Offering a unifying theoretical perspective not readily available in any other text, this innovative guide to econometrics uses simple geometrical arguments to develop students' intuitive understanding of basic and advanced topics, emphasizing throughout the practical applications of modern theory and nonlinear techniques of estimation. One theme of the text is the use of artificial regressions for estimation, reference, and specification testing of nonlinear models, including diagnostic tests for parameter constancy, serial correlation, heteroscedasticity, and other types of mis-specification. Explaining how estimates can be obtained and tests can be carried out, the authors go beyond a mere algebraic description to one that can be easily translated into the commands of a standard econometric software package. Covering an unprecedented range of problems with a consistent emphasis on those that arise in applied work, this accessible and coherent guide to the most vital topics in econometrics today is indispensable for advanced students of econometrics and students of statistics interested in regression and related topics. It will also suit practising econometricians who want to update their skills. Flexibly designed to accommodate a variety of course levels, it offers both complete coverage of the basic material and separate chapters on areas of specialized interest.

Estimation and Inference in Econometrics

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

We investigate the time-series properties of firm effects in the AKM models popularized by Abowd et al. (1999). We consider two approaches. The first approach â€” labelled as the rolling approach â€” estimates AKM models separately in each T = 2 adjacent time interval. The second approach is based on an extension of the original AKM â€” labelled as the Time Varying AKM Model (TV-AKM) â€” in which we allow for unrestricted interactions of year and firm dummies. We correct for biases in the resulting variance decompositions using the leave out correction of Kline et al. (2019). These approaches allow us to examine how firm effects evolve stochastically, their relation to the business cycle, and their contribution to changes in the wage structure at a higher frequency than previously possible. Using data from Washington State, we find that firm effects in earnings and hourly wages are highly persistent. The autocorrelation coefficient between firm effects for wage rates in 2002 and 2014 is 0.74, and between firm effects for earnings in 2002 and 2014 is 0.82. The rolling approach uncovers a significant degree of cyclicality in firm effects. Variability in firm premiums tended to increase during the great recession while the degree of worker and firm assortativity decreased. Time-varying firm effects explains 13% of the variance of log wages and 21% of the variance of log earnings in the Washington state over 2002â€“2014. Between 2002-2003 and 2013-2014 the variance of firm wage premia decreased by 10%, but this decline was offset by increases in the variance in individual premia and increases in assortative matching that resulted in an overall increase in the variance of wages. Auxiliary evidence suggests that misspecification in AKM models due to the drifting of firm effects is a second-order concern.

/pdf/do-firm-effects-drift-evidence-from-washington-3cii0v0llg.pdf

Do Firm Effects Drift? Evidence from Washington Administrative Data

IZA DP No. 15033 JANUARY 2022 The Unequal Cost of Job Loss across Countries We document the consequences of losing a job across countries using a harmonized research design. Workers in Denmark and Sweden experience the lowest earnings declines following job displacement, while workers in Italy, Spain, and Portugal experience losses three times as high. French and Austrian workers face earnings losses somewhere in-between. Key to these differences is that Southern European workers are less likely to find employment following displacement. Loss of employer-specific wage premiums accounts for 40% to 95% of within-country wage declines. The use of active labor market policies predicts a significant portion of the cross-country heterogeneity in earnings losses. JEL Classification: J30, J63, J64

/pdf/the-unequal-cost-of-job-loss-across-countries-2euxxftk.pdf

The Unequal Cost of Job Loss Across Countries

We combine matched employer-employee data with firms’ financial records tostudy a 2001 Italian reform that lifted constraints on the employment of temporary contract workers while maintaining rigid employment protection regulationsfor employees hired under permanent employment contracts. Exploiting the stag-gered implementation of the reform across different sectoral collective bargainingagreements, we find that this policy change led to an increase in the incidence oftemporary contracts but failed to raise employment significantly. The reform hadboth winners and losers. Firms appear to be the main winners as the reform wassuccessful in decreasing labor costs, leading to higher profits. By contrast, youngworkers are the main losers since their earnings were substantially depressed follow-ing the policy change. Rent-sharing estimates show that workers on a temporarycontract receive only 68% of the rents shared by firms with workers hired under apermanent contract, helping explain the post-reform labor cost reductions.

The Effects of Partial Employment Protection Reforms: Evidence from Italy

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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