This dissertation provides the developments and extensions of methodologies in panel, nonlinear, and high-dimensional econometrics. Chapter 1 of the dissertation introduces and summarizes the following chapters. Chapter 2 proposes a fixed-b approximation method for inference in a linear panel model with two-way clustering. Chapter 3 considers the same dependence structure in panel models with nonlinearity and high dimensionality. Chapter 4 revisits the use of linear models for binary responses, focusing on average partial effects. Chapter 5 considers models with endogenous controls and provides alternative identification methods for a large class of models.
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