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Unformatted text preview: LR.1 through LR.5 (in particular,
homoshedasticity is used). Melissa Tartari (Yale) Econometrics 19 / 27 Asymptotic Normality of the OLS Estimator WARNING:
if n is not very large, then the t distribution can be a poor
approximation to the distribution of the t statistics when u N .
the quality of the approximation depends not just on n, but on the
df = n K 1: with more indep vars in the model, a larger sample
size is usually needed to use the t approximation.
Theorem 5.2 requires LR.1 through LR.5 (in particular,
homoshedasticity is used). ˆ
Additional IMPLICATIONS: asymptotic normality of βj implies that
the F statistics has approximate F distribution in large sample sizes,
thus for testing exclusion restrictions or the other joint hypothesis,
nothing changes from what we have done before. Melissa Tartari (Yale) Econometrics 19 / 27 Asymptotic Normality of the OLS Estimator For notational simplicity we focus on Theorem 5.2 within the SLRM:
under ass.s LR.1-LR.5.
n β1 β1 jx N 0, σ2
3 2 ˆ
σ is a consistent estimator of σ2
( β1 β1 ) jx a
N (0, 1)
se ( β1 jx ) Melissa Tartari (Yale) Econometrics 20 / 27 Asymptotic Normality of the OLS Estimator: an intutive
Observe that p Melissa Tartari (Yale) ˆ
n β1 β1 p ∑n=1 (xi x ) ui
p n (xi x ) ui
= σ n∑
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This note was uploaded on 02/13/2014 for the course ECON 350 taught by Professor Donaldbrown during the Fall '10 term at Yale.
- Fall '10