Nonparametric Estimation and Inference in Econometrics

This dissertation includes two essays: The first one is on nonparametric inference in causal effect models, and the second one is on nonparametric estimation in financial economics. In the first essay, we propose a nonparametric test for unobserved heterogeneous treatment effects in a general framework, allowing for self-selection to the treatment. The proposed modified Kolmogorov-Smirnov-type test is consistent and simple to implement. Monte Carlo simulations show that our test performs well in finite samples. For illustration, we apply our test to study heterogeneous treatment effects of the Job Training Partnership Act on earnings and the impacts of fertility on family income. In the second essay, we provide an alternative to the existing estimations of implied volatility in option pricing. The use of state price densities to gather information about market sentiment and other empirical characteristics that describe important phenomena is popular in literature and in practice. The estimation of the implied volatility surface to extract these densities is a crucial intermediate step in the process, and the methods to do so are varied in literature. This essay proposes an estimation procedure that is relative new in nonparametric literature: `1 trend filtering. We show its advantages over typically used nonparametric and parametric methods, commonly used in literature and in practice, to deal with this particular estimation problem. Additionally, the method maintains smaller prediction errors than the comparison models across different number of observations and levels of noise