Time-varying Cointegration and the UK Great Ratios

Abstract

We re-examine the great ratios associated with balanced growth models and ask whether they have remained constant over time. We first use a benchmark DSGE model to explore how plausible smooth variations in structural parameters lead to movements in great ratios that are comparable to those seen in the UK data. We then employ a nonparametric methodology that allows for slowly varying coefficients to estimate trends over time. To formally test for stable relationships in the great ratios, we propose a statistical test based on these nonparametric estimators devised to detect time varying cointegrating relationships. Small sample properties of the test are explored in a small Monte Carlo exercise. Generally, we find no evidence for cointegration when parameters are constant, but strong evidence when allowing for time variation. The implications are that in macroeconometric models allowance should be made for shifting long-run relationships, including DSGE models where smooth variation should be allowed in the deep structural relationships.JEL Codes: C14, C26, C51, O4

Time-varying cointegration with an application to the UK Great Ratios

“…By contrast, the TV coefficient residuals are more plausible candidates for stationarity. It is hard to give a deep economic interpretation of movements in these long run relationships as we are not estimating a structural model, but in Kapetanios et al (2019)the broad changes in the ratios that we are finding here are interpretable in terms of shifting structural parameters in a benchmark equilibrium model.…”

“…An alternative would be to use some form of cross validation, for example by minimising the one-step ahead forecasts in or out of sample.5 Using the standard Newey-West estimate of the long-run variance.6 InKapetanios et al (2019), we also consider real series. 7 It cannot be rejected at 5% for the two trade ratios.…”