arXiv subjects

Paul Diegert

Publications and source records attributed to Paul Diegert.

4 recordsLinked to original sources

arXiv2026

Assessing Sensitivity to IV Exclusion and Exogeneity without First Stage Monotonicity

Exclusion and exogeneity are core assumptions in instrumental variable (IV) analyses, but their empirical validity is often debated. This paper develops new sensitivity analyses for these assumptions. Our results accommodate arbitrary heterogeneity in treatment effects and do not impose any monotonicity requirements on the first stage. Specifically, we derive identified sets for the marginal distributions of potential outcomes and their functionals, like average treatment effects, under a broad class of nonparametric relaxations of the exclusion and exogeneity assumptions. These identified sets are characterized as solutions to linear programs and have desirable theoretical properties. We explain how to estimate these solutions using computationally tractable methods even when the linear program is infinite-dimensional. We illustrate these methods with an empirical application to peer effects in movie viewership, using weather as a potentially imperfect instrument.

econ.EM↗

arXiv2025

An Axiomatic Approach to Comparing Sensitivity Parameters

Many methods are available for assessing the importance of omitted variables in linear regression. 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 new concepts of parameter consistency and monotonicity, and argue that a reasonable sensitivity parameter should satisfy both properties. We prove that the literature's most popular approach is inconsistent and non-monotonic, while several alternatives satisfy both.

econ.EM↗

arXiv2024

Heterogeneity, Uncertainty and Learning: Semiparametric Identification and Estimation

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.

econ.EM↗

arXiv2022

Assessing Omitted Variable Bias when the Controls are Endogenous

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 challenges that arise when the omitted variables are endogenous, meaning that they are correlated with the included controls. We develop a new approach to regression 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.

econ.EM↗