LinearRegression4

498079 0078609 0937351 inc 0774132 7627851 0000000

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Unformatted text preview: 8 sigma^2 = 1979.9734 Durbin-Watson = 1.9722 Nobs, Nvars = 2017, 6 *************************************************************** Variable Coefficient t-statistic t-probability intercept 1.498079 0.097835 0.922073 inc 0.774132 12.491476 0.000000 age -1.596178 -2.073415 0.038261 agesq 0.029003 3.210154 0.001348 male 2.473321 1.207553 0.227361 e401k 6.981118 3.271008 0.001090 White Heteroscedastic Consistent Estimates Dependent Variable = net tfa R-squared = 0.1280 Rbar-squared = 0.1258 sigma^2 = 1979.9734 Durbin-Watson = 1.9722 Nobs, Nvars = 2017, 6 VER. 10/23/2012. © P. KOLM 67 *************************************************************** Variable Coefficient t-statistic t-probability intercept 1.498079 0.078609 0.937351 inc 0.774132 7.627851 0.000000 age -1.596178 -1.476830 0.139878 agesq 0.029003 2.078857 0.037757 male 2.473321 1.205040 0.228330 e401k 6.981118 3.190378 0.001443 VER. 10/23/2012. © P. KOLM 68 (ii) Using the residuals from part (i), estimate a heteroscedasticity model , ˆ ˆ obtaining the h . What are the smallest and largest values of the h ? i i Solution: ˆ The smallest and largest hi are 12.83 and 58,059.71 respectively. Smallest h_i Largest h_i VER. 10/23/2012. © P. KOLM = = 12.83 58059.71 69 ˆ Estimate the model from part (i) using WLS, where the hi are obtained (iii) in part (ii). Obtain the usual WLS standard errors and the standard errors that are robust to misspecification of the heteroscedasticity function. Comment on how the two sets compare. Solution: In the following equation, estimated by WLS, the usual standard errors are in (⋅) and the heteroscedasticity-robust standard errors are in [⋅]: nettfa = −2.60 + 0.456inc − 0.613age + 0.013age 2 + 1.42male + 4.26e401k (9.94) (0.058) (0.541) (0.0071) (1.03) (1.23) [8.18] [0.062] [0.408] [0.0053] [0.823] [1.14] The differences between usual and robust standard errors for WLS regression are very small, unlike the large differences observed in the usual and robust standard errors for OLS regression. VER. 10/23/2012. © P. KOLM 70 Ordinary Least-squares Estimates Dependent Variable = net tfa R-squared = 0.0238 Rbar-squared = 0.0214 sigma^2 = 11.7132 Durbin-Watson = 1.9822 Nobs, Nvars = 2017, 6 *************************************************************** Variable Coefficient t-statistic t-probability intercept -2.579176 -0.259555 0.795234 inc 0.455972 7.832130 0.000000 age -0.613217 -1.132724 0.257465 agesq 0.013154 1.851951 0.064179 male 1.416934 1.369702 0.170933 e401k 4.264744 3.467134 0.000537 VER. 10/23/2012. © P. KOLM 71 White Heteroscedastic Consistent Estimates Dependent Variable = net tfa R-squared = 0.0238 Rbar-squared = 0.0214 sigma^2 = 11.7132 Durbin-Watson = 1.9822 Nobs, Nvars = 2017, 6 *************************************************************** Variable Coefficient t-statistic t-probability intercept -2.579176 -0.315262 0.752595 inc 0.455972 7.333519 0.000000 age -0.613217 -1.504026 0.132732 agesq 0.013154 2.499129 0.012529 male 1.416934 1.72...
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This document was uploaded on 02/17/2014 for the course COURANT G63.2751.0 at NYU.

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