This dissertation studies causal inference and its applications in empirical political economy. Chapter 1 studies a binary Imbens-Angrist instrumental variable model for persuasion. In the empirical study of persuasion, researchers often use a binary instrument to encourage individuals to consume information and take some action. We show that with the Imbens-Angrist instrumental variable model assumptions and the monotone treatment response assumption, it is possible to identify the joint distributions of potential outcomes among compliers. This is necessary to identify the percentage of persuaded individuals and their statistical characteristics. Specifically, we develop a weighting method that helps researchers identify the statistical characteristics of persuasion types: compliers and always-persuaded, compliers and persuaded, and compliers and never-persuaded. These findings extend the “Kappa weighting” results in Abadie (2003). We also provide a sharp test on the two sets of identification assumptions. The test boils down to testing whether there exists a nonnegative solution to a possibly under-determined system of linear equations with known coefficients. An application based on Green et al. (2003) is provided. The result shows that among compliers, roughly 10% voters are persuaded. The results are consistent with the findings that voters' voting behaviors are highly persistent. Chapter 2 applies the methods developed in the first chapter to three empirical examples (Enikolopov et al., 2011, Blattman and Annan, 2016, Chen and Yang, 2019). The results illustrate the usefulness of the methods. Re-analyzing Enikolopov et al. (2011) informed us that most of the voters were persuaded, and the persuaded voters were likely to be middle-aged and male. Re-analyzing Blattman and Annan (2016) informed us that around 20% of the Liberian ex-fighters were persuaded, and the persuaded ex-fighters were more likely to be risky type. Re-analyzing Chen and Yang (2019) informed us that roughly 20% of the students were persuaded, and the persuaded students were likely to come from wealthy families, come from coastal areas, less risk-loving, and less likely to believe in the inherent goodness of people. Chapter 3, coauthored with Hongchang Guo, studies when the validity of triple difference depends on functional form. Here, the functional form refers to the transformations on the outcome variables (e.g., taking the logarithm of the outcome variable). Build on Roth and Sant’Anna (2023), we provide a novel characterization: the “modified” parallel trends assumption in the triple difference design holds under all measurable transformations of the outcome if and only if a stronger “modified” parallel trends-type condition holds for the cumulative distribution function of untreated potential outcomes. Another equivalent condition for “modified” parallel trends to be insensitive to functional form is that the population can be partitioned into subgroups for which the treatment is effectively not (as-if) randomly assigned and a remaining part that is stable over time, which contrasts sharply to the decomposition results in Roth and Sant’Anna (2023). These conditions have testable implications on the distribution of the unobservable but identifiable untreated potential outcomes for the treated group in the treated period. Testing these implications boils down to testing a family of moment inequalities. We revisit Muralidharan and Prakash (2017) to illustrate the methodology we propose.