Application of Stochastic Frontier Production Function on Small Banana Growers of Kushtia District in Bangladesh

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1 J. Stat. Appl. Pro. 4, No., (015) 337 Journal of Statstcs Applcatons & Probablty An Internatonal Journal Applcaton of Stochastc Fronter Producton Functon on Small Banana Growers of Kushta Dstrct n Bangladesh Md. Moyazzem Hossan 1,*, Md. Asraful Alam 1 and Md. Kamal Uddn. 1 Department of Statstcs, Jahangrnagar Unversty, Savar, Dhaka-134, Bangladesh Department of Statstcs, Islamc Unversty, Kushta-7003, Bangladesh Receved: 13 Jan. 015, Revsed: 15 Mar. 015, Accepted: 19 Mar. 015 Publshed onlne: 1 Jul. 015 Abstract: Agrcultural productvty vares due to dfferences n producton technology, dfferences n the settng n whch producton occurs and dfferences n the effcency of the producton process. Effcency measurement has been the concern of researches wth an am to nvestgate the effcency levels of farmers engaged n agrcultural actvtes. Identfyng determnants of effcency levels s a major task n effcency analyss. Moreover, estmates on the extent and sources of neffcences could help mprove the effcency or develop new technology to rase the banana productvty. Thus the man objectve of ths paper s to estmate the effcency of the small banana grower n Kushta dstrct of Bangladesh. In ths study, econometrc fronter models were estmated under the specfcaton of the Cobb- Doulas producton functon model. Prmary data for ths study were collected by the use of well structured questonnare. Among the elastctes, the elastcty for land used for banana producton s the largest (0.3498). The second largest elastcty s cost on fertlzer whch s and the elastcty for the cost on labor s lowest (0.0495). From the results of the study, t s revealed that age and educaton level of the farmers has a postve effect on techncal effcency. Ths paper recommend that the Government should take an effectve step to control the prce system and prce spread of the market and make sure that the producers can get ther reasonable prce and also the consumer can also get the product n a reasonable prce. Government also should take necessary steps to mprove the knowledge of a farmer to the modern cultvaton technque and encouraged them to adopt the new technology to ncrease the producton. Keywords: Banana, Stochastc Fronter, Effcency, Bangladesh 1. Introducton: Banana (Musa paradsaca, famly Musaceae) s a central frut crop of the tropcal and subtropcal regons of the world grown on about 8.8 mllon hectares [1]. It s possbly the world's oldest cultvated crop []. Farmers n Southeast Asa and Papua New Gunea frst domestcated bananas. Recent archaeologcal and palaeoenvronmental evdence at Kuk Swamp n the estern Hghlands Provnce of Papua New Gunea suggests that banana cultvaton there goes back to at least 5000 BCE, and possbly to 8000 BCE [3]. It s lkely that other speces were later and ndependently domestcated elsewhere n Southeast Asa. Southeast Asa s the regon of prmary dversty of the banana. Areas of secondary dversty are found n Afrca, ndcatng a long hstory of banana cultvaton n the regon [4]. The banana frut s varable n sze, color and frmness, but s usually elongated and curved, wth soft flesh rch n starch covered wth a rnd whch may be green, yellow, red, purple, or brown when rpe. The fruts grow n clusters hangng from the top of the plant. As a det, banana s an affluent source of carbohydrate wth calorfc value of 67 calores per 100g frut and s one of the most well-lked and wdely traded fruts across the world [5, ]. Banana s manly cultvated for t s rpen fruts, cooked vegetables and leaves n Inda and many other countres ncludng Bangladesh [6]. It s the second largest produced frut after ctrus, contrbutng about 16% of the world s total frut producton [7]. Banana s hghly nutrtous [8] and s more easly dgestble than many other fruts ncludng apple [1]. Banana s a very popular frut and cultvated almost everywhere n Bangladesh round the year. However, the foremost banana growng areas are Rangamat, Barsal, Rangpur, Dnajpur, Noakhal, Fardpur, Tangal, Kushta and Khulna. Total producton of banana n Bangladesh was metrc tons n an area of acres whereas n Kushta the total producton of banana was metrc tons n an area of 86 acres n [9]. Also n * Correspondng author e-mal: mmhmm.justat@gmal.com 015 NSP

