slides_Ch5_W

1 through lr4 without any role played by

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Unformatted text preview: t; population parameters ( βo , β1 ); then I sort the estimates so obtained and graph them into 2 histograms. Melissa Tartari (Yale) Econometrics 25 / 27 Part II: Non-Normal Disturbances II ˆ ˆ Observe that, both the histograms for β1 and βo are centered about the true value of the parameters (namely 1 and 3): this is as it should since we know that unbiasedness of the OLS estimator holds under LR.1 through LR.4 without any role played by distributional assumptions on the disturbance u . Melissa Tartari (Yale) Econometrics 26 / 27 Part II: Non-Normal Disturbances II ˆ ˆ Observe that, both the histograms for β1 and βo are centered about the true value of the parameters (namely 1 and 3): this is as it should since we know that unbiasedness of the OLS estimator holds under LR.1 through LR.4 without any role played by distributional assumptions on the disturbance u . However, we also see that the two histograms resemble a Gaussian distribution: this is the implication of Theorem 5.2 on asymptotical normality of the OLS estimator (since the histogram estimates the distribution of the estimator). Melissa Tartari (Yale) Econometrics 26 / 27 Part II: Non-Normal Disturbances II ˆ ˆ Observe that, both the histograms for β1 and βo are centered about the true value of the parameters (namely 1 and 3): this is as it should since we know that unbiasedness of the OLS estimator holds under LR.1 through LR.4 without any role played by distributional assumptions on the disturbance u . However, we also see that the two histograms resemble a Gaussian distribution: this is the implication of Theorem 5.2 on asymptotical normality of the OLS estimator (since the histogram estimates the distribution of the estimator). Notice that by assumption/construction the disturbances are iid with …nite variance so the conditions for theorem 5.2 to apply are met. Melissa Tartari (Yale) Econometrics 26 / 27 Asymptotic E¢ ciency of OLS ˆ We know that under LR.1 through LR.5 βj is BLUE. Melissa Tartari (Yale) Econometrics 27 / 27 Asymptotic E¢ ciency of OLS ˆ We know that under LR.1 through LR.5 βj is BLUE. ˆ Under the same ass.s βj is also asymptotically e¢ cient among a certain class of estimators. Melissa Tartari (Yale) Econometrics 27 / 27...
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