arXiv subjects

Patrick Kline

Publications and source records attributed to Patrick Kline.

7 recordsLinked to original sources

arXiv2026

Repairing Locally Misspecified GMM: An Empirical Bayes Approach

Econometric models offer parsimonious but inexact approximations to data-generating processes. This paper studies the generalized method of moments (GMM) when exchangeable specification errors of order $n^{-1/2}$ contaminate the moment conditions. I develop estimators for the mean and variance of these specification errors, establishing their consistency in an asymptotic framework where the number of overidentifying restrictions grows with the sample size. These hyperparameter estimates are used to develop a feasible bias-corrected estimator of target parameters. I also propose an empirical Bayes estimator that weakly improves precision by subtracting a best linear predictor of the first-order estimation error from the bias-corrected estimator. Using a combinatorial central limit theorem, I establish asymptotic normality of both estimators and provide variance estimators that enable misspecification-aware frequentist inference. Simulation exercises indicate the procedures can meaningfully improve on standard two-stage least squares estimation when exclusion violations are present. Revisiting the influential study of Angrist and Krueger (1991), I consider an instrument set where exchangeable excludability violations are plausible. Repairing the two-stage least squares estimates of the returns to schooling moves them in the direction of ordinary least squares and reduces sensitivity to the specification of controls.

econ.EM↗

arXiv2025

Branching Fixed Effects: A Proposal for Communicating Uncertainty

Economists often rely on estimates of linear fixed effects models produced by other teams of researchers. Assessing the uncertainty in these estimates can be challenging. I propose a form of sample splitting for networks that partitions the data into statistically independent branches, each of which can be used to compute an unbiased estimate of the parameters of interest in two-way fixed effects models. These branches facilitate uncertainty quantification, moment estimation, and shrinkage. Drawing on results from the graph theory literature on tree packing, I develop algorithms to efficiently extract branches from large networks. I illustrate these techniques using a benchmark dataset from Veneto, Italy that has been widely used to study firm wage effects.

econ.EM↗

arXiv2023

A Discrimination Report Card

We develop an Empirical Bayes grading scheme that balances the informativeness of the assigned grades against the expected frequency of ranking errors. Applying the method to a massive correspondence experiment, we grade the racial biases of 97 U.S. employers. A four-grade ranking limits the chances that a randomly selected pair of firms is mis-ranked to 5% while explaining nearly half of the variation in firms' racial contact gaps. The grades are presented alongside measures of uncertainty about each firm's contact gap in an accessible rubric that is easily adapted to other settings where ranks and levels are of simultaneous interest.

econ.EM↗

arXiv2023

Adapting to Misspecification

Empirical research typically involves a robustness-efficiency tradeoff. A researcher seeking to estimate a scalar parameter can invoke strong assumptions to motivate a restricted estimator that is precise but may be heavily biased, or they can relax some of these assumptions to motivate a more robust, but variable, unrestricted estimator. When a bound on the bias of the restricted estimator is available, it is optimal to shrink the unrestricted estimator towards the restricted estimator. For settings where a bound on the bias of the restricted estimator is unknown, we propose adaptive estimators that minimize the percentage increase in worst case risk relative to an oracle that knows the bound. We show that adaptive estimators solve a weighted convex minimax problem and provide lookup tables facilitating their rapid computation. Revisiting some well known empirical studies where questions of model specification arise, we examine the advantages of adapting to -- rather than testing for -- misspecification.

econ.EM↗

arXiv2019

Audits as Evidence: Experiments, Ensembles, and Enforcement

We develop tools for utilizing correspondence experiments to detect illegal discrimination by individual employers. Employers violate US employment law if their propensity to contact applicants depends on protected characteristics such as race or sex. We establish identification of higher moments of the causal effects of protected characteristics on callback rates as a function of the number of fictitious applications sent to each job ad. These moments are used to bound the fraction of jobs that illegally discriminate. Applying our results to three experimental datasets, we find evidence of significant employer heterogeneity in discriminatory behavior, with the standard deviation of gaps in job-specific callback probabilities across protected groups averaging roughly twice the mean gap. In a recent experiment manipulating racially distinctive names, we estimate that at least 85% of jobs that contact both of two white applications and neither of two black applications are engaged in illegal discrimination. To assess the tradeoff between type I and II errors presented by these patterns, we consider the performance of a series of decision rules for investigating suspicious callback behavior under a simple two-type model that rationalizes the experimental data. Though, in our preferred specification, only 17% of employers are estimated to discriminate on the basis of race, we find that an experiment sending 10 applications to each job would enable accurate detection of 7-10% of discriminators while falsely accusing fewer than 0.2% of non-discriminators. A minimax decision rule acknowledging partial identification of the joint distribution of callback rates yields higher error rates but more investigations than our baseline two-type model. Our results suggest illegal labor market discrimination can be reliably monitored with relatively small modifications to existing audit designs.

econ.EM↗

arXiv2018

Leave-out estimation of variance components

We propose leave-out estimators of quadratic forms designed for the study of linear models with unrestricted heteroscedasticity. Applications include analysis of variance and tests of linear restrictions in models with many regressors. An approximation algorithm is provided that enables accurate computation of the estimator in very large datasets. We study the large sample properties of our estimator allowing the number of regressors to grow in proportion to the number of observations. Consistency is established in a variety of settings where plug-in methods and estimators predicated on homoscedasticity exhibit first-order biases. For quadratic forms of increasing rank, the limiting distribution can be represented by a linear combination of normal and non-central $\chi^2$ random variables, with normality ensuing under strong identification. Standard error estimators are proposed that enable tests of linear restrictions and the construction of uniformly valid confidence intervals for quadratic forms of interest. We find in Italian social security records that leave-out estimates of a variance decomposition in a two-way fixed effects model of wage determination yield substantially different conclusions regarding the relative contribution of workers, firms, and worker-firm sorting to wage inequality than conventional methods. Monte Carlo exercises corroborate the accuracy of our asymptotic approximations, with clear evidence of non-normality emerging when worker mobility between blocks of firms is limited.

econ.EM↗

arXiv2017

On Heckits, LATE, and Numerical Equivalence

Structural econometric methods are often criticized for being sensitive to functional form assumptions. We study parametric estimators of the local average treatment effect (LATE) derived from a widely used class of latent threshold crossing models and show they yield LATE estimates algebraically equivalent to the instrumental variables (IV) estimator. Our leading example is Heckman's (1979) two-step ("Heckit") control function estimator which, with two-sided non-compliance, can be used to compute estimates of a variety of causal parameters. Equivalence with IV is established for a semi-parametric family of control function estimators and shown to hold at interior solutions for a class of maximum likelihood estimators. Our results suggest differences between structural and IV estimates often stem from disagreements about the target parameter rather than from functional form assumptions per se. In cases where equivalence fails, reporting structural estimates of LATE alongside IV provides a simple means of assessing the credibility of structural extrapolation exercises.

stat.ME↗