Abstract
While there is disagreement concerning the integrated nature of US Gross domestic product (GDP) over the long-run, there is a consensus that it is best characterized as I(1) over the post-World War II period. In this article the existing literature is extended via the use of an exponential smooth transition autoregressive (ESTAR)-based unit root test. It is shown that in contrast to the conventionally applied ADF test and the more powerful GLS-based ADF test, introduction of an alternative hypothesis of ESTAR adjustment results in the overwhelming rejection of the presence of a unit root. Similar results are presented for UK GDP over the same period.
Notes
1Papell and Prodan (Citation2004) consider ADF tests incorporating two structural breaks, with ‘restricted structural change’ referring to the imposition of the restriction of offsetting breaks which sum to zero.
2For the trended series examined here, yt is detrended via regression upon an intercept and trend prior to estimating (6).
3The US data are measured in billions of chained 2000 dollars and were obtained from http://www.bea.doc.gov/bea/dn1.htm The UK data are chained volume measures of GDP obtained from http://www.statistics.gov.uk
4All the above tests are applied with four lags of the dependent variable included. A fixed degree of augmentation is employed as lag optimisation techniques have been shown to alter the finite-sample distributions of unit root tests, inducing a bias towards rejection of the unit root null (Cook and Manning Citation2004). It was also found that the chosen lag length resulted in no evidence of mis-specification for any of the estimated testing equations on the basis of Lagrange Multiplier (LM) tests of serial correlation and ARCH.
5The critical values for the ADF tests are derived from the response surface analysis of MacKinnon (Citation1991).
6The critical values for the GLS-based ADF tests are derived from the Elliott et al. (1986).
7The Monte-Carlo analysis was undertaken using the GAUSS programming language and the RNDNS pseudo-random number generator. The experimentation was performed over 50 000 replications. Further details are available upon request.
8Kapetanios et al. (Citation2003) note that the significance of θ cannot be tested in the usual manner via the t-distribution. However, the large t-ratios observed here are suggestive of significance.