Econometrics 7: Dummy Variables

Question 1

What are dummy variables and why do we use them?

Answer 1

Dummy variables (also called binary, indicator, or zero-one variables) take values of 0 or 1.
Used to encode qualitative information in regression models.
Examples:
Femaleᵢ = 1 if individual i is female, 0 otherwise.
Marriedᵢ = 1 if individual i is married.
Recessionₜ = 1 if the economy is in recession in quarter t.
Econometrically, choosing Femaleᵢ vs. Maleᵢ makes no difference, but interpretation depends on context.

Question 2

Explain how to interpret the coefficient on a dummy variable in a regression.

Answer 2

Question 3

Why does the choice of reference group matter in dummy variable models?

Answer 3

Question 4

How do we handle multiple categories in dummy variables?

Answer 4

Note: the m − 1 dummy variables must be
▶ Mutually exclusive
▶ Exhaustive

Question 5

What are multiplicative dummy variables and how do we interpret them?

Answer 5

Question 6

Describe the four regression outcomes based on interaction terms between dummy and continuous variables.

Answer 6

δ₀ = 0, δ₁ = 0 → Coincident regressions (same line).
δ₀ ≠ 0, δ₁ = 0 → Parallel regressions (same slope, different intercepts).
δ₀ = 0, δ₁ ≠ 0 → Concurrent regressions (same intercept, different slopes).
δ₀ ≠ 0, δ₁ ≠ 0 → Dissimilar regressions (different intercepts and slopes).

Question 7

How do we interpret interactions between two dummy variables?

Answer 7

Question 8

How does OLS estimate dummy variable coefficients?

Answer 8

Question 9

Define the Linear Probability Model and explain how it is used in econometrics.

Answer 9

Question 10

List and explain the limitations of using the Linear Probability Model.

Answer 10

Non-normality of errors:
Errors take only two values → not normally distributed.
But CLT helps with large samples.
Heteroscedasticity:
Variance of errors depends on Xᵢ.
Use robust standard errors.
Predicted probabilities outside [0,1]:
LPM doesn’t constrain predictions to valid probability range.
Constant marginal effects:
Assumes effect of Xᵢ on P(Dᵢ = 1) is the same across all Xᵢ.

Question 11

What are alternatives to the Linear Probability Model?

Answer 11

Logit and Probit models:
Designed for binary dependent variables.
Address LPM’s limitations (e.g., predicted probabilities, heteroscedastic