Econ 399 Chapter5 - 5.Consistency...

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5. Consistency We cannot always achieve unbiasedness of  estimators. -For example,  σ hat is not an unbiased  estimator of  σ -It is only consistent -Where unbiasedness cannot be achieved,  consistency is the minimum requirement for an  estimator -Consistency requires MLR. 1 through MLR.4, as  well as no correlation between x’s
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5. Intuitive Consistency While the actual proof of consistency is  complicated, it can be intuitively explained -Each sample of n observations produces a B j hat  with a given distribution -MLR. 1 through MLR. 4 cause this B j hat to be  unbiased with mean B j -If the estimator is consistent, as n increases the  distribution becomes more tightly distributed  around B j -as n tends to infinity, B j hat’s distribution  collapses to B
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In general, If obtaining more data DOES NOT get us closer  to our parameter of interest… We are using a poor (inconsistent) estimator. -Fortunately, the same assumptions imply 
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Econ 399 Chapter5 - 5.Consistency...

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