Question

1. The relationship between the monthly expenditure on housing (E) and household income (Y) for three age groups are as follows:

(1) Age less than 30: E = α0 + β1 Y + u1

(2) Age 31 to 55: E = β0 + β2 Y + u2

(3) Age 56 and over: E = γ0 + β3 Y + u3 a. Explain the meaning of β1, β2, and β3. b. What is the economic interpretation of the hypothesis β1 = β2 = β3? c. Describe step by step how the dummy variable approach could be used to test the hypothesis in part b.

Answer 1

a) 1,2, 3  are coefficients that explains how much expenditure on housing changes and the direction of this change (positive or negative) due to one unit increase in Income for age groups less than 30, age group 31-55 and age group >56 respectively.

b) If 1=2= 3 it means that for all the three age groups, INCOME is NOT SIGNIFICANTLY affecting housing expenditure any differently.

This means that the way income affects housing expenditure is same irrespective of the age group of a person.

c) Let us consider the following Dummy Variable Regression model.

where 1 = 1 if age group < 30 . 1 = 0 for others

2 = 1 for age group between 31-55 , 2 = 0 for others.

When there are 3 categories then 2 dummy variables are required to avoid PERFECT MULTICOLLIENARITY.

If 1 is significant then it will tell us the mean INCOME that affects housing expenditure for age group <30.

If 2 is significant then it will tell us the mean INCOME that affects housing expenditure for age group 31-55

Thus mean income that affects housing consumption is given by age group >56 . This is because when 1 and 2 are zero the model captures the mean income spent by age group >56

i.e.

If the coefficient values are very close to each other then there are no difference in how income affects housing expenditure.