Question

3. A possible modification of Model 2 in question 2 is being considered: log(wage) = ?? + ??female + ??educ + ??female.educ + ??exper + ?? exper" + ?? tenure + ?? tenure" + u (2) The following results were obtained for the same sample of workers as in question 2. The female.educ interaction term is denoted ‘femeduc’ in the Stata output. MODEL 3 . reg lwage female educ femeduc exper expersq tenure tenursq Source | SS df MS Number of obs = 526 ---------+------------------------------ F( 7, 518) = 58.37 Model | 65.4081534 7 9.34402192 Prob > F = 0.0000 Residual | 82.921598 518 .160080305 R-squared = 0.4410 ---------+------------------------------ Adj R-squared = 0.4334 Total | 148.329751 525 .28253286 Root MSE = .4001 ------------------------------------------------------------------------------ lwage | Coef. Std. Err. t P>|t| [95% Conf. Interval] ---------+-------------------------------------------------------------------- female | -.2267886 .1675394 -1.35 0.176 -.5559289 .1023517 educ | .0823692 .0084699 9.72 0.000 .0657296 .0990088 femeduc | -.0055645 .0130618 -0.43 0.670 -.0312252 .0200962 exper | .0293366 .0049842 5.89 0.000 .019545 .0391283 expersq | -.0005804 .0001075 -5.40 0.000 -.0007916 -.0003691 tenure | .0318967 .006864 4.65 0.000 .018412 .0453814 tenursq | -.00059 .0002352 -2.51 0.012 -.001052 -.000128 _cons | .388806 .1186871 3.28 0.001 .1556388 .6219732 ------------------------------------------------------------------------------ . corr lwage female educ femeduc exper tenure (obs=526) | lwage female educ femeduc exper tenure ---------+---------------------------------------------------------- lwage | 1.0000 female | -0.3737 1.0000 educ | 0.4311 -0.0850 1.0000 femeduc | -0.2937 0.9636 0.0832 1.0000 exper | 0.1114 -0.0416 -0.2995 -0.0823 1.0000 tenure | 0.3255 -0.1979 -0.0562 -0.1909 0.4993 1.0000 (a) In words, how would you interpret the parameters ?? and ??? [2 marks] (b) What are the estimated returns to education for men and for women? Is there any evidence to suggest that the return to education differs between men and women? Give reasons for your answer. [4 marks] (c) Compared to the models in question 2, the coefficient on female is no longer statistically significant at conventional significance levels. Should we therefore now conclude that there is no statistically significant evidence of lower pay for women (after controlling for education, experience and tenure) and opt for model 4 below? Explain your answer, including the details of any additional tests you could carry out that would aid your decision. [10 marks] MODEL 4 . reg lwage educ exper expersq tenure tenursq Source | SS df MS Number of obs = 526 ---------+------------------------------ F( 5, 520) = 60.26 Model | 54.4184647 5 10.8836929 Prob > F = 0.0000 Residual | 93.9112867 520 .180598628 R-squared = 0.3669 ---------+------------------------------ Adj R-squared = 0.3608 Total | 148.329751 525 .28253286 Root MSE = .42497 ------------------------------------------------------------------------------ lwage | Coef. Std. Err. t P>|t| [95% Conf. Interval] ---------+-------------------------------------------------------------------- educ | .0845258 .0071614 11.80 0.000 .070457 .0985946 exper | .029301 .0052885 5.54 0.000 .0189115 .0396905 expersq | -.0005918 .0001141 -5.19 0.000 -.0008159 -.0003677 tenure | .0371222 .0072432 5.13 0.000 .0228927 .0513517 tenursq | -.0006156 .0002495 -2.47 0.014 -.0011056 -.0001255 _cons | .2015715 .1014697 1.99 0.048 .0022306 .4009124 ------------------------------------------------------------------------------ (d) ‘‘Of the models considered in questions 3 and 4, Model 3 is the preferred model because it has the highest R".’’ Critically evaluate this argument, taking care to explain what information is conveyed by the R" values. [5 marks]

          3. A possible modification of Model 2 in question 2 is being considered:

log(wage) = ?? + ??female + ??educ + ??female.educ
+ ??exper + ?? exper" + ?? tenure + ?? tenure" + u (2)

The following results were obtained for the same sample of workers as in question 2.
The female.educ interaction term is denoted ‘femeduc’ in the Stata output.

