 v g (v σv ) = exp 1 / π σ (3) ( ) σ v v 1 1 u exp > f u 0 h(u σ ) = 1 / u (π) σ σ u u (4) 0 otherwse By assumng v and u are mutually ndependent, the jont PDF of ε s as follows (Wensten, 1964), ε ελ f ( ε σ, λ) = φ( ) 1 Φ( ) σ σ (5) σ where Φ(.) and φ(.) are the cumulatve densty functon and probablty densty functon of the standard normal random varable. λ -parameterzaton has advantages n seekng to obtan the ML estmates because the parameter space for γ can be searched for a sutable startng value n the teratve maxmzaton algorthm. Battese and Corra (1977) showed that the log-lkelhood functon, n terms of ths parameterzaton, s equal to N π π N 1 N ln L = ln log( σ ) + ln[1 Φ( S )] ) 1 1 (ln Y X β (6) = σ = (ln Y ε λ where X β) γ s = =. The ML estmates of β, σ s and γ are obtaned by fndng the σ 1 γ σ maxmum value of the log-lkelhood functon, defned n equaton (6). The ML estmators are consstent and asymptotcally effcent (Agner, Lovell, and Schmdt (1977), p.8). The computer program, FRONTIER Verson 4.1, can be used to obtan the ML estmates for the parameters of ths model. Ths program uses the three-step estmaton procedure that s specfed n Well, Rao, and Battese (1998, p ). Battese and Coell (199) propose a stochastc fronter producton functon for (unbalanced) panel data, whch has frm effects to be dstrbuted as truncated normal random varables, that are also permtted to vary systematcally over tme. Techncal Effcency Analyss of the Mlkfsh (Chanos chanos) Producton n Tawan - An Applcaton of the Stochastc Fronter Producton Functon PAGE

4 .3. Estmaton of Mean Techncal Effcency The mathematcal expectaton (mean) of techncal effcency, TE = exp(-u ), can be calculated, gven certan dstrbutonal assumptons. It can be shown that, f the u s are..d. half-normal random varables, as assumed above, then E[exp( u )] = [1 Φ( σ γ )] exp( γσ / ) (7) By revsng the concept of E(u ε ) proposed by Jondrow, Lovell, Materov and Schmdt (198), Battese and Coell (1988) pont out that the best predcton of exp(-u ) s obtaned by usng γε 1 Φ( σ A + ) σa σ A E[exp(-u ]_ exp( γε + ) (8) γε 1 Φ( ) σ A Where σ A = γ( 1 γ) σ, ε = ln(y ) x β. The rato of the observed output for the th frm, relatve to the * potental output, defned by the fronter functon, Y = exp(x β + v ), gven the nput vector, x, s used to defne the techncal effcency of the th frm: * TE = Y / Y = Y / exp(x β + v ) = exp( u ) = exp( z δ w ) (9).4. Hypothess Tests Because we have adopted the Battese and Corra (1977) parameterzaton, all hypotheses nvolvng γ need to be consdered here. For the Wald test, the rato of the γ estmate over ts estmated standard error s calculated. If H 0 : γ = 0 s true, ths test statstc s asymptotcally dstrbuted as a standard normal random varable. However, the test must be performed as a one-sded test because γ cannot take negatve values. Under the null hypothess, H 0 : γ = 0, the model s equvalent to the tradtonal average response functon, wthout the techncal neffcency effect u. The test statstc s, LR = -{ln{l(h 0 )/L(H 1 )}} = -{ln[l(h 0 )] - ln[l(h 1 )]} ~ χ (10) Where L(H 0 ) and L(H 1 ) are the values of the lkelhood functon under the null and alternatve hypotheses, H 0 and H 1, respectvely. If H 0 s true, ths test statstc s usually assumed to be asymptotcally dstrbuted as a ch-square random varable wth degrees of freedom equal to number of restrctons nvolved (n ths nstance one). However, dffcultes arse n testng H 0 : γ = 0 because γ = 0 les on the boundary of the parameter space for γ. In ths case, f H 0 : γ = 0 s true, the generalzed lkelhood-rato statstc, LR, has an asymptotc dstrbuton whch s a mxture of two ch-square dstrbutons, namely 1 1 χ 0 + χ 1, (Coell, 1995). Accordng to Kodde and Plam (1986), the sgnfcance level of the crtcal value