In a study of the relationship between real aggregate consumption and prices in a specific country based on a time series of 104 observations, the following OLS regression function was obtained (standard errors in parentheses), SER=2.85, C₂= 13.74 +0.24P, R² = 0.12, (0.35) (0.05) where C, is logarithm of consumption and P, is logarithm of price. Suppose that, in addition to a consumption equation C₁ =B₁ + B₁P₁+U₂ where the error u, is independently and identically distributed with mean 0 and variance o, a supply equation Q₁ = Yo + Y₁P₁+%₂Zt + vr is considered, where Q, is logarithm of production, Z, is a productivity vari- able independent of u, and ut, and the error term u, is independent of u and is independently and identically distributed with mean 0 and variance o2. Suppose that the equilibrium condition Q = Ct holds. Show that, if B₁ #71, then P₁ B₂-7₁2 (70-B0 + 7/2²/₁ +0₂-14). What is the implication of this relationship for the OLS estimation of the slope parameter 3₁

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In a study of the relationship between real aggregate consumption and prices
in a specific country based on a time series of 104 observations, the following
OLS regression function was obtained (standard errors in parentheses),
C₂ = 13.74 +0.24Pt, R² = 0.12, SER = 2.85,
(0.35) (0.05)
where C, is logarithm of consumption and P, is logarithm of price.
Suppose that, in addition to a consumption equation
C₁ = Bo+B₁P₁ + Us
where the error u is independently and identically distributed with mean 0
and variance o, a supply equation
Q₁ = 10 +1₁P₁+%₂²r + ve
is considered, where Q, is logarithm of production, Z, is a productivity vari-
able independent of u and ut, and the error term u, is independent of u and
is independently and identically distributed with mean 0 and variance o
Suppose that the equilibrium condition Q = Ct holds. Show that, if
171₁, then
P₁
B₁ - 7₁ (% − B₁ + 1⁄₂Z₁ + vr − 1).
71
What is the implication of this relationship for the OLS estimation of
the slope parameter 3₁
Transcribed Image Text:In a study of the relationship between real aggregate consumption and prices in a specific country based on a time series of 104 observations, the following OLS regression function was obtained (standard errors in parentheses), C₂ = 13.74 +0.24Pt, R² = 0.12, SER = 2.85, (0.35) (0.05) where C, is logarithm of consumption and P, is logarithm of price. Suppose that, in addition to a consumption equation C₁ = Bo+B₁P₁ + Us where the error u is independently and identically distributed with mean 0 and variance o, a supply equation Q₁ = 10 +1₁P₁+%₂²r + ve is considered, where Q, is logarithm of production, Z, is a productivity vari- able independent of u and ut, and the error term u, is independent of u and is independently and identically distributed with mean 0 and variance o Suppose that the equilibrium condition Q = Ct holds. Show that, if 171₁, then P₁ B₁ - 7₁ (% − B₁ + 1⁄₂Z₁ + vr − 1). 71 What is the implication of this relationship for the OLS estimation of the slope parameter 3₁
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