Question

You are interested in looking at the returns to experience (how much wages go up for each additional year a person works). There are several possible models you can run. Answer the questions related to the following models. Please note these values are not calculated from actual data.

wagei=10+6.2*experiancei+10*health+yXi+Ei

health is an indicator if an individual works in the healthcare industry. It is one if the person works in healthcare and zero if they work in a different industry.

a. How much would you expect your wage to go up by if you had an additional year of experience and worked in the health sector?

b. How much would you expect your wage to go up by if you had an additional year of experience and worked in an industry that was not health related?

c. How much would you expect your wage to go up by if you had an additional four years of experience and worked in the health sector?

d. In the output of the regression STATA indicates the p value for health is 0.03. At a 5% significance level does working in the healthcare industry have an impact on wages?

Answer 1

Given

wagei = 10 + 6.2 * exp + 10*health + y*Xi + Ei ---------------------- (1)

a.)

If we have extra year of experience and belongs to health sector, health = 1

new_wage = 10 + 6.2 * (exp + 1) + 10 * 1 + y*Xi + Ei

new_wage = 10 + 6.2 * exp + 6.2 + 10 + y*Xi + Ei ---------------------- (2)

Substracting 1 from 2, we get

new_wage - wage = 16.2 - 10 * health

Now, the individual belongs to health sector so health = 1. So equation becomes,

new_wage = 6.2 + wage

Hence new wage will increase by 6.2 units as compared to old wage

Note:

Now, Suppose intially the individual doesn't belong to health sector so health = 0 and later he shifted to health Industry, health = 1 . So equation becomes,

new_wage = 16.2 + wage

Hence new wage will increase by 16.2 units as compared to old wage in this special case

b.)

In this case, we have extra year of experience but doesn't belong to health sector. So,

new_wage = 10 + 6.2 * (exp + 1) + 10 * 0 + y*Xi + Ei

new_wage = 10 + 6.2 * exp + 6.2 + y*Xi + Ei ---------------------- (2)

Substracting 1 from 2, we get

new_wage - wage = 6.2 - 10 * health

There are 2 Cases now:

-> Suppose intially the individual doesn't belong to health sector so health = 0. So equation becomes,

new_wage = 6.2 + wage

Hence new wage will increase by 6.2 units as compared to old wage if individual experience increases by 1 year and if he doesn't belong to health sector

c.)

In this case, we have extra 4 years of experience and belongs to health sector. So,

new_wage = 10 + 6.2 * (exp + 4) + 10 * 1 + y*Xi + Ei

new_wage = 10 + 6.2 * exp + 24.8 + 10 + y*Xi + Ei ---------------------- (2)

Substracting 1 from 2, we get

new_wage - wage = 24.8- 10 * health

Now, the individual belongs to health sector so health = 1. So equation becomes,

new_wage = 14.8+ wage

Hence new wage will increase by 14.8 units as compared to old wage if individual experience increases by 4 years and if he belongs to health sector

Note:

There are chances of the special that i mentioned in part 1, That case is possible here as well

d.)

Given p value for health, p(health) = 0.03

At 5% significance level, = 0.05

So, p(health) < 0.03

Hence variable health is significant in detremining Wages at 5% significance level. It has significant impact on wages