Essays in Econometrics

Tabord-Meehan, Max

doi:https://doi.org/10.21985/n2-8vbn-fd29

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Essays in Econometrics

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This dissertation studies three distinct problems in econometrics. Chapter 1 proposes an adaptive randomization procedure for two-stage randomized controlled trials. The method uses data from a first-wave experiment in order to determine how to stratify in a second wave of the experiment, where the objective is to minimize the variance of an estimator for the average treatment effect (ATE). I consider selection from a class of stratified randomization procedures called stratification trees: these are procedures whose strata can be represented as decision trees, with differing treatment assignment probabilities across strata. By using the first wave to estimate a stratification tree, the method simultaneously selects which covari- ates to use for stratification, how to stratify over these covariates, as well as the assignment probabilities within these strata. My main result shows that using this randomization pro- cedure with an appropriate estimator results in an asymptotic variance which minimizes the variance bound for estimating the ATE, over an optimal stratification of the covariate space. Moreover, by extending techniques developed in Bugni et al. (2018), the results presented are able to accommodate a large class of assignment mechanisms within strata, including stratified block randomization. I also present extensions of the procedure to the setting of multiple treatments, and to the targeting of subgroup-specific effects. In a simulation study, I find that the method is most effective when the response model exhibits some amount of "sparsity" with respect to the covariates, but can be effective in other contexts as well, as long as the first-wave sample size used to estimate the stratification tree is not prohibitively small. The chapter concludes by applying the method to the study in Karlan and Wood (2017), where I estimate stratification trees using the first wave of their experiment. Chapter 2 (which is joint work with Eric Mbakop) studies a new statistical decision rule for the treatment assignment problem. Consider a utilitarian policy maker who must use sample data to allocate one of two treatments to members of a population, based on their observable characteristics. In practice, it is often the case that policy makers do not have full discretion on how these covariates can be used, for legal, ethical or political reasons. We treat this constrained problem as a statistical decision problem, where we evaluate the performance of decision rules by their maximum regret. We focus on settings in which the policy maker may want to select amongst a collection of such constrained classes: examples we consider include choosing the number of covariates over which to perform best-subset selection, and model selection when approximating a complicated class via a sieve. We adapt and extend results from statistical learning to develop a decision rule which we call the Penalized Welfare Maximization (PWM) rule. We establish an oracle inequality for the regret of the PWM rule which shows that it is able to perform model selection over the collection of available classes. We then use this oracle inequality to derive relevant bounds on maximum regret for PWM. We illustrate the model-selection capabilities of our method with a small simulation exercise, and conclude by applying our rule to data from the Job Training Partnership Act (JTPA) study. Chapter 3 studies inference in the linear model with dyadic data. Dyadic data are indexed by pairs of “units”, for example trade data between pairs of countries. Because of the potential for observations with a unit in common to be correlated, standard inference procedures may not perform as expected. I establish a range of conditions under which a t-statistic with the dyadic-robust variance estimator of Fafchamps and Gubert (2007) is asymptotically normal. Using these theoretical results as a guide, I perform a simulation exercise to study the validity of the normal approximation, as well as the performance of a novel finite-sample correction. The chapter concludes with guidelines for applied researchers wishing to use the dyadic-robust estimator for inference

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