This paper introduces a t-ratio type test for detecting bilinearity in a stochastic unit root process. It appears that such a process is a realistic approximation for many economic and ÿnancial time series. It is shown that, under the null of no bilinearity, the test statistics are asymptotically normally distributed. Proofs of these asymptotic normality results require the Gihman and Skorohod theory for multivariate di usion processes. Finite sample results describe speed of convergence, power of the tests and possible distortions to unit root testing which might appear due to the presence of bilinearity. It is concluded that the two-step testing procedure suggested here (the ÿrst step for the linear unit root and the second step for its bilinearity) is consistent in the sense that the size of the step one test is not a ected by the possible detection of bilinearity at step two. The empirical part of the paper describes testing unit root bilinearity for 65 GARCH-adjusted stock market indices from mature and emerging markets. It is shown that for at least 70% of these markets, the hypothesis of no unit root bilinearity has to be rejected. ? 2004 Elsevier B.V. All rights reserved. JEL classiÿcation: C12; C22; G15

The finding of the paper shows the relative effectiveness of the “one size fits all” policy of the European Central Bank. The paper provides strong evidence in favor of this by testing whether the monetary policy effects (footprints) found in inflation uncertainty converge to a common level. These footprints are measured as the fraction of the estimated policy‐induced reduction in this uncertainty. The testing was conducted by applying a bootstrap‐type test in a regression of the rate of growth of these fractions on their initial values, computed for 16 euro area countries. (JEL C33, E52, E58)

A class of stochastic unit-root bilinear processes, allowing for GARCH-type effects with asymmetries, is studied. Necessary and sufficient conditions for the strict and second-order stationarity of the error process are given. The strictly stationary solution is shown to be strongly mixing under mild additional assumptions. It follows that, in this model, the standard (non-stochastic) unit-root tests of Phillips-Perron and DickeyFuller are asymptotically valid to detect the presence of a (stochastic) unit-root. The finite sample properties of these tests are studied via Monte Carlo experiments.JEL classification: C22, C12, C52.

The article examines the relationship between the real effects of inflation and its level in countries with frequent episodes of high inflation. The real effects are computed as asymmetric impulse responses of output to inflation separately for the regimes with different signs of the differences between the expected inflation and the predicted output-neutral inflation. It is found that, with the increase in inflation, such effects increase for the regime with the positive sign, relatively to the effects for the regime with the negative sign. It is also shown that this finding is valid for most countries with high inflation episodes, where inflation is greater than 4.8% for at least 25% of quarterly observations. This leads to a simple policy prescription that, in economies with frequent high inflation episodes, anti-inflationary monetary decisions are least damaging for output if undertaken in the periods when the difference between the expected and output-neutral inflation is negative.