slides_Ch5_W

1 through lr4 without any role played by

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

This note was uploaded on 02/13/2014 for the course ECON 350 taught by Professor Donaldbrown during the Fall '10 term at Yale.

Ask a homework question - tutors are online