Do Farm Programs Explain Mean and Variance of Technical Efficiency? Stochastic Frontier Analysis

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1 Do Farm Programs Explan Mean and Varance of Techncal Effcency? Stochastc Fronter Analyss Rahul Ranjan Master Student Dept. of Agrbusness and Appled Economcs NDSU, Fargo, ND E-mal: Saleem Shak Rchard H Barry Hall Dept. of Agrbusness and Appled Economcs NDSU, Fargo, ND Phone: (701) ; Fax: (701) E-mal: saleem.shak@ndsu.edu Ashok K. Mshra 211 Agrculture Admnstraton Buldng Dept. of Agrcultural Economcs and Agrbusness LSU, Baton Rouge, LA Phone: (225) ; Fax: (225) E-mal: Amshra@lsu.edu Selected Paper prepared for presentaton at the Southern Agrcultural Economcs Assocaton Annual Meetng, Orlando, FL, February 6-9, 2010 Copyrght 2010 by Ranjan, Shak and Mshra. All rghts reserved. Readers may make verbatm copes of ths document for non-commercal purposes by any means, provded ths copyrght notce appears on all such copes. 1 Correspondng author

2 Abstract Past lterature has examned the mportance of farm programs on the volatlty and returns on general and agrculture economc growth. The objectve of ths study was to assess the mpact of farm program payments on techncal effcency. The study used aggregate state level panel data from the U.S agrcultural sector. Results ndcate producton ncreasng wth ncreasng unts of nputs. Results from ths study ndcate that farm program payments play an mportant role n techncal effcency. For example, farm program payments ndcate a negatve and postve effect on mean and varance of techncal effcency n the long-run and short-run, respectvely.

3 Do Farm Programs Explan Mean and Varance of Techncal Effcency? Stochastc Fronter Analyss 1. Introducton Among the frst peces of the New Deal legslaton proposed by ncomng Presdent Frankln D. Roosevelt n 1933 was a farm program desgned to address declnes n farm prces and net farm ncome. The federal crop nsurance program was ntated n 1938 to provde protecton to farmers aganst crop loss due to natural dsasters, ncludng drought, excessve mosture and unusual weather. Snce 1933, the desgn of federal agrcultural polces, ncludng farm programs and crop nsurance programs, are amended or new programs are ntroduced wth the authorzaton of a new farm bll. Although federal agrcultural polces n the Unted States are rarely ntended to alter the structure of agrculture, the effect of these polces and/or technology on the farm economc structure has long been an economc and poltcal concern. The wdely held vew s that a major, f not the most sgnfcant mechansm for changes n farm economc structure, s the effect of nsttutonal forces lke federal agrcultural polces. Whle the causes of the swtch to dfferent knds of programs are stll controversal, as are the predcted outcomes, there s strong nterest n the potental effects of farm programs and crop nsurance on the farm economc structure. Studes have examned the mportance of technology and farm programs on farm economc structural changes n nput use and output producton mx usng prmal producton functon, and dual cost functon or proft functon. Gven the changes n nput use and output producton, nterest has grown n understandng how technology and dfferent knd of federal farm polces have affected the techncal effcency of the U.S. agrculture sector.

4 2 Past lterature has examned the mportance of lqudty, solvency and effcency fnancal varables on the volatlty and returns on general and agrculture economc growth. However, the mportance of lqudty, solvency, and effcency, on techncal effcency and productvty 2 has yet to be documented. Therefore, the objectve of ths paper s to examne the mportance of farm programs varables on the techncal effcency of the U.S. agrculture sector usng stochastc fronter analyss framework. Specfc objectves nclude estmate the techncal effcency of the U.S. agrculture sector and second examne the role of farm program varables affectng techncal effcency. The study uses panel state data for the U.S agrcultural sector for the perod, Lterature revew of farm programs and techncal effcency Let us move towards the hstory of varous farm programs conducted n US farm whch s sad to be orgnated as the result of New Deal Legslaton proposed by Presdent Frankln D. Roosevelt n 1933 (whch s also consdered as one of the reasons for the change n the US farm productvty) to address the ssue of declnng Farm prce and Net farm ncome. Actually, t was the government s effort to deal wth the great depresson. The Adjustment act brought the major prce support (Bowers, Rasmussen, & Baker, 1984, p. v) for farmers by government. As a result, federal farm program orgnated to protect farmers aganst crop loss due to natural dsaster and stll s n force (Rasmussen, 1985; Shak, Helmers and Atwood, 2005). Though, there s a clear mpact of prce on productvty, t s emphaszed n dfferent papers that farm programs and crop nsurance have also altered the structure and productvty n US farm. 2 Two alternatve approaches - nonparametrc programmng and parametrc stochastc fronter analyss have ganed popularty due to ther own strength and weakness n effcency and productvty lterature. Wthn parametrc stochastc fronter analyss approach there has been ncreased emphass on the type of dstrbuton (exponental proposed by Agner, Lovell and Schmdt, 1977, normal-gamma proposed by Greene, 1990), methods (parametrc, sem-parametrc and Bayesan), dstngush between cross ndvdual heterogenety and neffcency (Greene, 2004) and fnally emprcal applcatons.

