Essays on Inference in Partially Identified ModelsPublic Deposited
This dissertation is composed of three chapters, each contributing to different aspects of the literature of partially identified econometric models. In the first chapter, I introduce a bootstrap procedure to perform inference in the class of partially identified econometric models defined by finitely many moment equalities and inequalities. I provide two different versions: one to cover each element of the identified set with a prespecified probability and the other to cover the identified set itself with a prespecified probability. I compare my bootstrap procedure, a competing asymptotic approximation and the subsampling procedure proposed by Chernozhukov, Hong and Tamer (2007) in terms of the rate at which they achieve the desired coverage level. Under certain conditions, I show that inference based on my bootstrap and asymptotic approximation should eventually be more precise than inference based on subsampling. A Monte Carlo study confirms this finding in a small sample simulation. In the second chapter, I adapt the specification test for functional data developed by Bugni, Hall, Horowitz and Neumann (2008) to the presence of missing observations. By using a worst case scenario approach, my method is able to extract all the information available in the data while being agnostic about the nature of the missing observations. Under the null hypothesis, my specification test will reject the null hypothesis with a probability that, in the limit, does not exceed the significance level of the test. Moreover, the power of the test converges to one whenever the distribution of the non-missing data conveys that the null hypothesis is false. The procedure is illustrated by using it to test the hypothesis that a sample of wage paths was generated by a specific equilibrium job search model. The third chapter explores the causal relationship between the child labor legislation dictated by several U.S. states between 1880 and 1910 and the spectacular decrease in child occupation rates during this period. Previous literature has studied this connection using differencing techniques in binary choice models, which I show to be inadequate. I develop a model with multiple equilibria to analyze the labor market mechanism by which the legislation affects the household's decision to send their children to work. Based on this model, it is possible to establish if the legislation was effective and if it constituted a benign policy or not, which sheds new light to previous results.