of a mxture of χ dstrbutons s defned as follows, 1 α = Pr[ χ (df 1) c] + Pr[ χ (df ) c] (11) where c s a constant and df are the degrees of freedom. The calculaton of the crtcal value for ths one-sded generalzed lkelhood-rato test of H 0 : γ = 0 versus H 1 : γ > 0 s qute smple. The crtcal value for a test of sze α s equal to the value of χ 1 (α), where ths s the value whch s exceeded by theχ1 random varable wth probablty equal to α. Thus the one-sded generalzed lkelhood-rato test of sze α s Reject H 0 : γ = 0 n favors of H 1 : γ > 0 f LR exceeds χ 1 (α). The crtcal value for a test of sze, α = 0. 05, s.71 rather than The followng hypotheses need to be tested wth generalzed lkelhood-rato tests to ensure that neffcency effects are absent form the model. k Note that χ 0 s the unt mass at zero. 3 The regular (two-sded) generalzed lkelhood-rato test was ncluded n the Monte Carlo experment n Coell (1995) and shown to have ncorrect sze (too small) as expected. Techncal Effcency Analyss of the Mlkfsh (Chanos chanos) Producton n Tawan - An Applcaton of the Stochastc Fronter Producton Functon PAGE 3

5 (1) H 0 : µ = 0, where the null hypothess specfes that a smpler half-normal dstrbuton s an adequate representaton of the data, gven the specfcatons of the generalzed truncated-normal model. Suppose the dstrbuton of the neffcency random factor u s obtaned and t s truncaton at zero wth a normal dstrbuton wth mean µ and varance σ u. The one-sded generalzed lkelhood-rato test, to test the null hypothess that there are no techncal neffcency effects n the half-normal hypothess, can be extended for use n the truncatednormal model. () H : γ = δ = δ =... = δ 0, the null hypothess specfes that neffcency effects are absent p = from the model at every level; (3) H 0 : γ = 0, the null hypothess specfes that the neffcency effects are not stochastc; and (4) H : δ = δ =... = δ 0, the null hypothess specfes that the neffcency effects are not a lnear 0 1 p = functon of each of the neffcency factors. 3. Emprcal Model Specfcaton 3.1. Data Source and Varable Defnton The Economc Survey database of 433 Offshore and Aquaculture Fshermen n Tawan s used n ths study. The nput cost and output revenue data for the varous classes of mlkfsh farmng ponds n four dfferent countes n the southern Tawan were obtaned from the database released by the Annual Economc Survey of Offshore Fsheres and Aquaculture (Tawan Fsheres Bureau, ). For the purpose of ths study, mlkfsh fshermen are defned as those who derve at least 60% of ther ncome from the sale of mlkfsh. Mlkfsh producton occurs prmarly n Chay, Tanan, and Kaohsung countes. The average nput costs for the ndustry fall roughly nto these categores: fry 17%, feed 51%, water, electrcty and fuel 13%, and other mscellaneous cost 0%. Ths study specfes the Translog SFPF for Tawan s mlkfsh ndustry as follows, lny = β 0 + β j lnx j + β jk lnx j lnx k + v u (1) j = 1 j k k = 1 where, represent the th mlkfsh farmer for = 1,,, 443 and X j represents the amount of nput j used by the th mlkfsh farmer. See Table 1 for nput defntons. If the β jk = 0 n equaton (1), then the model reduces to the Cobb-Douglas (C-D) SFPF model wth constant returns to scale as follows, 5 lny = β 0 + β j lnx j + v u (13) j = 1 The estmated parameters β 1, β,..., β5 n the above equaton (13) represent the output elastctes of the correspondng nputs, and the sum of these parameters equals the estmated output elastcty. Output elastcty, whch measures returns to scale, s defned as the percentage change of output for a 1% ncrease n all nput factors. For the output elastcty greater than one, there are ncreasng returns to scale for the ndustry. Suppose the techncal neffcency of each mlkfsh farmer depends on the manager s ablty and the pond