5 3 For emprcal mplementaton of the dstance functon, a functonal form must be specfed for ts emprcal representaton (Morrson et al., 2000). Researchers n ths area have used Cobb Douglas form for the estmaton of producton fronter whch keeps specal mportance n a mult-output and -nput context. Others have calculated effcency for farm programs usng cross-secton or panel data seres to estmate a fronter Cobb- Douglas producton functon for US Agrculture. Fronter estmaton model has also been used n the analyss of effcency patterns of New Zealand sheep and beef farmng wth panel data (Morrson et al., 2000). The past lterature uses two-stage lnear programmng followed by dscrete choce tobt model to examne the relatonshp between fnance and techncal or economc effcency of producton. The two-step process has been the subject of analyss by earler researchers. However, the two-step process mght be faced wth bas due to omtted or left out varables (see Wang and Schmdt 2002) or heteroskedastcty (Greene 2004). Hence, followng Greene (2004) nstead of a two-step process, a heterogenety stochastc fronter model s used to examne the mportance of farm fnancal varables on techncal effcency and productvty. Stochastc fronter model, ntroduced by Agner, Lovell, Schmdt; Meeusen, van den Broeck; and Battesse and Cora n 1977 decomposes the error term, nto random error, v and u neffcency. Stochastc fronter analyss has become a popular tool to model the producton relatonshp between nput and output quanttes and has been prmarly used to estmate the techncal effcency 3 of frm. In 1982, Jondrow, Materov, Lovell, and Schmdt suggested a 3 Effcency concept ntroduced by Farrell (1957) s defned as the dstance of the observaton from the producton fronter and measured by the observed output of a frm, state or country relatve to realzed output,.e., output that could be produced f t were 100 % effcent from a gven set of nputs.

6 4 method to estmate frm specfc neffcency measures. Snce t was ntroduced n 1977, the stochastc fronter analyss has been evolvng theoretcally wth surge n emprcal applcaton. Furthermore, progress has been made on extendng to fxed effects, random effects and random parameters panel models, tme nvarant and tme varant models, correctng for heteroskedastcty and heterogenety and alternatve dstrbutons (normal- half normal, normalexponental and normal-gamma) of u techncal effcency term. Addtonally, research has nvestgated the nfluence of a broader set of determnants of techncal effcency, namely geographc varables, market structure conduct and performance hypothess, polcy varables and sze of the frm. 2. Stochastc fronter model to nclude effcency Followng Greene (1993, 2004) the stochastc fronter model can be used to represent a Cobb- Douglas producton functon as (1) x; β y f v u where y s the output and x s a vector of nputs used n the producton functon, β s the vector 2 coeffcents assocated wth nputs, v represents the random error and ~ 0, v the one-sded neffcency and can be represent wth alternatve dstrbutons. v N, u represents Followng Shak and Mshra (2010), equaton (1) wth alternatve dstrbuton can be extended by ntroducng heterogenety n the varance of one-sded neffcency, u as

7 5 (2a) 2 u y f x; β v u exp Z or by ntroducng heterogenety n the mean of one-sded neffcency, u as (2b) u y f x; β v u exp Z 2 2 where u s the varance of the neffcency term, v s the varance of the random error. The 2 varance can be modeled as a functon of varables Z. Here we defned the u varance and mean of the neffcency term as a functon of level, short-run and long-run farm program rsk varables. u 2.1 Panel gamma SML stochastc fronter models The above tme-seres or cross-secton stochastc fronter model can be extended to one- and two-way fxed or random effects panel model. The basc panel stochastc fronter producton functon can be represented (5) y f x ; β v u or t t t t y f x ; β u v t t t t where 1,..., Ncross secton observatons and t 1,..., T number of years, y s the output and x s a vector of nputs used n the producton functon. Let us start wth one-way error dsturbance stochastc fronter producton functon (6) y f x ; β v u t t t t v t t

