Essays in Causal and Comparative Econometrics
My doctoral dissertation concerns causal and comparative econometrics. It comprises four separate essays with a common theme. They propose new metrics for causal or comparative inference and address problems with some ratios that are widely used for policy analysis. In the first chapter titled 'Stable Probability Weighting for Large-Sample Causal Analysis,' I propose new methods for causal analysis involving "Basu's elephants" (data with extreme selection on observables), which plague many empirical studies in both social and health sciences. I address this empirically relevant issue of limited overlap in settings where unconfoundedness holds and the conditional average treatment effect can be parameterized. I do so by developing a general principle called "Stable Probability Weighting" (SPW) that can be used as an alternative to the widely used Inverse Probability Weighting (IPW) technique, which relies on strong overlap. I show that IPW (or its augmented version), when valid, is a special case of the more general SPW (or its doubly robust version), which adjusts for the extremeness of the conditional probabilities of the treatment states. My approach also provides doubly robust alternatives to the widely used "Robinson transformation," which lacks double robustness. Large-sample causal analysis based on the SPW principle can be implemented using several established parametric or semiparametric procedures for conditional moment models. My framework extends to the setting of multivalued treatments. In the second chapter titled 'Finite-Sample Set-Estimation and Inference for Causal Analysis,' I develop new finite-sample methods that apply when unconfoundedness is plausible within fine strata. Since the widely used IPW technique relies on the problematic reciprocal of the estimated propensity score, I develop alternative set-estimators that are unbiased in a sense. I also propose new finite-sample inference methods for testing a general class of weak null hypotheses. The associated computationally convenient methods can be used to construct valid confidence sets and to bound the finite-sample confidence distribution. The third chapter is titled 'An Axiomatic Framework for Relative Cost–Benefit Analysis.' In recent years, the Marginal Value of Public Funds (MVPF) has become a popular tool for conducting cost–benefit analysis; the MVPF relies on the ratio of willingness-to-pay for a policy divided by its net fiscal cost. The MVPF gives policymakers important information about the equity–efficiency trade-off that is not necessarily conveyed by absolute welfare measures. However, I show in this chapter that the usefulness of MVPF for comparative welfare analysis is limited, because it suffers from several empirically important economic paradoxes and statistical irregularities. There are also several practical issues in using the MVPF to aggregate welfare across policies or across population subgroups. To address these problems, I develop a new axiomatic framework to construct a measure that quantifies the equity–efficiency trade-off in a better way. I do so without compromising on the core features of the MVPF: its unit-free property, and the main preference orderings underlying it. My axiomatic framework delivers a unique (econo)metric that I call the Relative Policy Value (RPV), which can be weighted to conduct both comparative and absolute welfare analyses (or a hybrid combination thereof) and to intuitively aggregate welfare (without encountering the issues in MVPF-based aggregation). I also propose computationally convenient methods to make uniformly valid statistical inferences on welfare measures. After reanalyzing several government policies using my new econometric methods, I conclude that there is substantial economic and statistical uncertainty about welfare of some policies that were previously reported to have very high or even "precisely estimated infinite" MVPF values. In the fourth chapter titled 'A Comparative Framework for Relative Multivariate Analysis,' I develop new methods for comparative analysis of multivariate data, such as multiple financial asset returns and user ratings of various products. My approach involves transforming the original data into bounded relative measures and is grounded in an axiomatic framework, which is inspired by the Ricardian notion of comparative advantage. I propose the Relative Sign Value (RSV), a generalization of the sign function, for relative multivariate analysis. The resulting statistical procedures based on it serve as general alternatives to some widely used nonparametric tests, such as the sign test, the signed-rank test, and the Friedman test. My methodology has applications in several areas. For example, it is useful for conducting sector or portfolio analysis in finance from a relative perspective to identify high-performing assets in a comparative manner. Users of online marketplaces or streaming services or review platforms may find relative ratings of products and services helpful. The general framework is also useful for multi-output model selection in a machine learning context. In addition, some of the proposed relative measures based on longitudinal data can themselves be practically treated as outcomes for causal analysis in some settings.
Applied Econometrics, Axiomatic Framework, Causal Inference, Comparative Framework, Cost–Benefit Analysis, Econometrics, Economics, Equity–Efficiency Tradeoff, Finance, Finite-Sample Inference, Finite-Sample Set-Estimation, Friedman Test, Limited Overlap, Marginal Value of Public Funds, Multi-Output Model Selection, Multivariate Analysis, Multivariate Statistics, Portfolio Analysis, Public Economics, Ratings Analysis, Relative Policy Value, Relative Sign Value, Sector Analysis, Semiparametric Econometrics, Sign Test, Signed-Rank Test, Stable Probability Weighting, Statistical Inference, Statistics, Uniformly Valid Inference, Welfare Aggregation, Welfare Analysis
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