RDP 9111: Monthly Movements in the Australian Dollar and Real Short-Term Interest Differentials: An Application of the Kalman Filter 1. Introduction

Despite an impressive volume of research, consensus on the forces responsible for the observed behaviour of real exchange rates is yet to be reached. Since the float of our dollar in December 1983, Australia's financial liberalization appears to have accentuated the role of financial markets in determining our exchange rate (Miller and Weller (1991)).

In particular, the relationship between the real exchange rate and real interest rates has fallen under scrutiny since the late 1980s. Over this period in Australia, real interest rates have generally been high relative to our major trading partners. At the same time, the Australian dollar has appreciated significantly in real terms. It would seem clear that the high domestic real interest rates contributed to the dollar's appreciation by attracting foreign capital. However, this link has not always been supported by observation in the shorter run. For example, domestic unofficial cash rates have been reduced by more than seven per cent since December 1989, substantially narrowing both nominal and real interest differentials. To date,^[1] the strength of the dollar has persisted.

This paper investigates the role of interest differentials in determining short-term activity in the dollar. In one scenario, where interest differentials matter, the foreign exchange market is efficient^[2] and therefore influenced, even in the short-term, by the behaviour of fundamentals.^[3] It therefore seems reasonable and tractable to approach this question from the theory of uncovered interest parity (UIP). UIP postulates that, given an efficient market in foreign exchange, risk-neutral traders and negligible transactions costs, the expected change in the real exchange rate reflects the expected real interest rate differential. UIP in its purest form has been rejected by empirical evidence.^[4] It has been suggested that its failure is due to the existence of a risk premium in the foreign exchange market.^[5] If we accept this as a reasonable proposition, then the theory of UIP can be retained. However, its underlying assumption that traders are risk-neutral must be relaxed to allow for the existence of a time-varying risk premium. This methodology was adopted by Campbell and Clarida (1987) to examine what proportion of the monthly movement in the real US dollar could be explained by real short-term interest differentials relative to a number of their trading partners. This paper estimates their rational expectations model with Australian data. Monthly statistics for Australia against the United States, Japan, West Germany, United Kingdom and a constructed trade weighted index^[6] are examined for the post-float period, extending from December 1983 to August 1990.

Monthly movement in the real exchange rate is simplified into two components. The first component is identified with ex ante^[7] real short-term interest differentials; the second with all remaining economic fundamentals^[8] as embodied in the expected long-run real exchange rate. Both of these explanatory variables are unobservable. Earlier studies^[9] have commonly assumed the long-run exchange rate constant, and adopted proxy measures for the ex ante short-term real interest differential.

Campbell and Clarida's (1987) model avoids such compromises by using a more flexible estimation technique able to accommodate models which include unobservable variables – the Kalman filtering prediction error technique. The Kalman filter is generally used to evaluate difficult likelihood functions. In this paper, however, it is used primarily to make variance decomposition statements about the unobservable components of the model.

The remainder of the paper is organised into five parts. Section 2 briefly discusses different schools of thought which have developed to explain the observed behaviour of the real exchange rate. Section 3 develops Campbell and Clarida's (1987) structural model from the principles of uncovered interest parity. Section 4 discusses the Kalman filter approach to estimation which requires this structural model to be cast in state space form. Variance decomposition techniques are primarily used to investigate the stochastic^[10] relationships between the real exchange rate and its unobservable components. Section 5 presents empirical results for the Australian data. We find that since the float of the Australian dollar in December 1983, ex ante real interest differentials have not accounted for the greater proportion of monthly variation in the real exchange rate. Therefore, given the specification of this model, movements in the dollar's real exchange rate have been dominated by unanticipated shifts in the expected long-run real exchange rate. Section 6 discusses the implications and limitations of Campbell and Clarida's (1987) methodology and identifies the direction in which we feel future research into the shorter-run dynamics of the Australian dollar should advance.