Question

Consider an economic model in which wages depend on years of experience (exper) and unobservable factors (ε) according to

wage = β˜₀ + β˜₁exper + ε.

i. Provide an expression for the change in wage if experience increases by 1, holding all other factors fixed.

ii. Suppose instead that the economic model is

wage = β˜₀ + β˜₁exper + β˜₂exper² + ε.

Provide an expression for the change in wage if exper increases from 10 to 11, holding all other factors fixed.

iii. We can use a derivative to describe the rate of change of wage as exper changes, all else equal. What is this derivative?

iv. Provide a condition that tells me when the derivative in part iii. is positive.

v. Suppose that we do not have data on years of experience, but instead months of experience (mexper). We consider the economic model

wage = β˜^∗₀ + β˜^∗₁mexper + ε ^∗ .

How is the parameter β˜^∗₁ related to the parameter β˜₁ used in part i. of this problem? (Hint: one of them is a multiple of the other.)

Answer 1

i) If experience increases by 1 wage will increase by β1. To see we can increase experience from 0 to 1.

exper =1, wage = β0 + β1. For exper = 0, wage = β0.

Change in wage = (β0 + β1) – β0 = β1

ii) Exper =10, wage = β0 + 10β1 +100β2.

For exper = 11, wage = β0 + 11β1 +121β2 .

Change in wage = (β0 + 11β1 +121β2)-( β0 + 10β1 +100β2) = β1 +21β2

iii) dwage/dexper = β1 + 2*β2

wage will change by β1 +2* β2.

iv) The condition is that both the β1 and β2 are positive.

*For solution to other parts please post as aseparate question. Supposed to do only four subparts to a question.