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Question 1

Assumptions for models with stochastic regressors

Answer 1

1) The model is linear in parameters and correctly specified

2) The values of the regressors are drawn randomly from fixed populations

3) No exact linear relationship exists among the regressors

4) The disturbance term has zero expectation: E(u_i) = 0 for all i
5) The disturbance term is homoscedastic, σ²_i = σ² for all i
6) The values of the disturbance term have independent distributions: u_i is distributed independently of u_i’ for all i’ ≠ i

7) The disturbance term is distributed independently of the regressors: u_i is distributed independently of X_ji’ for all i’ and all j

8) The disturbance term has zero conditional expectation: E(u_i I values of all the regressors in all observations) = 0

9) The disturbance term has a normal distributino

Question 2

Prove b₂^OLS is unbiased when the values of X are stochastic in model Yi