GMM Estimation of a Maximum Distribution With Interval Data
We develop a GMM estimator for the distribution of a variable where summary statistics are available only for intervals of the random variable. Without individual data, once cannot calculate the weighting matrix for the GMM estimator. Instead, we propose a simulated weighting matrix based on a first-step consistent estimate. When the functional form of the underlying distribution is unknown, we estimate it using a simple yet flexible maximum entropy density. our Monte Carlo simulations show that the proposed maximum entropy density is able to approximate various distributions extremely well. The two-step GMM estimator with a simulated weighting matrix improves the efficiency of the one-step GMM considerably. We use this method to estimate the U.S. income distribution and compare these results with those based on the underlyign raw income data.
|Date of creation:||01 Mar 2005|
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- Golan, Amos & Judge, George & Perloff, Jeffrey M, 1996.
"Estimating the Size Distribution of Firms Using Government Summary Statistics,"
Journal of Industrial Economics,
Wiley Blackwell, vol. 44(1), pages 69-80, March.
- Golan, Amos & Judge, George G. & Perloff, Jeffrey M., 1995. "Estimating the size distribution of firms using government summary statistics," Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series qt14b416tk, Department of Agricultural & Resource Economics, UC Berkeley.
- Wu, Ximing, 2003. "Calculation of maximum entropy densities with application to income distribution," Journal of Econometrics, Elsevier, vol. 115(2), pages 347-354, August.
- Jeffrey M. Perloff & Ximing Wu, 2004. "China's Income Distribution and Inequality," Econometric Society 2004 North American Summer Meetings 316, Econometric Society.
- Dalén, Jörgen, 1987. "Algebraic bounds on standardized sample moments," Statistics & Probability Letters, Elsevier, vol. 5(5), pages 329-331, August.
- Golan, Amos & Judge, George G. & Miller, Douglas, 1996. "Maximum Entropy Econometrics," Staff General Research Papers Archive 1488, Iowa State University, Department of Economics.
- Zellner, Arnold & Highfield, Richard A., 1988. "Calculation of maximum entropy distributions and approximation of marginalposterior distributions," Journal of Econometrics, Elsevier, vol. 37(2), pages 195-209, February.
- Thanasis Stengos & Ximing Wu, 2005. "Partially Adaptive Estimation via Maximum Entropy Densities," University of Cyprus Working Papers in Economics 6-2005, University of Cyprus Department of Economics.
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