Consider a product market with a supply function Qs i = b0 + b1 Pi + u s i, a demand function Qd i = g0 + u d i, and a market equilibrium condition Qs i = Qd i, where u s i and u d i are mutually independent i. i. d. random variables, both with a mean of zero. a. Show that Pi and u s i are correlated. b. Show that the OLS estimator of b1 is inconsistent. c. How would you estimate b0, b1, and g0? Stock, James H ... Introduction to Econometrics (Pearson Series in Economics (Hardcover)) (p. 463). Pearson Education. Kindle Edition.

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Business

Griffen

31 August, 18:33

Consider a product market with a supply function Qs i = b0 + b1 Pi + u s i, a demand function Qd i = g0 + u d i, and a market equilibrium condition Qs i = Qd i, where u s i and u d i are mutually independent i. i. d. random variables, both with a mean of zero. a. Show that Pi and u s i are correlated. b. Show that the OLS estimator of b1 is inconsistent. c. How would you estimate b0, b1, and g0? Stock, James H ... Introduction to Econometrics (Pearson Series in Economics (Hardcover)) (p. 463). Pearson Education. Kindle Edition.

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Townsend · Answer 1

A. Solving for P yields P = 0011dsiiuuγβββ--+; thus 21 (,) susCov P uσβ-=. Because Cov (P, u) ≠0, the OLS estimator is inconsistent.

B. We need an instrumental variable, something that is correlated with P but uncorrelated with us. In this case Q can serve as the instrument, because demand is completely inelastic (so that Q is not affected by shifts in supply). γ0can be estimated by OLS (equivalently as the sample mean of Qi