RDP 8910: An Analysis of the Determinants of Imports Appendix 2: Unit Root and Time Trend Tests
December 1989
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This appendix contains the results of sequentially testing for three unit roots, then two unit roots then one unit root in each series used in our estimation procedure. (The results for three unit roots are not shown below because they were always rejected.) In each case test statistics are presented which test firstly for a time trend or a constant, using standard t-tests, and then test the given hypothesis regarding the order of integration, using each of the three tests Dickey-Pantula (DP), Stock-Watson (SW) and Dickey-Fuller (DF). Four AR corrections have been made in testing each variable.
The following provides an example of how to read each section in each table. (e.g. lines 1 to 8 in Table 1.) Line 1 tests the null hypothesis of no time trend; line 5 tests the null hypothesis of no constant. The presence or absence of a time trend determines whether the tests in lines 2–4 or 6–8 are valid. If a time trend is detected (that is the null is rejected in line 5) then the three tests in lines 2–4 determine whether the hypothesis being tested in the section (in this case two unit roots versus at most one) can be accepted. If no time trend is detected then one uses the tests in lines 6–8.
Test |
Total Imports |
Endog Imports |
GDP |
GNE |
|
---|---|---|---|---|---|
H0 : Two Unit Roots vs H1: at most One Unit Root | |||||
time | 0.872 | 0.991 | 1.250 | 1.164 | (1) |
DP: | −4.223* | −4.223* | −3.453** | −4.028* | (2) |
SW: | −50.982* | −51.316* | −58.997* | −45.7.95* | (3) |
DF: | −3.883** | −4.152* | −3.409 | −3.846** | (4) |
constant | 2.040** | 2.190** | 3.316* | 2.604* | (5) |
DP: | −4.049* | −4.023* | −3.217** | −3.719* | (6) |
SW: | −50.161* | −50.570* | −58.140* | −44.121* | (7) |
DF: | −3.801* | −4.038* | −3.217** | −3.631* | (8) |
H0 : One Unit Root vs H1: No Unit Roots | |||||
time | 3.611* | 4.022* | 2.464** | 3.020* | |
DP: | −2.315 | −2.689 | −2.068 | −2.174 | |
SW: | −13.992 | −15.972 | −9.363 | −11.632 | |
DF: | −2.863 | −2.891 | −1.974 | −2.792 | |
constant | 0.024 | 0.021 | −0.667 | −0.656 | |
DP: | 0.750 | 0.783 | 0.964 | 1.202 | |
SW: | 0.431 | 0.581 | 0.566 | 0.733 | |
DF: | 0.246 | 0.406 | 0.946 | 0.781 |
For example, for Total Imports, at the 1% critical value we cannot reject the null hypotheses of no time trend and no constant. We can, however, reject the presence of two unit roots with each of the three tests (lines 6–8) and therefore accept that there is at most one unit root. Moving on to the second section of the table, we accept that a time trend exists and cannot reject the presence of one unit root for all three tests.
* indicates the null hypothesis is rejected at a 1% level of significance.
** indicates the
null hypothesis is rejected at a 5% level of significance.
Test |
RP Total Imports |
RP Endog Imports |
RP of Exports |
Overtime |
---|---|---|---|---|
H0 : Two Unit Roots vs H1: at most One Unit Root | ||||
time | −1.536 | −1.227 | −0.207 | 0.565 |
DP: | −3.524** | −3.073 | −4.048* | −2.688 |
SW: | −46.004* | −40.869* | −48.150* | −28.594** |
DF: | −3.081 | −2.576 | −3.238 | −2.913 |
constant | −0.275 | −0.306 | −0.741 | 1.691 |
DP: | −3.127** | −2.871** | −4.091* | −2.752 |
SW: | −44.409* | −40.245* | −48.039* | −28.714* |
DF: | −2.677 | −2.306 | −3.265** | −2.989** |
H0 : One Unit Root vs H1: No Unit Roots | ||||
Time | −1.428 | −1.759 | −2.202** | 1.662 |
DP: | −2.052 | −3.030 | −2.254 | −2.140 |
SW: | −7.863 | −8.935 | −13.840 | −7.734 |
DF: | −2.042 | −2.422 | −2.743 | −1.528 |
constant | 0.272 | 1.014 | −0.403 | 1.453 |
DP: | −2.256 | −2.539 | −0.974 | −0.562 |
SW: | −6.404 | −6.524 | −5.171 | −0.847 |
DF: | −2.154 | −2.063 | −1.305 | −0.343 |