where cov(Z, v) Suppose we have the following causal model Y = 3 +5Z+v, 0. However, a precise measure of Z is not available. Instead, we have a noisy measure X of Z, that is, X = Z + w with var(w) > 0. Suppose the error w is a classical measurement error so that cov(w, Z) = cov(w, v) = 0. What can you conclude about the limit of the OLS estimator, namely B = cov(X, Y)/var(X)? 3₁₁ = 0 B < 5 3* = 5 B < 0 OB₂ > 5 B > 0 O =

ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
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Chapter1: Making Economics Decisions
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=
3+5Z+v,
Suppose we have the following causal model Y
where cov(Z, v)
=
0. However, a precise measure of Z is not
available. Instead, we have a noisy measure X of Z, that is,
X = Z + w with var(w) > 0. Suppose the error w is a classical
measurement error so that cov(w, Z) = cov(w, v)
=
0. What
can you conclude about the limit of the OLS estimator, namely
ß₂2 = cov(X,
Y)/var(X)?
0 B² = 0
B < 5
3² = 5
B < 0
ß* > 5
OB > 0
U
Transcribed Image Text:= 3+5Z+v, Suppose we have the following causal model Y where cov(Z, v) = 0. However, a precise measure of Z is not available. Instead, we have a noisy measure X of Z, that is, X = Z + w with var(w) > 0. Suppose the error w is a classical measurement error so that cov(w, Z) = cov(w, v) = 0. What can you conclude about the limit of the OLS estimator, namely ß₂2 = cov(X, Y)/var(X)? 0 B² = 0 B < 5 3² = 5 B < 0 ß* > 5 OB > 0 U
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