Three essays on structural parameter estimation and bias correction for discrete choice models.

    In the last few decades, we have observed a growing body of economic research that focuses on structural economic models. Several authors, including Dubé et al. (2005), Reis and Wolak (2007), Keane et al. (2011), Low and Meghir (2017), highlight the importance of structural models in providing researchers with better insights on behaviors of economic agents, which cannot be captured by descriptive econometric models. The three main chapters in this thesis are independent essays on the estimation of structural parameters of two discrete choice models which are widely used in industrial organization economics. The first one is Berry, Levinsohn, and Pakes's (1995) random coefficient demand model, abbreviated as the BLP model. This model has well-deserved popularity for the analysis of demand for differentiated products since it accounts for the endogeneity of price and includes random coefficients to capture the heterogeneity of consumers' preferences. The second model is a dynamic discrete choice model which incorporates dynamic optimization of economic agents. In this model, the decision makers are assumed to be rational and forward-looking; the choices that they make today aim at maximizing the sequence of present and future payoffs.

    In chapter 2, "Limited information maximum likelihood estimation of random coefficient demand models with aggregate data", I propose to estimate the BLP model by means of the limited information maximum likelihood (LIML) estimation method. There are several estimation methods available for this model. The most commonly used is the generalized method of moments (GMM), as in Berry, Levinsohn, and Pakes (1995), Nevo (2000) and recently in Reynaert and Verboven (2014), where Chamberlain's (1987) optimal instruments are used. The GMM estimation with optimal instruments performs better than the other alternative estimation methods. Therefore, I use it as the benchmark for the comparison with the LIML estimation. The simulation results show that LIML produces estimates that are competitive with GMM, especially in terms of standard deviation. Furthermore, in order to examine the robustness of LIML, I present additional results in setups where the error terms are misspecified or where many instruments are included. LIML maintains good performance in these cases. In general, the simulation results are in line with the expected asymptotic properties of this estimator.

    Chapter 3, "Bias-corrected estimation of the BLP random coefficient model with fixed effects", touches upon another aspect of the BLP model. That is, BLP is extended to include market and product fixed effects, which allow the model to account for unobserved heterogeneity that is invariant across products and markets. The same estimation method, i.e., LIML, is also used in this chapter. The computation is slightly modified compared with the one used in the previous chapter. The main focus of this chapter is to correct for the incidental parameter bias, which arises when the number of fixed effects, or nuisance parameters, increases with the number of observations. The consequence of severe incidental parameter bias is anticipated: the estimation is inconsistent and standard LIML inference is misleading. The approach I propose is based on Dhaene and Jochmans (2015b), with which I examine the expected bias and possibility of bias spillover to other parameters. Based on this, I derive the corrected version of the concentrated log-likelihood function analytically. Monte Carlo simulations show that the method produces reasonably good estimates of the common parameters despite the presence of fixed effects. My focus is on correcting the incidental parameter bias problem when there are market fixed effects. However, a similar procedure can be applied for the case where product fixed effects are incorporated into the BLP model. I include an extension which presents how the incidental parameter bias arises in this case and how it can be resolved.

    In the last chapter, "Continuous-updating estimation of dynamic discrete choice models", I use Hansen, Heaton and Yaron's (1996) continuous-updating estimator (CUE) to estimate the structural parameters of a single-agent dynamic discrete choice model. The CUE is constructed using the theoretical results of Hotz and Miller (1993) and Aguirregabiria and Mira (2002). The algorithm is a two-step procedure where the contraction mapping for the conditional choice probabilities is incorporated as an inner loop. With this, the CUE avoids repeating the optimization procedure multiple times as implemented in the NPL algorithm of Aguirregabiria and Mira (2002). The contracting mapping plays the role of refining the estimates of the conditional choice probabilities; hence, it reduces the bias in the estimation of the model's structural parameters drastically. The CUE does not outperform the NPL estimator in common setups; however, it produces stable results even in cases where NPL is not reliable.