producton condtons and the manageral techncal neffcency u for each ndvdual mlkfsh farm s specfed n equaton (14) as follows, u = δ0 + δ1 Y98 + δ Y99 + δ3 MONO + δ4 FRESH + δ5 CHIAYI + δ6 TAINAN1 + δ7 SCALE _ 1 + δ8 SCALE _ 3 + δ9 EDUMONO + δ10 EDUHIGH + δ11 EXP + δ1 LABOR (14) The mlkfsh farmer s educaton and the years of producton experence are used to represent the management ablty. Pond sze, monoculture status, water source, county dummes, number of employees, and two yearly dummy varables, whch are all used to represent the pond producton condtons, are also ncluded to account for dfferences n effcency across varous mlkfsh farmers n dfferent years. 3.. Producton Elastcty, Substtuton Elastcty, and Return to Scale For each nput factor X j (j = 1,,..., 5), there s a correspondng output elastcty, whch s defned as the percentage change of th mlkfsh farm s output for a 1% ncrease n the j th nput factors whch s defned as EX j Techncal Effcency Analyss of the Mlkfsh (Chanos chanos) Producton n Tawan - An Applcaton of the Stochastc Fronter Producton Functon PAGE 4

6 and s defned as follows, EX = β + β ln X + β ln X (15) j j jj j k j jk j Under the Translog SFPF specfcaton, the output elastcty for each nput of varous mlkfsh farms actually dependents on the relatve nput levels used by varous mlkfsh farmers. If β jk = 0, the SFPF reduces to a C-D SFPF, the output elastcty for the jth nput s defned as β j, represent the output elastctes of the correspondng nputs, and the sum of these parameters equals the estmated returns to scale. Suppose the nput-output relatonshps of Tawan s mlkfsh ndustry are measured under fnancally proftable condtons, then all output elastctes for each of the nput factors should be postve. Hck s eleastcty of complementarty (HEC) under the Translog SFPF for each mlkfsh farm can be defned as follows, j j H jj = ( β jj + EX EX j ) / EX (16) The cross substtuton elastcty for factors j and k s defned as follows, H jk = ( β jk + EX j EXk ) /(EX j EX k ) (17) Snce EX j s dfferent for each mlkfsh farmer, ths study replaces EX j wth the sample mean for the ndustry EX j. A postve HEC value now mples that the factors j and k are jontly complementary. 4. Estmaton Results 4.1. Parameter Estmates Table shows the SFPF estmaton results for Tawan s mlkfsh ndustry, usng a C-D producton model. The hghest output elastcty s for feed, 0.39, mplyng that a 1% ncrease of feed nput wll ncrease producton by 0.39%. The other output elastctes are 0.16% for Acreage, 0.14% for Water and Electrcty, 0.11% for Fry cost, and 0.09% for Other Costs. The sum of all output elastctes s 0.9, ndcatng that on average the ndustry has dmnshng returns to scale. Put another way, f the ndustry ncreases all factor nputs by 1%, mlkfsh output would ncrease by only 0.9%, whch s clearly not a sensble economc decson. The estmaton results of the Translog producton functon are also reported n Table. The output elastcty s agan hghest for Food (- 0.51%). Output elastctes of Water and Electrcty, Acreage, Fry Cost, and Other mscellaneous nputs, are 0.13%, 0.1%, 0.1%, and 0.03% respectvely, so that the return to scale s 0.9. Comparng the output elastctes between the C-D and Translog specfcatons, there appears lttle dfference except that the output elastcty of the Feed cost. Under both specfcatons the sum of all output elastctes s around 0.90, whch ndcates dmnshng returns to scale. Under the Translog SFPF specfcaton, the error term for the techncal effcency λ σu / σ s 3.093, whch V shows that the varance of the frm specfc error term s bgger than the varance of the stochastc error term. More specfcally, snce γ = σ u /( σ v + σ u ) = , our estmaton shows that 90.5% of the producton varaton from the SFPF s due to manageral neffcency. Furthermore, the results from both models show that the manageral techncal neffcency ( σ ) s greater than the neffcency caused by stochastc factors ( σ ). 