Production Frontiers with Cross-sectional and Time-series Variation in Efficiency Levels*

In this paper we consider the efficient instrumental variables estimation of a panel data model with heterogeneity in slopes as well as intercepts. Using a panel of U.S. airlines, we apply our methodology to a frontier production function with cross-sectional and temporal variation in levels of technical efficiency. Our approach allows us to estimate time-varying efficiency levels for individual firms without invoking strong distributional assumptions for technical inefficiency or random noise. We do so by including in the production function a flexible function of time whose parameterization depends on the firm. We also generalize the results of Hausman and Taylor (1981) to exploit assumptions about the uncorrelatedness of certain exogenous variables with the temporal pattern of the firm’s technical inefficiency. Our empirical analysis of the airline industry over two periods of regulation yields believable evidence on the pattern of changes in efficiency across regulatory environments.