question archive 6) Use the following formula and the regression results below to test the joint null hypothesis that neither mother's nor father's education has an effect on wages (10 points) : F =_ (SSRr - SS Rur) /9 ~ Fan-k-1 SSRur/ (n - k - 1) What is the F-statistic, and what is the 18 critical value for that F-stat? What do you conclude? How can your conclusion be correct, given that neither of the relevant coefficients is significant at even 5% by itself? Regression 1) Source SS df MS Number of obs = 722 F( 8, 713) = 24
6) Use the following formula and the regression results below to test the joint null hypothesis that neither mother's nor father's education has an effect on wages (10 points) : F =_ (SSRr - SS Rur) /9 ~ Fan-k-1 SSRur/ (n - k - 1) What is the F-statistic, and what is the 18 critical value for that F-stat? What do you conclude? How can your conclusion be correct, given that neither of the relevant coefficients is significant at even 5% by itself? Regression 1) Source SS df MS Number of obs = 722 F( 8, 713) = 24
Subject:BusinessPrice:9.82 Bought3
6) Use the following formula and the regression results below to test the joint null hypothesis that neither mother's nor father's education has an effect on wages (10 points) : F =_ (SSRr - SS Rur) /9 ~ Fan-k-1 SSRur/ (n - k - 1) What is the F-statistic, and what is the 18 critical value for that F-stat? What do you conclude? How can your conclusion be correct, given that neither of the relevant coefficients is significant at even 5% by itself? Regression 1) Source SS df MS Number of obs = 722 F( 8, 713) = 24.84 Model | 27 . 6422885 8 3. 45528607 Prob > F = 0 . 0000 Residual | 99.1696272 713 . 139087836 R-squared = 0. 2180 -+ Adj R-squared = 0. 2092 Total | 126. 811916 721 . 175883378 Root MSE . 37294 1wage Coef. Std. Err. t P>It| [95% Conf. Interval] educ . 0562629 007967 7. 06 0 . 000 0406214 0719045 exper . 014224 . 0044905 3. 17 0 . 002 . 0054077 . 0230402 tenure . 009331 . 0029518 3.16 0 . 002 . 0035356 . 0151264 age . 0096873 . 0055133 1 . 76 0. 079 - . 001137 . 0205117 south - . 0807515 . 0305296 -2. 65 0 . 008 -. 1406902 - . 0208128 urban 1672097 . 0313994 5.33 0 . 000 . 1055634 . 228856 meduc . 0108041 . 0061195 1 . 77 0 . 078 - . 0012103 . 0228185 feduc . 0086483 . 0054328 1. 59 0. 112 - . 0020179 . 0193145 cons 5. 184015 . 1749834 29. 63 0. 000 4. 84047 5. 527559
Regression 2) Source | SS df MS Number of obs 722 -+- F ( 6, 715) = 30.89 Model 1 26.1070112 6 4 . 35116853 Prob > F = 0 . 0000 Residual 1 100 . 704905 715 . 14084602 R-squared = 0 . 2059 -+ Adj R-squared = 0 . 1992 Total | 126.811916 721 . 175883378 Root MSE = . 37529 Iwage | Coef. Std. Err. t P>It| [95% Conf. Interval] educ . 066289 . 007407 8. 95 0. 000 . 0517469 0808312 exper . 0139483 0045166 3 . 09 0 . 002 . 0050809 . 0228158 tenure . 0092854 . 0029681 3. 13 0 . 002 . 0034582 . 0151126 age . 008745 . 0055379 1 . 58 0 . 115 - . 0021275 . 0196175 south -. 0968346 . 0303248 -3. 19 0 . 001 -. 156371 - . 0372982 urban 17171 . 0314958 5 . 45 0 . 000 . 1098747 . 2335453 cons 5. 288836 . 1730791 30 .56 0 . 000 4. 949032 5 . 62864
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feduc = 0; meduc = 0, is Null hypothesis
feduc ! = 0; meduc ! = 0, can be Alternative hypothesis
Based on the unrestricted model,
n = 722,
k = 8
F-critical (q, n-k-1) = F ( 2, 722 - 8 - 1) = F (2, 713, 0.01) = 2.30259
F-critical (q, n-k-1, 0.05) = 2.9957
F-statistic = (RSS (unrestricted) - RSS (restricted) / q) / RSS (unrestricted) / (n - k - 1)
R squared (unrestricted) = 99.1696
R squared (restricted) = 100.7049
F-statistic =
(R squared unrestricted - R squared restricted) / q / ( 1 - R squared unrestricted) / ( n - k - 1)
R squared unrestricted = 0.2180
R squared restricted = 0.2059
((0.2180 - 0.2059) / 2 / ( 1 - 0.2180) / 713)
= 0.0121 / 2 / 0.782 / 713
= (0.0121) / 2 / (0.782 / 713)
= 0.00605 * (713 / 0.782) = 4.31365 / 0.782 = 5.5161
Conclusion;
True, the variables are not statistically significant at even 5%, but they do help the model fit; data can be added for significant coefficients.
The F-statistic is greater than the f-critical value. The null hypothesis can be rejected because the model fits well.
Educ is an endogenous variable; the variable depends on mother's education, and, father's education.
These are instrument variables to Educ if 2sls is carried out. 2sls estimation can be carried out in place of OLS.
