Essays on Political Methodology

Abstract

This dissertation consists of five independent essays in political methodology. First four essays propose statistical methodologies for causal inference, with particular emphasis on the analysis of repeated measurements and ordinal outcomes. The last essay develops a method for small area estimation with an application in American Politics.

In the first chapter, I introduce a method to conduct difference-in-difference analysis for ordinal outcomes. Unlike existing methods, the proposed method utilizes the latent variable framework to handle the non-numeric nature of the outcome, enabling identification and estimation of causal effects based on the assumption on the quantile of the latent continuous variable. The proposed method is applied to a study estimating the causal effect of mass shootings on the public's support for gun control.

In the second chapter, adapted from coauthor work in Egami and Yamauchi (2022), I develop a method to improve the difference-in-difference design and the staggered adoption design when multiple pre-treatment periods are available. I propose a new estimator, double DID, based on the generalized method of moments, which contains the two-way fixed effects regression as a special case. I show that the double DID requires a weaker assumption about outcome trends and is more efficient than existing DID estimators. The proposed method is illustrated with two empirical applications, covering both the basic DID and staggered adoption designs.

In the third chapter, I propose a sensitivity analysis for randomized experiments with non-ignorable attritions. The proposed method constructs confidence intervals for treatment effects that account for the possible violation of the conditional independence assumption. The method is based on a nonparametric inequality-based sensitivity analysis that bounds the ratio of quantiles of the potential outcomes. I apply the proposed method to two randomized experiments where the outcome is missing either due to panel attrition or due to the presence of the "don't know" option.

In the fourth chapter, I introduce an alternative estimand for analyzing experiments with ordinal outcomes. While the standard practice is to treat the outcome as continuous and defined the causal effect as a difference between two potential outcomes, I show that the standard estimand differentially weights each ordinal category, where the weight is a deterministic function of the number of categories. Instead, this chapter advocates the \emph{average relative effect} (ARE) as an alternative estimand of interest, which could provide a clear interpretation as a difference of two probabilities. To facilitate the practical use of ARE, I propose a method to improve the best available bound in the literature by imposing a mild condition on the joint distribution of the potential outcome, and by adjusting for baseline covariates. I further extend the result to the factorial design as well as to the difference-in-differences design.

In the final chapter, adapted from coauthored work in Kuriwaki and Yamauchi (2021), I propose a weighting method for small area estimation. The proposed method consists of two-step weighting: first to adjust differences across areas and then to adjust for differences between the sample and population. Unlike the conventional estimators, the proposed estimator can directly use the national weights that are often estimated from pollsters using proprietary information. I also clarify the assumptions needed for valid partial pooling, without imposing an outcome model. I apply the proposed method to estimate the support for immigration policies at the congressional district level in Florida.