4.. Testng for Model Specfcaton u A lkelhood rato test was conducted to test the null hypothess that the Translog SFPF can be reduced to a C-D SFPF. The test result statstc, as shown n Table 3: H : β = 0, H : β 0, has a lkelhood rato value of 0 jk 1 jk 89.8, whch mples a rejecton of the null hypothess at the 5% sgnfcance level,.e., the Translog SFPF s more sutable to the mlkfsh farm survey data and the substtuton elastctes for the varous nput factors are statstcally dfferent. Olson, Schmdt, and Waldman (1980), and Huang and Bag (1984) found that estmates of techncal effcency depend on the specfed functonal form. For example, both Kopp and Smth (1980) and Schmdt (1986) found the estmates of techncal effcency under a stochastc Translog functonal form are much hgher than the estmates of techncal effcency under a stochastc C-D functonal form. Consequently the remander of ths paper uses the Translog SFPF specfcaton to derve conclusons from Testng Manageral Techncal Ineffcency Assumptons (1) The frst techncal assumpton to be tested s that the neffcency factor error term u has a sem-normal v Techncal Effcency Analyss of the Mlkfsh (Chanos chanos) Producton n Tawan - An Applcaton of the Stochastc Fronter Producton Functon PAGE 5

7 dstrbuton wthµ = The test statstc for H 0 : µ = 0 s 9.7 whch leads to a rejecton of the null hypothess and mples that µ has a truncated normal dstrbuton. () The next hypothess tests the exstence of the neffcency factor. If H 0 : γ = δ0 = δ1 =... = δ1 = 0 s accepted then there s no neffcency n the ndustry. However, a sgnfcant lkelhood raton test value of 66 rejects H o and mples the exstence of neffcency across the mlkfsh ndustry. Conceptually, there exsts stochastc manageral neffcency,.e., wrong allocaton amount of resources. (3) The next hypothess tests for the presence of stochastc neffcency. The null hypothess s that H 0 : γ = 0,.e., the stochastc neffcency ( σ u ) s not exst. The test result rejects H o, mplyng that the tradtonal average response functon f not an adequate representaton of the data. (4) The last hypothess test establshes f the exstence of neffcency sgnfcantly affected techncal effcency. The null hypothess H 0 : δ 1 = δ =... = δ1 = 0 s rejected wth a test value of 46. Rejecton of the null hypothess mples that stochastc fronter model s sgnfcantly dfferent from the determnstc fronter model wth no random error sgnfcant techncal neffcency exsts. The lower half of Table shows the manageral neffcences where the negatve parameter values ndcatng greater effcency. The statstcally sgnfcant varables of the Translog SFPF affectng effcency are Year (Y98, Y99), mono/mult-speces cultured type (MONO), Water Source (FRESH), County (CHIAYI, TAINAN), Educaton (EDUNONE, EDUHIGH), Years of Experence (EXP) and Fxed Labor (LABOR). Postve parameter estmates ndcate relatve techncal neffcency whle negatve parameter estmates pont out relatve techncal effcency. The more the estmated value dffers from zero, the stronger ths effcency/neffcency. Consderng each of the parameter estmates provdes some nterestng nsghts. Effcency appears to vary from year to year. In 1998 ( δ 1 = 1.195) fshermen s techncal effcency was greater than durng the base year However, n 1999 when Y99 had a parameter value of δ s 0.441, producton was less effcent than n It s nterestng to know that the mlkfsh producton facng a bottleneck of mprovng ts effcency n The MONO varable whch measures f there s only one fsh speces or f there are multple speces rased on each mlkfsh farm, has a parameter value of δ 3 = Ths mples that specalzed mlkfsh farms tend to be more effcent