Consider the following simple macroeconomic model for the U.S. economy, say, for the period 1960-1999.*
Private consumption function:

Ct = α0 + α1 Yt + α2 Ct-1 + u1t                α1 > 0, 0 α2 1

Private gross investment function:

It = β0 + β1 Yt + β2 Rt + β3 It-1 + u2t      β1 > 0, β2 0, 0 β3 1

A money demand function:

Rt = λ0 + λ1 Yt + λ2 Mt-1 + λ3 Pt + λ4 Rt-1 + u3t      λ1 > 0, λ2 0, λ3 > 0, 0 λ4 1

Income identity: Yt = Ct + It + Gt

where C = real private consumption; I = real gross private investment, G = real government expenditure, Y = real GDP, M = M2 money supply at current prices, R = long-term interest rate (%), and P = Consumer Price Index. The endogenous variables are C, I, R, and Y. The predeter- mined variables are: Ct-1 , It-1 , Mt-1 , Pt , Rt-1 , and Gt plus the intercept term. The u's are the error terms.

a. Using the order condition of identi?cation, determine which of the four equations are identi?ed, either exact or over.

b. Which method(s) do you use to estimate the identi?ed equations?

c. Obtain suitable data from government and/or private sources, estimate the model, and comment on your results.