Income distribution functions with disturbances

Recent exercises in the maximum likelihood estimation of income distribution functions provide goodness of fit tests which lead to the rejection of most models. This result is usually ignored on the ground that the test is too strict, since it allows for sampling variation only. If income distribution functions, like other econometric models, are not meant to hold exactly, we should introduce disturbances in the statistical model. Here we treat observed income as the sum of a systematic component with a specific two-parameter distribution — Pareto, Gamma, or Lognormal — and an independent normal error. The ensuing models fit conventional U.S. income data much better than their traditional counterparts, but they still fail a goodness of fit test.