Introductory Econometrics: A Modern Approach 6th Edition by Jeffrey M Wooldridge

Exercise 14

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.)