Appendix B: The Behavioural Model of the Australian Real Exchange Rate – Integration Tests and Diagnostics | RDP 9608: Modelling the Australian Exchange Rate, Long Bond Yield and Inflationary Expectations

RDP 9608: Modelling the Australian Exchange Rate, Long Bond Yield and Inflationary Expectations Appendix B: The Behavioural Model of the Australian Real Exchange Rate – Integration Tests and Diagnostics

Alison Tarditi

November 1996

Download the Paper 171KB

Table B.1: Testing the Blundell-Wignall *et al*. (1993) Equation – Cumulative Current Account Deficit (CCAD) or Trend?
Model	Estimated coefficient^(a)
1985:Q1–1995:Q2	CCAD		Trend
Original specification – CCAD	−0.281	(−2.60*)
Adding a trend term	0.626	(1.49)	−0.012	(−2.15*)
Replacing CCAD with a trend term			−0.004	(−3.11**)
Notes: (a) Estimates are taken from the Bewley Transformation of an unrestricted error correction model. Figures in parenthesis denote t-statistics; * and ** denote significance at the 10% and 5% levels respectively.

Table B.2: Yield Gap Variable –Testing the Null of the Validity of the Implied Restrictions
Sample period	Test-statistic	Significance level
1985:Q1–1995:Q2	1.06	F(3,31)	0.38
1973:Q4–1995:Q2	0.77	F(3,76)	0.51

Table B.3a: Integration Tests (1973:Q4–1995:Q2)
	H₀: Non-stationarity					H₀: Stationarity
	Φ₃	τ_τ	τ_μ	DF-GLS_τ	DF-GLS_μ	KPSS_τ	KPSS_μ
Real exchange rate	5.48^*	−3.31^*	−1.77	−2.92^*	−2.03^**	0.05	0.78^***
Terms of trade	10.06^***	−4.07^***	−2.86^*	−5.67^***	−6.22^***	0.14^*	0.72^**
Prices	8.33^**	−2.32	−3.80^***	0.62	1.68	0.25^***	0.17
Current account	7.44^**	−3.86^**	−2.10	−4.013^***	−3.29^***	0.13^*	0.58^**
Debt	1.76	−1.87	−0.26	−3.18^**	0.03	0.09	1.06^***
Government deficit	6.97^**	−3.71^**	−3.31^**	−1.99	−2.12^**	0.08	0.23
Yield gap	5.00	−3.15^*	−3.17^**	−4.48^***	−4.11^***	0.13^*	0.14
Yield gap^*	5.01	−3.16^*	−2.78^*	−8.43^***	−8.83^***	0.05	0.26
Notes: , * and *** denote significance at the 10%, 5% and 1% levels respectively. Φ₃ refers to the likelihood ratio test of (α, β, ρ)=(α, 0, 1) in Y_t = α + β_t + ρY_t₋₁ + e_t. The critical values are from Dickey and Fuller (1981). τ refers to the Augmented Dickey-Fuller (ADF) ‘t-tests’; τ_τ includes a constant and trend and τ_μ includes a constant only. The critical values are from Fuller (1976). DF – GLS_τ and DF – GLS_μ are a modified trend and constant version, respectively, of the ADF tests proposed by Elliot et al. (1992). KPSS is a test proposed by Kwiatkowski et al. (1992) which tests the null hypothesis of stationarity. A truncation lag of 8 is used for the calculation of the estimate of the error variance.

