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. 2019 May 9;26(19):19389–19402. doi: 10.1007/s11356-019-05269-w

Table 5.

Results of the test for joint significance of coefficients and cointegration tests

Variable addition test (VAT) Test for joint significance of time-varying coefficients
Test statistics 1% CV 5% CV 10% CV Test statistics 1% CV 5% CV 10% CV
2.35*** 13.18 9.49 7.78 2.66 15.09 11.07 9.24

The left-hand side of the table shows the results of VAT cointegration test. The right-hand side of the table demonstrates results of the joint significance test of time-varying coefficients, in order to test whether or not the income elasticity is fixed or time varying. Triple asterisk and double asterisk stand for acceptance of the null in case of VAT test and rejection of the null in Chi-square test at 1% and 5% significance level, respectively