A sex discrimination suit alleges that a small college discriminated against women faculty in terms of salaries. A regression study considers the following variables: • Salary (base salary per year (thousands of dollars)) • Senior (seniority at the college (number of years working at the college)) • Gender = 1 for men; 0 for women • Doctorate = 1 for holders of doctorate degree; 0 for others • Rank There are four levels of \"rank\": full professors, associate professors, assistant professors, and instructors. Therefore, there are three indicator variables in the model defined as follows: ? RankD1 = 1 for full professors; 0 for others ? RankD2 = 1 for associate professors; 0 for others ? RankD3 = 1 for assistant professors; 0 for others Below is part of the regression output. Use the output to answer the questions that follow. Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 18.6784 1.3788 2e-16 Senior 0.5420 0.0762 2e-16 Gender 1.2074 0.0649 0.2685 RankD1 8.7779 1.9380 0.0002 RankD2 4.4211 1.7797 0.0207 RankD3 2.7165 1.4239 0.0690 Doctorate 0.9225 1.2589 0.4711 LP 15 WS Question 1 Homework • Unanswered THREE POINTS Write the least-squares regression equation. Define all terms in the equation. (Think about the \"rank\" variable and the fact that it has four categories.)
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I ran an OLS regression on a dataset in Stata using the following variables: Dependent Variable: hourlywage Hourly wage in dollars Independent Variables: bsdegree Does employee have a bachelor’s degree, Yes = 1 female Gender of employee. Female = 1 age Age in years . reg hourlywage bsdegree female age Source | SS df MS Number of obs = 7,440 -------------+---------------------------------- F(3, 7436) = 544.49 Model | 153004.257 3 51001.4191 Prob > F = 0.0000 Residual | 696510.725 7,436 93.6673917 R-squared = 0.1801 -------------+---------------------------------- Adj R-squared = 0.1798 Total | 849514.982 7,439 114.19747 Root MSE = 9.6782 ------------------------------------------------------------------------------ hourlywage | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- bsdegree | 8.318628 .227385 36.58 0.000 7.872889 8.764367 female | -3.810305 .2295979 -16.60 0.000 -4.260382 -3.360228 age | .510286 .0395206 12.91 0.000 .4328144 .5877576 _cons | 1.866198 1.187604 1.57 0.116 -.4618427 4.194238 ------------------------------------------------------------------------------ 4. Interpret the coefficients for statistically significant variables. Be precise. Do not use the word ‐‐units‐‐. 5. I wanted to know if there is a differential effect on hourly wage of having a bachelor’s degree for females vs males. My estimated equation follows: (HINT: Don’t forget about the intercept) hourlywage = ‐0.31 + 8.31(bsdegree) + 1.34(female) + 0.58(age) ‐ 3.73(fem_bsdegree) (se) (1.55) (.227) (2.382) (0.052) (0.081) a. How did I test for this? Be specific. b. Is there a differential effect of having a bachelor’s degree on hourly wage for males vs females? How do you know? c. What is the marginal effect of a bachelor’s degree for males? For females? What is the difference? HINT: ∂y/∂x d. What is the marginal effect of being female on hourly wage? HINT: ∂y/∂x e. What is the estimated hourly wage of a 40 year old male in this dataset without a bachelor’s degree? Show your work. f. What is the estimated hourly wage of a 40 year old male in this dataset with a bachelor’s degree? Show your work. g. What is the estimated hourly wage of a 40 year old female in this dataset without a bachelor’s degree? Show your work. h. What is the estimated hourly wage of a 40 year old female in this dataset with a bachelor’s degree? Show your work.
Sri K.
