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ABSTRACT:
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.

SUGGESTED CITATION:
Ximing Wu and Jeffrey M. Perloff, "GMM Estimation of a Maximum Distribution With Interval Data" (March 1, 2005). Institute for Research on Labor and Employment. Institute for Research on Labor and Employment Working Paper Series. Paper iirwps-112-05.
http://repositories.cdlib.org/iir/iirwps/iirwps-112-05