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3. A researcher is interested in analyzing earnings and she has data, together with basic summary statistics, on the following variables for a sample of 500 individuals: EARNINGS = current hourly earnings in $ S= years of schooling TENURE = years with current employer PREVEXP = years with previous employers EXP = total work experience ASVABC = composite IQ score, standardized to have a mean of 0, and a standard deviation of 1 MALE = gender of respondent (1 if male, 0 otherwise) ETHBLACK = African-American (1 if African-American, 0 otherwise) ETHHISP = Hispanic (1 if Hispanic, 0 otherwise) . sum EARNINGS S TENURE PREVEXP EXP ASVABC MALE ETHBLACK ETHHISP Variable Obs Mean Std. Dev. Min Max EARNINGS 500 18.46958 11.7299 2.13 96.15 SI TENURE PREVEXP EXP 500 500 500 500 14.336 3.784192 3.118731 6.902923 2.757228 2.680943 3.191452 2.817763 6 .2115385 -6.634615 .3653846 20 11.653 85 13.01923 14.26923 - .1669543 -2.863653 0 .5 ASVABC MALE ETHBLACK ETHHISP 500 500 500 500 9418386 .5005008 .3229312 .3344244 2.459217 1 1 1 . 118 . 128 HH 0 She estimates three different earnings equations and obtains the following results: . reg EARNINGS S EXP ASVABC MALE ETHBLACK ETHHISE Source SS df MS 1 10807.6933 578 49.9903 6 493 1801.28222 117.342779 Modell Residual -+- Total | Number of obs F(6, 493) Prob > F R-squared Adj R-squared Root MSE II II II II II II 500 15.35 0.0000 0.1574 0.1472 10.832 68 657.6836 499 137.590548 1 EARNINGS Coef Std. Err. t P>It! [95% Conf. Intervall - - S1 EXP ASVABC MALE ETHBLACK ETHHISP cons 1.535547 .7851167 1.644313 2.929096 -1.390122 1.369306 -10.71393 .2458793 .2054583 .6348966 .9849927 1.563134 1.493945 4.507981 6.25 3.82 2.59 2.97 -0.89 0.92 -2.38 0.000 0.000 0.010 0.003 0.374 0.360 0.018 1.052446 .3814348 .3968763 .993795 -4.461348 -1.565978 -19.57115 2.018647 1.188799 2.89175 4.864398 1.681104 4.30459 -1.856703 - - - reg EARNINGS S PREVEXP TENURE ASVABC MALE ETHBLACK ETHHISP Source SS df MS Model Residual 10941.2335 57716.4501 7 492 1563.03335 117.309858 Number of obs F(7, 492) Prob > F R-squared Adj R-squared Root MSE IIIIIIIIIIII 500 13.32 0.0000 0.1594 0.1474 10.831 Total | 68657.6836 499 137.590548 - 1 EARNINGS Coef. 101 Std. Err. t P>It! [95% Conf. Intervall - - - - - - - - SI PREVEXPL TENURET ASVABCI MALE ETHBLACK ETHHISP | cons 1.482 667 .6926119 .9023064 1.651307 2.932481 -1.363829 1.360287 -10.11562 .2507909 .2229762 .2329497 .6348413 .9848596 1.563109 1.493759 4.542098 5.91 3.11 3.87 2.60 2.98 -0.87 0.91 -2.23 0.000 0.002 0.000 0.010 0.003 0.383 0.363 0.026 .9899137 .2545088 .4446075 4039727 9974314 -4.435022 -1.574647 -19.03993 1.97542 1.130715 1.360005 2.898642 4.867531 1.707363 4.295221 -1.191323 reg EARNINGS S PREVEXP EXP ASVABC MALE ETHBLACK ETHHISP Source SS df MS = = Model Residual ! 10941.2335 57716.4501 7 492 1563.03336 117.309858 Number of obs F(7, 492) Prob > F R-squared Adj R-squared Root MSE 500 13.32 0.0000 0.1594 0.1474 10.831 = Total 1 68 657.6836 499 137.590548 - EARNINGS Coef. Std. Err. t P>It! [95% Conf. Intervall SI PREVEXP EXP | ASVABC MALET ETHBLACK ETHHISP1 cons 1.482667 -.2096945 .9023064 1.651307 2.932481 -1.363829 1.360287 -10.11562 .2507909 .1965388 .2329497 .6348413 .9848596 1.563109 1.493759 4.542098 5.91 -1.07 3.87 2.60 2.98 -0.87 0.91 - 2.23 0.000 0.287 0.000 0.010 0.003 0.383 0.363 0.026 .9899137 -.5958534 .4446075 4039727 .9974314 -4.435022 -1.574647 -19.03993 1.97542 .1764644 1.360005 2.898642 4.867531 1.707363 4.295221 -1.191323 . a) Show that the first specification of the earnings equation is a restricted version of the second specification and state the restriction. b) Test this restriction, using a suitable F-test. c) Explain how and why this same restriction can also be tested using a t-test of the significance of the parameter associated with the PREVEXP variable in the third specification. Be explicit d) Does the result of the test accord with your prior expectations? Explain. 