Comparing Malmquist and Hicks-Moorsteen productivity indices: Exploring the impact of unbalanced vs. balanced panel data

We explore the effect of balancing unbalanced panel data when estimating primal productivity indices using non-parametric frontier estimators. First, we list a series of pseudo-solutions aimed at making an unbalanced panel balanced. Then, we discuss some intermediate solutions (e.g., balancing 2-years by 2 years). Furthermore, we link this problem with a variety of literatures on infeasibilities, statistical inference of non-parametric frontier estimators, and the index theory literature focusing on the dynamics of entry and exit in industries. We then empirically illustrate these issues comparing both Malmquist and Hicks-Moorsteen productivity indices on two data sets. In particular, we test for the differences in distribution when comparing balanced and unbalanced results for a given index and when comparing Malmquist and Hicks-Moorsteen productivity indices for a given type of data set. The latter tests are crucial in answering the question to which extent the Malmquist index can approximate the Hicks-Moorsteen index that has a Total Factor Productivity (TFP) interpretation. Finally, we draw up a list of remaining issues that could benefit from further exploration.