Maximum likelihood estimates for the Hildreth-Houck random coefficients model

We explore maximum likelihood (ML) estimation of the Hildreth-Houck random coefficients model. We show that the global ML estimator can be inconsistent. We develop an alternative LML (local ML) estimator and prove that it is consistent and asymptotically efficient for points in the interior of the parameters. Properties of the LML and comparisons with common method of moments (MM) estimates are done via Monte Carlo. Boundary parameters lead to nonstandard asymptotic distributions for the LML which are described. The LML is used to develop a modification of the LR test for random coefficients. Simulations suggest that the LR test is more powerful for distant alternatives than the Breusch-Pagan (BP) Lagrange multiplier test. A simple modification of the BP test also appears to be more powerful than the BP. Copyright Royal Economic Society 2002