2 338 Md. M. Hossan et. al.: Applcaton of Stochastc Fronter Bangladesh, several studes have been conducted to analyze the banana producton [10, 11, 1, 13, 14, 15, 16, 17, 18]. Producton functons are wdely used to analyze effcency n terms of output for a gven level of nputs. In most mcroeconomc analyses, producton functons are estmated under the assumpton that producers are ratonal proft maxmzers that operate on ther producton fronters. However, Farrell [19], Agner et al. [0], Meeusen and Van den Broeck [1], and Battese and Coell [] support the vew that producers dffer n the measured output that they produce from a gven bundle of measured nput, or, alternatvely, n the nput requrements to produce a gven output. Stochastc fronter analyss (SFA) acknowledges such effcency dfferences among farmers. Producers operatng on ther producton fronter are referred to as techncally effcent and producers operatng below that fronter are called techncally neffcent. Stochastc fronter producton functons have been used extensvely n the past two decades to analyze techncal effcency. Bangladesh has long hstory of producng almost all agrcultural crops. Although farm households produce almost all agrcultural crops as they need, some regons n Bangladesh are advantageous or domnant to produce certan crops than other regons. Farm households n these regons are producng those crops whch are envronmental frendly and ensure more ncome or proft to them. But farm households are not strct to certan crops; they are always tryng to produce new crops whch ensure them promsng ncome. Thus land use patterns have been changng over the years [3]. In vew of the slow growth and ncreasng nstablty n producton, the banana producton of Kushta dstrct could be beneftted to a great deal from ts neffcency studes. Effcency measurement has been the concern of researches wth an am to nvestgate the effcency levels of farmers engaged n agrcultural actvtes. Identfyng determnants of effcency levels s a major task n effcency analyss. Thus, the man objectve of ths paper s to estmate the effcency of the small banana grower n Kushta dstrct of Bangladesh wth the help of Cobb-Douglas type stochastc fronter producton functon. Moreover, estmates on the extent and sources of neffcences could help mprove the effcency or develop new technology to rase the banana productvty n Kushta dstrct. Ths necesstates effcency analyss of the small banana grower across dfferent regons of the Kushta dstrct, whch n turn, wll help n formulatng the polcy measures to mtgate varous constrants n the banana producton of Bangladesh, partcularly n Kushta dstrct. The study n hand s orented towards the goal of achevng hgher productvty by mprovng techncal effcency of the banana farmers n Kushta dstrct of Bangladesh. The present paper s organzed as follows. After ths ntroducton Secton descrbes the methodology whch ncludes sample sze and samplng methods, Stochastc Fronter & Effcency measurements and models & varables. In Secton 3 we dscuss the results obtaned n ths study. Fnally, Secton 4 makes concluson of ths research. Methodology.1 Sample Sze and Samplng Methods: Ths s a feld study research whch has been made on the bass of a survey. A well structured questonnare has been developed after an ntensve revew of the lterature and practcal experence. The target populaton of the study s the small banana growers of Islamc Unversty thana of Kushta dstrct n Bangladesh. Purposvely we select the target area. The sample unt of ths study s the ndvdual farmer (small banana grower). The sample sze s 00 farmers. z pq The sample sze s determned by the formula, n, where n the desred sample sze, z the standard normal d devate, p the proporton n the target populaton estmated to cultvate the banana, q 1 p and d degree of accuracy desred (precson level of the estmate). From a plot survey of the target area we estmate as p We also consder z for 90% confdence level and d By usng these nformaton, we have, n Non-probablty convenence samplng procedure has been used to collect prmary data from small farmers who cultvate banana less than two acres of land. Research was conducted n 10 vllages from the Islamc Unversty thana of Kushta dstrct and ntervewed 0 farmers form each vllage. Data collecton was conducted on June-July of 014. Collected data was analyzed by IBM SPSS and FRONTIER Stochastc Fronters and Effcency Measurement: The measurement of the effcency of producton has been an mportant area of research over the last two decades. For ths purpose stochastc fronter producton functon has been used. Coell [4] observed that thrty out of forty studes on applcaton of fronter models to agrculture have used stochastc fronter producton functon. The advantage of usng stochastc fronter models are: (1) It ntroduces a dsturbance term representng statstcal nose, measurement error and exogenous shocks beyond the control of producton unts whch would other-wse be attrbuted to techncal neffcency, () It provdes the bass for conductng statstcal tests of hypothess regardng the producton structure and the degree of neffcency. The estmaton of fronter functon and effcency can be completed ether n one stage or n two stages. The two-stage analyss of explanng levels of techncal effcency (or neffcency) was crtczed by Battese and Coell [] as beng contradctory, n the assumptons made n the separate stages of the analyss. In ths 015 NSP

