Consider a finite distributed lag model for the relationship between inflation and the interest rate as given by the federal funds rate: yt $=$ $0+$ $1$ zt $+$ $2$ zt$1+$ $3$ zt$2+$ et $.$ Here yt represents inflation, and zt the interest rate, at different time periods t$.$ Observe that et represents inflationary shocks to the economy, for e$.$g$.$ oil price shocks. The theory of rational expectations states that the shock must be exogenous to all the past variables in the economy i$.$e$.$ E$[$et $|($zt$),($et$1,$ zt$1),($et$2,$ zt$2)...]=0.$ Let $$ denote the OLS estimator of $=($$0,$ $1,$ $2,$ $3)0.$