Unit roots, structural breaks and cointegration in the UK public finances, 1750–2004

Abstract

In this article, we report results from several traditional and more recently developed unit root and cointegration tests, allowing for structural breaks, which indicate that UK government revenue and spending during 1750–2004 were I(1) series and cointegrated, and that the UK public finances have been on a consistently sustainable path over the long run.

Notes

¹ Afonso (2005) provides a comprehensive discussion of the time series issues involved and a survey of many of the associated empirical studies.

² Perron (2006) provides an excellent survey of unit root and cointegration tests in the presence of structural changes.

³ The series are from Mitchell (1988) and the Annual Abstract of Statistics published by the UK National Statistics Office (NSO), and were deflated using the consumer price index compiled by O'Donoghue et al. (2004).

⁴ Clark and Dilnot (2002) note that between 1964 and 1970, UK government revenue increased from 33.6% of GDP to 42.1%, which was the largest significant and sustained increases in the tax burden in the 20th century that was not associated with a war or pre-war military build-up.

⁵ In some cases, second differences of the series have also been tested and the results (not reported here) suggest that an I(2) process can be excluded.

⁶ The Lumsdaine and Papell (1997) test, which, is an extension of the Perron and Vogelsang (1992) test to two breaks for the case of trending series, assumes no breaks under the unit root null and, as in the case of the ZA, may lead to spurious rejections of the unit root (i.e. the rejection of the null may still imply a presence of a unit root with breaks). The results of Lumsdaine–Papell test with two breaks (not reported here) are available from the authors upon request.

⁷ This is in line with the findings of Ahmed and Rogers (1995), who use only the Phillips and Perron (1988) and Perron (1989) tests, the latter of which is based on the assumption of a known single structural break (including for the year 1939, for which, however, Ahmed and Rogers reject the unit root null for the tax revenue series).

⁸ The results for sub-samples 1750–1913 and 1947–2004 are available from the authors upon request.

⁹ Leybourne and Newbold (2003) and Cook (2004) show in simulation studies that commonly employed tests of cointegration – Engle and Granger (1987), Johansen (1988), Banerjee et al. (1986) and Gregory and Hansen (1996a) – when applied to an independent I(1) processes with a structural change appear to spuriously reject the null of no cointegration in the presence of either breaks in level or trend. Furthermore, Noh and Kim (2003) argue that spurious cointegration can occur when there are breaks in the variances of the innovation errors of two independent time series, especially when the breaks occur early in the sample period.

¹⁰ Ahmed and Rogers (1995) use Engle and Granger (1987) and dynamic Ordinary Least Squares (OLS) procedures and find evidence of the long-term intertemporal budget balance. However, they caution about the stability of the results using simple regressions based on the cointegrating relation between revenue and expenditure and dummy variables for every break date during and around war years.

¹¹ The results of the residual-based misspecification tests (not reported here) are available from the authors upon request. Generally, more robust and stronger cointegration results are obtained when the logarithms of the revenue and spending series are used.

¹² No result is available in the literature for the models with slope shifts using the Saikkonen–Lütkepohl-type GLS detrending that results in a break date-free limit distribution of the test statistic.

¹³ The results for sub-samples 1750–1913 and 1947–2004 are available from the authors upon request.