The use of bootstrapped Malmquist indices to reassess productivity change findings: an application to a sample of Polish farms

Abstract

The paper assesses the extent to which sampling variation affects findings about Malmquist productivity change derived using Data Envelopment Analysis (DEA), in the first stage calculating productivity indices and in the second stage investigating the farm-specific change in productivity. Confidence intervals for Malmquist indices are constructed using Simar and Wilson’s (1999) bootstrapping procedure. The main contribution of the paper is to account in the second stage for the information provided by the first-stage bootstrap. The DEA standard errors of the Malmquist indices given by bootstrapping are employed in an innovative heteroscedastic panel regression, using a maximum likelihood procedure. The application is to a sample of 250 Polish farms over the period 1996-2000. The confidence intervals’ results suggest that the second half of 1990s for Polish farms was characterised not so much by productivity regress but rather by stagnation. As for the determinants of farm productivity change, we find that the integration of the DEA standard errors in the second-stage regression is significant in explaining a proportion of the variance in the error term. Although our heteroscedastic regression results differ with those from the standard OLS, in terms of significance and sign, they are consistent with theory and previous research.