We will explore how the cointegrating vector is only identified up to a particular normalization. Consider Xt and Yt , two cointegrated variables where Yt = 10 + Xt + et Xt = 1 + Xt−1 + ∈t et ∼ iidN(0, 1)

∈t ∼ iidN(0, 1)

as in Fig. 12.1. Generate 100 observations of this data. Graph these two variables, and verify visually that they seem cointegrated. Estimate the long-run relationship between them and verify that the cointegrating vector is [1, −1]

'

.

Now, generate Y '

t = 2Yt and X'

t = 2Xt . Graph these two new variables. Verify graphically that X'

t and Y '

t are cointegrated. Perform Engle-Granger two-step tests to verify formally that Xt and Yt are cointegrated and that X'

t and Y '

t are cointegrated. If X'

t and Y '

t are cointegrated, then we have shown that [2, −2]

' is also a valid cointegrating vector.