Question

log(wagei) = β0 + β1edui + β2log(experi) + β3marriedi + β4blacki + β5southi + β6urbani

Using log(wagei) = 5.354 + .0628edui + .134experi + .218marriedi + (-.198blacki) + (-.099southi) + .179urbani

1. What is the marginal effect of experience

2. A “marriage premium” means that married men earn, on average, more than nonmarried men. Holding education, experience, race, and geographic location constant, what is the approximate difference in monthly salary between married men and nonmarried men? Is this difference statistically significant at the 10% level? 1% level?

3. Modify the model by allowing log(wage) to differ across four groups of men: married and black, married and nonblack, single and black, and single and nonblack. What would it look like?

Answer 1

The structural model is given as:

The estimated model is:

where,

married is a dummy variable telling whether the person is married or not. If married=1, it means the person is married. If married=0, then he is non married,

black is a dummy variable telling whether the person is black or not. If black=1, it means the person is black. If black=0, then he is non black,

south is a dummy variable telling whether the person is living in the southern states or not. If south=1, it means the person is living in the southern states. If south=0, then he is not living in the southern states,

urban is a dummy variable telling whether the person is living in an urban area or not. If married=1, it means the person is living in an urban area. If married=0, then he is not living in an urban area,

1.

As both the experience and wage are in logarithmic form, the coefficients give the marginal effect in percentage terms. Hence, the marginal effect of experience can be explained as:

When experience of the i th individual increases by 100% , given the other things, wage of the ith individual rises by 13.4% on an average.

2.

Remember, married is used as a dummy variable which can take the values 0 and 1. When married=1, it represents the individual is not married, while married=1 represents the individual is married.

Note that as the coefficient is positive, it automatically implies a married men earns, on an average, more than non married men. This is defined as "marriage premium" here.

Hence this coefficient is gives us an idea about the approximate difference in monthly salary between married and non married men.

The coefficient implies that :

holding education, experience, race and geographical location constant, a married men earns about 100*(0.218) = 21.8% more than non married men, on an average, per month.

Thus, the approximate difference in the monthly salary between married and non married men is 21.8%.

For testing statistical significance of this difference, we must test:

The test statistic will follow a t distribution which will be of the form:

where,

is the estimated value of the parameter (we have this value from the estimated model), and

is the estimated standard error of

Now, since we have not given the value of the estimated standard errors, we can't compute the exact value of the test statistic.

However, we can discuss about the general way of testing here. I hope that will give you an idea!!

If the test statistic gotten is greater than the critical value obtained from the t table at the required significance level (10% or 1%) and appropriate degrees of freedom, we will reject the null hypothesis and conclude that the difference is statistically significant.

However, if the test statistic gotten is lesser than the critical value obtained from the t table at the required significance level (10% or 1%) and appropriate degrees of freedom, we will fail to reject the null hypothesis and conclude that the difference is not statistically significant.

3.

When we try to find the model for a particular group, we will change the value of the dummy variables accordingly.

For married and black,

put married=1 and black=1 in the estimated model.

This gives us the modified model:

or,

For married and non black,

put married=1 and black=0 in the estimated model.

This gives us the modified model:

or,

For single and black,

put married=0 and black=1 in the estimated model.

This gives us the modified model:

or,

For single and non black,

put married=0 and black=0 in the estimated model.

This gives us the modified model: