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Unformatted text preview: Asymptotic Properties of OLS Estimators ECON 399 Neil Hepburn Contents 1 Introduction 1 2 Asymptotic vs Finite Sample Properties 1 3 The Central Limit Theorem 6 1 Introduction Introduction A critical assumption in statistical inference is that the error terms are normally distributed This allows us to use the t-distribution as well as the 2 and F-distributions This may not always be a reasonable assumption Can we still use OLS and the usual hypothesis tests? Yes, under certain conditions. 2 Asymptotic vs Finite Sample Properties Asymptotic vs Finite Sample Properties The material that we have looked at so far developed properties for OLS estimators in finite samples We also need to consider what happens when the sample size becomes very large This is what the study of the asymptotic properties of OLS is all about. 1 Finite Sample Properties In our earlier look at OLS and the properties of OLS estimators, we were looking at finite sample properties We found that under a set of assumptions, that the OLS estimators are unbiased estimators of the true population parameter We also found the sampling distribution for the k Large Sample Properties We want to consider what the properties of OLS estimators are when the sample becomes very large (as n ) It turns out that large samples allow us to relax some of our earlier as- sumptions We can also, under certain circumstances, rely on classical hypothesis tests even if the error terms are not normally distributed Consistency vs Unbiasedness Earlier we found that OLS estimators were unbiased the expected value of an estimator is the true population parameter There is an analagous term in asymptotic theory consistency An estimator is consistent if its plim is equal to the true population pa- rameter plim? Whats a plim?...
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This note was uploaded on 10/04/2011 for the course ECONOMICS 399 taught by Professor Neil.h during the Spring '11 term at University of Alberta.
- Spring '11