Idea Transcript
PAD 705: Research Methods II · R. Karl Rethemeyer Department of Public Administration and Policy · Rockefeller College of Public Affair & Policy University at Albany · State University of New York Midterm Exam—Spring 2005 March 14, 2005 Name: ID Number:
Please put ONLY your ID number on the blue books. Tear off this page and turn it in separately.
Exam Instructions. You will have 90 minutes to complete this exam. The number of points corresponds to the number of minutes you should spend on each problem. Work the problems in your blue books. Use one blue book for Part I of the exam and one blue book for Part II of the exam. Show all of your work and reasoning – partial credit will be awarded on all questions. If you have a lot of scratch-throughs or computations, please circle your answer. Work quickly and try not to leave any questions unanswered.
Note: Making reference to a Stata command is usually NOT a complete answer – though it may get you partial credit For full credit, you must explain conceptually why your choice of a particular command is correct. You MUST stop writing IMMEDIATELY when time is called. Five (5) points will be deducted for the first and second warning to stop writing. Continuing to write after two warnings constitutes exam misconduct and will result in a score of zero (0) for the exam. Good Luck!!
Background Sociologists have long been interested in the factors that determine who obtain a high prestige job. To identify major correlates of job prestige we have extracted 908 individuals from General Social Survey (GSS). The GSS is the longest running survey of social, cultural and political indicators available in the United States (a version is now also administered in Canada). For Part I of the exam the data are drawn from the 1988 sample only. The regression results referenced in this section are found in Table I; the data definitions are in Table II. The dependent variable is the respondent’s job prestige score. Job prestige scores range from 0 to 100 points and are based on a scoring system developed and validated independently by other researchers. Part I 1. (5 points) Using regression (11): Is the constant statistically significant? Be sure to write down the hypothesis you are testing and its alternative. 2. (5 points) Using regression (3): How many prestige points does a 30 year old gain when they turn 31, all else held constant? 3. (5 points) Using regression (11): Are black men likely to have a prestige score that is at least 9.5 points lower than white men, all else held constant? 4. (5 points) Using regression (11): Holding all else constant, does being female and black tend to increase, decrease, or leave unaffected one’s prestige score compared to the base case? If it increased or decreased, by how much? If left unaffected, explain how you reached that conclusion (preferably using statistical tests as well as words). 5. (5 points) A colleague decided to divide the sample into two parts: those who finished high-school and those who did not. Using model (8), the colleague found that those who DID finish high school had a mean squared error (MSE) of 11.878; those who DID NOT finish high school had an MSE of 9.591. What does this finding suggest about the results (i.e., the magnitude of the coefficients estimated and their standard errors) in regression (8)? 6.
(10 points) A colleague wants to add the following variables to your model: mothers education (maeduc), father’s education (paeduc) and spouse education (speduc). She also hands you the following output from Stata: . corr educ paeduc maeduc speduc (obs=532) | educ paeduc maeduc speduc -------------+-----------------------------------educ | 1.0000 paeduc | 0.3990 1.0000 maeduc | 0.4130 0.6501 1.0000 speduc | 0.5787 0.3857 0.4275 1.0000
The colleague states that this table conclusively demonstrates that all regressions in Table I are biased. Another colleague, while accepting that this may be true, is nonetheless not sure whether the variables should be added and also states that the evidence is not conclusive. Discuss the issues that this table presents for the regression models in Table I.
7. (5 points) Interpret the coefficient for obey in regression (8). Holding all other factors constant, how much larger or smaller is the job prestige score of a person who states that “obeying” is the most important item on the list as compared to a person who states that “obeying” is the least important item on the list? 8. (5 points) A colleague ran a version of regression (5) using a logarithmic transformation of both age and education. In other words, the regression equation was: prestigei = β0 + β1ln(age) + β2ln(educ) + εi The resulting regression had an adjusted R2 of 0.2336. Which specification is better: the one above or the original one in regression (5)? Justify your answer. Then draw a graph showing (a) the hypothesized relationship between prestige and education in regression (5) and (b) the hypothesized relationship between prestige and education in the equation above. 9. (10 points) Using regression (13): Does being black affect the dependent variable in this regression? Justify your answer. Part II For Part II, let’s assume that you have been commissioned to do seven follow-up “waves” of interviews with the respondents to the 1988 GSS. The waves are conducted every two years, so your data set now consists of responses from 1988 – 2002. There are a total of 7,264 observations. The variables are the same ones listed in Table I except that (a) a variable named Year has been added to identify the year in which the observation was collected and (b) a variable named ID has been added to identify the data rows that belong to the same respondent. 1. (10 points) Discuss what sort of issues must be addressed in order to generate the best, linear unbiased estimate of the relationship between job prestige and the variables in regression (14) using the 1988-2002 panel data. Which panel data correction technique is most appropriate in this case? Be sure to provide an explanation for your answer. 2. (5 points) Let’s assume that the fixed effects model is appropriate in this case. If you only had access to the regress command in Stata (in other words, you DO NOT have access to the xtreg commands), what data construction steps would be necessary to do a fixed-effects regression? Be as specific as possible; making reference to Stata commands may be helpful here (but not required).
