RDP 9601: Why Does the Australian Dollar Move so Closely with the Terms of Trade? 3. Modelling the Real Exchange Rate

We construct a measure of Australia's real exchange rate as a trade-weighted arithmetic average of the real exchange rates of Australia's five largest trading partners, using trade weights derived from average annual trade flows over the two financial years 1984/85 and 1985/86.[3] With out-of-sample forecasting beginning in 1987:Q1, this choice of trade weights again ensures that model-generated forecasts are truly ex ante. The measure of the real exchange rate, qt, is therefore:

wj is the normalised country j trade weight, Qjt is the Australia-country j real exchange rate, Inline Equation and Inline Equation are consumer price indices in Australia and country j, and Ejt is the price of the Australian dollar in country j's currency on the last day of quarter t.

Two time-series models for this trade-weighted real exchange rate, qt, are estimated.[4] The first, Model A, simply assumes that real exchange rate changes are determined by contemporaneous changes in Australia's terms of trade:

To derive the second time-series model for Australia's real exchange rate, we begin with an unrestricted error-correction model (ECM):

This specification allows for a longer-run relationship between the log-levels of the terms of trade and the real exchange rate. It also includes a time-trend to allow for the possibility that the real exchange rate and the terms of trade do not share the same longer-term trend. Since the relationship between the real exchange rate and the terms of trade may change over time, we generate preferred specifications over five sample periods, each with a starting date of 1984:Q1, but with end-dates extending in annual increments from 1989:Q4 to 1993:Q4.[5]

For each sample period, we use a general-to-specific modelling approach. We test sequentially larger sets of exclusion restrictions on the regressors of the unrestricted ECM, leading eventually to identification of the statistically-significant regressors to be included in the estimated equation for the real exchange rate (see Appendix B for further details).

Three preferred regression specifications are identified. Thus, real exchange rate model B is given by:

for estimation periods ending 1986:Q4 to 1990:Q3,

for estimation periods ending 1990:Q4 to 1991:Q3,

for estimation periods ending 1991:Q4 to 1994:Q2.


Australia's five largest trading partners over the period, with normalised trade weights, were: Japan 0.4485, US 0.2896, UK 0.0969, W. Germany 0.0834, NZ 0.0816. [3]

We estimate the real exchange rate models over the post-float period; a sample so short that tests of non-stationarity generate ambiguous results. Tests on a longer sample of Australia's trade-weighted real exchange rate suggest it is stationary, possibly around a trend (Gruen and Shuetrim 1994). [4]

A preferred specification is assumed to remain the same for the three quarters following each end-date. Given the lack of degrees of freedom, we impose the model A specification given by equation (6) for sample periods ending before 1989:Q4. In these estimated equations, the coefficient on Δtott is always significant at the 5 per cent level. [5]