Consider the following demand-and-supply model for money:

Money demand: M^d_t = β₀ + β₁Y_t + β₂R_t + β₃P_t + u_1t

Money supply: M^s_t = α₀ + α₁Y_t + u_2t

Where

M =money

Y = income

R = rate of interest

P =price

u€™s = error terms

Assume that R and P are exogenous and M and Y are endogenous. The following table gives data on M (M2 definition), Y (GDP), R (3-month Treasury bill rate) and P (Consumer Price Index), for the United States for 1970€“2006.

a. Is the demand function identified?

b. Is the supply function identified?

c. Obtain the expressions for the reduced-form equations for M and Y.

d. Apply the test of simultaneity to the supply function.

e. How would we find out ifY in the money supply function is in fact endogenous?

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Observation M2 GDP TBRATE CPI 1970 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 10,675.8 11,003.4 11,319.4 38.8 626.5 6.458 1971 710.3 4.348 40.5 1972 802.3 4.071 41.8 1973 855.5 902.1 7.041 7.886 5.838 4.989 44.4 1974 49.3 1975 1,016.2 1,152.0 1,270.3 1,366.0 1,473.7 1,599.8 1,755.5 1,910.1 2,126.4 2,309.8 2,495.5 2,732.2 2,831.3 2,994.3 3,158.3 3,277.7 3,378.3 3,431.8 3,482.5 3,498.5 3,641.7 3,820.5 4,035.0 4,381.8 4,639.2 4,921.7 5,433.5 5,779.2 6,071.2 6,421.6 6,691.7 7,035.5 53.8 56.9 1976 1977 1978 5.265 60.6 7.221 10.041 65.2 1979 72.6 82.4 1980 11.506 1981 1982 1983 14.029 90.9 96.5 10.686 8.63 99.6 1984 1985 1986 1987 9.58 103.9 107.6 7.48 5.98 5.82 109.6 113.6 118.3 1988 1989 6.69 8.12 124.0 1990 7.51 130.7 1991 1992 5.42 136.2 3.45 140.3 1993 3.02 144.5 1994 1995 4.29 148.2 5.51 152.4 5.02 1996 156.9 1997 5.07 160.5 4.81 1998 163.0 4.66 1999 166.6 2000 5.85 3.45 1.62 172.2 2001 177.1 2002 2003 179.9 1.02 184.0 2004 1.38 188.9 2005 3.16 4.73 195.3 2006 201.6