Essays in causal inference methods designed for financial economics

In this paper, we propose a novel method for causal inference within the counterfactual and synthetic control framework, called the Covariate-projected Principal Component Analysis (CSC-CPCA) method. Our approach accommodates the Generalized Synthetic Control (GSC) method as a special case, thereby inheriting its key advantage of relaxing critical assumptions such as the parallel trends requirement in difference-in-differences designs. Beyond this, CSC-CPCA offers several improvements over GSC. By projecting covariates onto factor loadings through a projection matrix $\Gamma$, the method performs natural dimension reduction, enabling effective handling of high-dimensional datasets while keeping the model parsimonious. This covariate-projection also reduces exposure to model misspecification and improves predictive accuracy. In simulation studies, CSC-CPCA method demonstrates lower bias in the presence of unobserved covariates compared to mainstream alternatives. In an empirical application, we employ CSC-CPCA to evaluate the effect of Brexit on foreign direct investment in the United Kingdom, where the results highlight both the robustness and practical value of the method.