Reproduction: Koop, G., León-González, R., & Strachan, R. W. (2011). Bayesian inference in a time varying cointegration model.

Mon, 14 Sep 2026 00:00:00 +0000

The Fisher hypothesis says that nominal interest rates move one for one with expected inflation, so that the real interest rate is stationary. In a vector error correction model (VECM) of a short-term interest rate \(r_t\) and inflation \(\pi_t\) it implies a single cointegrating relationship with the vector \((1, -1)'\). Tests of it on long samples give mixed results, and one reason may be that the relationship is not the same throughout: a hypothesis that holds in some decades and fails in others is rejected by a model that insists on one answer for all of them.

Koop, León-González and Strachan (2011) develop a VECM whose cointegration space is allowed to change over time, and use it on exactly this question. The difficulty they solve is not computational but conceptual. The natural extension of a time varying parameter VAR – letting the cointegrating vectors follow a random walk – does not work, because only the space spanned by the vectors is identified, and a random walk on a normalised vector says nothing sensible about how that space moves. Their state equation instead implies that the space in one period is centred on the space of the period before, and that its marginal prior is uniform in every period.

This post reproduces the two results of the application with bvartools: the path of the cointegrating coefficient in the paper’s preferred model (Fig. 1) and the log predictive likelihoods of the model variants (Tables 1 and 2).

Time-Varying-Cointegration on r-econometrics

Reproduction: Koop, G., León-González, R., & Strachan, R. W. (2011). Bayesian inference in a time varying cointegration model.