PART A: Consider the following model of wage determination: wage = β0 + β1educ + β2exper + β3married + ε where: wage = hourly earnings in dollars educ = years of education exper = years of experience married = dummy equal to 1 if married, 0 otherwise Using data from the file ps2.dta, which contains wage data for a number of workers from across the United States, estimate the model shown above by OLS using the regress command in Stata. As always, be sure to include your Stata output (show the regression command used and the complete regression output). Why are we unable to determine which of the included variables is the most important determinant of wages by simply looking at the size (and perhaps significance) of the estimated coefficients (even if we were confident that these estimates reflected unbiased causal impacts)? PART B: Estimate the model again in Stata, but now include the "beta" option and explain how the additional information provided helps to provide insight into this issue discussed in part (c). As part of your answer, provide a clear interpretation of the new Stata output corresponding to the educ variable.
Dominador T.
E6.2 (a) Run a regression of years of completed education (ED) on distance to the nearest college (Dist). What is the estimated slope? (b) Run a regression of ED on Dist, but include some additional regressors to control for characteristics of the student, the student’s family, and the local labor market. In particular, include as additional regressors Bytest, Female, Black, Hispanic, Incomehi, Ownhome, DadColl, Cue80, and Stwmfg80. What is the estimated effect of Dist on ED? (c) Is the estimated effect of Dist on ED in the regression in (b) substantively different from the regression in (a)? Based on this, does the regression in (a) seem to suffer from important omitted variable bias? (d) Compare the fit of the regression in (a) and (b) using the regression standard errors. Why are the standard errors so similar in regression (b)? (e) The value of the coefficient on DadColl is positive. What does this coefficient measure? (f) Explain why Cue80 and Stwmfg80 appear in the regression. Are the signs of their estimated coefficients (+ or -) what you would have believed? Interpret the magnitudes of these coefficients. (g) Bob is a black male. His high school was 20 miles from the nearest college. His base-year composite test score (Bytest) was 58. His family income in 1980 was $26,000, and his family owned a home. His mother attended college, but his father did not. The unemployment rate in his county was 7.5%, and the state average manufacturing hourly wage was $9.75. Predict Bob’s years of completed schooling using the regression in (b). (h) Jim has the same characteristics as Bob except that his high school was 40 miles from the nearest college. Predict Jim’s years of completed schooling using the regression in (b). Data: Documentation for CollegeDistance Data These data are taken from the High School and Beyond survey conducted by the Department of Education in 1980, with a follow-up in 1986. The survey included students from approximately 1100 high schools. The data used here were supplied by Professor Cecilia Rouse of Princeton University and were used in her paper "Democratization or Diversion? The Effect of Community Colleges on Educational Attainment," Journal of Business and Economic Statistics, April 1995, Vol. 12, No. 2, pp 217-224. The data in CollegeDistance exclude students in the western states. The data in CollegeDistanceWest includes only those students in the western states. Series in Data Set Name Description ed Years of Education Completed (See below) female 1 = Female/0 = Male black 1 = Black/0 = Not-Black Hispanic 1 = Hispanic/0 = Not-Hispanic bytest Base Year Composite Test Score. (These are achievement tests given to high school seniors in the sample) dadcoll 1 = Father is a College Graduate/ 0 = Father is not a College Graduate momcoll 1 = Mother is a College Graduate/ 0 = Mother is not a College Graduate incomehi 1 = Family Income > $25,000 per year/ 0 = Income ≤ $25,000 per year. ownhome 1 = Family Owns Home / 0 = Family Does not Own Home urban 1 = School in Urban Area / 0 = School not in Urban Area cue80 County Unemployment rate in 1980 stwmfg80 State Hourly Wage in Manufacturing in 1980 dist Distance from 4yr College in 10's of miles tuition Avg. State 4yr College Tuition in $1000's Years of Education: Rouse computed years of education by assigning 12 years to all members of the senior class. Each additional year of secondary education counted as one year. Students with vocational degrees were assigned 13 years, AA degrees were assigned 14 years, BA degrees were assigned 16 years, those with some graduate education were assigned 17 years, and those with a graduate degree were assigned 18 years.
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