Estimating Mixtures of Normal Distributions and Switching Regressions

Abstract Since the likelihood function corresponding to finite mixtures of normal distributions is unbounded, maximum likelihood estimation may break down in practice. The article introduces the “moment generating function estimator” defined as the estimator which minimizes the sum of squares of differences between the theoretical and sample moment generating functions. The consistency and asymptotic normality of the estimator are proved and its finite sample behavior is compared to that of the standard method of moments estimator by Monte Carlo experiments. The estimator is applied to the Hamermesh model of wage bargain determination.