UNDERSTANDING REGRESSION VERSUS VARIANCE TESTS FOR SOCIAL INTERACTIONS

This article considers the relationship between the use of regressions and the use of variance contrast methods to uncover social interactions. We illustrate how these methods employ different identifying assumptions and are therefore complementary approaches. We also provide formal identification results that extend existing ones for the two methods. ( JEL C12, C21, C23, Z13)     

Strong Consistency of the Maximum Likelihood Estimator for Finite Mixtures of Location–Scale Distributions When Penalty is Imposed on the Ratios of the Scale Parameters

Abstract.  In finite mixtures of location–scale distributions, if there is no constraint or penalty on the parameters, then the maximum likelihood estimator does not exist because the likelihood is unbounded. To avoid this problem, we consider a penalized likelihood, where the penalty is a function of the minimum of the ratios of the scale parameters and the sample size. It is shown that the penalized maximum likelihood estimator is strongly consistent. We also analyse the consistency of a penalized maximum likelihood estimator where the penalty is imposed on the scale parameters themselves.