《计量经济学导论》ch5.pptVIP

Chapter 5 ;So far we focused on properties of OLS that hold for any sample Properties of OLS that hold for any sample/sample size Expected values/unbiasedness under MLR.1 – MLR.4 Variance formulas under MLR.1 – MLR.5 Gauss-Markov Theorem under MLR.1 – MLR.5 Exact sampling distributions/tests under MLR.1 – MLR.6 Properties of OLS that hold in large samples Consistency under MLR.1 – MLR.4 Asymptotic normality/tests under MLR.1 – MLR.5;Consistency Interpretation: Consistency means that the probability that the estimate is arbitrari- ly close to the true population value can be made arbitrarily high by increasing the sample size Consistency is a minimum requirement for sensible estimators ;Theorem 5.1 (Consistency of OLS) Special case of simple regression model Assumption MLR.4‘;For consistency of OLS, only the weaker MLR.4‘ is needed Asymptotic analog of omitted variable bias;Asymptotic normality and large sample inference In practice, the normality assumption MLR.6 is often questionable If MLR.6 does not hold, the results of t- or F-tests may be wrong Fortunately, F- and t-tests still work if the sample size is large enough Also, OLS estimates are normal in large samples even without MLR.6 Theorem 5.2 (Asymptotic normality of OLS) ;Converges to;Asymptotic analysis of the OLS sampling errors (cont.) This is why large samples are better Example: Standard errors in a birth weight equation