Let gGDPt denote the annual percentage change in gross domestic product and let intt denote a short-term interest rate. Suppose that gGDPt is related to interest rates by
gGDPt = a0 + (0intt, + (1int t-1 + ut,
Where ut is uncorrelated with int1, intt-1, and all other past values of interest rates. Suppose that the Federal Reserve follows the policy rule:
intt, = (0 + (1 (gGDt-1 - 3) + vt,
Where (1, > 0. (When last year's GDP growth is above 3%, the Fed increases interest rates to prevent an "overheated" economy.) If vt is uncorrelated with all past values of intt and ut, argue that intt must be correlated with ut-1. (Lag the first equation for one time period and substitute for gGDPt-1 in the second equation.) Which Gauss-Markov assumption does this violate?