SML Estimation Based on First Order Conditions

This paper describes a strategy for structural estimation of economic models that I will refer to as SML based on FOCs. In this approach, one uses simulated maximum likelihood (SML) to estimate the structural parameters that appear in the Euler or first order conditions (FOCs) solved by an optimizing economic agent. I will argue that the SML based on FOCs approach has certain advantages over the generalized method of moments (GMM) approach to structural estimation based on FOCs. Most importantly, the SML based on FOCs approach can easily handle economic models that involve multiple structural sources of error. In contrast, GMM requires that all the structural sources of error enter the FOCs additively, so that a single composite additive error term may be obtained. In models with multiple sources of error, very strong assumptions on functional form or on information structure are often necessary in order to put FOCs in this form. Thus, the SML based on FOCs approach gives the econometrician much more flexibility in terms of how he/she can specify utility functions and/or production functions, particularly in terms of how these functions may be heterogeneous across agents. Implementation of the SML based on FOCs approach requires the development of a number of new simulation algorithms that I develop here. These include two new recursive importance sampling algorithms that are the discrete/continuous and purely continuous data analogues the GHK algorithm for discrete data. These algorithms should have wide applicability to a range of econometric problems beyond the specific issues discussed here. I illustrate the SML based on FOCs approach by using it to estimate a structural model of the behavior of U.S. MNCs with affiliates in Canada. The model is estimated on confidential BEA firm level data on the activities of U.S. MNCs over the period 1983-96. The method appears to work well in practice. That is, the computation time was manageable, and the algorithm converged steadily to stable estimates that were not very sensitive to starting values or simulation size. The estimated model fits the data reasonably well, and there appeared to be little evidence against the distributional assumptions that were required to implement the SML