RDP 9508: Are Terms of Trade Rises Inflationary? Appendix 3: The Income Effect
November 1995
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The income effect associated with a rise in the terms of trade is estimated using the following regression model:
where GDP is real gross domestic product, RTWI is the real trade-weighted index of the Australian dollar, and RBR is the real 90-day bank bill rate and controls for the influence of monetary policy.^{[28]}
All data are quarterly and described in Appendix 1. The lag structure follows Gruen and Shuetrim (1994, p. 356) and allows for the possibility that past changes in GDP influence the current change in output, that changes in the terms of trade and the real exchange rate may take up to two years to influence GDP while real interest rates operate with a lag of two to six quarters. We test whether the nominated set of lags is significant collectively, rather than eliminating all insignificant lags. Ordinary Least Squares (OLS) estimation is used with standard errors estimated using a Newey-West correction allowing for fourth order autocorrelation.
Lags of the dependent variable were jointly insignificant and so were eliminated from the regression. In this reduced regression, lags of ΔRTWI were insignificant and were also eliminated.^{[29]} Results from the preferred specification are presented in Table A3.1. The sum of the coefficients on the lags is reported.
ΔTOT | −0.04^{###} |
---|---|
{lags} | {0 to 7} |
RBR | −0.14^{***} |
{lags} | {2 to 6} |
R^{2} | 0.80 |
0.38 | |
GDP impact | 0.11 |
Standard error of GDP impact | 0.05 |
Note: The sum of the coefficients on the lags are reported. The sample period is 1984:1 to 1994:2. ***, **, * indicate rejection at 1%, 5%, 10% level of the hypothesis that the sum of the coefficients on the lags is zero. ^{###} indicates rejection of the hypothesis that the coefficients are jointly zero at the 1% level. Hypothesis tests are based on standard errors estimated using a Newey-West correction allowing for fourth order autocorrelation. |
The sum of the coefficients on the terms of trade, while negative, is insignificantly different from zero. The coefficients on the first two lags are substantially positive, implying that a rise in the terms of trade provides an initial boost to GDP, after which the level of GDP returns to its long-run equilibrium. In other words, a terms of trade rise has only a temporary positive impact on output. The sum of the coefficients on RBR is of the expected negative sign and highly significant, indicating that a tightening of monetary policy reduces growth.
The per cent-years of real GDP gained within two years of a once-off change in the terms of trade, ΔTOT , is given by:
This formula cumulates the impact of a change in the terms of trade on GDP over two years (for which coefficient estimates for lags 0 to 7 are required). (Dividing by 4 converts the result from per cent-quarters to per cent-years.) The result of this calculation is reported in the table and indicates that for a 10 per cent rise in the terms of trade, the level of real GDP rises by 0.11×10=1.1 per cent-years.
The inflationary effect of the higher income is found by multiplying the real GDP impact by the parameter ϕ (see the text). Thus, for a 10 per cent rise in the terms of trade, the higher income causes an increase in inflation of 1.1× ϕ=1.1×0.4=0.44 percentage points.
Footnotes
GS conduct a similar exercise although their estimation period includes some of the pre-float period. For reasons explained by GS (p. 356), the specification chosen allows estimation of the average income effect from a terms of trade rise. [28]
In the original specification (A3.1), lags of the dependent variable and (the change in) the real TWI are jointly significant. We therefore checked the robustness of our results using a specification in which only lags of the dependent variable were eliminated from (A3.1). Setting ΔRTWI_{t}−_{j}=δΔTOT_{t}−_{j} and using either δ=0.51 or δ=0.885 gives estimates of the income effect of a terms of trade rise that are almost identical to those reported, although the standard errors are larger. [29]