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An Empirical Investigation of Fiscal Policy in New Zealand - WP 06/08

Appendix C: Normality and linearity tests

Appendix Table 4 – Test results for normality of residuals
  Net Tax G.E. GDP
  Statistics P-Value Statistics P-Value Statistics P-Value
Deterministic 0.111 0.946 19.387 0.000* 2.001 0.368
Stochastic 2.377 0.305 3.206 0.201 3.641 0.162
Hodrick-Prescott 1.651 0.438 19.453 0.000* 3.728 0.155
First Difference 1.700 0.427 4.593 0.101 4.763 0.092

* Indicates statistically significant non-normal distribution of residuals

Appendix Table 5 – Test results for linearity
D.T. S.T. H.P. F.D.
Net Tax Powers = 2 Statistics 0.702 0.185 0.027 0.233
P-Value 0.405 0.669 0.869 0.631
Powers = 2,3 Statistics 4.176 1.392 0.029* 1.417
P-Value 0.020* 0.256 0.972 0.250
Powers = 2,4 Statistics 2.763 1.122 0.448 1.099
P-Value 0.049* 0.346 0.720 0.356
G.E. Powers = 2 Statistics 0.340 1.898 0.067 3.139
P-Value 0.562 0.173 0.797 0.081*
Powers = 2,3 Statistics 0.173 1.177 0.046 1.872
P-Value 0.841 0.314 0.955 0.162
Powers = 2,4 Statistics 0.166 0.935 0.030 1.276
P-Value 0.919 0.429 0.993 0.290
GDP Powers = 2 Statistics 105.813 0.385 0.008 1.247
P-Value 0.000* 0.537 0.931 0.268
Powers = 2,3 Statistics 150.911 0.470 0.057 1.007
P-Value 0.000* 0.627 0.945 0.371
Powers = 2,4 Statistics 99.604 0.558 0.082 0.694
P-Value 0.000* 0.644 0.969 0.559

* Indicates significant non-linearity

* D.T. = Deterministic, S.T. = Stochastic, H.P. = Hodrick-Prescott and F.D. = First Difference

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