Consider fitting an Almon lag third degree polynomial i = a0+a1i+a2i2+a3i3 for i = 0, 1, . . . , 5, on the Consumption-Income relationship

Consider fitting an Almon lag third degree polynomial βi = a0+a1i+a2i2+a3i3 for i = 0, 1, . . . , 5, on the Consumption-Income relationship in logarithms. In this case, there are five lags on income, i.e., s = 5.

(a) Set up the estimating equation for the ai’s and report the estimates using OLS.

(b) What is your estimate of β3? What is the standard error? Can you relate the var(β3) to the variances and covariances of the ai’s?

(c) How would the OLS regression in part

(a) change if we impose the near end point constraint

β−1 = 0?

(d) Test the near end point constraint

(e) Test the Almon lag specification given in part

(a) against an unrestricted five year lag specification on income.