A New Optimization Approach to Maximum Likelihood Estimation of Structural Models

Maximum likelihood estimation of structural models is regarded as computationally difficult by many who want to apply the Nested Fixed-Point approach. We present a direct optimization approach to the problem and show that it is significantly faster than the NFXP approach when applied to the canonical Zurcher bus repair model. The NFXP approach is inappropriate for estimating games since it requires finding all Nash equilibria of a game for each parameter vector considered, a generally intractable computational problem. We reformulate the problem of maximum likelihood estimation of games as an optimization problem qualitatively no more difficult to solve than standard maximum likelihood estimation problems. The direct optimization approach is also applicable to other structural estimation problems such as auctions and RBC models, and also to other estimation strategies, such as the methods of moments. It is also easily implemented on standard software implementing state-of-the-art nonlinear programming algorithms