Consider the simultaneous equation of demand and supply given by D = a0 + apt +...

 

Transcribed Image Text:

Consider the simultaneous equation of demand and supply given by D₁ = a0 + a₁pt + a₂Yt + u₂₁ St= Bo + Bipt + B₂Ct + u{, (Demand equation) (Supply equation) where yt is the income level while c is the observable production cost shifter (e.g., wages and interest rates). Because a higher income leads to a higher demand, a2 > 0. A higher marginal cost lowers the quantity supplied so that 32 <0. We assume that (uDt, ust) is independent of (yt, Ct), and independently distributed over time. In equlibrium, we have qt = Dt = St. We observe the random sample of {qt, Pt, Yt, Ct1 generated from this equilibrium model. For your reference, we may define T = 01 - (1 - 1) 01-31 a1-3₁ (a) Suppose that we consider the following reduced-form specification: qt = To + 13t+T₂Ct + ugt. 1. (7 points) Express 7₁, 72, and uqt in terms of the structural parameter and the iid demand and supply shocks, upt and ust. 2. (7 points) Discuss whether the OLS estimator in (5) gives a consistent estimator of To, 71, and 72. (b) (8 points) Let o, 1, and 2 be the OLS estimate of (5) and let ât = 0 + 1yt + ₂Ct. Using ât, suppose we regress pt on constant, qt, and yt, i.e., we estimate 70, 71 and 2 by the following OLS regression: and I-1 = (3) -B₁ 01-31 01-3₁ = (5) (ao, a1, a2, Bo, B1, B₂) Pt70+ 19t + 72Yt + Et. Let 0, 1, and 2 be this OLS estimator. Is it possible to express the probability limit of 1 (i.e., 11) in terms of ao, a1, a2, Bo, B1, B₂? If so, show the relationship between the probability limit of 1 and ao, a1, a2, Bo, B1, B2. (c) (8 points) Suppose that we are interested in estimating the parameters B= (B0, B1, B2)' in supply equation (4). Provide a system of three equations in population whose solution gives the identification of 3 and express 3 in terms of the population moments. Consider the simultaneous equation of demand and supply given by D₁ = a0 + a₁pt + a₂Yt + u₂₁ St= Bo + Bipt + B₂Ct + u{, (Demand equation) (Supply equation) where yt is the income level while c is the observable production cost shifter (e.g., wages and interest rates). Because a higher income leads to a higher demand, a2 > 0. A higher marginal cost lowers the quantity supplied so that 32 <0. We assume that (uDt, ust) is independent of (yt, Ct), and independently distributed over time. In equlibrium, we have qt = Dt = St. We observe the random sample of {qt, Pt, Yt, Ct1 generated from this equilibrium model. For your reference, we may define T = 01 - (1 - 1) 01-31 a1-3₁ (a) Suppose that we consider the following reduced-form specification: qt = To + 13t+T₂Ct + ugt. 1. (7 points) Express 7₁, 72, and uqt in terms of the structural parameter and the iid demand and supply shocks, upt and ust. 2. (7 points) Discuss whether the OLS estimator in (5) gives a consistent estimator of To, 71, and 72. (b) (8 points) Let o, 1, and 2 be the OLS estimate of (5) and let ât = 0 + 1yt + ₂Ct. Using ât, suppose we regress pt on constant, qt, and yt, i.e., we estimate 70, 71 and 2 by the following OLS regression: and I-1 = (3) -B₁ 01-31 01-3₁ = (5) (ao, a1, a2, Bo, B1, B₂) Pt70+ 19t + 72Yt + Et. Let 0, 1, and 2 be this OLS estimator. Is it possible to express the probability limit of 1 (i.e., 11) in terms of ao, a1, a2, Bo, B1, B₂? If so, show the relationship between the probability limit of 1 and ao, a1, a2, Bo, B1, B2. (c) (8 points) Suppose that we are interested in estimating the parameters B= (B0, B1, B2)' in supply equation (4). Provide a system of three equations in population whose solution gives the identification of 3 and express 3 in terms of the population moments.

Answer rating: 100% (QA)

a It no 81yt 72Ct ugt 1 It can be shown that It no 81yt 72Ct ugt 20 ... View the full answer