Cointegration Test

Given that the two series are stationary in their differences (i. e., both are I(1)), the next step is to test whether they are cointegrated. In the discussion that follows, we return to reproducing results from POE4. To do this, use least squares to estimate the following regression.

aust = в usat + et


obtain the residuals, et, and then estimate

Aet = Yet-1 + ut


This is the “case 1 test” from chapter 12 of Hill et al. (2011) and the 5% critical value for the t-ratio is -2.76. The following script estimates the model cointegrating regression, saves the residuals, and estimates the regression required for the unit root test.

1 ols aus usa

2 series uhat = $uhat

3 ols diff(uhat) uhat(-1)

The result is:

Aet = -0.127937et_ 1 (13.7)


T = 123 R2 = 0.0640 F (1,122) = 8.3482 e = 0.5985
(standard errors in parentheses)

The t-ratio is -0.1279/.0443 = -2.889 which lies in the rejection region for this test. Therefore, you reject the null hypothesis of no cointegration.

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