Essays on Econometrics and Policy Evaluation

Abstract

This thesis consists of four chapters that study the statistical properties of synthetic control methods and their application to public policy evaluation and the digital economy.

The first chapter, co-written with Ahmet Gulek, proposes a Synthetic Instrumental Variables (SIV) estimator for panel data that combines the strengths of instrumental variables and synthetic controls to address unmeasured confounding. We derive conditions under which SIV is consistent and asymptotically normal, even when the standard IV estimator is not. Motivated by the finite sample properties of our estimator, we introduce an ensemble estimator that simultaneously addresses multiple sources of bias and provide a permutation-based inference procedure. We demonstrate the effectiveness of our methods through a calibrated simulation exercise, two shift-share empirical applications, and an application in digital economics that includes both observational data and data from a randomized control trial. In our primary empirical application, we examine the impact of the Syrian refugee crisis on Turkish labor markets. Here, the SIV estimator reveals significant effects that the standard IV does not capture. Similarly, in our digital economics application, the SIV estimator successfully recovers the experimental estimates, whereas the standard IV does not.

The second chapter, co-written with Ignacio Martinez, proposes a Bayesian alternative to the synthetic control method and explores the frequentist properties of the method in the context of linear factor models. In this chapter, we characterize the conditions on the factor model primitives (the factor loadings) for which the statistical risk minimizers are synthetic controls (in the simplex). Then, we propose a Bayesian alternative to the synthetic control method that preserves the main features of the standard method and provides a new way of doing valid inference. We explore a Bernstein-von Mises style result to link our Bayesian inference to the frequentist inference. For linear factor model frameworks we show that a maximum likelihood estimator (MLE) of the synthetic control weights can consistently estimate the predictive function of the potential outcomes for the treated unit and that our Bayes estimator is asymptotically close to the MLE in the total variation sense. Through simulations, we show that there is convergence between the Bayesian and frequentist approach even in sparse settings. Finally, we apply the method to re-visit the study of the economic costs of the German re-unification and the Catalan secession movement. The Bayesian synthetic control method is available in the bsynth R-package.

The third chapter, recognizes that synthetic control methods often rely on matching pre-treatment characteristics (called predictors) of the treated unit, and that the choice of predictors and how they are weighted plays a key role in the performance and interpretability of synthetic control estimators. This chapter proposes the use of a sparse synthetic control procedure that penalizes the number of predictors used in generating the counterfactual to select the most important predictors. I derive, in a linear factor model framework, a new model selection consistency result and show that the penalized procedure has a faster mean squared error convergence rate. Through a simulation study, I then show that the sparse synthetic control achieves lower bias and has better post-treatment performance than the unpenalized synthetic control. Finally, I apply the method to revisit the study of the passage of Proposition 99 in California in an augmented setting with a large number of predictors available.

The fourth chapter, co-written with Alberto Abadie, proposes a set of simple principles to guide empirical practice in synthetic control studies. The proposed principles follow from formal properties of synthetic control estimators, and pertain to the nature, implications, and prevention of over-fitting biases within a synthetic control framework, to the interpretability of the results, and to the availability of validation exercises. We discuss and visually demonstrate the relevance of the proposed principles under a variety of data configurations. JEL: C23, C26, C11, C52.