Heterogeneity, transient and persistent technical efficiency of Polish crop farms

  • Andrzej Pisulewski Cracow University of Economics, Dept. of Econometrics and Operational Research, ul. Rakowicka 27, 31-510 Kraków http://orcid.org/0000-0003-3937-4125
  • Jerzy Marzec Cracow University of Economics, Dept. of Econometrics and Operational Research, ul. Rakowicka 27, 31-510 Kraków
Keywords: panel data, stochastic frontier analysis, random effects


Accounting for heterogeneity in the measurement of farm efficiency is crucial to avoid biases related to climate and soil quality diversity in a given area. Therefore, this paper investigates the level of technical efficiency (TE) of Polish crop farms based on several stochastic frontier panel data models with different approaches to the measurement of unobserved heterogeneity, short- and long- run inefficiency. In our study, we show that ignoring farm heterogeneity can lead to underestimation of the level of TE in conventional stochastic frontier panel data models. Moreover, we have found empirically that not accounting for heterogeneity in the Generalized True Random Effects model may lead to incorrect estimates of persistent TE. The obtained results for Polish crop farms indicate that the level of transient TE (0.81) is lower than the level of persistent TE (0.88). This result suggests that Polish farms may have, for example, problems with adopting new technologies and poor managerial skills.


Download data is not yet available.


Abdulai A, Tietje H, 2007. Estimating technical efficiency under unobserved heterogeneity with stochastic frontier models: application to northern German dairy farms. Eur Rev Agric Econ 34 (3): 393-416. https://doi.org/10.1093/erae/jbm023

Aigner D, Lovell CAK, Schmidt P, 1977. Formulation and estimation of stochastic frontier production function models. J Econometrics 6 (1): 21-37. https://doi.org/10.1016/0304-4076(77)90052-5

Areal FJ, Balcombe K, Tiffin R, 2012. Integrating spatial dependence into stochastic frontier analysis. Aust J Agr Resour Ec 56 (4): 521-541. https://doi.org/10.1111/j.1467-8489.2012.00597.x

Badunenko O, Kumbhakar SC, 2017. Economies of scale, technical change and persistent and time-varying cost efficiency in Indian banking: Do ownership, regulation and heterogeneity matter? Eur J Oper Res 260 (2): 789-803. https://doi.org/10.1016/j.ejor.2017.01.025

Battese GE, Coelli TJ, 1988. Prediction of firm-level technical efficiencies with a generalized frontier production and panel data. J Econometrics 38 (3): 387-399. https://doi.org/10.1016/0304-4076(88)90053-X

Battese GE, Coelli TJ, 1992. Frontier production functions. technical efficiency and panel data: with application to paddy farmers in India. J Prod Anal 3 (1-2): 153-169. https://doi.org/10.1007/BF00158774

Battese GE, Coelli TJ, 1995. A model for technical inefficiency effects in a stochastic frontier production function for panel data. Empir Econ 20 (2): 325-332. https://doi.org/10.1007/BF01205442

Bojnec Š, Latruffe L, 2009. Determinants of technical efficiency of Slovenian farms. Post-Communist Econ 21 (1): 117-124. https://doi.org/10.1080/14631370802663737

Bojnec Š, Latruffe L, 2013. Farm size, agricultural subsidies and farm performance in Slovenia. Land Use Pol 32: 207-217. https://doi.org/10.1016/j.landusepol.2012.09.016

Brümmer B, Glauben T, Thijssen G, 2002. Decomposition of productivity growth using distance function: The case of dairy farms in three European countries. Am J Agr Econ 84 (3): 628-644. https://doi.org/10.1111/1467-8276.00324

Christensen LD, Jorgenson D, Lau LJ, 1973. Transcendental logarithmic production frontiers. Rev Econ Stats 55 (1): 28-45. https://doi.org/10.2307/1927992

Coelli T, 1995. Estimators and hypothesis tests for a stochastic frontier function: A Monte Carlo analysis. J Prod Anal 6 (3): 247-268. https://doi.org/10.1007/BF01076978

Coelli TJ, Prasada Rao DS, O'Donnell ChJ, Battese GE, 2005. An introduction to efficiency and productivity analysis, 2nd ed. Springer Science+Business Media, NY. 349 pp.

Colombi R, 2010. A skew normal stochastic frontier model for panel data. Proc 45th Sci Meeting of the Ital Stat Soc.

Colombi R, Martini G, Vittadini G, 2011. A stochastic frontier model with short-run and long-run inefficiency random effects. Working Paper no 01-2011. Dept Econ Technol Manage, Univ Bergamo, Italy.

