Consider the following model:

R_t = β₀ + β₁M_t + β₂Y_t + u_1t

Y_t = α₀ + α₁R_t + u_2t

where M_t (money supply) is exogenous, R_t is the interest rate, and Y_t is GDP.

a. How would you justify the model?

b. Are the equations identified?

c. Using the data given in the following table, estimate the parameters of the identified equations. Justify the method(s) you use.

GDP (Y1) 6 (X) Observation M2 (Y2) GPDI (X1) FEDEXP (X2) 3,771.9 3,898.6 4,105.0 4,341.5 4,319.6 4,311.2 4,540.9 4,750.5 5,015.0 5,173.4 5,161.7 5,291.7 5,189.3 5,423.8 5,813.6 6,053.7 6,263.6 6,475.1 6,742.7 6,981.4 7,112.5 7,100.5 7,336.6 7,532.7 7,835.5 8,031.7 8,328.9 8,703.5 9,066.9 9,470.3 9,817.0 9,890.7 10,048.8 10,301.0 10,703.5 11,048.6 427.1 475.7 201.1 1970 626.5 6.562 1971 710.3 220.0 4.511 1972 802.3 532.1 244.4 4.466 1973 7.178 855.5 594.4 261.7 1974 902.1 550.6 293.3 7.926 346.2 374.3 1,016.2 1,152.0 1,270.3 1,366.0 1,473.7 1,599.8 1,755.4 1,910.3 2,126.5 2,310.0 2,495.7 2,732.4 2,831.4 2,994.5 3,158.5 3,278.6 3,379.1 3,432.5 3,484.0 3,497.5 3,640.4 3,815.1 4,031.6 4,379.0 4,641.1 4,920.9 5,430.3 5,774.1 6,062.0 6,411.7 6,669.4 1975 453.1 6.122 1976 5.266 544.7 1977 627.0 407.5 5.510 702.6 1978 450.0 7.572 1979 725.0 497.5 10.017 1980 645.3 585.7 11.374 1981 704.9 672.7 13.776 1982 606.0 748.5 11.084 1983 662.5 815.4 8.75 877.1 1984 857.7 9.80 7.66 1985 849.7 948.2 1986 843.9 1,006.0 1,041.6 1,092.7 1,167.5 1,253.5 1,315.0 1,444.6 1,496.0 1,533.1 1,603.5 1,665.8 1,708.9 1,734.9 1,787.6 1,864.4 1,969.5 2,101.1 2,252.1 2,383.0 2,555.9 6.03 1987 870.0 6.05 890.5 1988 6.92 1989 926.2 8.04 1990 895.1 7.47 1991 822.2 5.49 1992 889.0 3.57 1993 968.3 3.14 1994 1,099.6 1,134.0 1,234.3 1,387.7 1,524.1 1,642.6 1,735.5 1,598.4 1,557.1 1,613.1 1,770.6 1,866.3 4.66 1995 5.59 1996 5.09 1997 5.18 1998 4.85 1999 4.76 2000 5.92 2001 3.39 2002 1.69 2003 1.06 2004 1.58 2005 3.40