Maximum Likelihood Estimation in Binary Data Models Using Panel Data Under Alternative Distributional Assumptions

This note considers a model of (recurrent) univariate binary outcomes which incorporates random individual effects. Given simplifying distributional assumptions, a likelihood can easily be obtained having the attractive feature of being the product of contributions which only involve sums and no numerical integration. A recent paper by Conaway (1990) considers the same problem but solves it by finding expressions for the probabilities of all the 2T possible sequences of the T recurrent binary outcomes, some of which will not be observed in a given data set. The approach adopted in this paper derives an expression for the appropriate likelihood given a particular set of data. The likelihood, score vector and hessian matrix can all be written in simple forms which readily permits the use of Newton-Raphsonigradient methods to locate the roots of the score equations. Simulation experiments suggest that convergence is rapid and also provide evidence on the robustness of the model to distributional misspecification.