Consider the following model: GNP t = 1 + 2 M t + 3

Consider the following model:

GNP_t = β₁ + β₂M_t + β₃M_t−1 + β₄(M_t −M_t−1) + u_t

where GNP_t = GNP at time t,M_t = money supply at time t, Mt₋₁ = money supply at time (t − 1), and (M_t −M_t−1) = change in the money supply between time t and time (t − 1). This model thus postulates that the level of GNP at time t is a function of the money supply at time t and time (t − 1) as well as the change in the money supply between these time periods.

a. Assuming you have the data to estimate the preceding model, would you succeed in estimating all the coefficients of this model? Why or why not?

b. If not, what coefficients can be estimated? 

c. Suppose that the β₃M_t−1 terms were absent from the model. Would your answer to (a) be the same?

d. Repeat (c), assuming that the terms β₂M_t were absent from the model.