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Appendix A

Table A1: Unit root test results
  ADF Philips-Perron
Government Spending -2.05* -1.64*
Net Tax -2.80* -1.74*
GDP -1.67* -1.67*
Inflation -2.54* -9.68
Interest Rate -2.58* -2.25*
Debt -2.36* -2.80*

Note: * indicates statistically significant unit root at 5 percent significance level. The lag lengths are selected based on Akaike Information Criteria (AIC). The ADF statistics for all variables are based on regressions including constant and linear trend with the exception of inflation which include constant only.

Table A2: Johansen cointegration test results

Selected (0.05 level*) Number of Cointegrating Relationships by Model
Data Trend: None None Linear Linear Quadratic
Test Type No Intercept Intercept Intercept Intercept Intercept
  No Trend No Trend No Trend Trend Trend
Trace 0 0 0 0 0
Max-Eig 0 0 0 0 0

*Critical values based on MacKinnon-Haug-Michelis (1999)

Information Criteria by Rank and Model
Data Trend: None None Linear Linear Quadratic
Rank or No. of Coint.Eqns. No Intercept Intercept Intercept Intercept Intercept
  No Trend No Trend No Trend Trend Trend

Log Likelihood by Rank (rows) and Model (columns)

          
0  421.2739  421.2739  423.0708  423.0708  425.0898
1  425.0364  425.5393  427.2717  428.6582  430.0346
2  425.8361  427.2742  427.2742  430.4015  430.4015

Akaike Information Criteria by Rank (rows) and Model (columns)

          
0 -7.722149 -7.722149 -7.718317 -7.718317 -7.718675
1 -7.717667 -7.708288 -7.722108 -7.729400  -7.736502*
2 -7.657284 -7.646684 -7.646684 -7.667954 -7.667954

Schwarz Criteria by Rank (rows) and Model (columns)

          
0 -7.420628* -7.420628* -7.366542 -7.366542 -7.316646
1 -7.315638 -7.281133 -7.269826 -7.251991 -7.233967
2 -7.154749 -7.093894 -7.093894 -7.064911 -7.064911

Note: The sample period is 1983:1-2010:2. The variables are logarithms of real per capita government spending and real per capita tax revenues net of transfers. The lag length for VAR is chosen as 3 based on AIC.

Selected (0.05 level*) Number of Cointegrating Relationships by Model
Data Trend: None None Linear Linear Quadratic
Test Type No Intercept Intercept Intercept Intercept Intercept
  No Trend No Trend No Trend Trend Trend
Trace 1 2 1 1 1
Max-Eig 1 0 0 1 1

 *Critical values based on MacKinnon-Haug-Michelis (1999)

Information Criteria by Rank and Model
Data Trend: None None Linear Linear Quadratic
Rank or No. of Coint Eqns. No Intercept Intercept Intercept Intercept Intercept
  No Trend No Trend No Trend Trend Trend

Log Likelihood by Rank (rows) and Model (columns)

          
0  1185.134  1185.134  1193.423  1193.423  1196.948
1  1198.959  1199.270  1206.883  1213.599  1216.820
2  1206.521  1211.581  1214.253  1222.422  1225.250
3  1208.871  1216.196  1217.842  1226.387  1228.979
4  1208.871  1218.492  1218.492  1229.728  1229.728

Akaike Information Criteria by Rank (rows) and Model (columns)

          
0 -20.96607 -20.96607 -21.04406 -21.04406 -21.03541
1 -21.07199 -21.05945 -21.14333 -21.24725 -21.25127
2 -21.06402 -21.11966 -21.13188 -21.24403  -21.25909*
3 -20.96128 -21.03992 -21.05168 -21.15249 -21.18145
4 -20.81585 -20.91804 -20.91804 -21.04960 -21.04960

Schwarz Criteria by Rank (rows) and Model (columns)

          
0 -20.18048* -20.18048* -20.16027 -20.16027 -20.05342
1 -20.08999 -20.05291 -20.06314 -20.14251 -20.07288
2 -19.88563 -19.89216 -19.85529 -19.91834 -19.88430
3 -19.58649 -19.59148 -19.57869 -19.60585 -19.61026
4 -19.24466 -19.24866 -19.24866 -19.28201 -19.28201

Note: The sample period is 1983:1-2010:2. The variables are logarithms of real per capita government spending, real per capita tax revenues net of transfers, real GDP per capita and 10 year interest rates. The lag length for VAR is chosen as 2 based on AIC.

Table A 3: VAR residual Portmanteau tests for autocorrelations

VAR residual Portmanteau tests for autocorrelations
Lags Q-Stat Prob. Adj Q-Stat Prob. df
1 3.767290 NA* 3.802831 NA* NA*
2 9.796390 NA* 9.946771 NA* NA*
3 29.70909 NA* 30.43387 NA* NA*
4 56.27069 0.1427 58.02700 0.1099 46
5 79.75032 0.2232 82.65758 0.1624 71
6 95.63549 0.4913 99.48643 0.3834 96
7 110.7778 0.7368 115.6887 0.6193 121
8 147.0489 0.4601 154.8908 0.2915 146
9 175.1920 0.3971 185.6184 0.2105 171
10 203.8717 0.3351 217.2548 0.1422 196
11 221.8366 0.4715 237.2782 0.2155 221
12 250.2876 0.4121 269.3231 0.1469 246

Note: Null hypothesis: no residual autocorrelations up to lag h. df is degrees of freedom for (approximate) chi-square distribution.

*The test is valid only for lags larger than the VAR lag order.

Table A 4: White test for heteroskedasticity

VAR Residual Heteroskedasticity Tests: No Cross Terms (only levels and squares), Sample: 1983:1 2010:2
Joint test:    
Chi-sq df Prob.
517.9624 480  0.1120

Note: Null hypothesis: no residual heteroskedasticity

Figure A1: Inverse roots of AR characteristic polynomial
Figure A1: Inverse roots of AR characteristic polynomial.
Source: Authors' calculations.
Figure A2: Residual quantile plots
Figure A2: Residual quantile plots.
Source: Authors' calculations.
Figure A3: CUSUM plots
Figure A3: CUSUM plots.
Source: Authors' calculations.
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