In this paper we propose a new variance estimator for OLS as well as for nonlinear estimators such as logit, probit and GMM. This variance estimator enables cluster-robust inference when there is two-way or multi-way clustering that is nonnested. 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.

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 overreject 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.

This paper considers regression models for cross-section data that exhibit crosssection dependence due to common shocks, such as macroeconomic shocks. The paper analyzes the properties of least squares (LS) estimators in this context. The results of the paper allow for any form of cross-section dependence and heterogeneity across population units. The probability limits of the LS estimators are determined, and necessary and sufficient conditions are given for consistency. The asymptotic distributions of the estimators are found to be mixed normal after recentering and scaling. The t� Wald, and F statistics are found to have asymptotic standard normal, χ2,andscaledχ2 distributions, respectively, under the null hypothesis when the conditions required for consistency of the parameter under test hold. However, the absolute values of t, Wald, and F statistics are found to diverge to infinity under the null hypothesis when these conditions fail. Confidence intervals exhibit similarly dichotomous behavior. Hence, common shocks are found to be innocuous in some circumstances, but quite problematic in others. Models with factor structures for errors and regressors are considered. Using the general results, conditions are determined under which consistency of the LS estimators holds and fails in models with factor structures. The results are extended to cover heterogeneous and functional factor structures in which common factors have different impacts on different population units.

. Klein gratefully acknowledges financial support from the

We provide novel evidence linking the level of creditor protection provided by law to the degree of usage of technologically older, vintage capital in the airline industry. Using a panel of aircraftlevel data around the world, we find that better creditor rights are associated with both aircraft of a younger vintage and newer technology as well as firms with larger aircraft fleets. Moreover, we find that more profitable airlines, airlines with lower leverage ratios, and airlines with less debt overhang are less sensitive to prevailing creditor rights in their country. We propose that by mitigating financial shortfalls, enhanced legal protection of creditors facilitates the ability of firms There is a large body of evidence that better legal rules covering protection of corporate shareholders and creditors are associated with more developed financial markets and higher economic growth (La

In this paper we survey methods to control for regression model error that is correlated within groups or clusters, but is uncorrelated across groups or clusters. Then failure to control for the clustering can lead to understatement of standard errors and overstatement of statistical significance, as emphasized most notably in empirical studies by Moulton (1990) and Bertrand, Duflo and Mullainathan (2004). We emphasize OLS estimation with statistical inference based on minimal assumptions regarding the error correlation process. Complications we consider include cluster-specific fixed effects, few clusters, multi-way clustering, more efficient feasible GLS estimation, and adaptation to nonlinear and instrumental variables estimators.

The result is that Juve and Milan can often rig the system to assign themselves the most mediocre, provincially minded referees, who are (subconsciously) more deferential towards their prestige clubs. [...] Other referees who have issued critical penalties against Juve have found themselves working games in the lowly Serie B. [...] Only on a few occasions have some

Abstract: Tax treaties are often viewed as a mechanism for eliminating tax competition, however this approach ignores the need for bargaining over the treaty’s terms. This paper focuses on how bargaining can affect the withholding taxes set under the treaty. In a simple framework, we develop hypotheses about patterns in treaty tax rates. A key determinant for these patterns is the relative size of bilateral foreign direct investment (FDI) activity. In plausible situations, more asymmetric countries will negotiate treaties with higher tax rates. This theory is then tested using 1997 data from U.S. bilateral tax treaties. Overall, the data supports the prediction that greater asymmetric FDI activity increases the negotiated tax rates. JEL Classification: F23, H25, K34.