Constrained Optimization Approaches to Estimation of Structural Models

Maximum likelihood estimation of structural models is regarded as computationally di-cult. This impression is due to a focus on the Nested Fixed-Point approach. We present a direct optimization approach to the problem and show that it is signiflcantly 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 flnding 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 into an optimization problem that is qualitatively no more di-cult to solve than standard 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. Structural estimation of economic models is an important technique for analyzing economic data. However, it is commonly believed that computational demands make it di-cult to implement the most powerful statistical methods. For example, maximum likelihood esti- mation is the gold standard in estimation and Rust (1987) provided a strategy for maximum likelihood estimation of economic models, an approach he dubbed the Nested Fixed-Point (NFXP) algorithm. Unfortunately, NFXP is computationally demanding since it repeat- edly takes a guess for the structural parameters and solves for the corresponding endogenous economic variables with high accuracy. While it is clear that NFXP is impractical in many contexts, particularly in the estimation of games, this does not mean that maximum like- lihood estimation is intractable. We present a direct optimization approach, called the MPEC (Mathematical Programming with Equilibrium Constraints) to structural estima- tion that avoids repetitive solution of the structural model; in fact, the only equilibrium ⁄ This version was prepared for the 2007 Chicago-Argonne Institute of Computational Economics, July 30-August 9. This version is incomplete. We welcome comments.