L. E. Gallaway and P. E. Smith developed a simple model for the United States economy, which is as follows:

Y = gross national product

C = personal consumption expenditure

I = gross private domestic investment

G = government expenditure plus net foreign investment

YD = disposable, or after-tax, income

M = money supply at the beginning of the quarter

Z = property income before taxes

t = time

u₁, u₂, and u₃ = stochastic disturbances

All variables are measured in the first-difference form.

From the quarterly data from 1948€“1957, the authors applied the least-squares method to each equation individually and obtained the following results:

CÌ‚_t = 0.09 + 0.43YD_tˆ’1 + 0.23M_t           R² = 0.23

IÌ‚_t = 0.08 + 0.43(Y_tˆ’1 ˆ’ Y_tˆ’2) + 0.48Z_t    R² = 0.40

GÌ‚_t = 0.13 + 0.67G_tˆ’1                            R² = 0.42

a. How would you justify the use of the single-equation least-squares method in this case?

b. Why are the R² values rather low?

Y; = C, + I; + G; C; = B1 + B2YD,1+ B3M, + u]; I, = B4 + Bs(Y,-1 Y;-2) + B6Z1 + u2: G = B7 + BsG,-1+U31