ECO220Y1 Midterm: ECO220Y1Y UTSG Term Test 220 5 APR18 Solution
ECO220Y1Y, Term Test #5, Prof. Murdock: SOLUTIONS
April 5, 2018, 9:10 – 11:00 am
(1) (a) Answering requires using Specification (2) in Table 1 because we are simply asked for the mean salary of full
professors, regardless of sex. As the reference (omitted) category is full professor, the constant term reveals that the
mean salary of full professors is $182,036.
(b) Regression (3) controls for job title whereas Regression (1) does not. Job title is clearly related to salary and must also
be related to sex – female faculty tend to be in lower ranked positions – such that once we control for it, more than half
of the salary difference by sex disappears: males are still paid more on average, but once we hold job title constant, the
sex-based discrepancy lessens. (Note: For the purposes of interpretation, remember that job title is a single categorical
variable. While we use a suite of dummy variables to include a categorical variable with multiple categories, remember
that these categories are mutually exclusive (aka disjoint).)
(c) From the formula sheets, we plug into: ±/ with degrees of freedom =−−1. The degrees of freedom
are = 1,067−5−1 = 1,061 and referencing the Student table we use 3.300 (to be conservative rather than using
3.291, which is for infinite degrees of freedom). Hence, we obtain 0.0403±3.300∗0.0108, which gives a lower
confidence limit of 0.005 and an upper confidence limit of 0.076.
We are 99.9% confident that after controlling for job title, male faculty members on average have salaries that are
between 0.5 percent to 7.6 percent higher than female faculty members. (Note: It is not correct to talk about
percentage point differences because salaries are measured in dollars. We only talk about percentage points when
talking about changes in something that is itself measured as a percent.)
(d) It would be 12,335.2 in Regression (1) and 0.0822 in Regression (4).
(e) The much higher in Regression (2) of 0.4513 means that about 45% of the variation in salaries of these faculty
members can be explained by variation in their job title. In contrast, the much lower in Regression (1) of 0.0260
means that only 2.6% of the salary variation can be explained by variation in the sex of the faculty member. In other
words, job title is much better predictor of salary than sex is (which is not surprising).
(f) There are zero female Clinical Lecturers. We can tell because the predicted salary of a female Clinical Lecturer is
$135,800 (=(177.3490 – 41.5487)*1000) and there are no dots there in the provided diagnostic plot.
(g) The value 1198.11625 is the variance of salary when we include the president and the square root of it is the
standard deviation of salaries, which is $34,614. It would be smaller for Regression (3) because that regression excludes
the president – a clear outlier with the highest salary – and hence the variance (and s.d.) of salaries would be smaller
without this extreme value.
(h) Answering requires using Regression (8). Since we included a dummy for the president, the regression will exactly
predict his salary, which is $400,000 = (177.349 + 5.831735 + 216.8193)*1000.
(i) : =0 versus : ≠0, which tests if there is statistically significant difference in the mean salaries of clinical
lecturers compared to full professors after controlling for sex (aka holding sex fixed). (You do not have to say anything
about the president dummy because that effectively eliminates the president: notice that the coefficient estimates and
standard errors are exactly the same in Regressions (3) and (8).)
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Document Summary
April 5, 2018, 9:10 11:00 am (1) (a) answering requires using specification (2) in table 1 because we are simply asked for the mean salary of full professors, regardless of sex. As the reference (omitted) category is full professor, the constant term reveals that the mean salary of full professors is ,036. (b) regression (3) controls for job title whereas regression (1) does not. While we use a suite of dummy variables to include a categorical variable with multiple categories, remember that these categories are mutually exclusive (aka disjoint). ) (c) from the formula sheets, we plug into: (cid:1854)(cid:3037) (cid:1872)(cid:3080)/(cid:2870)(cid:1871)(cid:3029)(cid:3285) with degrees of freedom (cid:2021)=(cid:1866) (cid:1863) 1. The degrees of freedom are (cid:1874)=1,067 5 1=1,061 and referencing the student (cid:1872) table we use 3. 300 (to be conservative rather than using. 3. 291, which is for infinite degrees of freedom). Hence, we obtain 0. 0403 3. 300 0. 0108, which gives a lower confidence limit of 0. 005 and an upper confidence limit of 0. 076.
