A Recursive Estimator for Random Coefficient Models

This paper describes a recursive method for estimating random coefficient models. Starting with a trial value for the moments of the distribution of coefficients in the population, draws are taken and then weighted to represent draws from the conditional distribution for each sampled agent (i.e., conditional on the agent’s observed dependent variable.) The moments of the weighted draws are calculated and then used as the new trial values, repeating the process to convergence. The recursion is a simulated EM algorithm that provides a method of simulated scores estimator. The estimator is asymptotically equivalent to the maximum likelihood estimator under specified conditions. The recursive procedure is faster than maximum simulated likelihood (MSL) with numerical gradients, easier to code than MSL with analytic gradients, assures a positive definite covariance matrix for the coefficients at each iteration, and avoids the numerical difficulties that often occur with gradient-based optimization. The method is illustrated with a mixed logit model of households’ choice among energy suppliers.