3 J. Stat. Appl. Pro. 4, No., (015) / paper, we follow the Battese and Coell [] approach of modelng both the stochastc and the techncal neffcency effects n the fronter, n terms of observable varables, and estmatng all parameters by the method of maxmum lkelhood, n a sngle-step analyss..3 Model and Varables: The study used the prmary data whch were collected from 00 small banana growers of Islamc Unversty thana of Kushta dstrct n Bangladesh. The Cobb-Douglas (CD) producton functon was found to be an adequate representaton of the data, gven the specfcatons of the correspondng translog fronter model. The stochastc fronter model s defned by: ln Y ln X ln X ln X ln X ln X ln X V U (1) Where ln represents the natural logarthm (base, e); the subscrpt, denotes the -th farmer n the sample, 1,,3,...,00 ; Banana producton, Y represents the total banana producton (n Taka, note that Taka s the currency of Bangladesh) for the farmer; banana area X 1 represents the total area of banana (n bgha, 1 acres=3bgha); cost on seed X represent the total cost for seed to produce sngle tme banana (n Taka); cost on labor X 3 represent the total cost for labor to produce sngle tme banana (n Taka); cost on rrgaton X 4 represents the cost of rrgaton water appled to produce sngle tme banana (n Taka); cost on fertlzer X 5 represents the cost on fertlzer appled to produce sngle tme banana (n Taka); cost on transport X represents the cost on transportaton for marketng the banana produced sngle tme (n Taka), the ; k 1,,..., 6 are unknown parameters for the producton functon; the V s are random errors assocated wth measurement errors n the producton of banana reported, or the combned effects of nput varables not ncluded n the producton functon, whereas V s are assumed to be ndependently and dentcally dstrbuted N 0, V random varables; the U s are non-negatve random varables, assocated wth techncal neffcency of producton of the farmers, assumed to be ndependently dstrbuted, such that the techncal neffcency effect for the -th farmer, U, s obtaned by truncaton (at zero) of the normal dstrbuton wth mean m, and varance, m 0 1Z1 Z 3Z3 4Z (), where, Z1 represents the age of farmers n years; k 6, such that Z represents Z the experence of a farmer to produce n years; Z3 represents the age of land producng banana n years; 4 represents the educaton of farmers n years of schoolng; and the s are unknown parameters to be estmated. The stochastc fronter model used n ths study s estmated usng the computer program, FRONTIER 4.1, wrtten by Coell [5]. The parameters of the fronter model are estmated, such that the varance parameters are: and, where the parameter has a value between zero and one. S 3 Results and Dscusson The annual producton, yeld and harvested area of banana n Bangladesh for dfferent year have been shown n the followng fgure: Area harvested (Ha) Yeld (Hg/Ha) S V Fgure 1: The annual producton, yeld and harvested area of banana n Bangladesh for dfferent years. Data source: The average harvested area, yeld and producton over the perod 197 to 01 n Bangladesh were Ha, Hg/Ha and tonnes respectvely. From Fgure 1, the annual banana productons n Bangladesh ncrease dramatcally after the year 000 and contnue up to 007. In ths study we are not able to dentfy the reason behnd ths. Agan, after the year 007 the annual banana producton s decreasng though the yeld and harvested area 015 NSP

4 340 Md. M. Hossan et. al.: Applcaton of Stochastc Fronter over the perod almost same. After the year 005, the yeld and harvested area slghtly ncrease and decrease after the year 011. The maxmum lkelhood estmates of the parameters of the stochastc fronter producton functon defned by equaton (1) and () are presented n Table 1, along wth ther standard errors and t-values. Table 1: Maxmum lkelhood Estmates for Parameters of Stochastc Fronter Producton Functon and Ineffcency Model for Banana Farmers n Kushta Dstrct of Bangladesh Varable Parameter Standard error t-value Constant ln of banana area ln of cost on seed ln of cost on labor ln of cost on rrgaton ln of cost on fertlzer ln of cost on transport Ineffcency Model Constant Age Experence to produce banana Age of land producng banana Educaton Varance Parameters sgma-square gamma Log lkelhood functon Lkelhood Rato Note: A negatve sgn of the parameters n the neffcency functon means that the assocated varable has a postve effect on techncal effcency, and vce versa. Source: