The time-series properties of Norwegian inflation and nominal interest rate

Abstract

This article investigates the time-series properties of Norwegian inflation and nominal interest rate using annual data from 1850 to 2004. A number of different univariate unit-root tests are employed to examine whether the time series are mean reverting or generated by unit-root processes. Results show very strong evidence in favour of mean reversion in inflation but a unit root in the nominal interest rate. This implies that there exists no long-run relationship between these two variables, a conclusion which is further supported by cointegration tests and estimated vector error correction models. The cointegration analysis also points to an important potential pitfall when using cointegration techniques on systems where some variables are stationary processes.

Acknowledgement

I am grateful to an anonymous referee for valuable comments on this article. Financial support from Jan Wallander's and Tom Hedelius’ foundation is gratefully acknowledged.

Notes

¹Whilst a constant or mean-reverting real interest rate has found plenty of support in the literature and is a common modelling choice, this assumption has also been questioned; see, for example, Mills and Stephenson (1985) and Rose (1988).

²An early reference pointing this out is Shiller and Perron (1985).

³As a comparison to the results based on the Norwegian dataset, we also conduct the same analysis using monthly US data ranging from April 1953 to July 2005.

⁴See, for example, Perron (1989).

⁵Moreover, unit-root tests that allow for structural breaks – such as Perron (1989), Zivot and Andrews (1992) and Vogelsang and Perron (1998) – have some well-documented shortcomings. One well-known problem is the risk of spurious rejection of the null hypothesis when the breakpoint is chosen endogenously; see, for example, Nunes et al. (1997) and Lee and Strazicich (2001).

⁶In an ESTAR model, the speed of mean reversion is not constant. Instead, the process can display unit-root behaviour in the region close to its equilibrium but strong mean reversion when the process is far from its mean.

⁷The value of the delay parameter has been set to d = 1. Just like Taylor et al. (2001), we believe that the delay parameter should be small.

⁸This finding would be consistent with the viewpoint of, for example, Cogley and Sargent (2001) and Stock and Watson (2006) that US inflation is a unit-root process.

⁹Note that even though the constant is interpreted as the equilibrium real interest rate in this setting, this does not mean that this variable needs to be stationary in practice. A unit root in the equilibrium real interest rate could accordingly be one reason for failing to find cointegration between the nominal interest rate and inflation.

¹⁰The constant term has been omitted for notational convenience.

¹¹We could – despite the overwhelming evidence from the unit root tests – also test the hypothesis to investigate whether the nominal interest rate is judged stationary. Doing this, we get a test statistic of 34.728; this null hypothesis is hence forcefully rejected by the data.