6 Robustness checks and diagnostics
In this section, we report the results from various robustness checks conducted to test the sensitivity of the results presented above to various model assumptions. In line with the main focus of the paper, we only report the sensitivities of the corresponding shocks and the fiscal multipliers. The full sets of impulse responses are also available on request.
Furthermore, we report the results from a selection of diagnostic tests performed to test the statistical validity of the model results. These include the tests for autocorrelation, heteroskedasticity, normality and model stability.
6.1 Sensitivity analysis
The purpose of the first robustness check is to check whether the results are sensitive to the sample size chosen for model estimation. We consider two episodes that could potentially lead to parameter instability. The first is the period following the global financial crisis (GFC).
To test whether the model results are robust to the inclusion of the crisis period in estimation, we re-estimate the model for the period 1983:1-2006:4 and calculate the impulse response functions. The results are shown in Figure 21. While the output response to the spending shock is more persistent in the shorter sample, the results are fairly robust particularly in the short-run.
- Figure 21: Sample size sensitivity (1983:1-2006:4)
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- Source: Authors' calculations.
The second sub-sample period we consider runs from 1992:1-2010:2. The period prior to 1992 is characterised by major policy changes in the economy such as the adaptation of inflation targeting regime and the amendment of the Fiscal Responsibility Act. We re-estimate the model for the later sub-sample and calculate the corresponding impulse responses. The results are displayed in Figure 22.
- Figure 22: Sample size sensitivity (1992:1-2010:2)
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- Source: Authors' calculations.
It can be seen that the government spending shocks have a smaller impact on output during this period. The effect of revenue shocks, on the other hand, is higher.
In another sensitivity analysis, we experiment with different values for the elasticities of government revenues and expenditures described in Section 3.1.
Firstly, we run the model by setting the price elasticity of real government spending, αg Δp, to zero. The impact of this change on the government spending shock and the corresponding output multiplier is shown in Figure 23. The impulse responses are qualitatively similar.
- Figure 23: Sensitivity to the price elasticity of government spending
- Source: Authors' calculations.
Secondly, we experiment with the elasticity of tax revenue with respect to GDP, aty by setting set its values to 1.5 and 2 respectively. The corresponding effects are displayed in Figure 24. The results appear broadly similar, although it is notable that the sign of the response of output to a net tax shock is almost entirely negative if the elasticity is set at 2. This is a more intuitive result, suggesting that it would be useful to investigate whether net taxes are more sensitive to GDP than is assumed in the base case.
- Figure 24: Sensitivity to the output elasticity of tax revenue
- Source: Authors' calculations.
6.2 Diagnostic tests
Tables A3-A4 and Figures A1-A3 in the Appendix show the results of various diagnostic tests. These tests are carried out to detect potential violations of the Gauss-Markov assumptions. Model stability tests show the model is stable-all the roots of the characteristic polynomial are less than one (Appendix Figure A1). The Portmanteau and the White tests do not indicate any significant autocorrelation and heteroskedasticity in the residuals of the model (Appendix Tables A3 and A4). The quantile plots for the residuals displayed in Appendix Figure A2 show that the residuals are normally distributed with only slight divergences. Finally, the cumulative sum of squares (CUSUM) test results displayed in Appendix Figure A3 is not suggestive of any parameter or variance instability in the model.
