On robust estimation of the location parameter

We develop a framework for difference-in-differences designs with staggered treatment adoption and heterogeneous causal effects. We show that conventional regression-based estimators fail to provide unbiased estimates of relevant estimands absent strong restrictions on treatment-effect homogeneity. We then derive the efficient estimator addressing this challenge, which takes an intuitive "imputation" form when treatment-effect heterogeneity is unrestricted. We characterize the asymptotic behavior of the estimator, propose tools for inference, and develop tests for identifying assumptions. Extensions include time-varying controls, triple-differences, and certain non-binary treatments. We show the practical relevance of these insights in a simulation study and an application. Studying the consumption response to tax rebates in the United States, we find that the notional marginal propensity to consume is between 8 and 11 percent in the first quarter -- about half as large as benchmark estimates used to calibrate macroeconomic models -- and predominantly occurs in the first month after the rebate. 

/pdf/revisiting-event-study-designs-robust-and-efficient-1dmeqgt7.pdf

Revisiting event study designs: robust and efficient estimation

Earnings inequality in the United States has increased rapidly over the last three decades, but little is
known about the role of firms in this trend. For example, how much of the rise in earnings inequality
can be attributed to rising dispersion between firms in the average wages they pay, and how much is
due to rising wage dispersion among workers within firms? Similarly, how did rising inequality affect
the wage earnings of different types of workers working for the same employer—men vs. women,
young vs. old, new hires vs. senior employees, and so on? To address questions like these, we begin
by constructing a matched employer-employee data set for the United States using administrative
records. Covering all U.S. firms between 1978 to 2012, we show that virtually all of the rise in
earnings dispersion between workers is accounted for by increasing dispersion in average wages paid
by the employers of these individuals. In contrast, pay differences within employers have remained
virtually unchanged, a finding that is robust across industries, geographical regions, and firm size
groups. Furthermore, the wage gap between the most highly paid employees within these firms (CEOs
and high level executives) and the average employee has increased only by a small amount, refuting
oft-made claims that such widening gaps account for a large fraction of rising inequality in the
population.

/pdf/firming-up-inequality-4o1phwaeic.pdf

Firming Up Inequality

Further Simulation Evidence on the Performance of the Poisson Pseudo-Maximum Likelihood Estimator

We develop a discrete heterogeneity framework for matched employer employee data. The framework allows for unrestricted interactions between worker and rm unobserved characteristics in the wage function, as well as unrestricted sorting based on these unobservables. Pooling cross-sectional observations together with information from the joint distribution of wages of job movers, we establish a series of nonparametric identication results in short panels. We evaluate our method on data simulated from a theoretical model under both positive and negative sorting. We apply our method to Swedish matched employer employee panel data and report estimated wage functions and sorting patterns.

/pdf/a-distributional-framework-for-matched-employer-employee-4atscfi8u7.pdf

A Distributional Framework for Matched Employer Employee Data

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 χ2 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.

/pdf/leave-out-estimation-of-variance-components-204ruh5r2r.pdf

Leave‐Out Estimation of Variance Components

This paper provides the first estimates of the long-run health eects of a universal infant health intervention. We examine the 1937 Danish home visiting program, which targeted all infants. Using administrative population data and exploiting variation in the timing of implementation across municipalities, we find that treated individuals are 5‐8 percent less likely to die in middle age (45‐57), experience fewer hospital nights and are less likely to be diagnosed with and die from cardiovascular disease. These results suggest that an improved nutrition and disease environment in infancy “programmed” individuals for lower predisposition to serious adult diseases.

https://pubs.aeaweb.org/doi/pdfplus/10.1257/app.20150087

Universal Investment in Infants and Long-Run Health: Evidence from Denmark's 1937 Home Visiting Program

We propose a hypothesis test that allows for many tested restrictions in a heteroskedastic linear regression model. The test compares the conventional F statistic to a critical value that corrects for many restrictions and conditional heteroskedasticity. The correction utilizes leave-one-out estimation to correctly center the critical value and leave-three-out estimation to appropriately scale it. Large sample properties of the test are established in an asymptotic framework where the number of tested restrictions may be fixed or may grow with the sample size and can even be proportional to the number of observations. We show that the test is asymptotically valid and has non-trivial asymptotic power against the same local alternatives as the exact F test when the latter is valid. Simulations corroborate the relevance of these theoretical findings and suggest excellent size control in moderately small samples also under strong heteroskedasticity.

Testing Many Restrictions Under Heteroskedasticity

Robust estimation with many instruments

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.

Leave-out estimation of variance components

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