Part III Another line of research suggests that there may be employer-related factors that cause some firms to add or subtract jobs with high prestige over time. To test this idea you have gotten company-wide average prestige scores from GE for the years 1954-2004. You then run a regression against these 60 observations using the following model (standard errors in parenthesis): prestigei = 28.456 + 0.503aget + 0.445compt - 2.79appliancest + 1.745Fint + εt (1.345) (0.020) (0.221) (1.125) (0.985)
DWstat = 1.332 where • • • • •
R2 = 0.867
prestige = average prestige of jobs at GE in year t age = average age of workers at GE in year t comp = millions of dollars of sales of computer software/hardware by GE in year t appliances = millions of dollars of sales of appliance sales by GE in year t Fin = millions of dollars of sales of financial services (loans, credit cards, etc.) sales by GE in year t
1. (5 points) Is there evidence that serial correlation is present in this regression? 2. (5 points) Let’s assume serial correlation is a problem in this regression. Provide at least two explanations for why serial correlation may occur. 3. (5 points) Again let’s assume that serial correlation is present in the regression. How might our results (i.e., estimated coefficients, standard errors, R2, DWstat) change after applying the Cochrane-Orcutt procedure? Can we assume that Cochrane-Orcutt will remove all serial correlation? 4. (5 points) Which variable is more important in determining the average prestige of jobs at GE: age or sales of computer software/hardware?
Table I: Job Prestige and Its Correlates DV: Job Prestige Score Standard errors in parenthesis constant age
(1) 43.395 (0.433)
(2) 42.935 (1.224) 0.01 (0.025)
age2
(3) 34.311 (3.471) 0.401 (0.15) -0.004 (0.001)
(4) 5.633 (3.354) 0.177 (0.128) -0.001 (0.001) 2.396 (0.131)
(5) 24.473 (5.465) 0.149 (0.127) -0.001 (0.001) -0.511 (0.682) 0.113 (0.026)
(6) 24.479 (5.469) 0.149 (0.127) -0.001 (0.001) -0.519 (0.687) 0.113 (0.026) 0.074 (0.746)
(7) 24.576 (5.459) 0.15 (0.127) -0.001 (0.001) -0.579 (0.687) 0.114 (0.026) 0.142 (0.745) 1.615 (0.791)
(8) 22.912 (5.500) 0.158 (0.127) -0.001 (0.001) -0.572 (0.685) 0.111 (0.026) 0.039 (0.745) 1.654 (0.789) 0.601 (0.274)
(9) 23.365 (5.534) 0.158 (0.127) -0.001 (0.001) -0.625 (0.689) 0.113 (0.026) 0.035 (0.745) 1.657 (0.789) 0.591 (0.274) -1.683 (2.200)
(10) 25.172 (5.529) 0.167 (0.126) -0.001 (0.001) -0.727 (0.686) 0.115 (0.026) 0.103 (0.741) 1.502 (0.786) 0.484 (0.275) -2.275 (2.195) -3.813 (1.143)
(11) 25.742 (5.518) 0.176 (0.126) -0.001 (0.001) -0.805 (0.684) 0.117 (0.026) -0.562 (0.786) 1.551 (0.784) 0.531 (0.275) -2.314 (2.188) -7.196 (1.776) 5.661 (2.28)
(12) 24.041 (5.775) 0.178 (0.126) -0.001 (0.001) -0.585 (0.719) 0.110 (0.027) -0.560 (0.786) 1.525 (0.785) 0.523 (0.275) -2.236 (2.19) -2.201 (5.303) 5.714 (2.280) -0.414 (0.414)
908
908
908
908
908
908
908
908
908
1217.6 152917 154135 0.0079 0.0057
42584.4 111551 154135 0.2763 0.2739
44864.7 109270 154135 0.2911 0.2879
44865.9 109269 154135 0.2911 0.2872
45369.6 108766 154135 0.2943 0.2897
45947.8 108187 154135 0.2981 0.2926
46018.1 108117 154135 0.2986 0.2923
47342.9 106792 154135 0.3072 0.3002
48072.0 106063 154135 0.3119 0.3042
educ educ2 female VHappy obey other black femblack blackeduc blackeduc2 908 908 N 0 27.6 Model SS 154135 154108 Residual SS 154135 154135 Total SS 2 0 0.0002 R 2 0 -0.0009 Adj R *Robust standard errors reported.
908
13 24.433 (5.972) 0.177 (0.126) -0.001 (0.001) -0.647 (0.758) 0.113 (0.029) -0.552 (0.787) 1.52 (0.786) 0.521 (0.275) -2.254 (2.192) -4.682 (10.94) 5.583 (2.337) 0.074 (1.924) -0.022 (0.084) 908
14* 24.433 (4.978) 0.177 (0.124) -0.001 (0.001) -0.647 (0.630) 0.113 (0.026) -0.552 (0.792) 1.52 (0.791) 0.521 (0.278) -2.254 (1.881) -4.682 (12.86) 5.583 (2.169) 0.074 (2.691) -0.022 (0.133) 908
48190.1 105945 154135 0.3126 0.3042
48198.0 105937 154135 0.3127 0.3035
48198.0 105937 154135 0.3127 0.3035
Variable age age2 educ educ2 female VHappy obey
other black femblack blackeduc blackeduc2
Definition Age of respondent Age squared of respondent Number of years of education completed by respondent Number of years of education completed by respondent squared 1= female 1 = very happy with life, 0 = somewhat happy or not happy 1 = of obeying authority, being popular, helping others, thinking for oneself, and working hard, obeying was the most important quality 2 = obeying was second most important quality 3 = obeying was third most important quality 4 = obeying was fourth most important quality 5 = obeying was the least important quality 1 = not white, not African-American 1 = African-American, not white 1 = if female and black black * educ (see definitions for black and educ) black * educ2 (see definitions for black and educ)