Question

Question 1) Ignore the values of Fand DW, for a fourth year seminar course, you decide to investigate the relationship between childhood health and adult wages. Your hypothesis is that healthier children do better in school, and are consequently more successful in adulthood. You estimate the following regression on a sample of adult workers in a developing country (standard errors in parentheses): InW; = 2.35+0.25HEIGHT: +0.36WEIGHT, +0.05 AGE; – 0.003 AGE (0.85) (0.2) (0.3) (0.015) (0.001) R2 = 0.65 n = 1500 F = 306 DW = 1.98 where W; is the current wage of adult worker i; HEIGHT; measures the worker's height (in centimeters) at age 5; WEIGHT; measures the worker's weight (in kilograms) at age 5; and AGE; is the worker's current age. Your specification relies on the fact that in developing economies, childhood height and weight are strongly correlated with overall health (i.e., taller and heavier children are healthier on average). a) What is the marginal effect of age 5 height on adult wages? Test the null hypothesis that it is not positive at the 5% level of significance and interpret the result. Does the result surprise you? Explain. b) What is the marginal effect of age 5 weight on adult wages? Test the null hypothesis that it is not positive at the 5% level of significance and interpret the result. Does the result surprise you? Explain.

Answer 1

1. Let the
AGE
and
WEIGHT,
be fixed as 30years and 17kg respectively. Now the marginal effect of
HEIGHT,
on current wage can be calculated by varying the
HEIGHT,
by 1 unit.

It is told that the null hypothesis (i.e., the coefficient of  
HEIGHT,
= 0) is not positive. Which means we reject the null hypothesis at 0.05 level of significance. Hence the coefficient of  
HEIGHT,
= 0.25

Now let us find the adult wage for  
HEIGHT,
=105cm and  
HEIGHT,
=106cm.

When the =105cm, After substitution of values, we get

HEIGHT,

$$ln$W_i$ = 32.8 that is, $W_i$ =3.48

Similarly, when the =106cm, After substitution of values, we get

HEIGHT,

$$ln$W_i$ = 33.05 that is, $W_i$ =3.49

From this, we can infer that a unit change in height will make a difference of 0.01 in the current wage. The result surprises that there is a relationship between the Height at age 5 and the current wage but, the marginal shows there is only a very small increase in the current wage which can be due to chances.

2.Let the
AGE
and
HEIGHT,
be fixed as 30years and 105cm respectively. Now the marginal effect of
WEIGHT,
on current wage can be calculated by varying the
WEIGHT,
  by 1 unit.

It is told that the null hypothesis (i.e., the coefficient of  
WEIGHT,
=0) is not positive. Which means we reject the null hypothesis at 0.05 level of significance. Hence the coefficient of  
WEIGHT,
= 0.36

Now let us find the adult wage for  
WEIGHT,
=17kg and  
WEIGHT,
=18kg.

When the =17kg , After substitution of values, we get

WEIGHT,

$$ln$W_i$ = 33.52 that is, $W_i$ =3.51

Similarly, when the =18kg , After substitution of values, we get

WEIGHT,

$$ln$W_i$ = 33.88 that is, $W_i$ =3.52

From this, we can infer that a unit change in weight will make a difference of 0.01 in the current wage which is same as compared to the height. Both has same effect.