The good, the bad and the technology: Endogeneity in environmental production models

In this paper we consider an environmental production process in which firms intend to produce outputs (which we label as desirable/good) but the production process is such that it automatically produces some other unintentional but inevitable undesirable (bad) outputs as by-products (emission of pollutants). Like stochastic production frontier, by-production technology specifies that there is a minimal amount of the by-product that is produced, given the quantities of inputs and desirable outputs. The presence of (environmental) inefficiency in by-production therefore means that more than this minimal amount of the undesirable output is produced. Similarly, the presence of technical inefficiency implies that, given inputs, less than the maximal possible amount of desirable outputs is produced. Alternatively, it means that more than the minimal amounts of inputs are used to produce a given level of desirable output. We use the "by-production technology" approach which is a composition of production technology of desirable outputs and the technology of by-products, and estimate both technical and environmental efficiency. Given that electricity, the good output in our application, is demand determined, we treat it as exogenous and address the endogeneity of inputs by using the first-order conditions of cost minimization. Some of our models automatically take endogeneity of bad outputs into account. We use an efficient Bayesian MCMC technique to estimate both good and bad output technologies and both types of inefficiency. We also compare results with some alternative models with and without endogeneity corrections.