than mlkfsh farms growng several types of fsh. Note that MONO has the greatest parameter estmate, ndcatng that the crtera whether to farm one or more types of fsh has a greater mpact on effcency than any other nput factor. The type of water used n producton s also statstcally sgnfcant. FRESH has a parameter value of δ 4 = and suggests that the mlkfsh farms operated n bracksh water shows a better technology than the mlkfsh farms operated n fresh water. The county n whch producton occurs s another sgnfcant varable. CHIAYI and TAINAN have parameter estmates of δ 5 = and δ 6 = 1. 9 to ndcate that mlkfsh farmer n KOAHSIUNG are relatvely more effcent. The area under producton tends not to mpact effcency. However, educaton affects effcency wth the least educated mlkfsh farmers beng more effcent whch mples more educated mlkfsh farmers may not are effcent than those less educated mlkfsh farmers. Smlarly odd s that more experenced mlkfsh farmers/managers are less effcent than farmers wth fewer years n producton. The new farmers wth progressve producton practces may enter the ndustry and mplementng effcent changes n producton practces and some of the older farmers stay n producton even though they are neffcent because they are nearng retrement and have few alternatve employment optons. Also nterestng s that farms wth more labor are less effcent. Ths suggests that small owner operators are more motvated than ther hred employees. Table 4 breaks down techncal effcency by county, type of water supply, mono/mult-speces cultured and water depth. All of the monoculture producton s more effcent than spreadng resources over several speces. The hghest techncal effcency s found for the deep bracksh water monoculture ponds n Kaohsung (0.9), followed by Chay (0.91) and then Tanan (0.89). Agan the techncal effcency n the deep freshwater monoculture pond n Kaohsung (0.91) s also hgher than Chay (0.86) and Tanan (0.69). The result s the same as shown n Table for both Chay and Tanan are neffcent than Kaohsung. Hcks complementary elastcty estmates for mlkfsh farms usng a Translog SFPF are shown n Table 5. Negatve complementary elastcty estmates, such as for Acreage-Fry Cost, Acreage-Other Costs, Fry Cost-Feed Techncal Effcency Analyss of the Mlkfsh (Chanos chanos) Producton n Tawan - An Applcaton of the Stochastc Fronter Producton Functon PAGE 6

8 Cost, Fry Cost-Other Costs, Feed Cost-Water & Electrcty, and Water & Electrcty-Other Costs mply that these two nput categores need to be rased or lowered together. For example, f producton ncreases are to be acheved by ncreasng Acreage, then the Fry Cost and Other Costs wll also ncrease. Lkewse, f a rse n producton s to be acheved by stockng the ponds wth more Fry then Feed costs and Other Costs wll also ncrease. Postve complementary elastctes mply that a gven output can be mantaned by swtchng nputs between the two resources. For example, f Acreage s ncreased, Feed Costs would drop whle total output and the other varables reman constant Estmates of Techncal Effcency A scatter dagram (Fgure 1) shows the relatonshp between estmated potental output Y * and the actual output Y. Let techncal effcency be defned as TE =Y /Y *, and any pont along the 45 0 dagonal s perfectly effcent. The more dstant a pont (farm) from the dagonal, the less effcent the farm. The 0-50 M.T. group has 4 bad outlers but the rest of the group seems to be closer to the dagonal than the bggest produces. Techncal neffcency seems to be more apparent for these 4 bad mlkfsh farms wth output levels between 0 to 50 M.T. Usng the Translog SFPF TE across all mlkfsh farms s estmated to be at The most effcent mlkfsh farm has a TE of 0.96 whle the less effcent mlkfsh farm has TE of The medan TE s The best 36% of mlkfsh