This dissertation studies the estimation and statistical inference of a few methods that are commonly used in empirical studies of economics, when the data is dependent. Chapter 1 studies the linear IV models with clustering dependence, which are widely used in empirical studies. The common solution, the cluster covariance estimator, often produces undesirable inferential results, especially with weak instruments. I propose a method that is robust to both weak IV and (potentially heterogeneous) clustering dependence. The proposed method is based on the idea of Fama-MacBeth estimation, with group-level estimators being a truncated version of the unbiased IV estimator. Asymptotic validity is shown under both strong and weak IV sequences, as well as under general requirements. Simulation results indicate that the method has good finite-sample performance in both size and power. The proposed method is applied to study the effect of city compactness on population density. Chapter 2, coauthored with Damian Kozbur, Christian Hansen, and Lucciano Villacorta, presents and analyzes an approach to inference for dependent data. The primary setting considered here is with spatially indexed data in which the dependence structure of observed random variables is characterized by an observed dissimilarity measure over spatial indexes. Observations are partitioned into clusters with the use of an unsupervised clustering algorithm applied to the dissimilarity measure. Once the partition into clusters is learned, a cluster-based inference procedure is applied to a statistical hypothesis test. The procedure proposed in the paper allows the number of clusters to depend on the data, which gives re- searchers a principled method for choosing an appropriate clustering level. The paper gives conditions under which the proposed procedure asymptotically attains the correct size. Chapter 3, coauthored with Connor Dowd, studies the synthetic control methods in the presence of spillover effects. The synthetic control method is often used in treatment effect estimation with panel data where only a few units are treated, and a small number of post- treatment periods are available. Current estimation and inference procedures for synthetic control methods do not allow for the existence of spillover effects, which are plausible in many applications. In this chapter, we consider estimation and inference for synthetic control methods, allowing for spillover effects. We propose estimators for both direct treatment effects and spillover effects and show that they are asymptotically unbiased. In addition, we propose an inferential procedure and show that it is asymptotically unbiased. Our estimation and inference procedure applies to cases with multiple treated units and/or multiple post- treatment periods, and to ones where the underlying factor model is either stationary or cointegrated.




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