[SOLVED] ECON772 Homework 5 -Simultaneous Equations

Simultaneous Equations

• Consider

qt                     = β0 + β1pt + β2yt + udt qt       = α0 + α1pt + α2wt + ust

as a system of equations for supply and demand of bananas.                Suggest how to

test

H₀ : β₂ = α₂ = 0 vs. H_A : β₂ =6 α₂ 6= 0.

• Consider the model

y = Xβ + u

where some of the X variables are potentially endogenous. Let Z be a valid set of instruments for X.

1. Show that the OLS estimator of β is asymptotically biased if any of the X variables are endogenous and asymptotically unbiased otherwise.
2. Show that the IV estimator of β is asymptotically unbiased whether or

not the X variables are endogenous.

1. Use this to construct a test statistic forH₀ : X is exogenous vs. H_A : X is endogenous.

• Consider the model:

where y_i is output at rm i, X_i is input at rm i, and A_i is a rm-speci c productivity factor.

1. Suggest how to estimate α using OLS.
2. Suggest why, if rms are pro t maximizing, X_i would be endogenous and

show the precise relationship between X_i and the error.

1. Suggest a reasonable instrument for X_i. Explain why it is a valid instru-

ment.

1