UCLA

The dissertation consists of three chapters on different econometric topics. The first chapter studies jackknife bias reduction for simulated maximum likelihood estimator of discrete choice models. We propose to reduce asymptotic biases of simulated maximum likelihood estimators (SMLE) by using a jackknife method similar to Dhaene and Jochmans (2015), which was originally proposed to reduce bias in nonlinear panel models. Lee (1995) investigates the asymptotic bias of the SMLE, and derives the analytical formula of higher order bias due to simulation. However, implementation of Lee (1995)’s method requires analytical characterization of the higher order bias, which may not be convenient for practice. Because the jackknife method does not require an explicit characterization of the bias, it may be a practically attractive alternative to Lee (1995)’s estimator. The second chapter studies estimation of average treatment effects for massively unbalanced binary outcomes. The maximum likelihood estimator (MLE) of the average treatment effects (ATE) in the logit model for binary outcomes may have a significant second order bias if the event has a low probability. The analysis of rare events is relevant for economics because some of the big data sets are collected from online sources where the number of events (such as “ clicks” and “ purchases”) is much smaller than the number of nonevents. The literature about rare events (King and Zeng, 2001; Chen and Giles, 2012; Rilstone, 1996; Wang, 2020) does not shed light on the finite sample behavior of logit MLE and ATE if events are rare. In this chapter, we also derive the second order bias of the logit ATE estimator and propose bias-corrected estimators of the ATE. We also propose a variation on the logit model with parameters that are elasticities. Finally, we propose a computational trick that avoids numerical instability in the case of estimation for rare events. The third chapter studies a Vuong test (Vuong, 1989) for panel data models with fixed effects. This chapter generalizes the Vuong test to nonlinear panel models where the dimension of incidental parameters grows with the sample size. The incidental parameters (Neyman and Scott, 1948) that affect the unbiasedness of the parameters of interest are also important for panel data models as they capture unobserved heterogeneity. The discrepancy in incidental parameters plays an important role in model selection; for example, as noted by MacKinnon et al. (2020), there is a vast literature on the cluster-robust inference that assumes the structure of the clusters is correctly specified, which is often violated. In the presence of incidental parameters, we cannot easily apply the classical Vuong test to select a panel data model. This chapter proposes a new model selection test for panel data models by extending the classical Vuong test, which selects from two parametric likelihood models based on their Kullback–Leibler information criterion (KLIC). This chapter proposes three different test statistics for researchers who need to deal with all possible relationships between candidate models: overlapping models, nested models, and strictly nonnested models. These three model relationships are classified according to the structure of low-dimensional parameter of interest and high-dimensional incidental parameters. We allow for disagreements about incidental parameters and obtain specification tests based on a modified likelihood function.