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The generalised score and Wald tests are described and related to their nongeneralised versions. Two interesting applications are discussed. In the first a new test for the Behrens-Fisher problem is derived. The second is testing homogeneity of variances from multiple univariate normal populations.

This paper develops new methods for determining the cointegration rank in a nonstationary fractionally integrated system, extending univariate optimal methods for testing the degree of integration. We propose a simple Wald test based on the singular value decomposition of the unrestricted estimate of the long run multiplier matrix. When the "strength" of the cointegrating relationship is less than 1/2, the test statistic has a standard asymptotic distribution, like Lagrange Multiplier tests exploiting local properties. We consider the behavior of our test under estimation of short run parameters and local alternatives. We compare our procedure with other cointegration tests based on different principles and find that the new method has better properties in a range of situations by using information on the alternative obtained through a preliminary estimate of the cointegration strength.

We develop a test for equality of variances given two independent random samples of observations. The test can be expected to perform well when both sample sizes are at least moderate and the sample variances are asymptotically equivalent to the maximum likelihood estimators of the population variances. The test is motivated by and is here assessed for the case when both populations sampled are assumed to be normal. Popular choices of test would be the two-sample test if normality can be assumed and Levene's test if this assumption is dubious. Another competitor is the Wald test for the difference in the population variances. We give a nonparametric analogue of this test and call it the test. In an indicative empirical study when both populations are normal, we find that when both sample sizes are at least 25 the test is nearly as robust as Levene's test and nearly as powerful as the test.

AbstractDistinguishing substantively meaningful spillover effects from correlated residuals is of great importance in cross-sectional studies. Both forms of spatial dependence not only hold different implications for the choice of an unbiased estimator but also for the validity of inferences. To guide model specification, different empirical strategies involve the estimation of an unrestricted spatial Durbin model and subsequently use the Wald test to scrutinize the nonlinear restriction of common factors implied by pure error dependence. However, the Wald test's sensitivity to algebraically equivalent formulations of the null hypothesis receives scant attention in the context of cross-sectional analyses. This article shows analytically that the noninvariance of the Wald test to such reparameterizations stems from the application of a Taylor series expansion to approximate the restriction's sampling distribution. While asymptotically valid, Monte Carlo simulations reveal that alternative formulations of the common factor restriction frequently produce conflicting conclusions in finite samples. An empirical example illustrates the substantive implications of this problem. Consequently, researchers should either base inferences on bootstrap critical values for the Wald statistic or use the likelihood ratio test which is invariant to such reparameterizations when deciding on the model specification that adequately reflects the spatial process generating the data.

Mit dem Ziel, zu den wichtigen Dingen des Lebens zurückzufinden, kehrte Henry Thoreau der Zivilisation den Rücken. "Walden" ist sein eindringliches Plädoyer für Freiheit und ein selbstbestimmtes Dasein. Der Wirtschafts- und Sozialkritiker Henry Thoreau (1817-1862) sah, wie seine Mitmenschen unter der Last des Arbeitsalltags litten. Diesem Schicksal wollte er entgehen, wollte die materiellen Schwierigkeiten des mittellosen Schriftstellers überwinden. 1845 entschloß er sich zum freiwilligen Auszug aus der Zivilisation in die Stille und Freiheit der Natur, um "mit Vorbedacht zu leben, es nur mit den Grundtatsachen des Lebens zu tun zu haben und zu sehen, ob ich nicht lernen könne, was es zu lernen gibt, damit mir in der Stunde des Todes die Entdeckung erspart bleibe, nicht gelebt zu haben". Henry Thoreau hat in seinem Leben nicht weniger als neununddreißig Bände mit Tagebucheintragungen gefüllt. Berühmt gemacht hat ihn jedoch diese Chronik seines Hüttenlebens. Sie zeigt die Natur rund um den Waldensee in ihrer ganzen Widersprüchlichkeit, Schönheit und Komplexität. Mit seinen sensiblen, poetischen Naturbeschreibungen begründete er die Tradition amerikanischer Naturessayistik und sicherte dem Werk seinen Platz unter den einflußreichsten Texten des 19. Jahrhunderts.

Social scientists often study the differential effects of explanatory variables among multiple social groups such as race, ethnic group, and nation.This paper examines the Wald test for testing equality of logit coefficients from models of multiple social groups. I propose a Wald statistic that can perform some joint tests of group comparisons that the usual likelihood ratio test cannot. Two examples apply the Wald statistic for testing various hypotheses, and show that the Wald test is flexible and straightforward for making comparisons across social groups, and that the proposed Wald test may find wide applications in the social sciences.