Abstract
ABSTRACTThis article proposes wild and the independent and identically distibuted (i.i.d.) parametric bootstrap implementations of the time-varying cointegration test of Bierens and Martins (2010). The bootstrap statistics and the original likelihood ratio test share the same first-order asymptotic null distribution. Monte Carlo results suggest that the bootstrap approximation to the finite-sample distribution is very accurate, in particular for the wild bootstrap case. The tests are applied to study the purchasing power parity hypothesis for twelve Organisation for Economic Cooperation and Development (OECD) countries and we only find evidence of a constant long-term equilibrium for the U.S.–U.K. relationship.
Highlights
Structural change is of key importance in economics and econometrics, especially for cointegration analysis, as it normally involves long term historical trends, which, are likely to display breaks in their equilibrium relationship
In Bierens and Martins (2010), the original time-varying cointegration (TVC) test statistic was applied to the purchasing power parity (PPP) hypothesis: In its absolute form, it means that the same bundle of goods, measured in real terms, should have the same value across countries
The data we use to illustrate the usefulness of the bootstrap TVC tests in empirical work is the same as in Falk and Wang (2003), downloaded from the Journal of Applied Econometrics data archives web site
Summary
Structural change is of key importance in economics and econometrics, especially for cointegration analysis, as it normally involves long term historical trends, which, are likely to display breaks in their equilibrium relationship. As in many other estimation and inference contexts, in our case the bootstrap distribution is an accurate approximation to the ...nite-sample one under the null hypothesis of constant cointegration vectors, as initially presented by Johansen (1988, 1991 and 1995). It has extensively been shown in the literature that bootstrap methods provide higher order asymptotic re...nements and, better results in bias reduction, con...dence interval construction and hypothesis testing in ...nite-samples, even in the cases where analytical results are known.
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