Refer to formulas (11.2.2) and (11.2.3). Assume Ï 2 i = Ï 2 k i where Ï

Refer to formulas (11.2.2) and (11.2.3). Assume

σ²_i = σ²k_i

where σ² is a constant and where k_i are known weights, not necessarily all equal.

Using this assumption, show that the variance given in Eq. (11.2.2) can be expressed as

The first term on the right side is the variance formula given in Eq. (11.2.3), that is, var (β̂₂) under homoscedasticity. What can you say about the nature of the relationship between var (β̂₂) under heteroscedasticity and under homoscedasticity? (Examine the second term on the right side of the preceding formula.) Can you draw any general conclusions about the relationships between Eqs. (11.2.2) and (11.2.3)?

Transcribed Image Text:

σ Σk Σ Σ var (β3)