MODEL 3
. reg lwage female educ femeduc exper expersq tenure tenursq

Source | SS df MS Number of obs = 526
---------+------------------------------ F( 7, 518) = 58.37
Model | 65.4081534 7 9.34402192 Prob > F = 0.0000
Residual | 82.921598 518 .160080305 R-squared = 0.4410
---------+------------------------------ Adj R-squared = 0.4334
Total | 148.329751 525 .28253286 Root MSE = .4001

------------------------------------------------------------------------------
lwage | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------+--------------------------------------------------------------------
female | -.2267886 .1675394 -1.35 0.176 -.5559289 .1023517
educ | .0823692 .0084699 9.72 0.000 .0657296 .0990088
femeduc | -.0055645 .0130618 -0.43 0.670 -.0312252 .0200962
exper | .0293366 .0049842 5.89 0.000 .019545 .0391283
expersq | -.0005804 .0001075 -5.40 0.000 -.0007916 -.0003691
tenure | .0318967 .006864 4.65 0.000 .018412 .0453814
tenursq | -.00059 .0002352 -2.51 0.012 -.001052 -.000128
_cons | .388806 .1186871 3.28 0.001 .1556388 .6219732
------------------------------------------------------------------------------

. corr lwage female educ femeduc exper tenure
(obs=526)

| lwage female educ femeduc exper tenure
---------+----------------------------------------------------------
lwage | 1.0000
female | -0.3737 1.0000
educ | 0.4311 -0.0850 1.0000
femeduc | -0.2937 0.9636 0.0832 1.0000
exper | 0.1114 -0.0416 -0.2995 -0.0823 1.0000
tenure | 0.3255 -0.1979 -0.0562 -0.1909 0.4993 1.0000

(a) In words, how would you interpret the parameters ?? and ??? [2 marks]
(b) What are the estimated returns to education for men and for women? Is there any evidence to suggest that the return to education differs between men and women? Give reasons for your answer. [4 marks]
(c) Compared to the models in question 2, the coefficient on female is no longer statistically significant at conventional significance levels. Should we therefore now conclude that there is no statistically significant evidence of lower pay for women (after controlling for education, experience and tenure) and opt for model 4 below? Explain your answer, including the details of any additional tests you could carry out that would aid your decision. [10 marks]

MODEL 4
. reg lwage educ exper expersq tenure tenursq

Source | SS df MS Number of obs = 526
---------+------------------------------ F( 5, 520) = 60.26
Model | 54.4184647 5 10.8836929 Prob > F = 0.0000
Residual | 93.9112867 520 .180598628 R-squared = 0.3669
---------+------------------------------ Adj R-squared = 0.3608
Total | 148.329751 525 .28253286 Root MSE = .42497

------------------------------------------------------------------------------
lwage | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------+--------------------------------------------------------------------
educ | .0845258 .0071614 11.80 0.000 .070457 .0985946
exper | .029301 .0052885 5.54 0.000 .0189115 .0396905
expersq | -.0005918 .0001141 -5.19 0.000 -.0008159 -.0003677
tenure | .0371222 .0072432 5.13 0.000 .0228927 .0513517
tenursq | -.0006156 .0002495 -2.47 0.014 -.0011056 -.0001255
_cons | .2015715 .1014697 1.99 0.048 .0022306 .4009124
------------------------------------------------------------------------------

(d) ‘‘Of the models considered in questions 3 and 4, Model 3 is the preferred model because it has the highest R".’’ Critically evaluate this argument, taking care to explain what information is conveyed by the R" values. [5 marks]

3. A possible modification of Model 2 in question 2 is being considered:

log(wage) = ?? + ??female + ??educ + ??female.educ
+ ??exper + ?? exper" + ?? tenure + ?? tenure" + u (2)

The following results were obtained for the same sample of workers as in question 2.
The female.educ interaction term is denoted ‘femeduc’ in the Stata output.