8 6 where represents the temporally nvarant cross-secton or spatal effect and t represents the remander random error. If representng ndvdual cross-sectonal unts are assumed to be fxed, a one-way fxed effects stochastc fronter producton functon can be wrtten as y f ;, Z ; u t (7) x β t t t where Z s a vector of ndvdual cross-sectonal dummes and are the assocate parameters of the cross-sectonal dummes. Instead of estmatng too many parameters (dummes), t s possble to assume as random leadng to one-way random effects model. The one-way random panel stochastc fronter producton functon can be represented as y f u (8) x β t t; t t where s the temporally nvarant spatal error, normally dstrbuted wth mean zero, varance 2, t the remander error s normally dstrbuted wth mean zero, varance 2, and are ndependent of t. Further, xt are ndependent of and t for all and t. represented as Smlarly, the two-way error dsturbance stochastc fronter producton functon can be (9) y f x ; β v u t t t t v t t t

9 7 where represents the temporally nvarant cross-secton or spatal effect, t represents the spatally nvarant tme-seres or temporal effect, and t represents the remander random error. If and t representng ndvdual cross-sectonal and tme-seres unts, respectvely are assumed to be fxed, a two-way fxed effects stochastc fronter producton functon can be wrtten as (10) x β Z t y f ;, Z ;, ; u t t t t where Z s a vector of ndvdual cross-sectonal dummes and are the assocate parameters of the cross-sectonal dummes, Z s a vector of ndvdual tme-seres dummes and t are the assocate parameters of the tmes-seres dummes. Smlarly, t s possble to assume and t as random leadng to two-way random effect model. The two-way random panel stochastc fronter producton functon can be represented as y f u (11) x β t t; t t t where s temporally nvarant spatal error and ~ N 0,, t s spatally nvarant temporal error and ~ 0, t N, and of, t and t for all and t., t and t are ndependent. Further, x s ndependent t

10 8 3. Data and varables used n the analyss The U.S. Department of Agrculture s Economc Research Servce (ERS) constructs and publshes the state and aggregate producton accounts for the farm sector 4. The features of the state and natonal producton accounts are consstent wth gross output model of producton and are well documented n Ball et al. (1999). Output s defned as gross producton leavng the farm, as opposed to real value added. Prce of land s based on hedonc regressons. Specfcally the prce of land n a state s regressed aganst land characterstcs and locaton (state dummy). Prces of captal nputs are obtaned on nvestment goods prces, takng nto account the flow of captal servces per unt of captal stock n each state (Ball et al, 2001). Table 1 presents the summary statstcs of the output, nput and farm program payment rsk varables. 4. Emprcal applcaton and results To examne the mportance of farm program payments, short-run and long-run farm program rsk on the mean and varance of techncal effcency of U.S. agrculture sector panel stochastc fronter model s estmated. The output and nputs n the producton functon equaton s estmated usng the logs of the varables and the farm program payments, long-run and short-run farm program rsk varables n the mean and varance neffcency functon s estmated n levels. A Cobb-Douglas functonal form was specfed for panel stochastc fronter models. The long and short-run farm program rsk varable was specfed n the neffcency mean and varance functon. The Cobb-Douglas functonal form wth varance functon specfed as 4 The data are avalable at the USDA/ERS webste

11 9 (12a) Output Captal Land Labor Chemcals t 0 1 t 2 t 3 t 4 t Energy Materals Year 5 t 6 t 7 t FP LR FP rsk SR FP rsk 2 u 0, u 1, u t 1, u t 2, u t and the mean neffcency functon specfed as (12b) Output Captal Land Labor Chemcals t 0 1 t 2 t 3 t 4 t Energy Materals Year 5 t 6 t 7 t FP LR FP rsk SR FP rsk u 0, u 1, u t 1, u t 2, u t Where LR FP rsk s the long run farm program rsk defned as the cumulatve standard devaton of the fnancal varables, SR FPrsk s the short run farm program rsk defned as a fve-year movng standard devaton of the farm program payment varables. 4.1 Results Parameter coeffcents of stochastc fronter producton functon are presented n Table 2 for mean and varance farm program neffcency functon. A nce feature about usng logarthms s that the slope coeffcent measures the elastcty of endogenous varable wth respect to exogenous varaton, that s, by the percentage change n endogenous varable gven a percentage change n exogenous varaton. Column 2 of table 2 presents estmates of varance functon. Results n table 2 suggest the nput varables n the producton are all postve and sgnfcantly related to output producton. The producton functon results are consstent wth producton theory,.e., an ncrease n the quantty of nput leads to ncrease n quantty of output produced. The results from the model ndcate an nput elastcty of for materal whch s relatve hgher to the other nputs. A 100 percent ncrease n the use of materal nput would ncrease the output by 45 percent, whch ndcates agrcultural producton can be ncreased 45