Feld survey, 014. The estmate for the varance parameter,, ndcates that the varance,, assocated wth the neffcacy effect s S about 86% of the two varances. Estmated output elastctes for all the nputs all dffered from zero at the 5% sgnfcance level. Among the elastctes, the elastcty for land used for banana producton s the largest (0.3498). Ths means a 10% ncrease n the land used for banana producton wll gve rse to a 3.498% ncrease n output. The second largest elastcty s cost on fertlzer whch s Among the elastctes, the elastcty for the cost on labor s lowest (0.0495). Soco-economc, demographc factors, farm characterstcs, envronmental factors and nonphyscal factors are lkely to affect the effcency [6, 7]. The results of techncal neffcency effects are also presented n the lower part of Table 1. From our results, t s revealed that age and educaton level of the farmers has a postve effect on techncal effcency. Also, experence of banana producng of a farmer and age of the land banana producng has negatve effect on techncal effcency. Though n our study, experence of banana producng of a farmer has negatve effect on techncal effcency but n general we expect t has postve effect on techncal effcency. Table : Summery Statstcs of Effcency Estmates from the Stochastc Fronter Model Statstc Effcency Score Statstc Effcency Score Mean Standard Devaton Mnmum Kurtoss Maxmum Skewness The average techncal effcency for the sample s about 89 percent, wth a mnmum of about 65 percent and maxmum 98 percent (Table ). Ths mples that on average the respondents are able to obtan 89 percent of potental output from a gven mx of producton nputs. Thus, n the short run, there s a scope for ncreasng banana producton 015 NSP

5 Estmated Effcency J. Stat. Appl. Pro. 4, No., (015) / n Kushta dstrct of Bangladesh by 11 percent, by adoptng the technology and the technques used by the best practce banana farms. Frm Fgure : Estmated Effcency of the Frms It s observed that the estmated frm effcency almost nearer to one. Only 6 percent of the frm has effcency score less than About 60 percent of the frm consdered n ths study operate wth effcency level greater than 0.90 (Fgure ). Table 3: Frequency Dstrbuton of Techncal Effcency Estmates from the Stochastc Fronter Model. Effcency Score Number of Frms Percentage of Frms The frequency dstrbuton of the effcency estmates obtaned from the stochastc fronter model n presented n Table 3. About 43 percent of the frms operate wth effcency level greater than 90 percent as can be seen from the table. Only 14 percent of the frms operate wth effcency level less than 80 percent. 4 Concluson Agrcultural productvty vares due to dfferences n producton technology, dfferences n the settng n whch producton occurs and dfferences n the effcency of the producton process. Effcency measurement has been the concern of researches wth an am to nvestgate the effcency levels of farmers engaged n agrcultural actvtes. Identfyng determnants of effcency levels s a major task n effcency analyss. Emprcal studes suggest that farmers n developng countres fal to explot fully the potental of a technology makng neffcency decsons. Polcy makers have started to recognze that one mportant source of growth for the agrcultural sector s effcency gan through greater techncal effcency. It s observed that among the elastctes, the elastcty for land used for banana producton s the largest (0.3498). The second largest elastcty s cost on fertlzer whch s and the elastcty for the cost on labor s lowest (0.0495). Results of ths study revealed that age and educaton level of the farmers has a postve effect on techncal effcency. Also, experence of banana producng of a farmer and age of the land banana producng has negatve effect on techncal effcency. Though n our study, experence of banana producng of a farmer has negatve effect on techncal effcency but n general we expect t has postve effect on techncal effcency. Banana s not only mportant source of nutrton but also an mportant source of cash ncome to producers and traders. Moreover, a large number of people were nvolved n the producton and marketng of banana. So the farmers and ntermedares could be more benefted fnancally f producton and marketng of banana are to be well expanded. Government should take an effectve step to control the prce system and prce spread of the market and make sure that the producers can get ther reasonable prce and also the consumer can also get the product n a reasonable prce. Government also should take necessary steps to mprove the knowledge of a farmer to the modern cultvaton technque and encouraged them to adopt the new technology to ncrease the producton. 015 NSP

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