Introductory Econometrics 4th Edition by Jeffrey Wooldridge

Exercise 13

Suppose the process {(xt, yt): t = 0, 1, 2,...} satisfies the equations
yt = xt + ut
and
xt = xt-1+vt
where E(ut|I+) = E(vt|I+) = 0, It-1 contains information on x and y dated at time t - 1 and earlier, 0, and | | 1 [so that xt, and therefore yt, is Show that these two equations imply an error correction model of the form
yt = xt-1 + (yt-1 - xt-1) + et
where 1 = , = -1, and et = ut + 3vt. (Hint: First subtract yt-1 from both sides of the first equation. Then, add and subtract xt-1 from the right-hand side and rearrange. Finally, use the second equation to get the error correction model that contains xt-1.)