Consider the Model Y_i = β₁X_i + U_i, Where U_i $x _ { i } ^ { 2 }$

question 24

Essay

Consider the model Y_i = β₁X_i + u_i, where u_i = c $x _ { i } ^ { 2 }$ e_i and all of the X's and e's are i.i.d. and distributed N(0,1).
(a)Which of the Extended Least Squares Assumptions are satisfied here? Prove your assertions.
(b)Would an OLS estimator of β₁ be efficient here?
(c)How would you estimate β₁ by WLS?

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Definitions:

Streetlights

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Marginal Social Benefit

The additional benefit to society from consuming or producing one more unit of a good or service.

Marginal Social Cost

Marginal social cost is the total cost to society of producing one additional unit of a good or service, including both private costs and any externalities.

Common Resources

Resources that are accessible to all members of a society but are limited in availability and can be depleted by overuse.