L7/8 - Panel data

Question 1

What is the main idea of Pooled OLS?

Answer 1

Ignores the panel structure

Question 2

What is the main idea of Random Effects GLS?

Answer 2

Treats αᵢ as uncorrelated with regressors

Question 3

What is the main idea of Fixed Effects OLS?

Answer 3

OLS on the unit de-meaned equation

Question 4

What is the main idea of First Difference OLS?

Answer 4

OLS on the first difference equation

Question 5

What is the Pooled OLS estimator?

Answer 5

(XᵀX)⁻¹XᵀY

Question 6

What is the RE estimator?

Answer 6

(XᵀV⁻¹X)⁻¹ XᵀV⁻¹Y

Question 7

What is the FE estimator?

Answer 7

(X̃ᵀX̃)X̃ᵀỸ

Where:
ỹ = yᵢₜ - ȳᵢ
x̃ = xᵢₜ - x̄ᵢ

Question 8

What is the FD estimator?

Answer 8

(X̃ᵀX̃)X̃ᵀỸ

Where:
ỹ = yᵢₜ - yᵢ,ₜ₋₁
x̃ = xᵢₜ - xᵢ,ₜ₋₁

Question 9

For what OLS estimators must be E[αᵢ|Xᵢ] = 0 and for what estimators can be E[αᵢ|Xᵢ] ≠ 0

Answer 9

For E[αᵢ|Xᵢ] = 0:
1) Pooled OLS
2) FE OLS

For E[αᵢ|Xᵢ] ≠ 0:
3) FE OLS
4) FD OLS

Question 10

Under what conditions is Pooled OLS consistent?

Answer 10

E[αᵢ|Xᵢ] = 0

Question 11

Under what conditions is RE OLS consistent?

Answer 11

E[αᵢ|Xᵢ] = 0

Question 12

Under what conditions is FE OLS consistent?

Answer 12

E[uᵢₜ|xᵢₛ] = 0
Strong exogeneity

Question 13

Under what conditions is FD OLS consistent?

Answer 13

E[uᵢₜ|xᵢₜ,xᵢₜ₋₁] = 0
Strong exogeneity

Question 14

Under what specific condition are all estimator consistent?

Answer 14

E[uᵢ|Xᵢ] = 0 and E[αᵢ|Xᵢ] = 0