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GE-Logit: A New Regular-Flexible Cost Function
Presented by:
Tom Rutherford
Department of Agricultural and Applied Economics
University of Wisconsin - Madison
Wednesday, October 30, 2024
12:00 pm-1:15 pm
Taylor-Hibbard Seminar Room (Rm103)
The nested constant-elasticity-of-substitution (CES) function has been the dominant functional form used to model relationships across production inputs and outputs in calibrated economic equilibrium models for over 50 years. This paper introduces an alternative – the GE-Logit. The paper derives the logit specification from core principles which portray the production process as a set of N tasks, each of which is performed with one of n factors of production. Random variations in factor cost for each task are generated by a Gumbel distribution. In the partial equilibrium setting this leads to the conventional multinomial logit which has been widely applied in transport and spatial equilibrium models. A reformulation of the conventional model is required to represent an n-factor, constant-returns-to-scale (CRTS) cost function. The paper shows how to implement the logit in applied general equilibrium models, including calibration, input demand functions and an equation which implicitly defines unit cost. Comparative static formulae characterizing local behavior of the logit specification reveal local equivalence to the CES model. Hence, based on Perroni and Rutherford (1995), the nested GE-Logit model can be calibrated to any negative semidefinite Slutsky matrix, and the resulting model remains monotone and convex over the full price simplex. In conclusion, the paper provides three numerical comparisons of the GE-logit with the standard nested CES. Illustrative numerical examples are provided for a small spatial economic equilibrium model, for Kehoe’s multiple equilibrium example and a optimal tariff calculations in a 65 sector / 10 region model. These findings highlight the usefulness of this new functional form for second order sensitivity analysis of policy simulation results.