Colombi R, Kumbhakar SC, Martini G, Vittadini G, 2014. Closed-skew normality in stochastic frontiers with individual effects and long/short-run efficiency. J Prod Anal 42 (2): 123-136. https://doi.org/10.1007/s11123-014-0386-y

CSO, 2016. Statistical Yearbook of Agriculture 2016. Central Statistical Office, Warsaw, Poland.

EC, 2008. Commission Regulation no 1242/2008 of 8 December 2008 establishing a Community typology for agricultural holdings: Annex I, part C. Definition of types of farming. European Commission.

Ellman M, 1981. Agricultural productivity under socialism. World Dev 9 (9-10): 979-989. https://doi.org/10.1016/0305-750X(81)90054-1

Fandel P, 2003. Technical and scale efficiency of corporate farms in Slovakia. Agr Econ-Czech 49 (8): 375-383. https://doi.org/10.17221/5417-AGRICECON

Farsi M, Filippini M, Kuenzle M, 2005. Unobserved heterogeneity in stochastic cost frontiers models: an application to Swiss nursing homes. Appl Econ 37 (18): 2127-2141. https://doi.org/10.1080/00036840500293201

Filippini M, Greene WH, 2016. Persistent and transient productive inefficiency: a maximum simulated likelihood approach. J Prod Anal 45 (2): 187-196. https://doi.org/10.1007/s11123-015-0446-y

Geweke J, 1989. Bayesian inference in econometric models using Monte Carlo integration, Econometrica 57 (6): 1317-1339. https://doi.org/10.2307/1913710

Gourieroux C, Holly A, Monfort A, 1982. Likelihood ratio test, Wald test, and Kuhn-Tucker test in linear models with inequality constraints on the regression parameters. Econometrica 50 (1): 63-80. https://doi.org/10.2307/1912529

Greene WH, 2005a. Fixed and random effects in stochastic frontier models. J Prod Anal 23 (1): 7-32. https://doi.org/10.1007/s11123-004-8545-1

Greene WH, 2005b. Reconsidering heterogeneity in panel data estimators of the stochastic frontier model. J Econometrics 126 (2): 269-303. https://doi.org/10.1016/j.jeconom.2004.05.003

Greene WH, 2008. The econometric approach to efficiency analysis. In: The measurement of productivity efficiency and productivity growth; Fried HO, Lovell CAK, Shelton SS (eds.), pp: 92-250. Oxford Univ Press, UK. https://doi.org/10.1093/acprof:oso/9780195183528.003.0002

Greene WH, 2012. Econometric Analysis, 7th ed. Pearson Education.

Hajivassiliou V, 1990. Smooth simulation estimation of panel data LDV models. Dept Econ, Yale Univ.

Hajivassiliou VA, 2000. Some practical issues in maximum simulated likelihood. In: Simulation-based inference in econometrics: Methods and applications; Mariano R, Schuermann T, Weeks MJ (eds.), pp: 71-99. Cambridge Univ Press, UK. https://doi.org/10.1017/CBO9780511751981.006

Hartvigsen M, 2014. Land reform and land fragmentation in Central and Eastern Europe. Land Use Pol 36: 330-341. https://doi.org/10.1016/j.landusepol.2013.08.016

Henningsen A, 2009. Why is the Polish farm sector still so underdeveloped? Post-Communist Econ 21 (1): 47-64. https://doi.org/10.1080/14631370802663646

Jondrow J, Lovell CAK, Materov I, Schmidt P, 1982. On the estimation of technical inefficiency in the stochastic frontier production function model. J Econometrics 19 (2-3): 233-238. https://doi.org/10.1016/0304-4076(82)90004-5

Keane M, 1994. A computationally practical simulation estimator for panel data. Econometrica 62 (1): 95-116. https://doi.org/10.2307/2951477

Kodde DA, Palm FC, 1986. Wald criteria for jointly testing equality and inequality restrictions. Econometrica 54 (5): 1243-1248. https://doi.org/10.2307/1912331

Kumbhakar SC, 1990. Production frontiers, panel data, and time-varying technical inefficiency. J Econometrics 46 (1-2): 201-211. https://doi.org/10.1016/0304-4076(90)90055-X

Kumbhakar SC, Heshmati A, 1995. Efficiency measurement in Swedish dairy farms: An application of rotating panel data 1976-88. Am J Agr Econ 77 (3): 660-674. https://doi.org/10.2307/1243233

Kumbhakar SC, Lien G, Hardaker JB, 2014. Technical efficiency in competing panel data models: A study of Norwegian grain farming. J Prod Anal 41 (2): 321-337. https://doi.org/10.1007/s11123-012-0303-1

Lachaud MA, Bravo-Ureta BE, Ludena CE, 2015. Agricultural productivity growth in Latin America and the Caribbean and other world regions: An analysis of climatic effects, convergence and catch-up. Int-Am Dev Bank Working Paper No. 607 (IDB-WP-607), Washington DC.

