Based on the US data for 1965 Q1 to 1983Q4 (n=76), James Doti and Esmael Adibi o

Question

Based on the US data for 1965 Q1 to 1983Q4 (n=76), James Doti and Esmael Adibi obtained the following regression to explain personal consumption expenditure (PCE) in the US. 6, =-10.96 + 0.93x2t-2.09 X3t t-values (3.33) (249.06) (-3.09) R =0.9996 F 83,753.7 where y = the PCE (billions of $) X2 disposable income (billions of $) Xs = the prime interest rate charged by banks a. b. c. d. What is the marginal propensity to consume (MPC)? is the MPC statistically different from 1? is the coefficient on the prime interest rate significantly different than -1.5? Test the hypothesis that both coefficients are jointly equal to zero.

Explanation / Answer

Solution:-

a)

MPC is coefficient of disposable income,

i.e, X2t = 0.93

b)

Since t value of X2t is 249.06 which is very large and t value for 75 degree of freedom ( df = n-1 = 76 -1 = 75) for 5% confidence interval is 1.990.

So since the calculated value 249.06 is greater than the table value 1.990 .So MPC is significant . So it is statistically different from 1.

c)  

It is good to include prime interest rate variable in the model because the coefficient of prime interest rate variable is significant so it affecting the PCE in significant way .Also the R2 value of the model is very high which shows that the model overall is a very good fitt model.

Negative sign here indicates that as the prime rate increases than the PCE decreases which is true in the real world as rate of interest increases then the expenditure of the people decreases.

d)

Checking the hypoyhesis that R2= 0 , is same thing as checking whether the F-test is significant or not. because R2 and F test are directly related by a formula.

f-statistic for joint significsnce can be calculated by (R2 / k) / [(1 - R2) / (n-k-1)]

= (0.9996/2) / [(1-0.9996)/(76 - 2 - 1)]

= 91213

since here we can see that F calculated value is very very large which will be always greater than he table value so F-test is significant .

So we fail to reject the null hypothesis that R2 is not equal to 0 .

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