RDP 2000-05: A Small Model of the Australian Macroeconomy Appendix B: Testing for a Structural Break

Meredith Beechey, Nargis Bharucha, Adam Cagliarini, David Gruen and Christopher Thompson

June 2000

Lucas (1976) pointed out that coefficients in reduced-form macroeconomic equations may change if there is a policy-regime shift, rendering the equations unreliable in the new regime. To assess the relevance of the Lucas critique for the model, we test for structural change in the equations, using 1993:Q1 as the break point (for reasons explained in the text). To do this, each of the equations is estimated (in its restricted form where appropriate) augmented by each variable multiplied by a dummy, which takes the value 1 from 1993:Q1 onward.

The results are shown in the following tables. In each case, the first column repeats the estimates presented in Section 3 of the paper. The second column reports the full-sample coefficients from the augmented regression and the third column reports the coefficients on the post-break dummy variables. Tests of joint significance of the coefficients on the post-break dummy variables are also shown in the tables.

There is little evidence of structural breaks in the equations in early 1993. Most of the post-break dummy variables are individually insignificant and the hypothesis that the post-break coefficients are jointly zero is easily accepted in each equation.

This suggests that the introduction of the inflation-targeting regime around 1993 has not led to significant changes in the estimated relationships. This gives us some confidence that we can use the equations to generate forecasts, and to conduct policy experiments, provided those experiments do not involve policy regimes that are ‘too far removed’ from the range of policies that have been operating over the estimation period.

Table B1: Australian Non-farm Output(a)
  Original equation Augmented equation
 
    Coefficients on full-sample variables
 		 Coefficients on post-break dummy variables
 
Constant −189.827*** (50.263) −144.163
(138.576)		 −212.543
(165.484)
Real cash rate (lags 2 to 7)(b) −0.052***
{0.001}		 −0.056
{0.322}		 −0.008
{0.677}
Non-farm GDP (lag 1) −0.389***
(0.090)		 −0.302
(0.229)		 −0.483
(0.296)
US GDP (lag 1) 0.425***
(0.104)		 0.327
(0.277)		 0.498
(0.342)
De-trended real share prices (lag 1) 0.045***
(0.010)		 0.043***
(0.013)		 0.014
(0.029)
Non-farm GDP growth (lags 1 and 2)(c) −0.201**
(0.091)		 −0.154
(0.168)		 −0.208
(0.256)
OECD industrial production growth (lags 3 to 6) (c) 0.089**
(0.043)		 0.031
(0.102)		 0.201
(0.141)
Inline Equation 0.506 0.497
Standard error of the residuals 0.547 0.552
F-test for joint significance of coefficients on post-break dummy variables   {0.528}

Notes: (a) The equations are estimated by ordinary least squares using quarterly data over the period 1985:Q1–1999:Q3. Numbers in parentheses () are standard errors. Numbers in braces {} are p-values. ***, ** and * represent significance at the 1, 5 and 10 per cent levels. All variables in log levels are multiplied by 100 (so growth rates are in percentages).
(b) The mean coefficient is reported for the real cash rate to summarise the coefficients on its lags. The p-value is derived from an F-test of the joint significance of the lags.
(c) For these variables, the restriction that the coefficients on each lag are equal is accepted and imposed.
Table B2: Real Exchange Rate(a)
  Original equation Augmented equation
 
    Coefficients on full-sample variables
 		 Coefficients on post-break dummy variables
 
Constant −2.019
(32.118)		 13.059
(34.941)		 −177.687
(124.480)
Real exchange rate (lag 1) −0.484***
(0.096)		 −0.474***
(0.133)		 −0.105
(0.239)
Terms of trade (lag 1) 0.473***
(0.124)		 0.429***
(0.154)		 0.498
(0.430)
Real interest rate differential (lag 1) 0.590**
(0.252)		 0.734**
(0.340)		 −1.328
(1.268)
Terms of trade growth (lag 0) 1.290***
(0.176)		 1.348***
(0.212)		 −0.129
(0.451)
Inline Equation 0.605 0.587
Standard error of the residuals 2.819 2.883
F-test for joint significance of coefficients on post-break dummy variables   {0.758}

Note: (a) The equations are estimated by ordinary least squares using quarterly data over the period 1985:Q1–1999:Q3. Numbers in parentheses () are standard errors. Numbers in braces {} are p-values. ***, ** and * represent significance at the 1, 5 and 10 per cent levels. All variables in log levels are multiplied by 100 (so growth rates are in percentages).
Table B3: Import Prices(a)(b)
  Original equation Augmented equation(c)
 
    Coefficients on full-sample variables
 		 Coefficients on post-break dummy variables
 
Constant 153.271***
(40.275)		 150.309**
(65.194)		 −10.833
(74.013)
Change in the nominal exchange rate (lag 0) −0.657***
(0.030)		 −0.647***
(0.042)		 −0.046
(0.060)
Change in the nominal exchange rate (lag 1) −0.010**
(0.046)		 −0.111
(0.074)		 0.036
(0.084)
Change in foreign export prices (lag 0) 0.567***
(0.212)		 0.244 (0.405) 0.605
(0.424)
Change in foreign export prices (lag 1) 0.389*
(0.211)		 0.605
(0.409)		 −0.351
(0.426)
Import prices (lag 1) −0.335***
(0.089)		 −0.329**
(0.145)		 0.029
(0.164)
Foreign export prices (lag 1) 0.335***
(0.089)		 0.329**
(0.145)		 −0.029
(0.164)
Nominal exchange rate (lag 1) −0.335***
(0.089)		 −0.329**
(0.145)		 0.029
(0.164)
Trend −0.108***
(0.026)		 −0.102**
(0.041)		 −0.012
(0.050)
Dummy 1998:Q2–1999:Q3 −2.796***
(0.696)		 −2.280***
(0.421)		  
Inline Equation 0.920 0.915
Standard error of the residuals 0.934 0.960
F-test for joint significance of coefficients on post-break dummy variables   {0.740}