MODEL 3
. reg lwage female educ femeduc exper expersq tenure tenursq

Source | SS df MS Number of obs = 526
———+—————————— F( 7, 518) = 58.37
Model | 65.4081534 7 9.34402192 Prob > F = 0.0000
Residual | 82.921598 518 .160080305 R-squared = 0.4410
———+—————————— Adj R-squared = 0.4334
Total | 148.329751 525 .28253286 Root MSE = .4001

——————————————————————————
lwage | Coef. Std. Err. t P>|t| [95% Conf. Interval]
———+——————————————————————–
female | -.2267886 .1675394 -1.35 0.176 -.5559289 .1023517
educ | .0823692 .0084699 9.72 0.000 .0657296 .0990088
femeduc | -.0055645 .0130618 -0.43 0.670 -.0312252 .0200962
exper | .0293366 .0049842 5.89 0.000 .019545 .0391283
expersq | -.0005804 .0001075 -5.40 0.000 -.0007916 -.0003691
tenure | .0318967 .006864 4.65 0.000 .018412 .0453814
tenursq | -.00059 .0002352 -2.51 0.012 -.001052 -.000128
cons | .388806 .1186871 3.28 0.001 .1556388 .6219732
——————————————————————————

. corr lwage female educ femeduc exper tenure
(obs=526)

| lwage female educ femeduc exper tenure
———+———————————————————-
lwage | 1.0000
female | -0.3737 1.0000
educ | 0.4311 -0.0850 1.0000
femeduc | -0.2937 0.9636 0.0832 1.0000
exper | 0.1114 -0.0416 -0.2995 -0.0823 1.0000
tenure | 0.3255 -0.1979 -0.0562 -0.1909 0.4993 1.0000

(a) In words, how would you interpret the parameters ?? and ??? [2 marks]
(b) What are the estimated returns to education for men and for women? Is there any evidence to suggest that the return to education differs between men and women? Give reasons for your answer. [4 marks]
(c) Compared to the models in question 2, the coefficient on female is no longer statistically significant at conventional significance levels. Should we therefore now conclude that there is no statistically significant evidence of lower pay for women (after controlling for education, experience and tenure) and opt for model 4 below? Explain your answer, including the details of any additional tests you could carry out that would aid your decision. [10 marks]

MODEL 4
. reg lwage educ exper expersq tenure tenursq

Source | SS df MS Number of obs = 526
———+—————————— F( 5, 520) = 60.26
Model | 54.4184647 5 10.8836929 Prob > F = 0.0000
Residual | 93.9112867 520 .180598628 R-squared = 0.3669
———+—————————— Adj R-squared = 0.3608
Total | 148.329751 525 .28253286 Root MSE = .42497

——————————————————————————
lwage | Coef. Std. Err. t P>|t| [95% Conf. Interval]
———+——————————————————————–
educ | .0845258 .0071614 11.80 0.000 .070457 .0985946
exper | .029301 .0052885 5.54 0.000 .0189115 .0396905
expersq | -.0005918 .0001141 -5.19 0.000 -.0008159 -.0003677
tenure | .0371222 .0072432 5.13 0.000 .0228927 .0513517
tenursq | -.0006156 .0002495 -2.47 0.014 -.0011056 -.0001255
cons | .2015715 .1014697 1.99 0.048 .0022306 .4009124
——————————————————————————

(d) ‘‘Of the models considered in questions 3 and 4, Model 3 is the preferred model because it has the highest R".’’ Critically evaluate this argument, taking care to explain what information is conveyed by the R" values. [5 marks]

Added by Eva T.

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