Table B.3b: Integration Tests (1984:Q1–1995:Q2)
	H₀: Non-stationarity					H₀: Stationarity
	Φ₃	τ_τ	τ_μ	DF-GLS_τ	DF-GLS_μ	KPSS_τ	KPSS_μ
Real exchange rate	3.03	−2.36	−2.26	−4.93^***	−2.22^**	0.08	0.16
Terms of trade	8.96^**	−4.17^***	−4.24^***	−3.63^**	−3.43^***	0.07	0.08
Prices	6.67^*	−1.99	−3.60^***	−1.14	1.12	0.17^**	0.61^**
Current account	6.13^*	−3.43^*	−3.37^**	−4.78^***	−5.56^***	0.07	0.12
Debt	11.35^***	−4.74^***	−0.07	−3.39^**	0.76	0.06	0.63^**
Government deficit	6.61^**	−3.31^*	−3.23^**	−1.27	−1.55	0.15^**	0.15
Yield gap	6.78^**	−3.63^**	−2.46	−5.48^***	−6.14^***	0.13^*	0.32
Yield gap^*	2.78	−2.29	−2.37	−4.08^***	−5.02^***	0.13^*	0.13
Notes: , * and *** denote significance at the 10%, 5% and 1% levels respectively. Φ₃ refers to the likelihood ratio test of (α, β, ρ)=(α, 0, 1) in Y_t = α + β_t + ρY_t₋₁ + e_t. The critical values are from Dickey and Fuller (1981). τ refers to the Augmented Dickey-Fuller (ADF) ‘t-tests’; τ_τ includes a constant and trend and τ_μ includes a constant only. The critical values are from Fuller (1976). DF – GLS_τ and DF – GLS_μ are a modified trend and constant version, respectively, of the ADF tests proposed by Elliot et al. (1992). KPSS is a test proposed by Kwiatkowski et al. (1992) which tests the null hypothesis of stationarity. A truncation lag of 8 is used for the calculation of the estimate of the error variance.

The DF-GLS test (Elliot et al. 1992) is a modified version of the Augmented Dickey-Fuller (ADF) t-test, having the advantages that it exhibits superior power properties and suffers from only small size distortions in finite samples. The testing procedure involves firstly demeaning or detrending the series using Generalised Least Squares and then running the ADF test regression using that series. The constant and time trend terms are omitted from the test regression. The t-statistic on (ρ−1) is then used to test for significance against the appropriate critical value. The demeaned case (DF-GLS^μ) is comparable to including a constant term in the ADF test; the critical values are taken from Fuller (1976) and the no-constant variant of the MacKinnon (1991) table. The detrended case (DF-GLS^τ) is comparable to including a constant and a time trend in the ADF test; the critical values have been tabulated by Elliot et al.

The KPSS (1992) test is applied in the following way. All series can be written as the sum of a trend (ξ_t), a random walk (r_t), and a stationary component (ε_t) such that:

If the series is stationary (that is, there is no random walk component), the variance of ut will be zero. The test statistic for the null hypothesis of no unit root is an LM statistic which is a function of estimated residuals and an estimate of the long-run error variance. These residuals are either the demeaned series (η_μ) or the demeaned and detrended series (η_τ). The critical values for these tests are detailed in Kwiatkowski et al. (1992, p.166).

These tests provide evidence over the full sample period (1973:Q4–1995:Q2) that the real exchange rate; terms of trade; interest differentials; yield gaps; current account deficit; government budget balance; and relative productivity differentials are 1(0), with the first two series exhibiting this stationarity around a trend. These conclusions are also supportable over the shorter sample period (1984:Q1–1995:Q2).

Table B.4: A Comparison of the Statistical Significance of Competing Measures of Interest Rates in the Real Exchange Rate Equation^(a)
1985:Q1–1995:Q2)
Interest differential term	Estimated coefficient	t-statistic (p-value)
	1.10	3.10	(0.00)
	0.90	2.62	(0.01)
as per the BW equation.	1.11	1.82	(0.08)
	1.81	2.47	(0.02)
Notes: (a) The real TWI exchange rate model is specified as a function of the terms of trade; the cumulated current account deficit; an interest differential term; and a fiscal policy variable. (b) The real long interest differential is here tested in the BW specification which expresses the real TWI as a function of the terms of trade; the cumulated current account deficit as a proportion of GDP; and the real long interest rate differential.