Notes: (a) The equations are estimated by ordinary least squares using quarterly data over the period 1985:Q1–1999:Q3. Numbers in parentheses () are standard errors. Numbers in braces {} are p-values. ***, ** and * represent significance at the 1, 5 and 10 per cent levels. All variables in log levels are multiplied by 100 (so growth rates are in percentages).
(b) Given the evidence of heteroskedasticity (see Table above), the standard errors reported are White heteroskedasticity-consistent standard errors.
(c) The assumption of purchasing power parity for traded goods prices is imposed both before and after the break.
Table B4: Unit Labour Costs(a)
  Original equation Augmented equation(b)
 
    Coefficients on full-sample variables
 		 Coefficients on post-break dummy variables
 
Dummy 1985:Q1–1995:Q4 0.304
(0.537)		 0.407
(0.792)		 0.171
(0.702)
Four-quarter-ended rate of inflation (lag 1) 0.298***
(0.104)		 0.317***
(0.110)		 −0.217
(0.268)
Four-quarter-ended rate of unit labour cost growth (lag 1) 0.473*** (0.110) 0.476***
(0.117)		 −0.141
(0.239)
Quarterly unit labour cost growth (lag 4) −0.969***
(0.130)		 −1.110***
(0.148)		 0.751**
(0.311)
(lag 5) −0.316***
(0.116)		 −0.361***
(0.140)		 0.060
(0.274)
Output gap (lag 4) 0.528***
(0.114)		 0.595***
(0.125)		 0.188
(0.182)
Bond market inflation expectations 0.319***
(0.101)		 0.324***
(0.117)		 0.218
(0.232)
Average inflation over past three years (lag 1) (1996:Q1 to sample end) 0.231***
(0.084)		 0.250**
(0.117)		  
Inline Equation 0.446 0.446
Standard error of the residuals 0.909 0.886
F-test for joint significance of coefficients on post-break dummy variables   {0.400}

Notes: (a) The equations are estimated by ordinary least squares using quarterly data over the period 1985:Q1–1999:Q3. Numbers in parentheses () are standard errors. Numbers in braces {} are p-values. ***, ** and * represent significance at the 1, 5 and 10 per cent levels. All variables in log levels are multiplied by 100 (so growth rates are in percentages).
(b) In the augmented equation, the long-run vertical Phillips curve is imposed post 1996:Q1, as in the original equation. No restrictions are imposed on the coefficients of the post-break dummy variables.
Table B5: Consumer Prices(a)
  Original equation(b) Augmented equation(c)
 
    Coefficients on full-sample variables
 		 Coefficients on post-break dummy variables
 
Constant −0.541
(0.379)		 −0.859*
(0.462)		 2.103
(1.329)
Consumer prices (lag 1) −0.073***
(0.008)		 −0.069***
(0.017)		 −0.102
(0.082)
Unit labour costs (lag 1) 0.043***
(0.013)		 0.034
(0.022)		 0.125
(0.090)
Adjusted import prices (lag 1) 0.030***
(0.006)		 0.036***
(0.007)		 −0.022
(0.014)
Unit labour cost growth (lag 0) 0.103***
(0.032)		 0.076*
(0.041)		 0.099
(0.083)
Adjusted import prices growth (lag 0) 0.032**
(0.013)		 0.046***
(0.016)		 −0.031
(0.028)
Oil price growth (lag 1) 0.008***
(0.003)		 0.003
(0.004)		 0.006
(0.007)
Output gap (lag 3) 0.142***
(0.026)		 0.165***
(0.033)		 0.045
(0.121)
Change in the output gap (lag 0, 1 and 2)(d) 0.072**
(0.032)		 0.099**
(0.041)		 0.011
(0.101)
Dummy 1990:Q4 1.084***
(0.291)		 1.279***
(0.324)		  
Dummy 1991:Q1 −1.254***
(0.290)		 −1.095***
(0.322)		  
Inline Equation 0.880 0.879
Standard error of the residuals 0.250 0.251
F-test for joint significance of coefficients on post-break dummy variables   {0.490}

Notes: (a) The equations are estimated by ordinary least squares using quarterly data over the period 1985:Q1–1999:Q3. Numbers in parentheses () are standard errors. Numbers in braces {} are p-values. ***, ** and * represent significance at the 1, 5 and 10 per cent levels. All variables in log levels are multiplied by 100 (so growth rates are in percentages).
(b) The standard errors reported for this equation are White heteroskedasticity-consistent standard errors.
(c) In the augmented equation, the long-run restriction of static homogeneity is imposed both before and after the break. This equation does not exhibit heteroskedasticity, so OLS standard errors are used.
(d) For these variables, the restriction that the coefficients on each lag are equal is accepted and imposed.