Question

You have data on birth weights and a number of child, mother, and family characteristics. In particular, you are interested in the relationship between birth weight in ounces (bwght) and the sex of the child (male = 1 if baby is male and = 0 if baby is female), the number of years of mother’s education (motheduc), and family income in $1000s (faminc). An “l” prefix indicates the natural log of the variable. For example, lbwght is log(bwght).

The general model is of the form b w g h t i = β 0 + β 1 ⋅ m a l e i + β 2 ⋅ m o t h e d u c i + β 3 ⋅ f a m i n c i + ϵ i where birth weight or family income may be logged. In all cases, n = 1387.

a.) (10 points) Consider the following OLS estimates of the model without logs:

E ( b w e i g h t i ) = 111.36 + 3.13 ⋅ m a l e i + 0.19 ⋅ m o t h e d u c i + 0.11 ⋅ f a m i n c i

Interpret the constant and the coefficients on each of the explanatory variables.

b.) (5 points) Consider OLS estimates of the model with log family income

E ( b w e i g h t i ) = 107.29 + 3.10 ⋅ m a l e i + 0.25 ⋅ m o t h e d u c i + 2.15 ⋅ l f a m i n c i

Interpret the coefficient on lfaminc.

c.) (10 points) Consider OLS estimates of the model with log birth weight

E ( l b w e i g h t i ) = 4.70 + 0.03 ⋅ m a l e i + 0.002 ⋅ m o t h e d u c i + 0.001 ⋅ f a m i n c i

Interpret the coefficients on male and faminc.

d.) (5 points) Consider the model with log birth weight and log family income

E ( l b w e i g h t i ) = 4.66 + 0.03 ⋅ m a l e i + 0.002 ⋅ m o t h e d u c i + 0.02 ⋅ l f a m i n c i

Interpret the coefficient on lfaminc.

Answer 1

a)The birthweight of the child is expected to be a minimum of 111.36 irrespective of any other factors.

The birthweight of the chid is expected to be more by 3.13 of a male than a female.

The birthweight of the child is expected to increase by 0.19 for every one year of extra mothers education.

The birthweight of the child is expected to increase by 0.11 for every 1000 increase in family income

b)The birthweight of the child is expected to increase by 2.15 for every 1% increase in family income

c)The natural logarithm of the birthweight is expected to increase by 0.03 if the child is a male

The natural logarithm of the birthweight is expected to increase by 0.001 for every 1000 increase in family income.

d)The natural logarithm of the child birthweight is expected to increase by 0.02 for every 1% increase in family income