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Melissa tartari yale econometrics 84 93 the variance

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Unformatted text preview: stimate β1 Melissa Tartari (Yale) Econometrics 82 / 93 The Variance of the OLS Estimator - Estimation I Premise: is there any di¤erence between the unobservables and the residuals? YES! Melissa Tartari (Yale) Econometrics 83 / 93 The Variance of the OLS Estimator - Estimation I Premise: is there any di¤erence between the unobservables and the residuals? YES! in yi = βo + β1 xi + ui the unobservable for observation i is ui : the unobservable appears in the equation containing the population parameters; the unobservables are never observed Melissa Tartari (Yale) Econometrics 83 / 93 The Variance of the OLS Estimator - Estimation I Premise: is there any di¤erence between the unobservables and the residuals? YES! in yi = βo + β1 xi + ui the unobservable for observation i is ui : the unobservable appears in the equation containing the population parameters; the unobservables are never observed ˆ ˆ in yi = βo + β1 xi + ui the residual for observation i is ui : the residual ˆ b shows up in the estimated equation containing the estimates of the population parameters; the residuals are computed from the data Melissa Tartari (Yale) Econometrics 83 / 93 The Variance of the OLS Estimator - Estimation I Premise: is there any di¤erence between the unobservables and the residuals? YES! in yi = βo + β1 xi + ui the unobservable for observation i is ui : the unobservable appears in the equation containing the population parameters; the unobservables are never observed ˆ ˆ in yi = βo + β1 xi + ui the residual for observation i is ui : the residual ˆ b shows up in the estimated equation containing the estimates of the population parameters; the residuals are computed from the data here is an equation that explicitly gives the di¤erence between ui and ui ˆ ui ui ˆ | {z } = ˆ βo βo ˆ β1 β 1 xi (2.59) in Expected value it is 0 Melissa Tartari (Yale) Econometrics 83 / 93 The Variance of the OLS Estimator - Estimation I ˆ ˆ Notice that Var β1 jx and Var βo jx depend on σ2 and σ2 is ˆ ˆ unknown; thus, Var β1 jx and Var βo jx are...
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