Sven Schreiber

The Hausman Test Statistic can be Negative even Asymptotically

Summary We show that under the alternative hypothesis the Hausman chi-square test statistic can be negative not only in small samples but even asymptotically. Therefore in large samples such a result is only compatible with the alternative and should be interpreted accordingly. Applying a known insight from finite samples, this can only occur if the different estimation precisions (often the residual variance estimates) under the null and the alternative both enter the test statistic. In finite samples, using the absolute value of the test statistic is a remedy that does not alter the null distribution and is thus admissible. Even for positive test statistics the relevant covariance matrix difference should be routinely checked for positive semi-definiteness, because we also show that otherwise test results may be misleading. Of course the preferable solution still is to impose the same nuisance parameter (i.e., residual variance) estimate under the null and alternative hypotheses, if the model context permits that with relative ease. We complement the likelihood-based exposition by a formal proof in an omitted-variable context, we present simulation evidence for the test of panel random effects, and we illustrate the problems with a panel homogeneity test.

Testing the effectiveness of the French work-sharing reform: a forecasting approach

The macroeconomic impact of the French work-sharing reform of 2000 (a reduction of standard working hours in combination with wage subsidies) is analysed. Using a vector error correction model (VECM) for several labour market variables, as well as inflation and output, out-of-sample forecasts for 2000/2001 are produced. A comparison of these forecasts – which serve as a benchmark simulation without structural shifts – to the realized values (with shifts) suggests significant beneficial employment effects of the policy mix. Other shifts were absent and thus cannot explain the outcome. Output, productivity, hourly labour costs, and inflation are only transitorily affected or not at all.

Estimating the natural rate of unemployment in euro-area countries with co-integrated systems

Given that for France, Germany, Italy and the Netherlands the unemployment rates are best classified as I(1), we apply permanent-transitory decompositions based on co-integrated Vector Autoregressions (VAR) with relevant variables (labour productivity, wages, tax wedges, foreign relative prices) to estimate the time-varying natural unemployment rates. In general all variables seem to matter, and the results are quite different from published Organization for Economic Co-operation and Development (OECD) Nairus. Our implied unemployment gaps are better than the OECD gaps in predicting unemployment changes and inflation gaps, but they are (except for Italy) as bad as the OECD gaps for forecasting inflation changes.

Pensions and Insider-Outsider Unemployment

If workers gain an insider position through past activity, young workers will bear the resulting outsider unemployment burden. In a world where productivity of employed workers rises because of learning-by-doing, and where labor demand is sufficiently elastic, preventing this unemployment (by lowering wages) leads to a higher income tax base in the future. Thus the institution of certain intergenerational transfer schemes provides an incentive for insiders to lower wages. In a stylized overlapping-generations model I show that this effect partially or fully abolishes unemployment in the steady-state equilibria.