DOI: 10.25549/usctheses-c40-326408
title: MPEC and sequential Monte Carlo method to structural estimation

description: Modern empirical economic research constantly faces challenges from structural estimation. The conventional estimation algorithm for structural models involves unconstrained optimization to a complicated criterion function with multiple local optima, an approach that is not only slow-computing but also has questionable convergence properties. To improve estimation efficiency and accuracy, I propose two alternative algorithms to implement structural estimation: a quasi-Bayesian approach, density-tempered Sequential Monte Carlo, to estimate random coefficient demand models, as well as a conditional optimization algorithm, Mathematical Programming with Equilibrium Constraints (MPEC), to estimate structural matching models. I also conduct Monte Carlo experiments to investigate the consequences of a misspecified demand estimation. ❧ In the first chapter, I propose a quasi-Bayesian approach that formulates the quasi-posterior in the spirit of Chernozhukov and Hong (2003) and implements the sampling with a density-tempered sequential Monte Carlo (SMC) approach. The advantage of this algorithm lies in both the stochastic exploratory nature of the process that is not vulnerable to the presence of multiple local optima and the fact that it preserves the original assumptions of the BLP IV-GMM estimator. Extending the simulation framework developed by Dube Fox and Su (2012), I demonstrate the usefulness of the SMC method in contrast to MPEC and a comparable Markov chain Monte Carlo approach. SMC not only provides a reliable and informative estimation for each scenario, but in addition has the merit of fast computation due to the utilization of modern parallel computing technology. ❧ In the second chapter, I study the consequences of demand misspecification. To demonstrate how misspecification leads to biases in both estimated elasticities and counterfactual merger simulations, I conduct Monte Carlo experiments to three state-of-art demand models with GMM estimation: the fixed-coefficient logit model, the random-coefficient logit model with and without observable demographics. They are a nested family of demand models. I find that the simpler models, even if misspecified, have more explanatory power. For the elasticity estimation, the fixed-coefficient model or the random-coefficient model without demographics yield small mean squared errors (MSEs). Regarding the post-merger price predictions, it is the simplest fixed-coefficient model that always outperforms the two random-coefficient models. Furthermore, in several scenarios, the biases of the estimates by the two specifications with lower MSEs have opposite signs, suggesting that a weighted average of the estimates may be a more reliable strategy. ❧ The third chapter applies MPEC to structural matching models, in an attempt to improve the performance of the integer projected fixed point algorithm. To do so, I derive the Jacobians of the analytical matching function for both the transferrable utility case and non-transferrable utility case, and use the Jabobians to code the MPEC algorithm. A preliminary result shows that MPEC combined with the state-of-art KNITRO solver is capable of converging to local optima with far less computation time than the conventional method.