Research

Abstract:   A large literature argues that technological change since the 1980s altered the demand for workers' skills, increasing wage inequality and polarization. By estimating a model of occupational choice using panel data from the Survey of Income and Program Participation (SIPP), I find that changes in the supply of workers' skills were also major driving factors in increasing inequality and polarization. Specifically, I find that (1) as tasks in high-skill jobs have become increasingly complex, the distribution of workers' ability to perform those tasks has become more dispersed, (2) workers' ability to perform low-skill work tasks has become more homogeneous, and (3) workers have increasingly sorted into occupations by skill level, even if this does not maximize their income. These results suggest that skill formation has been a key channel through which long run changes in the nature of work have affected wage inequality. Finally, to obtain my estimates I prove a new identification result in a multi-dimensional potential outcome model and show how to robustly estimate it semiparametrically adapting results from mixture models.    

Abstract: Many methods are available for assessing the importance of omitted variables. These methods typically make different, non-falsifiable assumptions. Hence the data alone cannot tell us which method is most appropriate. Since it is unreasonable to expect results to be robust against all possible robustness checks, researchers often use methods deemed "interpretable", a subjective criterion with no formal definition. In contrast, we develop the first formal, axiomatic framework for comparing and selecting among these methods. Our framework is analogous to the standard approach for comparing estimators based on their sampling distributions. We propose that sensitivity parameters be selected based on their covariate sampling distributions, a design distribution of parameter values induced by an assumption on how covariates are assigned to be observed or unobserved. Using this idea, we define a new concept of parameter consistency, and argue that a reasonable sensitivity parameter should be consistent. We prove that the literature's most popular approach is inconsistent, while several alternatives are consistent. 

Note: This material first appeared in our retired and superseded drafts arXiv:2206.02303v3 (May 2023) and arXiv:2206.02303v4 (July 2023). Those drafts also contained additional results which are now in the companion paper, "Assessing Omitted Variable Bias when the Controls are Endogenous." 

Abstract: Omitted variables are one of the most important threats to the identification of causal effects. Several widely used methods assess the impact of omitted variables on empirical conclusions by comparing measures of selection on observables with measures of selection on unobservables. The recent literature has discussed various limitations of these existing methods, however. This includes a companion paper of ours which explains issues that arise when the omitted variables are endogenous, meaning that they are correlated with the included controls. In the present paper, we develop a new approach to sensitivity analysis that avoids those limitations, while still allowing researchers to calibrate sensitivity parameters by comparing the magnitude of selection on observables with the magnitude of selection on unobservables as in previous methods. We illustrate our results in an empirical study of the effect of historical American frontier life on modern cultural beliefs. Finally, we implement these methods in the companion Stata module regsensitivity for easy use in practice. 

Note: A previous draft contained material that is no longer in the current draft; it is now in the companion paper, "An Axiomatic Approach to Comparing Sensitivity Parameters." 

Abstract: We provide identification results for a broad class of learning models in which continuous outcomes depend on three types of unobservables: known heterogeneity, initially unknown heterogeneity that may be revealed over time, and transitory uncertainty. We consider a common environment where the researcher only has access to a short panel on choices and realized outcomes. We establish identification of the outcome equation parameters and the distribution of the unobservables, under the standard assumption that unknown heterogeneity and uncertainty are normally distributed. We also show that, absent known heterogeneity, the model is identified without making any distributional assumption. We then derive the asymptotic properties of a sieve MLE estimator for the model parameters, and devise a tractable profile likelihood-based estimation procedure. Our estimator exhibits good finite-sample properties. Finally, we illustrate our approach with an application to ability learning in the context of occupational choice. Our results point to substantial ability learning based on realized wages.

Abstract: Consider dyadic random variables on units from a given population. It is common to assume that these variables are jointly exchangeable and dissociated. In this case they admit a non-separable specification with two-way unobserved heterogeneity. The analysis of this type of structure is of considerable interest but little is known about their nonparametric identifiability, especially when the unobserved heterogeneity is continuous. We provide conditions under which both the distribution of the observed random variables conditional on the unit-specific heterogeneity and the distribution of the unit-specific heterogeneity itself are uniquely recoverable from knowledge of the joint marginal distribution of the observable random variables alone without imposing parametric restrictions.