12 10 percent by ncreasng the use of materal nputs n agrcultural producton. Energy nput has an elastcty of and ranks second wth respect to the magntude of contrbutons to agrcultural output. Farmland wth an elastcty of ranks thrd and chemcals wth an elastcty of ranks fourth n terms of contrbutons to agrcultural output. Captal wth an elastcty of and labor wth an elastcty of are at the bottom, showng that these nputs have a smaller postve nfluence on agrcultural output. Year proxy for technology s postvely related to agrcultural output. The agrculture producton returns to scale s and 0.815, respectvely wthout and wth the ncluson of technology. The nput elastctes estmated are not that dfferent between the mean functon and varance functon stochastc fronter models. The long-run farm program rsk (varablty n farm program payments) varable n the neffcency mean and varance functon s postve and sgnfcant. Ths ndcates wth an ncrease n the varaton of farm program payments ncreases the mean and varaton n the neffcency n the long run. In contrast, short-run farm program rsk varable has a negatve and sgnfcant mpact on the neffcency varance. The negatve sgn ndcates short-run varaton n farm program payment would decrease the varaton n the neffcency varance. The level farm program payment dd not sgnfcantly affect the mean or varance neffcency functon. 5. Concluson Farms have to a certan extent used farm program payments n assessng, benchmarkng and montorng farm performance. Past lterature has examned the mportance of farm programs on the volatlty and returns on general and agrculture economc growth. The objectve of ths study was to assess the mpact of farm program payments on techncal effcency. The study used aggregate state level panel data from the U.S agrcultural sector. Results ndcate producton ncreasng wth ncreasng unts of nputs. Results from ths study ndcate that farm program

13 11 payments play an mportant role n techncal effcency. For example, farm program payments ndcate a negatve and postve effect on mean and varance of techncal effcency n the longrun and short-run, respectvely.

14 12 References Agner, D.J., Lovell, C.A.K. and Schmdt, P., Formulaton and Estmaton of Stochastc Fronter Producton Functon Models. Journal of Econometrcs, 6, Ball, V. Eldon, Jean-Chrstophe Bureau, Jean-Perre Butault, and Rchard Nehrng Levels of Farm Sector Productvty: An Internatonal Comparson. Journal of Productvty Analyss 15:5-29. Ball, V. Eldon, Frank Gollop, Alson Kelly-Hawke, and Gregory Swnand "Patterns of Productvty Growth n the U.S. Farm Sector: Lnkng State and Aggregate Models," Amercan Journal of Agrcultural Economcs, 81: Battese, G. and G.Corra, Estmaton of a producton fronter model: Wth applcaton for the pastoral zone of eastern Australa. Australan Journal of Agrcultural Economcs, 21, Farrell, M.J., The Measurement of Productve Effcency. Journal of the Royal Statstcal Socety Seres A, 120, pp Greene, W.H., The Econometrc Approach to Effcency Analyss. n Fred, H.O., Lovell, C.A.K. and Schmdt, S.S.(Eds), The Measurement of Productve Effcency, Oxford Unversty Press, New York, Greene, W. Dstngushng Between Heterogenety and Ineffcency: Stochastc Fronter Analyss of the World Health Organzaton's Panel Data on Natonal Health Care Systems. Health Economcs 13 (10), (2004):

15 13 Greene, W. LIMDEP Computer Program: Verson 9.0. Econometrc Software. Planvew, NY, Jondrow, J., I. Materov, K. Lovell and P. Schmdt, "On the Estmaton of Techncal Ineffcency n the Stochastc Fronter Producton Functon Model," Journal of Econometrcs, 1982, 19, pp Meeusen, W. and van den Broeck, J., Effcency Estmaton from Cobb-Douglas Producton Functons wth Composed Error. Internatonal Economc Revew, 18, Shak, Saleem., and Ashok Mshra, Alternatve Panel Estmators of Gamma SML Estmaton: Role of Fnancal Varables on Techncal effcency and Productvty. In press. Wang, H. and P. Schmdt, One-Step and Two-Step Estmaton of the Effects of Exogenous Varables on Techncal Effcency Levels. Journal of Productvty Analyss 18, , Input and Farm Program varables of U.S. agrculture sector,

16 14 Table 1. Summary statstcs of Output, Input and Farm Program varables of U.S. agrculture sector, Mean Std. dev Mnmum Maxmum Output Captal Land Labor Chemcals Energy Materals Year Farm program (FP) payments 103, , ,970 Short-run FP rsk 80, , ,366 Long-run FP rsk

17 15 Table 2. Panel Stochastc Fronter Producton Functon results for mean and varance of farm program payment rsk varables. Varance (neffcency) Mean (neffcency) Coeffcent P[ Z >z] Coeffcent P[ Z >z] Constant < < 0 Captal < < 0 Land < < 0 Labor < < 0 Chemcals < < 0 Energy < < 0 Materals < < 0 Year < < 0 Ineffcency (u) Constant < Farm program(fp) Long-run FP rsk < Short-run FP rsk