How can I solve this? 3. Let cand y denote the (natural) logarithms of consumpti

Question

How can I solve this?

3. Let cand y denote the (natural) logarithms of consumption and income respectively. Fron a sample of n = 50 the following estimates for the consumption function c = 0 + 1 y+11 was obtained -(292) + (02)y c= 2.3 +0.8 0.92) (0.2) with R2 0.85. Standard errors are in the parentheses a) What is the interpretation of the slope coefficient? b) Test whether the slope coefficient is equal to one. If thenul hy- pothesis is accepted, what is the interpretation of the end result? (You can use the 5% significance level for the testing, where the approximate threshold value for the one sided test is 1.64 and for the 2-sided test 1.96. If you do not have a calculator, it is enough to show the necessary formulas in your calculations.)

Explanation / Answer

a) The slope coefficient shows how much the log of consumption increases due to a unit change in the log of income. Thus the 0.8 shows that consumption will increase by 0.8 if income increases by 1 unit.

b) Thus we use the Z stat here. So the null hypothesis is H0: B=1,H1:B not equal to 1. Thus Z=(0.8-1)/0.2=-1. Thus as the result is insignificant as 1<1.64<1.96, we accept the null hypothesis. This means that it can be accepted that the slope coefficient = 1.

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