For Which Countries did PPP hold? A Multiple Testing Approach

We use recent advances in multiple testing to identify the countries for which Purchasing Power Parity (PPP) held over the last century. The approach controls the multiplicity problem inherent in simultaneously testing for PPP on several time series, thereby avoiding spurious rejections. It has higher power than traditional multiple testing techniques by exploiting the dependence structure between the countries with a bootstrap approach. We use a sieve bootstrap approach to account for nonstationarity under the null hypothesis. Our empirical results show that, plausibly, controlling for multiplicity in this way leads to a number of rejections of the null of no PPP that is intermediate between that of traditional multiple testing techniques and that which results if one tests the null on each single time series at some level. --Multiple Testing,Bootstrap,PPP,Panel Data

The Error-in-Rejection Probability of Meta-Analytic Panel Tests

Meta-analytic panel unit root tests such as Fisher?s X2 test, which consist of pooling the p-values of time series unit root tests, are widely applied in practice. Recently, several Monte Carlo studies have found these tests? Error-in-Rejection Probabilities (or, synonymously, size distortion) to increase with the number of series in the panel. We investigate this puzzling finding by modelling the finite sample p-value distribution of the time series tests with local deviations from the asymptotic p-value distribution. We find that the size distortions of the panel tests can be explained as the cumulative effect of small size distortions in the time series tests. --Panel Unit Root Tests,Meta-Analysis,Error-in-Rejection Probability

A meta analytic approach to testing for panel cointegration

We propose new tests for panel cointegration by extending the panel unit root of Choi [2001] and Maddala and Wu [1999] to the panel cointegration case. The tests are flexible, intuitively appealing and relatively easy to compute. We investigate the finite sample behavior in a simulation study. Several variants of the tests compare favorably in terms of both size and power with other widely used panel cointegration tests. --panel cointegration tests,Monte Carlo study,meta analysis

Cross-Sectional Correlation Robust Tests for Panel Cointegration

We use meta analytic combination procedures to develop new tests for panel cointegration. The main idea consists in combining p-values from time series cointegration tests on the different units of the panel. The tests are robust to heterogeneity as well as to cross-sectional dependence between the different units of the panel. To achieve the latter, we employ a sieve bootstrap procedure with joint resampling of the residuals of the different units. A simulation study shows that the suggested bootstrap tests can have substantially smaller error-in-rejection probabilities than tests ignoring the presence of cross-sectional dependence while preserving high power. We apply the tests to a panel of Post-Bretton Woods data to test for weak Purchasing Power Parity (PPP). --panel cointegration tests,cross-sectional dependence,sieve bootstrap

Mixed Signals Among Panel Cointegration Tests

Time series cointegration tests, even in the presence of large sample sizes, often yield conflicting conclusions (?mixed signals?) as measured by, inter alia, a low correlation of empirical p-values [see Gregory et al., 2004, Journal of Applied Econometrics]. Using their methodology, we present evidence suggesting that the problem of mixed signals persists for popular panel cointegration tests. As expected, there is weaker correlation between residual and system-based tests than between tests of the same group. --Panel cointegration tests,Monte Carlo comparison

Now, whose schools are really better (or weaker) than Germany's? A multiple testing approach

Using PIRLS (Progress in International Reading Literacy Study) data, we investigate which countries' schools can be be classified as significantly better or weaker than Germany's as regards the reading literacy of primary school children. The `standard' approach is to conduct separate tests for each country relative to the reference country (Germany) and to reject the null of equally good schools for all those countries whose $p$-value satisfies p_iPIRLS; Multiple Testing; Multi-Country Comparisons

Is Double Trouble? – How to Combine Cointegration Tests

This paper suggests a combination procedure to exploit the imperfect correlation of cointegration tests to develop a more powerful meta test.To exemplify, we combine Engle and Granger (1987) and Johansen (1988) tests. Either of these underlying tests can be more powerful than the other one depending on the nature of the data-generating process. The new meta test is at least as powerful as the more powerful one of the underlying tests irrespective of the very nature of the data generating process. At the same time, our new meta test avoids the arbitrary decision which test to use if single test results conflict. Moreover it avoids the size distortion inherent in separately applying multiple tests for cointegration to the same data set. We apply our test to 143 data sets from published cointegration studies. There, in one third of all cases single tests give conflicting results whereas our meta test provides an unambiguous test decision.Cointegration, meta test, multiple testing

More on the F-test under nonspherical disturbances

We show that the F-test can be both liberal and conservative in the context of a particular type of nonspherical behaviour induced by spatial autocorrelation, and that the conservative variant is more likely to occur for extreme values of the spatial autocorrelation parameter. In particular, it will wipe out the progressive one as the sample size increases. --F-test,spatial autocorrelation

OLS-based estimation of the disturbance variance under spatial autocorrelation

We investigate the OLS-based estimator s2 of the disturbance variance in the standard linear regression model with cross section data when the disturbances are homoskedastic, but spatially correlated. For the most popular model of spatially autoregressive disturbances, we show that s2 can be severely biased in finite samples, but is asymptotically unbiased and consistent for most types of spatial weighting matrices as sample size increases. --regression,spatial error correlation,bias,variance

Is Double Trouble? How to Combine Cointegration Tests

This paper suggests a combination procedure to exploit the imperfect correlation of cointegration tests to develop a more powerful meta test. To exemplify, we combine Engle and Granger (1987) and Johansen (1988) tests. Either of these underlying tests can be more powerful than the other one depending on the nature of the data-generating process. The new meta test is at least as powerful as the more powerful one of the underlying tests irrespective of the very nature of the data generating process. At the same time, our new meta test avoids the arbitrary decision which test to use if single test results conflict. Moreover it avoids the size distortion inherent in separately applying multiple tests for cointegration to the same data set. We apply our test to 143 data sets from published cointegration studies. There, in one third of all cases single tests give conflicting results whereas our meta tests provides an unambiguous test decision.Economics ;