Measurement Error on x; nagine you want to estimate the following model: Yi = B1 + B2r; + Ei, nere Eler] = 0. The issue is that you do not observe r, but observe = x + wi, where the measurement error, uwi, is such that E[wz;] = 0, and [wi, E] = 0. You estimate: %3D Yi = B1 + B2ai + vị OLS. Show that B20? o? + o2 plim(b2) = ere o? = var(r;) and o = var(w,).

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3.
Measurement Error on x;
Imagine you want to estimate the following model:
Yi = B1 + B2x; + Ei,
where Ele,x:] = 0. The issue is that you do not observe , but observe
T: = x + wi, where the measurement error, wi, is such that Elwr] = 0, and
cov(wi, ei] = 0. You estimate:
Yi = B1 + B2ai + vị
by OLS. Show that
plim(b2) =
o? + o%
where o? = var(x;) and o =var(w;).
%3D
Transcribed Image Text:3. Measurement Error on x; Imagine you want to estimate the following model: Yi = B1 + B2x; + Ei, where Ele,x:] = 0. The issue is that you do not observe , but observe T: = x + wi, where the measurement error, wi, is such that Elwr] = 0, and cov(wi, ei] = 0. You estimate: Yi = B1 + B2ai + vị by OLS. Show that plim(b2) = o? + o% where o? = var(x;) and o =var(w;). %3D
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