Working Papers
"Reinforcing RCTs with Multiple Priors while Learning about External Validity", with F. Finan.
Updated December, 2021. {pdf}
Abstract: This paper presents a framework for how to incorporate prior sources of information into the design of a sequential experiment. These sources can include previous experiments, expert opinions, or the experimenter's own introspection. We formalize this problem using a multi-prior Bayesian approach that maps each source to a Bayesian model. These models are aggregated according to their associated posterior probabilities. We evaluate a broad of policy rules according to three criteria: whether the experimenter learns the parameters of the payoff distributions, the probability that the experimenter chooses the wrong treatment when deciding to stop the experiment, and the average rewards. We show that our framework exhibits several nice finite sample properties, including robustness to any source that is not externally valid.
"Inference for multi-valued heterogenous treatment effects when the number of treated units is small", with M. Dias.
Updated: May, 2021. {pdf}
Abstract: We propose a method for conducting asymptotically valid inference for treatment effects in a multi-valued treatment framework where the number of units in the treatment arms can be small and do not grow with the sample size. We accomplish this by casting the model as a semi-/non-parametric conditional quantile model and using known finite sample results about the law of the indicator function that defines the conditional quantile. Our framework allows for structural functions that are non-additively separable, with flexible functional forms and heteroskedasticy in the residuals, and it also encompasses commonly used designs like difference in difference. We study the finite sample behavior of our test in a Monte Carlo study and we also apply our results to assessing the effect of weather events on GDP growth.
"Some Large Sample Results for the Method of Regularized Estimators”, with M. Jansson.
Updated: July, 2020. {pdf}
Abstract: We present a general framework for studying regularized estimators; i.e., estimation problems wherein "plug-in" type estimators are either ill-defined or ill-behaved. We derive primitive conditions that imply consistency and asymptotic linear representation for regularized estimators, allowing for slower than square-root n estimators as well as infinite dimensional parameters. We also provide data-driven methods for choosing tuning parameters that, under some conditions, achieve the aforementioned results. We illustrate the scope of our approach by studying a wide range of applications, revisiting known results and deriving new ones.
“On the Non-Asymptotic Properties of Regularized M-estimators”.
Updated: May, 2016. {pdf}
Abstract: We propose a general framework for regularization in M-estimation problems under time dependent (absolutely regular-mixing) data which encompasses many of the existing estimators. We derive non-asymptotic concentration bounds for the regularized M-estimator. Our results exhibit a "variance-bias" trade-off, with the "variance" term being governed by a novel measure of the "size" of the parameter set. We also show that the mixing structure affect the variance term by scaling the number of observations; depending on the decay rate of the mixing coefficients, this scaling can even affect the asymptotic behavior. Finally, we propose a data-driven method for choosing the tuning parameters of the regularized estimator which yield the same (up to constants) concentration bound as one that optimally balances the "(squared) bias" and "variance" terms. We illustrate the results with several canonical examples of, both, non-parametric and high-dimensional models.
Updated December, 2021. {pdf}
Abstract: This paper presents a framework for how to incorporate prior sources of information into the design of a sequential experiment. These sources can include previous experiments, expert opinions, or the experimenter's own introspection. We formalize this problem using a multi-prior Bayesian approach that maps each source to a Bayesian model. These models are aggregated according to their associated posterior probabilities. We evaluate a broad of policy rules according to three criteria: whether the experimenter learns the parameters of the payoff distributions, the probability that the experimenter chooses the wrong treatment when deciding to stop the experiment, and the average rewards. We show that our framework exhibits several nice finite sample properties, including robustness to any source that is not externally valid.
"Inference for multi-valued heterogenous treatment effects when the number of treated units is small", with M. Dias.
Updated: May, 2021. {pdf}
Abstract: We propose a method for conducting asymptotically valid inference for treatment effects in a multi-valued treatment framework where the number of units in the treatment arms can be small and do not grow with the sample size. We accomplish this by casting the model as a semi-/non-parametric conditional quantile model and using known finite sample results about the law of the indicator function that defines the conditional quantile. Our framework allows for structural functions that are non-additively separable, with flexible functional forms and heteroskedasticy in the residuals, and it also encompasses commonly used designs like difference in difference. We study the finite sample behavior of our test in a Monte Carlo study and we also apply our results to assessing the effect of weather events on GDP growth.
"Some Large Sample Results for the Method of Regularized Estimators”, with M. Jansson.
Updated: July, 2020. {pdf}
Abstract: We present a general framework for studying regularized estimators; i.e., estimation problems wherein "plug-in" type estimators are either ill-defined or ill-behaved. We derive primitive conditions that imply consistency and asymptotic linear representation for regularized estimators, allowing for slower than square-root n estimators as well as infinite dimensional parameters. We also provide data-driven methods for choosing tuning parameters that, under some conditions, achieve the aforementioned results. We illustrate the scope of our approach by studying a wide range of applications, revisiting known results and deriving new ones.
“On the Non-Asymptotic Properties of Regularized M-estimators”.
Updated: May, 2016. {pdf}
Abstract: We propose a general framework for regularization in M-estimation problems under time dependent (absolutely regular-mixing) data which encompasses many of the existing estimators. We derive non-asymptotic concentration bounds for the regularized M-estimator. Our results exhibit a "variance-bias" trade-off, with the "variance" term being governed by a novel measure of the "size" of the parameter set. We also show that the mixing structure affect the variance term by scaling the number of observations; depending on the decay rate of the mixing coefficients, this scaling can even affect the asymptotic behavior. Finally, we propose a data-driven method for choosing the tuning parameters of the regularized estimator which yield the same (up to constants) concentration bound as one that optimally balances the "(squared) bias" and "variance" terms. We illustrate the results with several canonical examples of, both, non-parametric and high-dimensional models.
Non-Active Working Papers
“Learning foundation and equilibrium selection in voting environments with private information”, with Ignacio Esponda. Updated: January 25, 2012. { pdf } This paper is obsolete, mostly incorporated in the papers "Conditional Retrospective Voting in Large Elections" and "Retrospective Voting and Party Polarization"
Abstract: We use a dynamic learning model to investigate different behavioral assumptions in voting environments with private information. We show that a simple rule, where players learn based on the outcomes of past elections in which they were pivotal but requires no prior knowledge of the payoff structure or of the rules followed by other players, provides a foundation for Nash equilibrium. In contrast, a rule where voters learn from all past elections provides a foundation for a new notion of naive voting where players vote sincerely but have endogenously-determined beliefs. Finally, we use the model to select among multiple equilibria in the jury model. We find that the well-known result that elections aggregate information under Nash equilibrium relies on the selection of symmetric equilibria which are unstable. Nevertheless, we show that there exist (possibly asymmetric) Nash equilibria that are asymptotically stable and aggregate information.
Abstract: We use a dynamic learning model to investigate different behavioral assumptions in voting environments with private information. We show that a simple rule, where players learn based on the outcomes of past elections in which they were pivotal but requires no prior knowledge of the payoff structure or of the rules followed by other players, provides a foundation for Nash equilibrium. In contrast, a rule where voters learn from all past elections provides a foundation for a new notion of naive voting where players vote sincerely but have endogenously-determined beliefs. Finally, we use the model to select among multiple equilibria in the jury model. We find that the well-known result that elections aggregate information under Nash equilibrium relies on the selection of symmetric equilibria which are unstable. Nevertheless, we show that there exist (possibly asymmetric) Nash equilibria that are asymptotically stable and aggregate information.