A rapidly growing literature claims to reject the efficient market hypothesis by producing large estimates of long-term abnormal returns following major corporate events. The preferred methodology in this literature is to calculate average multi-year buy-and-hold abnormal returns and conduct inferences via a bootstrapping procedure. We show that this methodology is severely flawed because it assumes independence of multi-year abnormal returns for event firms, producing test statistics that are up to four times too large. After accounting for the positive cross-correlations of event firm abnormal returns we find virtually no evidence of reliable abnormal performance for our samples.

We derive the asymptotic sampling distribution of various estimators frequently used to order distributions in terms of poverty, welfare and inequality. This includes estimators of most of the poverty indices currently in use, as well as estimators of the curves used to infer stochastic dominance of any order. These curves can be used to determine whether poverty, inequality or social welfare is greater in one distribution than in another for general classes of indices. We also derive the sampling distribution of the maximal poverty lines (or income censoring thresholds) up to which we may con dently assert that poverty or social welfare is greater in one distribution than in another. The sampling distribution of convenient estimators for dual approaches to the measurement ofpoverty is also established. The

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.

The bootstrap is a method for estimating the distribution of an estimator or test statistic by resampling one’s data. It amounts to treating the data as if they were the population for the purpose of evaluating the distribution of interest. Under mild regularity conditions, the bootstrap yields an approximation to the distribution of an estimator or test statistic that is at least as accurate as the

The authors thank three anonymous referees and the Editor Badi Baltagi for several useful comments. This work was supported by the Bank of Canada and by grants from the Canadian Network of Centres of Excellence [program on Mathematics

an earlier draft. We also thank Orley Ashenfelter for his help in getting this project off The work of Levine and Renelt (1992) and Sala-i-Martin (1997a, b) which attempted to test the robustness of various determinants of growth rates of per capita GDP among countries using two variants of Edward Leamer’s extreme-bounds analysis is reexamined. In a realistic Monte Carlo experiment in which the universe of potential determinants is drawn from those in Levine and Renelt’s study, both versions of the extreme-bounds analysis are evaluated for their ability to recover the true specification. Levine and Renelt’s method is shown to have low size and extremely low power: nothing is robust; while Sala-i-Martin’s method is shown to have high size and high power: it is undiscriminating. Both methods are compared to a cross-sectional version of the generalto-specific search methodology associated with the LSE approach to econometrics. It is shown to have size near nominal size and high power. Sala-i-Martin’s method and the general-to-specific method are then applied to the actual data from the original two studies. The results are consistent with the Monte Carlo results and are suggestive that the factors that most affect differences of growth rates are ones that are beyond the control of policymakers.

Tests of statistical hypotheses can be based on either of two critical values: the Type I critical value or the size-corrected critical value. The former usually depends on unknown population parameters and cannot be evaluated exactly in applications, but it can often be estimated very accurately by using the bootstrap. The latter does not depend on unknown population parameters but is likely to yield a test with low power. The critical values used in most Monte Carlo studies of the powers of tests are neither Type I nor size-corrected. They are irrelevant to empirical research. Key words: Hypothesis test, critical value, size, Type I error, bootstrap JEL classification: C12, C15 ___________________________________________________________________________ Corresponding author: Joel L. Horowitz, Department of Economics, University of Iowa, Iowa City, IA, 54442. Tel: (319) 335-0844. Fax: (319) 335-1956. E-mail: joelhorowitz @uiowa.edu. We thank Art Goldberger, Beth Ingram, Tom Rothenberg,...

This paper considers the problem of constructing tests and confidence intervals (CIs) that have correct asymptotic size in a broad class of non-regular models. The models considered are non-regular in the sense that standard test statistics have asymptotic distributions that are discontinuous in some parameters. It is shown in Andrews and Guggenberger (2005a) that standard fixed critical value, subsample, and b<n bootstrap methods often have incorrect size in such models. This paper introduces general methods of constructing tests and CIs that have correct size. First, procedures are introduced that are a hybrid of subsample and fixed critical value methods. The resulting hybrid procedures are easy to compute and have correct size asymptotically in many, but not all, cases of interest. Second, the paper introduces size-correction and “plug-in” size-correction methods for fixed critical value, subsample, and hybrid tests. The paper also introduces finite-sample adjustments to the asymptotic results of Andrews and Guggenberger (2005a) for subsample and hybrid methods and employs these

We show that the power of a bootstrap test will generally be very close to the level-adjusted power of the asymptotic test on which it is based, provided the latter is calculated properly. Our result, when combined with previous results on approximating the rejection frequency of bootstrap tests, provides a way to simulate the power of both asymptotic and bootstrap tests easily and inexpensively. Some Monte Carlo results for omitted variable tests in logit models illustrate the theoretical results of the paper, demonstrate that the level-adjusted power of asymptotic tests can vary greatly depending on the method used for level adjustment, and show how useful our approximate method can be.

The paper proposes a framework for modelling cointegration in fractionally integrated processes, and considers methods for testing the existence of cointegrating relationships using the parametric bootstrap. In these procedures, ARFIMA models are fitted to the data, and the estimates used to simulate the null hypothesis of non-cointegration in a vector autoregressive modelling framework. The simulations are used to estimate p-values for alternative regression-based test statistics, including the F goodness-of-fit statistic, the Durbin-Watson statistic and estimates of the residual d. The bootstrap distributions are economical to compute, being conditioned on the actual sample values of all but the dependent variable in the regression. The procedures are easily adapted to test stronger null hypotheses, such as statistical independence. The tests are not in general asymptotically pivotal, but implemented by the bootstrap, are shown to be consistent against alternatives with both stationary and nonstationary cointegrating residuals. As an example, the tests are applied to the series for UK consumption and disposable income. The power properties of the tests are studied by simulations of artificial cointegrating relationships based on the sample data. The F test performs better in these experiments than the residual-based tests, although the Durbin-Watson in turn dominates the test based on the residual d.