Time varying cointegration and the UK Great Ratios

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.