Nonparametric Models of Production: Efficiency Estimation and Statistical Inference

Production theory is based on an economic model where we define the production set, i.e. the set of the combinations of inputs and outputs that are technically feasible. The efficiency of a particular unit is measured by its distance to the efficient frontier of the production set, based on a selected direction. Nonparametric models are particularly appealing because they do not rely on restrictive assumptions about the shape of the efficient frontier nor on the processes that may give rise to inefficiencies. Since these quantities are typically unknown, they must be estimated from a sample of observed units. The most widely used non-parametric approaches are based on envelopment estimators such as Data Envelopment Analysis (DEA) or Free Disposal Hull (FDH), making the derived measures of efficiency for a given unit dependent on these envelopment estimators. In recent decades, substantial results have been derived regarding the statistical properties of these non-parametric estimators. These advancements facilitate statistical inference regarding the efficiency scores of individual units acrossdifferent contexts or efficiency comparison between groups of units, as well as testing procedures concerning the shape of the attainable set (whether convex or non-convex), or assumptions about returns to scale. It is shown how crucial the assumptions made on the DGP are, incorrect assumptions may lead to inconsistent estimators and wrong inference. These results have now been extended to dynamic settings, including inference on Malmquist Productivity Indices (and other well-known productivity indices) and their components. In this paper, we provide a comprehensive up-to-date survey of various approaches.