Modelling the duration of interest rate spells under inflation targeting in Canada

Abstract

We use survival models to analyse the duration of the spells associated with the interest rate used by the Bank of Canada as its monetary policy instrument. Both nonparametric and parametric models are estimated, allowing for right-censoring of the data, and time-varying covariates. We find that the data are explained well by an accelerated failure time Weibull model, with the annual rate of inflation and the quarterly rate of growth in Gross domestic product (GDP) as covariates. The model indicates that there is positive duration dependence in the interest rate spells, and that unemployment and exchange rate effects are insignificant.

Acknowledgement

We are grateful to a referee, Graham Voss, and participants at the 6th Hawaii International Conference on Statistics, Mathematics & Related Disciplines for helpful comments on an earlier version of this work.

Notes

¹Details about inflation targeting in transition countries are given by Jonas and Mishkin (2005).

²Once the band is breached, the Bank will take some actions to pull the inflation back to the band.

³For more details, see the official website of the Bank of Canada, and particularly the helpful material at http://www.bankofcanada.ca/en/monetary/monetary_framework.html.

⁴Ties occur when two or more observations have the same duration.

⁵See http://www.bankofcanada.ca/en/monetary/monetary_stats.html, http://www.bankofcanada.ca/en/cpi.htm, and http://dc2.chass.utoronto.ca/cansimdim/English/

⁶The sample mean is 2.3 months, with a maximum spell-length of 8 months.

⁷See Greene (2003, p.797) for the expression of the conditional mean for the Weibull and other models.

⁸Using the estimated coefficients for INFCA and GDPM and the estimates for θ and p, for model 4 in Table 3, the marginal effects for INFCA and GDPM are calculated as and .

⁹These authors estimated policy rules, and did not consider the duration of interest rate spells per se.