Econometrics-I-7

&#152&#152˜™ ™ 24/35 part 7

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Unformatted text preview: ˜˜˜™ ™ 24/35 Part 7: Estimating the Variance of b ˜˜˜™ ™ 25/35 Part 7: Estimating the Variance of b The NIST Filipelli Problem ˜˜˜™ ™ 26/35 Part 7: Estimating the Variance of b Certified Filipelli Results ˜˜˜˜™ ™ 27/35 Part 7: Estimating the Variance of b Stata Filipelli Results ˜˜˜˜™ ™ 28/35 Part 7: Estimating the Variance of b Regression of x2 on all other variables ˜˜˜˜™ ™ 29/35 Part 7: Estimating the Variance of b Using QR Decomposition ˜˜˜˜™ ™ 30/35 Part 7: Estimating the Variance of b Multicollinearity There is no “cure” for collinearity. Estimating something else is not helpful (principal components, for example). There are “measures” of multicollinearity, such as the condition number of X and the variance inflation factor. Best approach: Be cognizant of it. Understand its implications for estimation. What is better: Include a variable that causes collinearity, or drop the variable and suffer from a biased estimator? Mean squared error would be the basis for comparison. Some generalities. ˜˜˜˜ 1™ ™ 31/35 Part 7: Estimating the Variance of b Specification and Functional Form: Nonlinearity 2 2 1 2 3 4 1 2 3 4 2 3 2 3 2 2 Population Estimators ˆ [ | , ] ˆ 2 2 ˆ Estimator of the variance of ˆ . [ ] [ ] 4 x x x x y x x z y b b x b x b z E y x z x b b x x Est Var Var b x Va = β + β + β + β + ε = + + + ∂ δ = = β + β δ = + ∂ δ δ = + 3 2 3 [ ] 4 [ , ] r b xCov b b + ˜˜˜˜ ˜™ 32/35 Part 7: Estimating the Variance of b Log Income Equation---------------------------------------------------------------------- Ordinary least squares regression ............ LHS=LOGY Mean = -1.15746 Estimated Cov[b1,b2] Standard deviation = .49149 Number of observs. = 27322 Model size Parameters = 7 Degrees of freedom = 27315 Residuals Sum of squares = 5462.03686 Standard error of e = .44717 Fit R-squared = .17237--------+------------------------------------------------------------- Variable| Coefficient Standard Error b/St.Er. P[|Z|>z] Mean of X--------+------------------------------------------------------------- AGE| .06225*** .00213 29.189 .0000 43.5272 AGESQ| -.00074*** .242482D-04 -30.576 .0000 2022.99 Constant| -3.19130*** .04567 -69.884 .0000 MARRIED| .32153*** .00703 45.767 .0000 .75869 HHKIDS| -.11134*** .00655 -17.002 .0000 .40272 FEMALE| -.00491 .00552 -.889 .3739 .47881 EDUC| .05542*** .00120 46.050 .0000 11.3202--------+------------------------------------------------------------- Average Age = 43.5272. Estimated Partial effect = .066225 – 2(.00074)43.5272 = .00018....
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&#152&#152˜™ ™ 24/35 Part 7 Estimating...

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