Bootstrap-Based Improvements for Inference with Clustered Errors

Microeconometrics researchers have increasingly realized the essential need to account for any within-group dependence in estimating standard errors of regression parameter estimates. The typical preferred solution is to calculate cluster-robust or sandwich standard errors that permit quite general heteroskedasticity and within-cluster error correlation, but presume that the number of clusters is large. In applications with few (5-30) clusters, standard asymptotic tests can over-reject considerably. We investigate more accurate inference using cluster bootstrap-t procedures that provide asymptotic refinement. These procedures are evaluated using Monte Carlos, including the much-cited differences-in-differences example of Bertrand, Mullainathan and Duflo (2004). In situations where standard methods lead to rejection rates in excess of ten percent (or more) for tests of nominal size 0.05, our methods can reduce this to five percent. In principle a pairs cluster bootstrap should work well, but in practice a Wild cluster bootstrap performs better.clustered errors; random effects; cluster robust; sandwich; bootstrap; bootstrap-t; clustered bootstrap; pairs bootstrap; wild bootstrap.

Robust Inference with Multi-way Clustering

In this paper we propose a new variance estimator for OLS as well as for nonlinear estimators such as logit, probit and GMM, that provcides cluster-robust inference when there is two-way or multi-way clustering that is non-nested. The variance estimator extends the standard cluster-robust variance estimator or sandwich estimator for one-way clustering (e.g. Liang and Zeger (1986), Arellano (1987)) and relies on similar relatively weak distributional assumptions. Our method is easily implemented in statistical packages, such as Stata and SAS, that already offer cluster-robust standard errors when there is one-way clustering. The method is demonstrated by a Monte Carlo analysis for a two-way random effects model; a Monte Carlo analysis of a placebo law that extends the state-year effects example of Bertrand et al. (2004) to two dimensions; and by application to two studies in the empirical public/labor literature where two-way clustering is present.

Distributional Impacts of the Self-Sufficiency Project

A large literature has been concerned with the impacts of recent welfare reforms on income, earnings, transfers, and labor-force attachment. While one strand of this literature relies on observational studies conducted with large survey-sample data sets, a second makes use of data generated by experimental evaluations of changes to means-tested programs. Much of the overall literature has focused on mean impacts. In this paper, we use random-assignment experimental data from Canada’s Self-Sufficiency Project (SSP) to look at impacts of this unique reform on the distributions of income, earnings, and transfers. SSP offered members of the treatment group a generous subsidy for working full time. Quantile treatment effect (QTE) estimates show there was considerable heterogeneity in the impacts of SSP on the distributions of earnings, transfers, and total income; heterogeneity that would be missed by looking only at average treatment effects. Moreover, these heterogeneous impacts are consistent with the predictions of labor supply theory. During the period when the subsidy is available, the SSP impact on the earnings distribution is zero for the bottom half of the distribution. The SSP earnings distribution is higher for much of the upper third of the distribution except at the very top, where the earnings distribution is the same under either program or possibly lower under SSP. Further, during the period when SSP receipt was possible, the impacts on the distributions of transfer payments (IA plus the subsidy) and total income (earnings plus transfers) are also different at different points of the distribution. In particular, positive impacts on the transfer distribution are concentrated at the lower end of the transfer distribution while positive impacts on the income distribution are concentrated in the upper end of the income distribution. Impacts of SSP on these distributions were essentially zero after the subsidy was no longer availablewefare reforms, labor force

What We Don\u27t Know About Class Actions but Hope to Know Soon

Legislation that would alter class action practice in the federal courts has been pending in Congress. Nearly a decade’s worth of U.S. Supreme Court cases have restricted the scope and ease of use of the class action device. Class action critics argue that class litigation is a “racket” that fails to compensate plaintiffs and instead enriches plaintiffs’ lawyers at the expense of legitimate business practices. On the other hand, defenders of class actions decry the legislative and judicial forces aligned against them, warning that trends in class action law will eviscerate the practical rights held by consumers and workers. In short, there is considerable controversy over whether class actions are an economic menace or a boon to the little guys. We have two purposes in this brief Article. First, we wish to focus continuing attention on the need for more empirical information about the actual functioning of the federal class action system. Second, we wish to share our current efforts to use a one-of-a-kind collection of docket reports, originally harvested from Public Access to Court Electronic Records (PACER), to fill the empirical gap. Presentation of empirical findings resulting from this effort awaits a future article. However, this Article includes suggestions as to how the federal judiciary and Administrative Office of the United States Courts (“AO”) could improve data management and data reporting so as to make information about federal class actions more accessible to scholars and others interested in how the class action device operates in practice and what reforms, if any, would be advisable

Bootstrap-Based Improvements for Inference with Clustered Errors

Researchers have increasingly realized the need to account for within-group dependence in estimating standard errors of regression parameter estimates. The usual solution is to calculate cluster-robust standard errors that permit heteroskedasticity and within-cluster error correlation, but presume that the number of clusters is large. Standard asymptotic tests can over-reject, however, with few (5-30) clusters. We investigate inference using cluster bootstrap-t procedures that provide asymptotic refinement. These procedures are evaluated using Monte Carlos, including the example of Bertrand, Duflo and Mullainathan (2004). Rejection rates of ten percent using standard methods can be reduced to the nominal size of five percent using our methods.

Empirical Law and Economics

Empirical work has grown in importance in law and economics. This growth coincides with improvements in research designs in empirical microeconomics more generally. In this essay, we provide a stylized discussion of some trends over the last two or three decades, linking the credibility revolution in empirical micro to the ascendancy of empirical work in law and economics. We then provide some methodological observations about a number of commonly used approaches to estimating policy effects. The literature on the economics of crime and criminal procedure illustrates the ways in which many of these techniques have been used successfully. Other fields, including corporate law and economics and the law and economics of civil procedure, have lagged behind in methodological terms

\u3ci\u3eAmerican Pipe\u3c/i\u3e Tolling, Statutes of Repose, and Protective Filings: An Empirical Study

This paper offers a conceptual and empirical analysis of a key issue that overhangs CalPERS v. ANZ Securities, soon to be decided by the Supreme Court. In particular, the paper offers an empirical estimate of the plausible quantity of wasteful protective filings that putative class members might make if the Court were to hold that American Pipe tolling does not apply to statutes of repose in the federal securities laws

The Law and Economics of Proportionality in Discovery

This paper analyzes the proportionality standard in discovery. Many believe the Advisory Committee\u27s renewed emphasis on this standard has the potential to infuse litigation practice with considerably more attention to questions related to the costs and benefits of discovery. We discuss the history and rationale of proportionality\u27s inclusion in Rule 26, adopting an analytical framework that focuses on how costs and benefits can diverge in litigation generally, and discovery in particular. Finally, we use this framework to understand the mechanics and challenges involved in deploying the six factors included in the proportionality standard. Throughout, we emphasize that the proportionality standard requires both difficult-to-answer positive questions and unavoidably normative judgments