Problem 2. (SW 12.8.) Consider a product market with a supply function Q = Bo + B₁ P₁ + už, a demand function Q = %o +u, and an equilibrium condition Q = Q, where u and u are mutually independent i.i.d. random variables, both with a mean of 0. (a) Show that P₁ and us are correlated. OLS (b) Show that the OLS estimator of ₁ is inconsistent. Hint: The standard strategy for showing inconsistency: first, argue that Cov(QP), second, use Var(P) calculations to show that Cov(Q²,P) #B₁. will converge in large samples to Var(P)
Problem 2. (SW 12.8.) Consider a product market with a supply function Q = Bo + B₁ P₁ + už, a demand function Q = %o +u, and an equilibrium condition Q = Q, where u and u are mutually independent i.i.d. random variables, both with a mean of 0. (a) Show that P₁ and us are correlated. OLS (b) Show that the OLS estimator of ₁ is inconsistent. Hint: The standard strategy for showing inconsistency: first, argue that Cov(QP), second, use Var(P) calculations to show that Cov(Q²,P) #B₁. will converge in large samples to Var(P)
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Just part B. Please write it out on paper. Typing it back to back is difficult to understand what you mean.
Transcribed Image Text:Problem 2. (SW 12.8.) Consider a product market with a supply function Q₁ = B₁ + B₁P₁ + už,
a demand function Q = 7o+u, and an equilibrium condition Q = Q, where u and u are
mutually independent i.i.d. random variables, both with a mean of 0.
(a) Show that P; and us are correlated.
(b) Show that the OLS estimator of ₁ is inconsistent. Hint: The standard strategy for showing
in large samples to Co, second, use
Cov(Q,P)
OLS
inconsistency: first, argue that ₁ will converge
# B₁.
calculations to show that Cov(QP)
Var(P)
(c) How would you estimate Bo, B₁, and ?
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