slides_Ch5_W[1]

Let j be the ols estimator for j for each sample size

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Unformatted text preview: gain an intuitive understanding behind consistency of OLS estimators? ˆ Let βj be the OLS estimator for βj . For each sample size n, we saw ˆ that β has a certain pdf, denote this distribution f n for clarity ˆ βj j (notice the indexing to the sample size ). ˆ Under LR.1 to LR.4 βj is unbiased, then it must be that the mean of n is the true β . fβ ˆ j j Melissa Tartari (Yale) Econometrics 9 / 27 Consistency of the OLS Estimator Can we gain an intuitive understanding behind consistency of OLS estimators? ˆ Let βj be the OLS estimator for βj . For each sample size n, we saw ˆ that β has a certain pdf, denote this distribution f n for clarity ˆ βj j (notice the indexing to the sample size ). ˆ Under LR.1 to LR.4 βj is unbiased, then it must be that the mean of n is the true β . fβ ˆ j j n ˆ If βj is also consistent, then fβ becomes more and more tightly ˆ j n distributed around βj as n grows; as n ! ∞, fβ collapses to the ˆ j single point βj . Melissa Tartari (Yale) Econome...
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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.

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