We are interested in the long run multiplier in the model Assume that xt is an autoregressive series, xt = rxt??1 + vt where |r | a. What is the long run multiplier in this model?

b. How would you estimate the long-run multiplier in this model?

c. Suppose you that the preceding is the true model but you linearly regress yt only on a constant and the first 5 lags of xt. How does this affect your estimate of the long run multiplier?

d. Same as c. for 4 lags instead of 5.

e. Using the macroeconomic data in Appendix F5.1, let yt be the log of real investment and xt be the log of real output. Carry out the computations suggested and report your findings. Specifically, how does the omission of a lagged value affect estimates of the short-run and long-run multipliers in the unrestricted lag model?

Y = Bo + Bix-; + &. j-0