Measurement of production inefficiency in a technology and inefficiency heterogeneity setting

ABSTRACT

This study shows how the estimates of production inefficiency and of the marginal effects of its determinants can be distorted if not accounting for technology and inefficiency heterogeneity. This is achieved by employing a hierarchical stochastic frontier model with random parameters both in the production frontier and in the inefficiency distribution and comparing its results with a conventional frontier model. German dairy farming is used as a case study and estimation is performed in a Bayesian framework. The results reveal significant differences in the inefficiencies and the calculated marginal effects of its determinants across the two models. Specifically, it is shown that inefficiency is overestimated when heterogeneity is not accounted for. An inflation of the means and the variances of the marginal effects is also observed, with the latter result suggesting that technology heterogeneity dominates inefficiency heterogeneity. According to Bayes factors, the employed hierarchical frontier model is favoured by the data when compared to the conventional frontier model.

KEYWORDS:

• Production inefficiency
• heterogeneity
• marginal effects
• Bayesian techniques

JEL CLASSIFICATION:

• C11
• C23
• D24
• Q12

Disclosure Statement

No potential conflict of interest was reported by the author.

Notes

¹ Price indices from EUROSTAT are used for the deflation of revenues and values of outputs and inputs.

² The hierarchical frontier is also estimated using a translog specification. However, most second-order terms are ‘statistically insignificant’, while the posterior model probabilities present overwhelming evidence in favour of the Cobb-Douglas specification of the hierarchical frontier. The results can be provided upon request. Note also that the robustness checks with regards to the model specification and the performed test concern only the hierarchical frontier as results from the simple frontier are only presented for comparison.

³ The posterior mean of $\mathbf{\Omega }$ from the hierarchical frontier model is presented in Table A1 in the Appendix.

⁴ The posterior mean of $\mathbf{\Psi }$ from the hierarchical frontier model appears in Table A2 in the Appendix.