slides_Ch5_W[1]

Recall however that lr6 plays no role in the

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Unformatted text preview: to test hypothesis about the βj0 s . ˆ The exact normality of βj hinges crucially on the normality of the unobservable u in the population: if ui iid from some distribution other than N , ˆ βj N , and the t and the F statistics will NOT have the t and F distributions. ˆ Recall however that LR.6 plays no role in the unbiasedness of βj , nor ˆ does it a¤ect the conclusion that βj is BLUE under LR.1-LR.5. It is just exact inference based on t and the F statistics that requires LR.6. Melissa Tartari (Yale) Econometrics 16 / 27 Large Sample Inference in the MLRM II How can we perform inference when LR.6 fails? Should we abandon the t and the F statistics? What shall we use in their place? Melissa Tartari (Yale) Econometrics 17 / 27 Large Sample Inference in the MLRM II How can we perform inference when LR.6 fails? Should we abandon the t and the F statistics? What shall we use in their place? Even though the ui0 s (hence the yi0 s ) are not normal when LR.6 does ˆ not hold, we can invoke the CLT and conclude t...
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