farms have TE s between , another 43% of mlkfsh farms have TE s between , 11% have TE s between and 10% have TE s below Estmates of Maxmum Potental Output Farmers and government offcals may fnd t useful to compare mlkfsh aquaculture farms by potental output. Snce the locatons where the mlkfsh farm set-up dctate certan constrants, farms are separated by these and other nput factors n Table 6. Notce that the average maxmum potental mlkfsh output for the perod s estmated at 9.8 M.T., whch compares to an actual output of 8.3 M.T. The maxmum potental output s 18% above actual producton. Output under a monoculture regme output could possbly ncrease to 10.8 M.T./ha or 11%, whle output on farms that produce a varety of speces could potentally ncrease to 8.6 M.T./ha or by 9%. Clearly such dramatc ncreases can only be acheved f the producton logstcs are feasble. Mlkfsh farms usng fresh and bracksh water should be able to ncrease ther output to 1 M.T. and 8.5 M.T. or by 15% and 0% respectvely. Producton gans should be greater n Kaoshung county and greatest for the largest mlkfsh farms. 5. Concludng Remarks Faced wth a lmted land resource, Tawanese mlkfsh farmers need to be lookng at ncreasng effcency to rase ther producton levels. Ths study specfes a stochastc translog fronter producton functon to estmate potental mlkfsh farm output and producton effcency. Usng data from 433 mlkfsh farms gathered between , ths study detals how to determne possble potental yelds for the ndustry and under dfferent producton constrants. Especally, the manageral manager s ablty and the pond producton condtons, whch ndcated by the type of mono/mult-speces cultured, water source, locaton, educaton, and years of experence statstcally sgnfcant capture the neffcency effects whch represent about 90.5% of the producton varaton,.e., the manageral techncal neffcency actually hampers producton. Hypothess testng results shows that the translog stochastc fronter producton functon model fts the data better and the mlkfsh farmng n Tawan already exhbts dmnshng returns to scale,.e. the output wouldn t ncrease as much as we ncrease the major nput factors. Hence, ths study also documents the cross-elastcty estmates to provde gudance where mlkfsh farmers should shft nput resources to acheve producton gans. The estmates of maxmum potental yeld ndcate that about 80% of all mlkfsh farms reach a techncal effcency level of 0.8. Average techncal effcency s 0.8. By elmnatng the techncal neffcency, the producton per hectare could ncrease by 18% or the maxmum output could reach 9.8 M.T. per hectare n average. In addton, a comparson of the estmated maxmum potental mlkfsh producton per hectare under varous pond condtons could provde managers about how to swtch n nput resources could boost effcency. Techncal Effcency Analyss of the Mlkfsh (Chanos chanos) Producton n Tawan - An Applcaton of the Stochastc Fronter Producton Functon PAGE 7

9 References Ager, D.J. and S.F. Chu On Estmatng the Industry Producton Functon. Amercan Economc Revew. 58(4), Ager, D.J., C.A.K. Lovell and P. Schmdt Formulaton and Estmaton of Stochastc Fronter Producton Models. Journal of Econometrcs. 6, Battese, G.E., and G.S. Corra Estmaton of a Producton Fronter Model: wth Applcaton to the Pastoral Zone of Eastern Australa. Australan Journal of Agrcultural Economcs. 1, Battese, G.E., and T.J. Coell Predcton of Frm-Level Techncal Effcences Wth a Generalzed Fronter Producton Functon and Panel Data. Journal of Econometrcs. 38, Battese, G.E., and T.J. Coell Fronter Producton Functons, Techncal Effcency and Panel Data: Wth Applcaton to Paddy Farmers n Inda. Journal of Productvty Analyss. 3, Battese, G.E. and T.J. Coell A Stochastc Fronter Producton Functon Incorporatng a Model for Techncal Ineffcency Effects. Workng Papers n Econometrcs and Appled Statstcs. 