Wild Bootstrap Tests for IV RegressionJournal articleRussell Davidson et James G. MacKinnon, Journal of Business & Economic Statistics, Volume 28, Issue 1, pp. 128-144, 2010

We propose a wild bootstrap procedure for linear regression models estimated by instrumental variables. Like other bootstrap procedures that we have proposed elsewhere, it uses efficient estimates of the reduced-form equation(s). Unlike them, it takes account of possible heteroskedasticity of unknown form. We apply this procedure to t tests, including heteroskedasticity-robust t tests, and provide simulation evidence that it works far better than older methods, such as the pairs bootstrap. We also show how to obtain reliable confidence intervals by inverting bootstrap tests. An empirical example illustrates the utility of these procedures.

The fourth special issue on Computational EconometricsJournal articleRussell Davidson, David A. Belsley, Erricos John Kontoghiorghes, James G. MacKinnon et Herman K. van Dijk, Computational Statistics & Data Analysis, Volume 53, Issue 6, pp. 1923-1924, 2009

No abstract is available for this item.

Econometric Theory and Methods: International EditionBookRussell Davidson, OUP Catalogue, 2009, 768 pages, Oxford University Press, 2009

Econometric Theory and Methods International Edition provides a unified treatment of modern econometric theory and practical econometric methods. The geometrical approach to least squares is emphasized, as is the method of moments, which is used to motivate a wide variety of estimators and tests. Simulation methods, including the bootstrap, are introduced early and used extensively. The book deals with a large number of modern topics. In addition to bootstrap and Monte Carlo tests, these include sandwich covariance matrix estimators, artificial regressions, estimating functions and the generalized method of moments, indirect inference, and kernel estimation. Every chapter incorporates numerous exercises, some theoretical, some empirical, and many involving simulation.

Reliable inference for the Gini indexJournal articleRussell Davidson, Journal of Econometrics, Volume 150, Issue 1, pp. 30-40, 2009

Although attention has been given to obtaining reliable standard errors for the plug-in estimator of the Gini index, all standard errors suggested until now are either complicated or quite unreliable. An approximation is derived for the estimator by which it is expressed as a sum of IID random variables. This approximation allows us to develop a reliable standard error that is simple to compute. A simple but effective bias correction is also derived. The quality of inference based on the approximation is checked in a number of simulation experiments, and is found to be very good unless the tail of the underlying distribution is heavy. Bootstrap methods are presented which alleviate this problem except in cases in which the variance is very large or fails to exist. Similar methods can be used to find reliable standard errors of other indices which are not simply linear functionals of the distribution function, such as Sen's poverty index and its modification known as the Sen-Shorrocks-Thon index.

Testing for Restricted Stochastic Dominance: Some Further ResultsJournal articleRussell Davidson, Review of Economic Analysis, Volume 1, Issue 1, pp. 34-59, 2009

Extensions are presented to the results of Davidson and Duclos (2007), whereby the null hypothesis of restricted stochastic non dominance can be tested by both asymptotic and bootstrap tests, the latter having considerably better properties as regards both size and power. In this paper, the methodology is extended to tests of higher-order stochastic dom- inance. It is seen that, unlike the first-order case, a numerical nonlinear optimisation prob- lem has to be solved in order to construct the bootstrap DGP. Conditions are provided for a solution to exist for this problem, and efficient numerical algorithms are laid out. The em- pirically important case in which the samples to be compared are correlated is also treated, both for first-order and for higher-order dominance. For all of these extensions, the boot- strap algorithm is presented. Simulation experiments show that the bootstrap tests perform considerably better than asymptotic tests, and yield reliable inference in moderately sized samples.

Chow testBook chapterRussell Davidson, In: International encyclopedia of the social sciences, William A. Darity (Eds.), 2008, Volume 1, pp. 529-530, Macmillan Reference USA, 2008


The wild bootstrap, tamed at lastJournal articleRussell Davidson et Emmanuel Flachaire, Journal of Econometrics, Volume 146, Issue 1, pp. 162-169, 2008

The wild bootstrap is studied in the context of regression models with heteroskedastic disturbances. We show that, in one very specific case, perfect bootstrap inference is possible, and a substantial reduction in the error in the rejection probability of a bootstrap test is available much more generally. However, the version of the wild bootstrap with this desirable property is without the skewness correction afforded by the currently most popular version of the wild bootstrap. Simulation experiments show that this does not prevent the preferred version from having the smallest error in rejection probability in small and medium-sized samples.

Bootstrap inference in a linear equation estimated by instrumental variablesJournal articleRussell Davidson et James G. MacKinnon, Econometrics Journal, Volume 11, Issue 3, pp. 443-477, 2008

We study several tests for the coefficient of the single right-hand-side endogenous variable in a linear equation estimated by instrumental variables. We show that writing all the test statistics–Student's t, Anderson–Rubin, the LM statistic of Kleibergen and Moreira (K), and likelihood ratio (LR)–as functions of six random quantities leads to a number of interesting results about the properties of the tests under weak-instrument asymptotics. We then propose several new procedures for bootstrapping the three non-exact test statistics and also a new conditional bootstrap version of the LR test. These use more efficient estimates of the parameters of the reduced-form equation than existing procedures. When the best of these new procedures is used, both the K and conditional bootstrap LR tests have excellent performance under the null. However, power considerations suggest that the latter is probably the method of choice. Copyright The Author(s). Journal compilation Royal Economic Society 2008

stochastic dominanceBook chapterRussell Davidson, In: The New Palgrave Dictionary of Economics, Steven N. Durlauf et Lawrence E. Blume (Eds.), 2008-02, pp. 921-925, Nature Publishing Group, 2008

Stochastic dominance is a term which refers to a set of relations that may hold between a pair of distributions. A very common application of stochastic dominance is to the analysis of income distributions and income inequality, the main focus in this article. The concept can, however, be applied in many other domains, in particular financial economics, where the distributions considered are usually those of the random returns to various financial assets. In what follows, there are often clear analogies between things expressed in terms of income distributions and financial counterparts.

Asymptotic and bootstrap inference for inequality and poverty measuresJournal articleRussell Davidson et Emmanuel Flachaire, Journal of Econometrics, Volume 141, Issue 1, pp. 141-166, 2007

A random sample drawn from a population would appear to offer an ideal opportunity to use the bootstrap in order to perform accurate inference, since the observations of the sample are IID. In this paper, Monte Carlo results suggest that bootstrapping a commonly used index of inequality leads to inference that is not accurate even in very large samples. Bootstrapping a poverty measure, on the other hand, gives accurate inference in small samples. We investigate the reasons for the poor performance of the bootstrap, and find that the major cause is the extreme sensitivity of many inequality indices to the exact nature of the upper tail of the income distribution. Consequently, a bootstrap sample in which nothing is resampled from the tail can have properties very different from those of the population. This leads us to study two non-standard bootstraps, the m out of n bootstrap, which is valid in some situations where the standard bootstrap fails, and a bootstrap in which the upper tail is modelled parametrically. Monte Carlo results suggest that accurate inference can be achieved with this last method in moderately large samples.