4.2  Diagnostic tests

To assess the stability of parameter estimates, Hansen’s (1992) stability test can be used. A key advantage of this test is that it does not require selecting potential structural break points. Moreover, no special treatment of lagged dependent variables is required (Hansen, 1992). However, the test requires variables to be stationary.

The Hansen stability test produces two types of statistic: a joint test statistic and individual test statistics. Individual test statistics represent the stability of each parameter in the reduced-form equations in (1), while the joint test assesses the stability of all the parameters jointly in each of the equations in (1). The null hypothesis of stable estimates is rejected if the individual or joint test statistics are significant, i.e. the p-values are low. The results for the baseline and alternative models, which are reported in Appendix B, show that, overall, the parameter estimates are fairly stable for both the individual and joint tests. Although some parameters are unstable individually, they appear to be stable jointly over time.

To test for model stability we verify the stationary condition of the fiscal VAR models. This formally tests that the impulse responses converge following a fiscal shock. We compute the value of root from the eigenvalues of the companion matrix derived from the parameter estimates. A value of root of greater than one indicates that a model is systematically unstable. The results, also reported in Appendix B, show that the baseline and alternative models are stationary. The values of roots are less than one although they are larger for the deterministic and Hodrick-Prescott models compared to the stochastic trend and first difference models.

To detect possible misspecification of the models we test that the residuals from the reduced-form equations in (1) are normally distributed using Jarque and Bera’s (1987) test of normality. The results, reported in Appendix C, show that the equations have normally distributed errors except for the government expenditure equation in the deterministic and the Hodrick-Prescott model.

We also use Ramsey’s (1969) RESET test of specification error to determine possible misspecification of the models. The RESET test allows assessing the linearity assumption in the reduced-form equations in (1). The results, also reported in Appendix C, show that the hypothesis of model misspecification is rejected for all equations except for the deterministic model. This finding and the results from the normality tests strongly suggest that the deterministic model does not fit the New Zealand data well. The finding is in line with the unit root tests, which suggest that a model specification that assumes non-stationary variables is more appropriate for New Zealand.

4.3  Alternative ordering of variables and elasticities

In the baseline model, net tax is ordered before government spending. To assess the sensitivity of the impulse responses the ordering is reversed and government spending is placed before net tax. The results, which are plotted in Appendix D, show that the impulse responses from the alternative ordering are similar. For the stochastic and first difference models, there is only a minor difference that the immediate response of each fiscal variable from the shock to the other fiscal variable is somewhat larger when net tax are ordered first.

For the Hodrick-Prescott specification, there are small differences in the immediate response of net tax to a government spending shock, and the immediate response of government spending to a net tax shock. With the alternative ordering, where government spending is placed before net tax, government spending no longer declines following a net tax shock. Moreover, with the alternative ordering net tax immediately declines in response to an increase in government spending. The opposite occurs with the baseline Hodrick-Prescott specification.

To test the sensitivity of the fiscal VAR to the tax-output elasticity, two alternative elasticities of 0.5 and 1.5 are used instead of 1. The tax-output elasticity is a key variable in forming the cyclically adjusted net tax residuals that are used as instrumental variables to estimate the contemporaneous effect of a change in net tax on output. The impulse responses with the alternative elasticities are plotted in Appendix E for the stochastic, first difference and Hodrick-Prescott models. The results show that the impact of increasing the tax-output elasticity from 1 to 1.5 is to marginally increase the impact that a net tax shock has on output for all three models. The result of decreasing the tax-output elasticity from 1 to 0.5 is to reduce the negative impact on GDP over the short term of the net tax shock. Overall, despite substantial changes in the tax-output elasticity, the responses of GDP to the net tax shock are similar.

4.4  Comparison with other models and economies

Finally, we compare the New Zealand results to that from other models and economies. Table 3 summarises the fiscal multipliers estimated from the New Zealand VAR and prior work by Blanchard and Perotti (2002), and Perotti (2004). Contemporaneous, peak and long term responses are reported.[8]

While there is considerable variation between economies in the contemporaneous responses of GDP to fiscal shocks, they are generally positive for government spending and negative for a net tax shock. However, in absolute terms the impact of a government spending shock on GDP tends to be larger than a net tax shock. The peak and long-term responses of GDP to government spending shocks differ substantially across economies, being positive in some countries and negative in others. Results for the United States suggest that the peak and long-term government spending multipliers are sensitive to the time period and whether or not inflation and the 10 year nominal interest rate are included in the VAR model. The peak and long-term tax multipliers are generally negative, although again there is considerably variation across economies.

Note that for Australia and New Zealand, which are both small open economies, the fiscal multipliers are relatively small compared with the larger economies, possibly reflecting the role that imports, private savings, interest and exchange rates play in influencing the way these economies adjust to fiscal shocks.

* Long-term is taken to be after 20 quarters.

** Peak is the largest absolute deviation from zero.

*** Model includes 5 variables: government spending, net tax, output, inflation and a nominal interest rate.

DT, ST, FD and HP indicate at a deterministic trend, stochastic trend, first difference and a Hodrick-Prescott trend.

The contemporaneous response of GDP to fiscal shocks displayed in Table 3 does not capture the dynamic response of GDP to these shocks. Therefore, to compare the dynamic response of GDP to fiscal shocks across the various VAR models, Table 4 reports the cumulative response of GDP after four and twelve quarters. Consistent with prior work, the twelve quarter cumulated response is referred to as the long-run multiplier. Table 4 shows that government spending tends to also have a positive effect on GDP in the medium and long run. However, the immediate negative effect on GDP of a net tax shock does not persist for all countries in the long run. Net tax increases because of an increase in tax revenue and/or a decline in transfer payments. A positive response of GDP to a discretionary net tax shock may therefore be the result of a decline in transfer payments having a positive effect on GDP that more than offsets any negative effects of increased taxation. Alternatively, an increase in net tax may be the result of tax policy reform that has raised tax revenue but at the same time has reduced the distortionary effects of taxation, for example, by broadening the tax base.

In summary, the results from the sensitivity analysis and robustness testing suggest that the fiscal VAR with a specification that assumes non-stationary variables is well specified and appropriate for New Zealand. Moreover, the estimated effects of fiscal policy on output fall within the range of international evidence. In fact, our results suggest that the New Zealand data may actually fit the Blanchard and Perotti (2002) model better than the US data. Performing the same sensitivity analysis and robustness testing for the US model as for the New Zealand fiscal VAR, we found evidence of parameter and model instability and potential model misspecification for the US model. For example, the equations for the US model have non-normally distributed errors, especially for the net tax equation. In addition, we found that the US equations with temporary tax cut dummy variables have unstable estimates for the joint test although the equations become stable once the dummy variables are removed from the equations.[9]

* Model includes 5 variables: government spending, net tax, output, inflation and a nominal interest rate.

DT, ST, FD and HP indicate at a deterministic trend, stochastic trend, first difference and a Hodrick-Prescott trend.