Using Moment Constraints in GME Estimation
In this contribution, we explore the sensitivity of parameter estimates derived through the generalized maximum entropy (GME) approach under alternative specifications of the width of the error term supports. Although many recommend a “three-sigma” rule for setting the width of this term, there can be noticeable differences in the results if it is expanded beyond that, as others in the literature have suggested. We use a Monte Carlo analysis to see how imposing a moment-based condition into the GME problem, as an additional constraint, affects the results. We find that it removes the sensitivity of the parameter estimates to the width of the supports for the error term and that this remains robust even when the data is ill-conditioned. Based on this, we recommend that researchers impose this condition when doing GME-based estimation, to improve the performance of the estimator.
- Brooke, A., Kendrick, D., & Meeraus, A. (1988). GAMS: A users’s guide. The Scientific Press.Google Scholar
- Fragaso, R. M., & Carvalho, M. L. (2012). Estimation of joint costs allocation coefficients using the maximum entropy: A case of mediterranean farms. Journal of Quantitative Economics, 10(2), 91–111.Google Scholar
- Gohin, A. (2000). Positive mathematical programming and maximum entropy: Economic tools for applied production analysis. In INRA-ESR-Rennes Economics, Paris.Google Scholar
- Golan, A., Judge, G., & Miller, D. (1996b). Maximum entropy econometrics: Robust estimation with limited data. New York: Wiley.Google Scholar
- Golan, A., Judge, G. & Karp, L. (1996b). A maximum entropy approach to estimation and inference in dynamic models or counting fish in the sea using maximum entropy. Journal of Economic Dynamics and Control 20(4): 559–582.Google Scholar
- Mittelhammer, R. C., Judge, G. G., & Miller, D. J. (2000). Econometric foundations. New York: Cambridge University Press.Google Scholar
- Paris, Q. (2001, April). MELE: Maximum entropy leuven estimators. Working Paper 01-003. UC Davis: Department of Agricultural and Resource Economics, UCD. Retrieved from https://escholarship.org/uc/item/66q143ht.
- Paris, Q., & Caputo, M. R. (2001, August). Sensitivity of the GME estimates to support bounds. Working Paper 01–008. Davis: Dept of Agricultural & Resource Economics, University of California.Google Scholar
- Pukelsheim, F. (1994). The 3-sigma rule. American statistician, 48(2), 88–91.Google Scholar
- Van Akkeren, Judge, M. G., & Mittelhammer, R. (2002). Generalized moment based estimation and inference. Journal of Econometrics 107 (1–2): 127–148.Google Scholar
- Wu, X. (2009). A weighted generalized maximum entropy estimator with a data-driven weight. Entropy, 11. https://doi.org/10.3390/e11040917.