Long memory properties of international ex post and ex ante real interest rates : Asian, Pacific and European countries : a research thesis submitted in fulfilment of the requirements for the degree of Master of Applied Economics at Massey University, Department of Applied and International Economics, College of Business, Massey University, New Zealand
According to the Fisher equation efficient capital markets should compensate for changes in the purchasing power of money. This implies that in the long-run, the nominal interest rate and expected inflation should move together one-for-one. However, because expected inflation is unobservable, testing the Fisher relationship is problematic and an appropriate proxy for expected inflation must be employed. Empirical results in the literature of the Fisher relationship have produced mixed findings concerning the validity of this relationship. Many recent studies have focused on the stationarity of the ex ante real rate in determining the acceptability of the long-run Fisher relationship. For the long-run Fisher effect to hold the ex ante real interest rate should display mean-reversion. Mean-reversion is characterised by the tendency of a time series to return to its mean after a shock. Most studies that have examined the stationarity of the ex ante real rate have concentrated on testing for restrictive integer orders of integration. This is restrictive because mean-reversion is confined to the covariance stationary I(0) process. However, an I(0) process is not the only process that displays mean-reversion. Fractional orders of integration can characterise a wider form of mean-reversion. Many studies that observe the order of integration of the real interest rate use actual or realised inflation for expected inflation in order to generate the ex post real rate, which differs from the ex ante real rate only by a stationary forecast error. These studies have then used the ex post real rate to infer the dynamic behaviour of the ex ante real rate. However, because the difference between the ex post and ex ante real rates is unexpected, the large volatility of the forecast error can mask the more persistent behaviour of the ex ante real rate. The additional volatility is inherited by the ex post real rate and therefore estimates of the order of integration are biased downwards. In this research the order of integration is estimated for real interest rates of nineteen European, Asian and Pacific countries. Two different econometric techniques are used in order to generate proxies for expected inflation, and it is found that these proxies exhibit a more persistent dynamic when compared to actual inflation. Employing an autoregressive fractionally integrated moving average (ARFIMA) model, the order of integration is estimated by using a maximum likelihood (ML) estimation technique. This estimation technique is applied to the two estimated ex ante real rates as well as the ex post real rate for each country studied. The empirical results show that estimated orders of integration display a distinct pattern. That is, the ex post real rate is found to be significantly less persistent when compared to either of the ex ante real rates estimated in this study. This is due to the additional volatility that is inherited within the ex post real rate of interest. The Fisher relationship has also been extended to international capital and goods markets. Real interest rate parity (RIP) theory postulates that if international capital (through uncovered interest rate parity) and goods (through relative purchasing power parity) markets are efficient then the real interest rate on two perfectly comparable assets between countries and across time should equalise. Similar to the Fisher relationship, RIP has also had mixed empirical results. Early studies found limited support for RIP, on the other hand more recent studies have found evidence of real interest rate integration. In this research, a preliminary study was conducted of RIP between New Zealand and Australia. Using the same methodology mentioned above, RIP was examined for three real interest rate differentials of New Zealand and Australia. Again, these differentials differ in the method used to model expected inflation. The empirical results of RIP between New Zealand and Australia are not overwhelmingly conclusive. The order of integration of the real interest rate differentials do not differ from the order of integration of the real interest rates of New Zealand and Australia, which does not support RIP. This analysis however, does generate many possibilities for further research including data and methodological extensions.