More uncertainty: on the trending nature of real GDP in the US and UK

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 (2004) 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, y_t 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 2004). 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 (1991).

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. (2003) 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.