Testing for Fractional Cointegration: The Relationship between Government Popularity and Economic Performance in the UK

Summary This paper investigates the relationship between the quarterly opinion poll lead of UK governments over the period 1955–1996, and a set of economic indicators. The hypothesis of a causal link between these variables is often debated, but there is a difficulty in testing the link by conventional econometric methods. These require either stationarity or the I(1) property, but there is strong evidence from a number of different studies that opinion poll series are fractionally integrated, being nonstationary but also mean-reverting. This paper tests the hypothesis of fractional cointegration using bootstrap methods. It first discusses the problem of defining a cointegrating relationship between series that may not have the same order of integration, and suggests a generalized cointegration model that might account for this case. Bootstrap tests of the regular and generalized (non-)cointegration hypotheses are performed, as well as tests of the null hypothesis that cointegration of either type exists. Both the regular and double bootstrap statistics are calculated, the latter method providing a correction to the finite sample size distortion to the estimation of unknown parameters. The tests reveal little or no evidence of a link between the political and economic cycles, a conclusion that reinforces the results of earlier work suggesting that the political cycle is generated by the internal dynamics of the opinion formation process. The findings are reinforced by a case-specific Monte Carlo study, showing that the methods have ample power to reveal cointegrating relations, if they exist.