Econometrics information sheet

Econometrics information sheet - 1) Gauss-Markov Theorem...

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Gauss-Markov Theorem – Under 4 assumptions + homoskedasticity, OLS is BLUE 1) Linear in Parameters – Population model is 0 1 y x u β = + + Violations: Including irrelevant variables does not affect unbiasedness but increases variance if correlated with relevant variable of interest. Omitting relevant variable will bias estimator and generally decrease variance unless uncorrelated with all included variables. 2) Random Sampling 3) Zero Conditional Mean - E( | ) E( ) 0 u x u = = Corr( , ) 0 u x = a Cov( , ) 0 u x = a Cov( , ) Corr( , ) or sd( )sd( ) u x u x u x u x u x u x σ ρ σ σ = = Represents two assumptions in one: E( | ) E( ) u x u = and E( ) 0 u = . u and x are assumed to be random variables that follow a joint probability distribution The assumption E( | ) E( ) u x u = is very important; it implies, among other things, that u and x are uncorrelated (i.e., not linearly related). The assumption E( ) 0 u = is not crucial as long as an intercept term is included in the equation (intuitive explanation). Violations:
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