Econometric Estimation of Distance Functions and Associated Measures of Productivity and Efficiency Change

The economically-relevant characteristics of multi-input multi-output production technologies can be represented using distance functions. The econometric approach to estimating these functions typically involves factoring out one of the outputs or inputs and estimating the resulting equation using maximum likelihood methods. A problem with this approach is that the outputs or inputs that are not factored out may be correlated with the composite error term. Fernandez, Koop and Steel (2000, p. 58) have developed a Bayesian solution to this so-called ‘endogeneity’ problem. O'Donnell (2007) has adapted the approach to the estimation of directional distance functions. This paper shows how the approach can be used to estimate Shephard (1953) distance functions and an associated index of total factor productivity (TFP) change. The TFP index is a new multiplicatively-complete index that satisfies most, if not all, economically-relevant tests and axioms from index number theory. The fact that it is multiplicatively-complete means it can be exhaustively decomposed into a measure of technical change and various measures of efficiency change. The decomposition can be implemented without the use of price data and without making any assumptions concerning either the optimising behaviour of firms or the degree of competition in product markets. The methodology is illustrated using state-level quantity data on U.S. agricultural inputs and outputs over the period 1960-2004. Results are summarised in terms of the characteristics (e.g., means) of estimated probability densities for measures of TFP change, technical change and output-oriented measures of efficiency change.