Consider the following demand function for money in the United States for the period 1980€“1998:

M_t = β₁ Y^β2_t r^β3_t e^ut

where M = real money demand, using the M₂ definition of money
Y = real GDP
r = interest rate

To estimate the above demand for money function, you are given the data in the following table.

a. Given the data, estimate the above demand function. What are the income and interest rate elasticities of demand for money?

b. Instead of estimating the above demand function, suppose you were to fit the function (M/Y)_t = α₁r_t^α2e^ut. How would you interpret the results? Show the necessary calculations.

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Observation GDP M2 CPI LTRATE TBRATE 11.27 1980 2795.6 1600.4 82.4 11.506 90.9 14.029 1981 3131.3 1756.1 13.45 1982 10.686 3259.2 1911.2 96.5 99.6 12.76 1983 3534.9 2127.8 11.18 8.630 1984 3932.7 103.9 12.41 2311.7 9.580 1985 4213.0 2497.4 107.6 10.79 7.480 7.78 1986 4452.9 2734.0 109.6 5.980 5.820 1987 4742.5 2832.8 113.6 8.59 1988 5108.3 2995.8 118.3 8.96 6.690 124.0 1989 5489.1 3159.9 8.45 8.120 1990 5803.2 3279.1 130.7 8.61 7.510 1991 3379.8 5986.2 136.2 8.14 5.420 3.450 3.020 1992 6318.9 3434.1 140.3 7.67 144.5 148.2 6642.3 1993 3487.5 6.59 7.37 1994 7054.3 3502.2 4.290 1995 7400.5 3649.3 152.4 6.88 5.510 1996 7813.2 3824.2 156.9 6.71 5.020 8300.8 1997 4046.7 160.5 6.61 5.070 4401.4 163.0 5.58 1998 8759.9 4.810