Detection of Functional Form Misspeci–cation in Cointegrating….pdfVIP

Detection of Functional Form MisspeciÖcation in Cointegrating Relations Ioannis Kasparis University of Nottingham 18 December 2004 Abstract A simple speciÖcation test based on fully modiÖed residuals and the CUSUM test for cointegration of Xiao and Phillips (2002) are considered as means of testing for functional form in long-run cointegrating relations. It is shown that both tests are consistent under functional form misspeciÖcation and lack of cointegration. An extensive simulation study is carried out to asess the prop- erties of the tests in Önite samples. The Dickey-Fuller test is also considered. The simulation results reveal that the Örst two tests perform well. On the other hand the Dickey-Fuller test performs poorly in many cases, not only when there is functional form misspeciÖcation, but also when there is lack of cointegration and the spurious regression is nonlinear. 1 Introduction The theory of cointegration was developed nearly Öfteen years ago. Cointegration has probably been, the most popular approach in modeling macroeconomic relations since it was introduced. Although the concept of cointegration is very appealing from an economic theory point of view, a lot of data sets have failed to show evidence supporting the existence of long-run macroeconomic equilibria. Lack of evidence for cointegration in certain data sets has created doubts about the validity of the classi- cal linear cointegration models and led some researchers to consider the possibility of nonlinearities in macroeconomic relations. Recent work e.g. Corradi, Swanson and White (2000), Ter‰svirta and Ellianson (2001) among others, c