Specification and estimation of primal production models
While estimating production technology in a primal framework production function, input and output distance functions and input requirement functions are widely used in the empirical literature. This paper shows that these popular primal based models are algebraically equivalent in the sense that they can be derived from the same underlying transformation (production possibility) function. By assuming that producers maximize profit, we show that in all cases, except one, the use of ordinary least squares (OLS) gives inconsistent estimates irrespective of whether the production, input distance and input requirement functions are used. Based on several specifications of the production and input distance function models, we conclude that one can estimate the input elasticities and returns to scale consistently using instruments on only one regressor. No instruments are needed if either it is assumed that producers know the technology entirely (including the so-called error term) or a system approach is used. We used Norwegian timber harvesting data to illustrate workings of various model specifications.
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- James Levinsohn & Amil Petrin, 2000.
"Estimating Production Functions Using Inputs to Control for Unobservables,"
NBER Working Papers
7819, National Bureau of Economic Research, Inc.
- James Levinsohn & Amil Petrin, 2003. "Estimating Production Functions Using Inputs to Control for Unobservables," Review of Economic Studies, Wiley Blackwell, vol. 70(2), pages 317-341, 04.
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- COELLI, Tim, 2000. "On the econometric estimation of the distance function representation of a production technology," CORE Discussion Papers 2000042, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- James Levinsohn & Amil Petrin, 2003. "Estimating Production Functions Using Inputs to Control for Unobservables," Review of Economic Studies, Oxford University Press, vol. 70(2), pages 317-341.
- Boussemart, Jean-Philippe & Briec, Walter & Peypoch, Nicolas & Tavéra, Christophe, 2009. "[alpha]-Returns to scale and multi-output production technologies," European Journal of Operational Research, Elsevier, vol. 197(1), pages 332-339, August.
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