4  Sensitivity analysis

This section reports some sensitivity analysis of the baseline three variable fiscal VAR. To test the robustness of the results, we estimate two alternative fiscal VAR models. We then provide diagnostic tests and consider alternative ordering of variables and elasticities for the baseline model. We also compare the New Zealand results to that from other models and economies.

4.1  Alternative specifications

Unit root tests discussed in section 2 suggest that net tax, government spending, and GDP are non-stationary and that the stochastic specification may be more appropriate than the deterministic model. This section considers two alternative stochastic trend specifications. First, net tax, government spending and GDP are included in first differences. Second, the data are detrended by removing time varying stochastic trends using the Hodrik-Prescott filter.

The parameter estimates of the contemporaneous relationships shown in equations (2) to (4) for the first difference and Hodrick-Prescott trend specification of the fiscal VAR are reported in Table 2. As with the baseline deterministic and stochastic specifications, the tax to output elasticity (^a1) is set equal to one and the government spending to output elasticity (^b1) is set equal to zero.

A comparison of the estimated contemporaneous coefficients from the baseline deterministic and stochastic models (Table 1) with the estimates from the two alternative specifications (Table 2) shows broadly similar results. The contemporaneous effect of a net tax shock on GDP (^c 1) is negative, while the contemporaneous effect of a government spending shock on GDP (_{^c 2) is positive. The coefficient estimates for the first difference model are almost identical to the estimates from the baseline stochastic model. For the Hodrick-Prescott specification, the estimate for ^c 1 is slightly smaller than for the first difference, deterministic and stochastic specifications and the estimate for ^c 2 is smaller than for the other models.}

Figure 5 – Responses to a net tax and government spending shock: first difference model – net tax shock (left) and government spending shock (right)

The impulse responses of net tax, government spending and GDP to a one dollar net tax and government spending shock are plotted in Figure 5 for the first difference model and in Figure 6 for the Hodrick-Prescott specification. Figure 5 shows that the impulse responses of the first difference and baseline stochastic trend model are virtually identical.

For the Hodrick-Prescott specification, Figure 6 shows that the fiscal shocks lead to temporary deviations of variables from their long-run time varying trend (as measured by the Hodrick-Prescott filter) but eventually the impulse responses converge back to zero, as is the case for the deterministic model. For the Hodrick-Prescott specification, the reduction in GDP caused by the net tax shock persists for around two quarters, before the economy experiences a period where GDP is above trend. As suggested earlier, this period where GDP increases above its long-run path could be owing to the influence of other macroeconomic variables (such as interest and exchange rates) that change in response to the initial net tax shock. The decline in GDP may also cause the small decrease in government spending. Following the net tax shock, government spending initially declines (as in the case of the deterministic, stochastic and first difference specifications). This result is further discussed in section 4.3.

Figure 6 – Responses to a net tax and government spending shock: Hodrick-Prescott specification – net tax shock (left) and government spending shock (right)

One noticeable difference is that the government spending shock is less persistent for the Hodrick-Prescott specification than the deterministic model. The one dollar government spending shock dissipates over the first year. The positive effect on GDP from the government spending shock lasts for less than one year, before the economy experiences a period where GDP falls below its trend path. The impact of the government spending shock on net tax is broadly similar to the deterministic specification.