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2. (2 points) Rachel is a graduate student at Mac who is interested in issues related to labor market discrimination. As such, she plans to write a term paper regarding the male-female wage gap for one of her graduate courses. As a starting point, she performs a simple Oaxaca decomposition using a public dataset that she acquired online. First, she starts with the simplest specification as follows: Specification 1: In(hourly wage) = a + b x (years of education) Using a statistical software, she gets the following Oaxaca decomposition results: oaxaca Inwage educ, by(female) weight(@) Blinder-Oaxaca decomposition Number of obs 1, 434 1: female = 0 2: female = 1 Inwage Coof . Std. Err. Z P> |ZI [95% Conf. Interval] Differential Prediction_1 3.440222 0174724 196.89 3.405977 3.474467 Prediction_2 3.266761 . 0218257 149. 68 0.090 3.223984 3.309539 Difference . 1734607 .0279579 6.20 0.000 1186642 . 2282573 Decomposition Explained 0457899 0112163 4.08 0.080 0238064 0677734 Unexplained .1276708 0266898 4.78 0.080 0753598 1799818 Next, she tries a different specification with additional controls: Specification 2: In(hourly wage) = a + b x (years of education) + c x (years of labor market experience) + d x (years of job tenure) With the second specification, she gets the following decomposition results: . oaxaca Inwage educ exper tenure, by(female) weight(@) Blinder-Oaxaca decomposition Number of obs 1,434 1: female = 0 2: female = 1 Inwage Coef. Std. Err. P>|21 [95% Conf. Interval] Differential Prediction_1 3. 440222 .0174874 196.73 0.090 3.405947 3.474497 Prediction_2 3.266761 . 0218522 149.49 0.090 3.223932 3.309591 Difference .1734607 .027988 6.20 . 1186052 . 2283163 Decomposition Explained 0852798 015693 5.43 0.090 0545222 .1160375 Unexplained 0881809 826692 3.30 0358655 1404963 Based on these results, choose two of the following interpretations that are the least reasonable. a) On average, the hourly wage of men is approximately 17.3% higher than that of women. b) Under Specification 1, about 0.046 log points are due to average differences in education years between men and women. c) Under Specification 2, about 0.085 log points are due to average differences in education years between men and women. d) Under Specification 2, roughly half of the male-female wage gap is due to factors that are unexplained by observable productivity characteristics. e) The difference in the unexplained portion under Specification I and 2 implies that Specification 2 is the correct one that Rachel should use and thus, Rachel should interpret that the 0.088 log points difference in the male-female wage gap is due to labor market discrimination against women. Explain why the two arguments that you chose are flawed