69, Department of Economcs, Unversty of New England, Armdale, Australa. Battese, G.E. and T.J. Coell A Model for Techncal Ineffcency Effects n a Stochastc Fronter Producton Functon for Panel data. Emprcal Economcs. 0, Coell, T.J Estmators and Hypothess Tests for a Stochastc Fronter Functon: A Monte Carlo Analyss. Journal of Productvty Analyss. 6, Coell, T., P.D.S. Rao, and G.E. Battese An Introducton to Effcency and Productvty Analyss. Kluwer Academc Publshers, Boston/Dordrecht/London. Farrel, M.J The Measurement of Productve Effcency. Journal of the Royal Statstcal Socety. 10 (Part 3), Greene, W.H Maxmum Lkelhood Estmaton of Econometrc Fronter Functons. Journal of Econometrcs. 13(1), Huang, C. and F.S. Bag Techncal Effcency on Indvdual Farms n Northwest Inda. Southern Economc Journal. 51(1), Jondrow, J., C.A.K. Lovell, I.S. Materov, and P. Schmdt On the Estmaton of Techncal Ineffcency n the Stochastc Fronter Producton Functon Model. Journal of Econometrcs. 19, Kodde, D.A. and F.C. Palm Wald Crtera for Jontly Testng Equalty and Inequalty Restrctons. Econometrca. 54, Kopp, R.J. and V.K. Smth Fronter Producton Functon Estmates for Steam Electrc Generaton: A Comparatve Analyss. Southern Economc Journal. 46(4), Kumbhakar, S.C., S. Ghosh, and J.T. McGuckn A Generalzed Producton Fronter Approach for Estmatng Determnants of Ineffcency n U.S. Dary Farms. Journal of Busness and Economc Statstcs. 9, Meeusen, W. and J. van den Broek Effcency Estmaton From Cobb-Douglas Producton Functon wth Composed Error. Internatonal Economc Revew. 18, Olesen, J.A., P. Schmdt, and D.M. Waldman A Monte Carlo Study of Estmators of Stochastc Fronter Producton Functon. Journal of Econometrcs. 13, Ptt, M.M. and M-F. Lee Measurement and Sources of Techncal Ineffcency Vewpont n the Indonesan Weavng Industry. Journal of Development Economcs. 9, Refschneder, D. and R. Stevenson Systematc Departures from the Fronter: A Framework for the Analyss of Frm Ineffcency. Internatonal Economc Revew. 3, Schmdt, P Fronter Producton Functons. Econometrcs Revew. 4, Tawan Fsheres Bureau Fsheres Yearbook n Tawan Area. Fsheres Admnstraton, Councl of Agrculture, Tawan: Republc of Chna. Varous Issues Annual Economcs Survey of Offshore Fsheres and Aquaculture n Tawan. Department of Agrculture and Forestry, Tawan: Republc of Chna. Tmmer, C.P Usng a Probablstc Fronter Functon to Measure Techncal Effcency. Journal of Poltcal Economy. 79, Techncal Effcency Analyss of the Mlkfsh (Chanos chanos) Producton n Tawan - An Applcaton of the Stochastc Fronter Producton Functon PAGE 8

10 Table 1. Varable Defntons and Measurement Unts for the Emprcal Model Varable Defntons Unt Y Mlkfsh producton quantty of the th farm. M.T. X 1 Pond hectares of the th farm, representng the level of captal nvestment. Hectares X Fry cost of the th farm. NT$1,000 X 3 Feed cost of the th farm. NT$1,000 X 4 Water, electrcty and ol costs of the th farm. NT$1,000 X 5 Other mscellaneous costs, ncludng part-tme labor, medcne, pond mantenance fee, equpment mantenance fee, rent, nsurance, transportaton NT$1,000 cost. X 6 Multculture rato of the mlkfsh producton value. Y98 Y98 = 1, for farm survey data collected n 1998; otherwse Y98 = 0. Y99 Y99 = 1 for farm survey data collected n 1999; otherwse Y99 = 0. MONO MONO = 1 f the farm s a monoculture farm; MONO=0 f more than one speces s produced. FRESH FRESH = 1 f the water source of the pond s fresh water, otherwse FRESH=0. CHIAYI CHIAYI = 1 f the th mlkfsh farm s located n Chay county; otherwse CHIAYI=0. TAINAN TAINAN = 1 f the th mlkfsh farm s located n Tanan county; otherwse TAINAN=0. SCALE_1 SCALE_1 = 1 f the th mlkfsh farm s pond sze s under one hectare; otherwse SCALE_1=0. SCALE_3 SCALE_3 = 1 f the th mlkfsh farm s pond sze s 1 to 3 hectare; otherwse SCALE_3=0. EDUNONE EDUNONE = 1 f the manager s not able to read; otherwse EDUNONE=0. EDUHIGH EDUHIGH = 1 f the manager s educaton s above senor hgh school level; otherwse EDUHIGH =0. EXP Years of experence Years LABOR Number of hred employees, ncludng famly members. Persons Techncal Effcency Analyss of the Mlkfsh (Chanos chanos) Producton n Tawan - An Applcaton of the Stochastc Fronter Producton Functon PAGE 9

