Essays in Econometric Theory and Applied Econometrics

My dissertation consists of three chapters that concerns topics in econometric theory and applied econometrics. The first two chapters analyze identification and estimation in models with endogeneity. The second chapter is joint work with Edward Vytlacil. The final chapter reexamines methods for dealing truncated dataset in economic history.;The first chapter of my dissertation analyzes the effect of weak instruments on identification, estimation, and inference in a nonparametric setting. This analysis is considered to be the first attempt in the literature. The consequences of weak instruments have been extensively studied in the literature with linear simultaneous equations models. One might conjecture that the problem of weak instruments becomes even more important when studying endogenous explanatory variables in nonparametric models, as more flexible models generally require stronger identification power, and hence plausibly stronger instruments.;To address this problem, in this chapter, we consider a triangular simultaneous equations model, and follow the control function approach for identification and estimation. We derive a necessary and sufficient rank condition for identification, based on which weak identification is established. Then, nonparametric weak instruments are defined as a sequence of reduced form functions that converges to a constant function. We characterize weak instruments as a multicollinearity problem or, more generally, as an inverse problem, which motivates the introduction of a regularization scheme. We propose a series estimation method with penalization to alleviate the effects of weak instruments. We derive the rate of convergence of the resulting penalized series estimator. Consistency and asymptotic normality are achieved with "mildly" weak instruments and a "rapidly" shrinking penalization parameter. Monte Carlo results show that the finite sample performance of the penalized estimator is appealing. The results of this chapter are applied to an empirical example, where the effect of class size on test scores is estimated nonparametrically.;The second chapter, which is joint work with Edward Vytlacil, studies the identification problem in bivariate probit models with endogenous binary regressors. We find that an exclusion restriction is sufficient to globally identify parameters in a simple bivariate probit model. We find that identification is still achieved in a model without the exclusion restriction but with common exogenous regressors that are present in both probit equations. We show that our identification result extends beyond the bivariate probit model to a larger class of bivariate threshold crossing models characterized by latent error terms that are distributed according to a normal copula while having arbitrary (but known) marginal distributions.;The third chapter studies the long-term trend in the standard of living during the Industrial Revolution in Britain. In particular, we investigate methods and findings in Komlos's (1993) study. As a proxy for the living standard, he estimates the trend in the mean heights of subgroups of the population, and concludes that the living standard has deteriorated throughout the period. In this chapter, we reexamine his findings by analyzing the two-step procedure that Komlos employs to deal with the sample that is truncated due to institutional policies. We find that, in each step of the procedure, Komlos requires a set of strong assumptions that is not consistent with the data. We show, however, that the first step procedure is justified under weaker assumptions, which implies that the result obtained from this procedure is robust. In doing so, we develop a generalized version of the main theorem based on which Komlos employs his procedure. Despite the validity of the first step, we show that a fairly general distributional assumption that justifies the first step creates bias in the second step. We also find that, even with the same data and the two-step procedure that Komlos uses, one of his reported graphs, which is most supportive to his conclusions, cannot be replicated. Lastly, by decomposing the first and second step of Komlos's procedure, we find that his final results are mainly driven by the second step procedure. We calculate an alternative trend using a method that does not create bias in the second step, which does not present a downward trend. According to the result, the living standard during the period has not deteriorated.