Is the real interest rate parity condition affected by the method of calculating real interest rates?

Abstract

Although the real interest rate parity (RIRP) hypothesis has been extensively tested, there are no conclusive findings. We argue that the mixed findings are a result of the different methods used to calculate the real interest rate. In this article, we examine whether the RIRP holds for four OECD countries using five different methods for computing the real interest rate. The results indicate that the connection between real interest rates tends to be sensitive to the computational method of the real interest rate. Thus, authors have to be careful when comparing results across existing studies, since the type of computational method might be responsible for differences in conclusions of the validity of the RIRP.

Notes

¹ A different way of resolving the past mixed results, is to relax the assumption that real interest rates are distributed as zero or unit integrated process. For example, Tsay (2000) show that the US real interest rate may be a fractional process. Smallwood and Norrbin (2007) find that an encompassing test of the RIRP shows stronger support when the real interest rate is relaxed to be a Gegenbauer autoregressive moving average process. However, these studies also have mixed results.

² Specifically, the data come from the International Financial Statistics CD-ROM by the IMF. The interest rates and CPI are series 60ea and 64, respectively. The Paris interbank offer rate is used for pound sterling. For other currencies, the London interbank offer rates are used. The eurocurrencies are used to avoid governmental restrictions.

³ The agent is assumed to use a five-year forecast window in the rolling regression framework, thus eliminating the first 5 years of data. Therefore, the sample period is adjusted to 1983:08 to 2004:06 for comparability from different approaches of measuring the real interest rate.

⁴ Junttila (2001), for example, uses a rolling regression technique to approximate the inflation forecast. The purpose is to take into account the possibility that agents would be able to learn from the most recent information on inflation available at the time of the forecast.

⁵ Our data on the nominal interest rate are for a three-month holding period. Therefore, the annualization of the inflation rate is calculated as .

⁶ The fitted ARMA(p, q) models for each country's inflation rate are the following: Japan–ARMA(2,3), Switzerland–ARMA(2,3), UK–ARMA(4,3) and US–ARMA(1,4).

⁷ Under the assumption of rational expectations, given the probabilities and parameter estimates, the ex ante real interest rate can be estimated in the following way: E(y_t|y˜_{t − 1}) = E(μs_t|y˜_t ) + Φ ₁ E(y_{t − 1} − μ_{st − 1} |y˜_t ) + Φ ₂ E(y_{t − 2} − μ_{st − 2} |y˜_t ) where y˜_t = [y ₁ … y _t ].

⁸ A first-order Markov–switching process , ∑ _j = 1³ p _ij  = 1. To determine the log-likelihood function, we use the Gibbs-sampling procedure that generates a sample from the marginal density without requiring the marginal density distribution itself. See Casella and George (1992) for examples and applications of the Gibbs-sampling algorithm.

⁹ See Elliott et al. (1996) for details on the DF-GLS test.

¹⁰ We have also examined other testing methodologies suggested by Phillips and Perron (1988) and Perron and Ng (1996). We find similar results in that the time-series properties depend on the computational methodology used to compute the real interest rate.

¹¹ The test statistic for ADF test is evaluated using the t-ratio for α and MacKinnon's updated version of critical values.

¹² We only briefly discuss cointegration, because it is frequently used in the literature. For a more general discussion, see Johansen (1988).

¹³ Since the Johansen cointegration test relies on the assumption of Gaussian error term in a VAR system, the lag order must be selected a priori in order to correct for serial correlation. The selection of lag length is based on the Hannan-Quinn information criterion (HQC) with a maximum lag of 12, and then residuals of the VAR model for the chosen lag are tested for serial correlation with the LM test,.

¹⁴ The researcher ought to continue to check for a second cointegrating vector. However, many times researchers stop their search for the number of cointegrating vector once they find one cointegrating vector.

¹⁵ Note that as γ → ∞, the transition function G(s_t ;γ, c) approaches the indicator function and becomes instantaneous, and the LSTAR model reduces to a two-regime threshold autoregressive (TAR) model. Similarly when γ approaches 0, the transition function becomes a constant and the LSTAR model collapses to a linear autoregressive model.

¹⁶ The LSTAR and ESTAR models are scaled by standard deviations and variance, respectively, as the following: