Consider a model where the return to education depends upon the amount of work experience (and vice versa): log(wage) = β0 + β1educ + β2exper + β3educ ∗ exper+u

Question

What is the return to experience for someone who has 12 years of education? Explain your answer.

Answer 1

log(wage) = β₀ + β₁educ + β₂exper + β₃educ*exper + u

This problem involves two important econometric concepts:

1. Log-Level Regression
2. Interaction Term

LOG-LEVEL REGRESSION

A log-level regression involves a logarithmically-transformed variable being regressed on an unaltered variable or variables. The interpretation of an estimated coefficient is:

If X changes by one unit, we'd expect to see an associated percent change in Y equal to (β₁*100).

Note: This is an approximation; the actual percent change in Y is equal to 100*(e^β - 1) but the approximation works fine in most cases.

Suppose we were dealing with this simple regression:

log(wage) = β₀ + β₁educ + u

If education increased by 10 years, we'd expect to see an associated percent increase in wage equal to 10*(β₁*100).

INTERACTION TERM

The next important concept is the interaction term. Suppose we were dealing with this level-level (no log) version of the model:

wage = β₀ + β₁educ + β₂exper + β₃educ*exper + u

Here, if education increased by 10 years, we'd expect to see an associated increase in wage equal to [10*β₁ + 10β₃exper] = 10[β₁ + β₃exper]. Note, since the independent variable is wage, this change would be in dollars.

PUTTING IT ALL TOGETHER

Returning to the original model:

log(wage) = β₀ + β₁educ + β₂exper + β₃educ*exper + u

An increase of 12 years of education would lead to an associated percent increase in wage equal to 12[(β₁ + β₃exper)*100]