11 Table. Estmaton Results Output Elastctes and Techncal Ineffcences Cobb-Douglas Producton functon Translog Producton Functon Item Parameter t Value Parameter t Value Output Elastcty Acreage (X 1 ) EX EX Fry Cost (X ) EX EX 0.1 Feed Cost (X 3 ) EX EX Water & Electr._X 4 _ EX EX Other Costs (X 5 ) EX EX Return to Scale RTS 0.90 Techncal Ineffcency factors RTS SSS Y98 δ δ1 Y99 δ δ MONO δ δ3 FRESH δ δ4 CHIAYI δ δ5 TAINAN δ δ6 SCALE_1 δ δ7 SCALE_3 δ δ8 EDUNONE δ δ9 EDUHIGH δ _ 1.76 δ10 EXP δ δ11 LABOR δ δ1 σ σ γ γ _ σ v 0.07 σ u 0.17 λ 1.63 λ 3.09 Note: t-values are n the parentheses. ***, **, and * represents sgnfcance at the 1%, 5%, and 10% level respectvely. σ v σ u Techncal Effcency Analyss of the Mlkfsh (Chanos chanos) Producton n Tawan - An Applcaton of the Stochastc Fronter Producton Functon PAGE 10

12 Table 3. Hypothess Tests for Model Specfcaton and Statstcal Assumptons Item and H 0 H (1) H 0 1 : β : β jk jk = 0 = 0 Lkelhood Value of the Reduced Model Lkelhood Value of the Full Model * 05 χ 0. Lkelhood Mxture Rato Test (LR) Crtcal Value Degrees of Freedom Concluson Reject H 0 () H 0 : µ = Reject H 0 H0 : γ = δ0 = δ (3) =... = δ = Reject H 0 (4) H 0 : γ = Reject H 0 H 0 : δ1 = δ (5) =... = δ = Reject H 0 _ χ s obtaned from Davd A. Kodde and Franz C. Plam, Econometrca, Vol. 54, No.5, p.146. Table 4. Techncal Effcences of Mlkfsh Farms by County, Water Type, Number of Speces Produced and Water Depth Deep Freshwater Pond Bracksh Water Pond County Monoculture Multculture Deep Pond Shallow Pond Monoculture Multculture Monoculture Multculture Chay Tanan Kaohsung Table 5. Hcks Complementary Elastctes for Inputs used n Mlkfsh Producton Item Substtute Elastcty Acreage - Fry Cost H Acreage - Feed Cost H Acreage - Water & Electrcty H Acreage - Other Cost H Fry-Cost - Feed Cost H Fry-Cost - Water and Electrcty H Fry-Cost - Other Cost H Feed Cost - Water & Electrcty H Feed Cost - Other Cost H Water & Electrcty - Other Cost H Techncal Effcency Analyss of the Mlkfsh (Chanos chanos) Producton n Tawan - An Applcaton of the Stochastc Fronter Producton Functon PAGE 11

13 Table 6. Percentage Incensement of Mlkfsh Farm Output f there were no Techncal Ineffcency Percentage of mlkfsh farm output n crease f there were no techncal neffcency (%) Total Maxmum Mlkfsh Farm Output per Hectare wthout Techncal Ineffcency (MT) (MT) (MT) (MT) All Knd of Mlkfsh Farms Mono/Mult-Speces Cultured Pond Monoculture Mult-Speces Water Source Freshwater Blacksh County Chay Tanan Kaohsung Scale Under 1ha ha Above 3 ha All Knd of Aquafarms 0% 10% 6% 18% Monoculture 1% 9% 14% 11% Mxed Speces 3% 1% 36% 9% Water Source Freshwater 13% 10% 3% 15% Blacksh 6% 10% 30% 0% County Chay % 15% 13% 18% Tanan 17% 10% 4% % Kaohsung 1% 8% 9% 14% Scale Under 1ha. 1% 9% 9% 10% 1-3 ha. 14% 10% 3% 17% Above 3 ha. 30% 1% 7% 5% Techncal Effcency Analyss of the Mlkfsh (Chanos chanos) Producton n Tawan - An Applcaton of the Stochastc Fronter Producton Functon PAGE 1

14 Expected Output Y* (MT) Actual Output Y (MT) Fgure 1. Scatter Dagram of the Relatonshp between Potental Ou and Actual Output for all Mlkfsh Farmers n Tawan ( Techncal Effcency Analyss of the Mlkfsh (Chanos chanos) Producton n Tawan - An Applcaton of the Stochastc Fronter Producton Functon PAGE 13