3. A researcher is interested in analyzing earnings and she has data, together with basic summary statistics, on the following variables for a sample of 500 individuals: EARNINGS = current hourly earnings in $ S= years of schooling TENURE = years with current employer PREVEXP = years with previous employers EXP = total work experience ASVABC = composite IQ score, standardized to have a mean of 0, and a standard deviation of 1 MALE = gender of respondent (1 if male, 0 otherwise) ETHBLACK = African-American (1 if African-American, 0 otherwise) ETHHISP = Hispanic (1 if Hispanic, 0 otherwise) . sum EARNINGS S TENURE PREVEXP EXP ASVABC MALE ETHBLACK ETHHISP Variable Obs Mean Std. Dev. Min Max EARNINGS 500 18.46958 11.7299 2.13 96.15 SI TENURE PREVEXP EXP 500 500 500 500 14.336 3.784192 3.118731 6.902923 2.757228 2.680943 3.191452 2.817763 6 .2115385 -6.634615 .3653846 20 11.653 85 13.01923 14.26923 - .1669543 -2.863653 0 .5 ASVABC MALE ETHBLACK ETHHISP 500 500 500 500 9418386 .5005008 .3229312 .3344244 2.459217 1 1 1 . 118 . 128 HH 0 She estimates three different earnings equations and obtains the following results: . reg EARNINGS S EXP ASVABC MALE ETHBLACK ETHHISE Source SS df MS 1 10807.6933 578 49.9903 6 493 1801.28222 117.342779 Modell Residual -+- Total | Number of obs F(6, 493) Prob > F R-squared Adj R-squared Root MSE II II II II II II 500 15.35 0.0000 0.1574 0.1472 10.832 68 657.6836 499 137.590548 1 EARNINGS Coef Std. Err. t P>It! [95% Conf. Intervall - - S1 EXP ASVABC MALE ETHBLACK ETHHISP cons 1.535547 .7851167 1.644313 2.929096 -1.390122 1.369306 -10.71393 .2458793 .2054583 .6348966 .9849927 1.563134 1.493945 4.507981 6.25 3.82 2.59 2.97 -0.89 0.92 -2.38 0.000 0.000 0.010 0.003 0.374 0.360 0.018 1.052446 .3814348 .3968763 .993795 -4.461348 -1.565978 -19.57115 2.018647 1.188799 2.89175 4.864398 1.681104 4.30459 -1.856703 - - - reg EARNINGS S PREVEXP TENURE ASVABC MALE ETHBLACK ETHHISP Source SS df MS Model Residual 10941.2335 57716.4501 7 492 1563.03335 117.309858 Number of obs F(7, 492) Prob > F R-squared Adj R-squared Root MSE IIIIIIIIIIII 500 13.32 0.0000 0.1594 0.1474 10.831 Total | 68657.6836 499 137.590548 - 1 EARNINGS Coef. 101 Std. Err. t P>It! [95% Conf. Intervall - - - - - - - - SI PREVEXPL TENURET ASVABCI MALE ETHBLACK ETHHISP | cons 1.482 667 .6926119 .9023064 1.651307 2.932481 -1.363829 1.360287 -10.11562 .2507909 .2229762 .2329497 .6348413 .9848596 1.563109 1.493759 4.542098 5.91 3.11 3.87 2.60 2.98 -0.87 0.91 -2.23 0.000 0.002 0.000 0.010 0.003 0.383 0.363 0.026 .9899137 .2545088 .4446075 4039727 9974314 -4.435022 -1.574647 -19.03993 1.97542 1.130715 1.360005 2.898642 4.867531 1.707363 4.295221 -1.191323 reg EARNINGS S PREVEXP EXP ASVABC MALE ETHBLACK ETHHISP Source SS df MS = = Model Residual ! 10941.2335 57716.4501 7 492 1563.03336 117.309858 Number of obs F(7, 492) Prob > F R-squared Adj R-squared Root MSE 500 13.32 0.0000 0.1594 0.1474 10.831 = Total 1 68 657.6836 499 137.590548 - EARNINGS Coef. Std. Err. t P>It! [95% Conf. Intervall SI PREVEXP EXP | ASVABC MALET ETHBLACK ETHHISP1 cons 1.482667 -.2096945 .9023064 1.651307 2.932481 -1.363829 1.360287 -10.11562 .2507909 .1965388 .2329497 .6348413 .9848596 1.563109 1.493759 4.542098 5.91 -1.07 3.87 2.60 2.98 -0.87 0.91 - 2.23 0.000 0.287 0.000 0.010 0.003 0.383 0.363 0.026 .9899137 -.5958534 .4446075 4039727 .9974314 -4.435022 -1.574647 -19.03993 1.97542 .1764644 1.360005 2.898642 4.867531 1.707363 4.295221 -1.191323 . a) Show that the first specification of the earnings equation is a restricted version of the second specification and state the restriction. b) Test this restriction, using a suitable F-test. c) Explain how and why this same restriction can also be tested using a t-test of the significance of the parameter associated with the PREVEXP variable in the third specification. Be explicit d) Does the result of the test accord with your prior expectations? Explain