Latruffe L, Balcombe K, Davidova S, Zawalińska K, 2004. Determinants of technical efficiency of crop and livestock farms in Poland. Appl Econ 36 (12): 1255-1263. https://doi.org/10.1080/0003684042000176793

Latruffe L, Balcombe K, Davidova S, Zawalińska K, 2005. Technical and scale efficiency of crop and livestock farms in Poland: Does specialization matter? Agr Econ 32 (3): 281-296. https://doi.org/10.1111/j.1574-0862.2005.00322.x

Latruffe L, Davidova S, Balcombe K, 2008. Application of a double bootstrap to investigation of determinants of technical efficiency of farms in Central Europe. J Prod Anal 29 (2): 183-191. https://doi.org/10.1007/s11123-007-0074-2

Latruffe L, Fogarasi J, Desjeux Y, 2012. Efficiency, productivity and technology comparison for farms in Central and Western Europe: The case of field crop and dairy farming in Hungary and France. Econ Syst 36 (2): 264-278. https://doi.org/10.1016/j.ecosys.2011.07.002

Makieła K, 2017. Bayesian inference and Gibbs sampling in generalized true random-effects models. Cent Eur J Econ Mod Econ 9 (1): 69-95. https://doi.org/10.24425/cejeme.2017.122200

Makieła K, Marzec J, Pisulewski A, 2017. Productivity change analysis in dairy farms following Polish accession to the EU – An output growth decomposition approach. Outlook Agr 46 (4): 295-301. https://doi.org/10.1177/0030727017742557

Marzec J, Pisulewski A, 2017. The effect of CAP subsidies on the technical efficiency of Polish dairy farms. Cent Eur J Econ Mod Econom 9 (3): 243-273. https://doi.org/10.24425/cejeme.2017.122210

Marzec J, Pisulewski A, 2019. The measurement of time-varying technical efficiency and productivity change in Polish crop farms. Ger J Agr Econ 68 (1): 15-27. http://www.gjae-online.de/inhaltsverzeichnisse/pages/index.prl

Meeusen W, van den Broeck J, 1977. Efficiency estimation from Cobb-Douglas production functions with composed error. Int Econ Rev 18 (2): 435-444. https://doi.org/10.2307/2525757

Njuki E, Bravo-Ureta BE, 2015. The economic costs of environmental regulation in U.S. dairy farming: a directional distance function approach. Am J Agr Econ 97 (4): 1087-1106. https://doi.org/10.1093/ajae/aav007

Pede VO, Areal FJ, Singbo A, McKinley J, Kajisa K, 2018. Spatial dependency and technical efficiency: An application of a Bayesian stochastic frontier model to irrigated and rainfed farmers in Bohol, Phillipines. Agr Econ 49 (3): 301-312. https://doi.org/10.1111/agec.12417

Pitt M, Lee L, 1981. Measurement of sources of technical inefficiency in the Indonesian weaving industry. J Dev Econ 9 (1): 43-64. https://doi.org/10.1016/0304-3878(81)90004-3

PORDATA, 2017: Labour productivity per hour (Euro) – Europe. http://www.pordata.pt/en/Europe/Labour+productivity+per+hour+(Euro)-3019 [5 Jan 2019].

Schmidt AM, Moreira ARB, Helfand SM, Fonseca TCO, 2009. Spatial stochastic frontier models: Accounting for unobserved local determinants of inefficiency. J Prod Anal 31 (2): 101-112. https://doi.org/10.1007/s11123-008-0122-6

Stevenson RE, 1980. Likelihood functions for generalized stochastic frontier estimation. J Econometrics 13 (1): 57-66. https://doi.org/10.1016/0304-4076(80)90042-1

Train K, 2009. Discrete choice methods with simulation. Cambridge Univ Press, UK. 378 pp. https://doi.org/10.1017/CBO9780511805271

Tsionas EG, 2002. Stochastic frontier models with random coefficients. J Appl Econom 17 (2): 127-147. https://doi.org/10.1002/jae.637

Tsionas EG, Kumbhakar SC, 2014. Firm heterogeneity, persistent and transient technical inefficiency: A generalized true random-effects model. J Appl Econom 29 (1): 110-132. https://doi.org/10.1002/jae.2300

Zhu X, Lansink AO, 2010. Impact of CAP subsidies on technical efficiency of crop farms in Germany, the Netherlands and Sweden. J Agr Econ 61 (3): 545-564. https://doi.org/10.1111/j.1477-9552.2010.00254.x

How to Cite
PisulewskiA., & MarzecJ. (2019). Heterogeneity, transient and persistent technical efficiency of Polish crop farms. Spanish Journal of Agricultural Research, 17(1), e0106. https://doi.org/10.5424/sjar/2019171-13926
Agricultural economics