Calculation of Maximum Entropy Densities with Application to Income Distribtuions

Abstract

This paper shows that there exits a unique maximum entropy density for any finite sample when arithmetic sample moments are used as side conditions. A sequential updating method to calculate the maxent entropy density subject to known moment constraints is proposed. Instead of imposing the moment constraints simultaneously, the sequential updating method incorporates the moment constraints into the calculation from lower to higher moments and updates the density estimates sequentially. The proposed method is employed to approximate the size distribution of U.S. family income. Numerical experiments and empirical evidence demonstrate the efficiency of this method.

Keywords: Maximum Entropy, Density, Optimization, Income Distribution

JEL Classification: C4, C6, D3