Measurement of technical efficiency in the case of heterogeneity of technologies used between firms – Based on evidence from Polish crop farms
In the present study, we have investigated several competing stochastic frontier models which differ in terms of the form of the production function (Cobb-Douglas or translog), inefficiency distribution (half-normal or exponential distribution) and type of prior distribution for the parameters (hierarchical or non-hierarchical from the Bayesian point of view). This last distinction corresponds to a difference between random coefficients and fixed coefficients models. Consequently, this study aims to examine to what extent inferences about estimates of farms' efficiency depend on the above assumptions. Moreover, the study intends to investigate how far the production function's characteristics are affected by the choice of the type of prior distribution for the parameters. First of all, it was found that the form of the production function does not impact the efficiency scores. Secondly, we found that measures of technical efficiency are sensitive to distributional assumptions about the inefficiency term. Finally, we have revealed that estimates of technical efficiency are reasonably robust to the prior information about the parameters of crop farms' production technology. There is also a resemblance in the elasticity of output with respect to inputs between the models considered in this paper. Additionally, the measurement of returns to scale is not sensitive to model specification.
Aigner D., Lovell C.A.K., Schmidt P. (1977): Formulation and estimation of stochastic frontier production function models. Journal of Econometrics, 6: 21–37. https://doi.org/10.1016/0304-4076(77)90052-5
Alvarez A., Arias C., Greene W. (2004): Accounting for unobservables in production models: Management and inefficiency. Economic Working Papers No., 72. Seville, Centro de Estudios Andaluces.
Areal F.J., Balcombe K., Tiffin R. (2012): Integrating spatial dependence into stochastic frontier analysis. Australian Journal of Agricultural Resource Economics, 56: 521–541. https://doi.org/10.1111/j.1467-8489.2012.00597.x
Baráth L., Ferto I., Bojnec S. (2018): Are farms in less favoured areas less efficient? Agricultural Economics, 49: 3–12.
Bojnec Š., Latruffe L. (2009): Determinants of technical efficiency of Slovenian farms. Post-Communist Economies, 21: 117–124. https://doi.org/10.1080/14631370802663737
Broeck van den J., Koop G., Osiewalski J., Steel M.F.J. (1994): Stochastic frontier models: A Bayesian perspective. Journal of Econometrics, 61: 273–303. https://doi.org/10.1016/0304-4076(94)90087-6
Caudill S.B. (2003): Estimating a mixture of stochastic frontier regression models via the EM algorithm: A multiproduct cost function application. Empirical Economics, 28: 581–598. https://doi.org/10.1007/s001810200147
Čechura L. (2010): Estimation of technical efficiency in Czech agriculture with respect to firm heterogeneity. Agricultural Economics – Czech, 56: 183–191. https://doi.org/10.17221/23/2010-AGRICECON
Čechura L., Hockmann H., Malý M., Kroupová Z. (2015): Comparison of technology and technical efficiency in cereal production among EU countries. Agris on-line Papers in Economics and Informatics, 7: 27–37. https://doi.org/10.7160/aol.2015.070203
Čechura L., Grau A., Hockman H., Levkovych I., Kroupova Z. (2017): Catching up or falling behind in European agriculture: The case of milk production. Journal of Agricultural Economics, 68: 206–227. https://doi.org/10.1111/1477-9552.12193
Chib S. (1995): Marginal likelihood from Gibbs output. Journal of the American Statistical Association, 90: 1313–1321. https://doi.org/10.1080/01621459.1995.10476635
Emvalomatis G. (2012): Productivity growth in German dairy farming using a flexible modelling approach. Journal of Agricultural Economics, 63: 83–101. https://doi.org/10.1111/j.1477-9552.2011.00312.x
FADN (2020): Polish Farm Accountancy Data Network. [Dataset]. Unpublished Data.
Feng G., Zhang X. (2012): Productivity and efficiency at large community banks in the US: A Bayesian true random effects stochastic distance frontier analysis. Journal of Banking and Finance, 36: 1883–1895. https://doi.org/10.1016/j.jbankfin.2012.02.008
Greene W.H. (2005): Reconsidering heterogeneity in panel data estimators of the stochastic frontier model. Journal of Econometrics, 126: 269–303. https://doi.org/10.1016/j.jeconom.2004.05.003
Greene W.H. (2012): Econometric Analysis. 7th Ed. Essex, England, Pearson Education: 1–1228.
Hildreth C., Houck J.P. (1968): Some estimators for a linear model with random coefficients. Journal of the American Statistical Association, 63: 584–595.
Kalirajan K.P., Obwona M.B. (1994): Frontier production function: The stochastic coefficients approach. Oxford Bulletin of Economics and Statistics, 56: 87–96. https://doi.org/10.1111/j.1468-0084.1994.mp56001007.x
Koop G., Osiewalski J., Steel M. (1997): Bayesian efficiency analysis through individual effects: Hospital cost frontiers. Journal of Econometrics, 76: 77–105. https://doi.org/10.1016/0304-4076(95)01783-6
Latruffe L., Balcombe K., Davidova S., Zawalińska K. (2004): Determinants of technical efficiency of crop and livestock farms in Poland. Applied Economics, 36: 1255–1263. https://doi.org/10.1080/0003684042000176793
Marzec J., Pisulewski A. (2017): The effect of CAP subsidies on the technical efficiency of Polish dairy farms. Central European Journal of Economic Modelling and Econometrics, 9: 243–273.
Marzec J., Pisulewski A. (2019): The measurement of time-varying technical efficiency and productivity change in Polish crop farms. German Journal of Agricultural Economics, 68: 15–27.
Njuki E., Bravo-Ureta B.E., O'Donnell C.J. (2019): Decomposing agricultural productivity growth using a random-parameters stochastic production frontier. Empirical Economics, 57: 839–860. https://doi.org/10.1007/s00181-018-1469-9
Orea L., Kumbhakar S.C. (2004): Efficiency measurement using a latent class stochastic frontier model. Empirical Economics, 29: 169–183. https://doi.org/10.1007/s00181-003-0184-2
Pisulewski A., Marzec J. (2019): Heterogeneity, transient and persistent technical efficiency of Polish crop farms. Spanish Journal of Agricultural Research, 17: 1–14. https://doi.org/10.5424/sjar/2019171-13926
Rossi P., Allenby G., McCulloch R. (2005): Bayesian Statistics and Marketing. Chichester, England, John Wiley & Sons: 1–348.
Skevas I., Emvalomatis G., Brümmer B. (2018): Productivity growth measurement and decomposition under a dynamic inefficiency specification: The case of German dairy farms. European Journal of Operational Research, 271: 250–261. https://doi.org/10.1016/j.ejor.2018.04.050
Skevas I. (2019): A hierarchical stochastic frontier model for efficiency measurement under technology heterogeneity. Journal of Quantitative Economics, 17: 513–524. https://doi.org/10.1007/s40953-018-0144-5
Swamy P.A. (1970): Efficient inference in a random coefficient regression model. Econometrica, 38: 311‒323. https://doi.org/10.2307/1913012
Tsionas E.G. (2002): Stochastic frontier models with random coefficients. Journal of Applied Econometrics, 17: 127–147. https://doi.org/10.1002/jae.637
Zhu X., Lansink A.O. (2010): Impact of CAP ubsidies on technical efficiency of crop farms in Germany, the Netherlands and Sweden. Journal of Agricultural Economics, 61: 545–564. https://doi.org/10.1111/j.1477-9552.2010.00254.x