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# 1. Use the data in WAGE'I for this problem. (a) Use OLS to estimate the equation log (wage) = o + leduc + 32 exper + rgwxper'2 + u and report the

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1. Use the data in WAGE‘I for this problem. (a) Use OLS to estimate the equation
log (wage) = ﬁo + ﬁleduc + 32 exper + ﬁrgwxper'2 + u and report the results using the usual format.
(b) Is experz statistically signiﬁcant at the 1% level?
(c) Using the approximation %AWE§E % 100(32 + 23gexper)Aexper, ﬁnd the approximate return to the ﬁfth year of experiencel. What is the approximate return to
the twentieth2 year of experience? Put a 95% conﬁdence interval around the predicted returns
at both the ﬁfth and twentieth year of experience. (d) At what value of exper does additional experience actually lower predicted log(wage)? How
many people have more experience in this sample? Hint: Check problem 4d in PS5.

2. Use the data in VOTE1 for this exercise, which contains data on election outcomes and campaign
expenditures for 173 two-party races for the US. House of Representatives in 1988. Let voteA be the
percentage of the votes received by candidate A, expendA and expendB the campaign expenditures
by candidate A and B respectively, and partystrA is a measure of party strength for Candidate A (the
percentage of the most recent presidential vote that went to A’s party). (a) Consider a model with an interaction between expenditures:
voteA = [30 + ﬁ1pﬂystrA + ﬁgexpendA + ﬁg expendB + ﬁ4expendA X expendB + at What is the partial effect of expendB on voteB, holding pnystrA and expendA ﬁxed? What is the
partial effect of expendA on voteA? Is the expected sign for [34 obvious? 1That is, going from 4 years to 5 years.
2Again, this is going from 19 to 20 years. ECO 321 2 of3 (b) Estimate the equation in part (a) and report the results in the usual form. Is the interaction
term statistically signiﬁcant? (c) Find the average of expend/l in the sample. Fix expend/i at 300 (for \$300,000). What is the
estimated effect of another \$100,000 spent by Candidate B on voteA? Is this a large effect? (d) Now ﬁx expendB at \$100. What is the estimated effect of Aexpend = 100 on voteA? Does this
make sense? Estimate a 99% conﬁdence interval around the predicted change on vote/l. (e) Now, estimate a model that replaces the interaction with shareA, candidate A’s percentage share
of total campaign expenditures. Report the results in the usual form. Does it make sense to

(e) Now, estlmate a model that replaces the mteractlon w1tn snareA, candidate A 5 percentage share
of total campaign expenditures. Report the results in the usual form. Does it make sense to
hold both expend/1 and expendB ﬁxed, while changing shareA? How would you interpret the coefﬁcient on shareA? Hint: Notice that shareA = 100% so when you change, say expendA, shareA also moves, and similarly when you change expendB. (f) In the model from part (6), ﬁnd the partial effect of expendB on voteA, holding prtystrA and
expendA ﬁxed. Evaluate this at expendA = 300 and expendB = 0 and compute a 95 conﬁ- dence interval around this partial effect. Comment on the results. Hint: Notice that shareA = 100 W, so when computing the partial effect3 of expendB you will need to take this into account. (g) Now consider the following speciﬁcation of the model voteA = 3/0 + ylprtystTA + y; log(expendA) + y310g(expendB) + u. What is the interpretation of 3/2? (h) In tenns of the parameters, state the null hypothesis that a 1% increase in A’s expenditures is
offset by a 1% increase in B’s expenditures. (i) Estimate the model and report the results in the usual fonn. Do A’s expenditures affect the
outcome? What about 3’5 expenditures? (j) Test the hypothesis from part (2h) using a two—sided alternative at the 5% and 1% conﬁdence
levels. What do you conclude? (k) Which model between (2a) and (2g) do you prefer? Please give sensible arguments when an—
swering this question.

3. The data set N BASAL contains salary information and career statistics for 269 players in the National
Basketball Association (NBA). (a) Estimate a model relating points-per—game (points) to years in the league (exper), age, and years
played in college (coll). Include a quadratic in exper; the other variables should appear in level
form. Report the results in the usual way. (b) Holding college years and age ﬁxed, at what value of experience does the next year of experi-
ence actually reduce points-per—game? Does this makes sense? (c) Why do you think call has a negative and statistically signiﬁcant coefﬁcient? (Hint: NBA players
can be drafted before ﬁnishing their college careers and even directly out of high school.4) (d) Add a quadratic in age to the equation. Is it needed? What does this appear to imply about the
effects of age, once experience and education are controlled for? 3Partial effect means partial derivative.
4Like was the case for Kobe Bryant. ECO 321 3 of3 (e) Now regress log(wage) on points, exper, experz, age and call. Report the results in the usual
format. (f) Test whether age and call are jointly signiﬁcant in the regression from part (Be). What does
this imply about whether age and education have separate effects on wage, once productivity
and seniority are accounted for?

4. What is the effect of physical attractiveness on wage? Hamermesh and Biddle (1994)5 used measures
of physical attractiveness in a wage equation. In this exercise you will use the ﬁle BEAUTY which
contains a subset of the variables (but more usable observations) reported by Hamermesh and Biddle
(1994). Each person in the sample was ranked by an interviewer for physical attractiveness, using
ﬁve categories (homely, quite plain, average, good looking, and strikingly beautiful or handsome).
Because there are so few people at the two extremes, the authors put people into one of three groups
for the analysis: average, below average and above average, where the base group is average. (3) Using the data pooled for men and women, estimate the equation log(wage) = ﬁg + )9 1belavg + ﬁzabvavg + ﬁg female + ﬁ4educ + I35 exper + ﬁ5 expert2 and report the results in the usual way. Are any of the coeﬁ'icients surprising in either their
signs or magnitudes? Is the coefﬁcient on female practically large and statistically signiﬁcant? (b) Explain in words what the hypothesis H0 : ﬂl = 0 against Ha : [31 &lt; 0 means and ﬁnd the
p—value. (c) Add interactions of female with all other explanatory variables in the equation from part (4a)
(ﬁve interactions in all). Compute the F—test of joint signiﬁcance of the ﬁve interactions. What
do you conclude? (d) In the full model with interactions, determine whether those involving the looks variables— femalex belavg and femalexabvavg—are jointly signiﬁcant. Are their coeﬂicients practically
small? (e) Is there convincing evidence that women with above average looks earn more than women with average looks? Explain.

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