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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"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.
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