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

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. The bootstrap tests of the regular and generalized cointegration hypotheses make use of a size correction that compensates for the biases due to estimating the parameters of the model for the bootstrap replications. The tests reveal 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 Monte Carlo study, showing that the methods have ample power to detect cointegrating relations, even in cases where the residuals are noisy and persistent