Economics 2557
Fall 2021
Exam II
加拿大经济代考 The Admissions Office of an unnamed college had a policy of not considering an applicant who scores below 500 on the verbal portion of the SAT exam.
Show all your work. Don’t panic! Good luck.
1.(6points) 加拿大经济代考
The Admissions Office of an unnamed college had a policy of not considering an applicant who scores below 500 on the verbal portion of the SAT exam. Suppose verbalscores of applicants are normally distributed with a mean of 550 and a standard deviationof 100. Because of declining enrollment in 2021, the administration lowered the cutoffscore to 450. If the college has 5,000 applicants for the class, how many more will be accepted because of the revised policy?
2.(10points)
The maximum patent life for a new drug is 17 years. Subtracting the length of time required for testing and approval of the drug by the Food and Drug Administration you obtain the actual patent life of the drug—that is, the length of time that a company has to recover research and development costs and make a profit. Suppose that the distribution of the length of actual patent life for new drugs is as shown below:
| Years | X | p(x) |
| 5 | .10 | |
| 6 | .12 | |
| 7 加拿大经济代考 | .12 | |
| 8 | .15 | |
| 9 | .10 | |
| 10 | .30 | |
| 11 | .08 | |
| 12 | .03 |
a.Findthe expected number of years of patent life for a new drug, E(X).
b.If R and D costs are such that it takes 8 years just to break even, what is the probability that a new drug will make a profit?
3.(10points) A believer in the “random walk” theory of stock markets thinks that an index of stock prices has a .65 probability of increasing in any year. 加拿大经济代考
Moreover, the change in the index in any given year is not influenced by whether it rose or fell in the earlier years. Let X be the number of years among the next 3 years in which the index
a.Whatare the possible values that X can take on?
b.Findthe probability of each value of X. Draw the probability distribution of X.
c.Whatis the mean and standard deviation of this distribution?
4.(10points) Economists Autor, Figlio, Karbownik, Roth, and Wasserman published a paper in 2019 in the journal American Economic Journal: 加拿大经济代考
Applied Economics in whichthey examine the gender gap in school performance. In a number of measures of schoolperformance, they show that boys do worse than girls. This much was already well known. But what these authors add to our understanding is that boys born to disadvantaged families (think low income) do even worse in various school/life outcomesthan girls born to disadvantaged families. Thus, gender and low income combined particularly disadvantage boys. 加拿大经济代考
I want you to think about the regression model they have run to come to this conclusion.Let the school performance measure be absence rate in grades 3 to 8. Use AB to denoteabsence rate. Assume we have data on AB and on the child’s age CHILDAGE, mother’sage MOMAGE, marital status of the child’s parents at the time of the child’s birthMOMMARRIED, the child’s gender BOY, and a continuous measure of parental income SES. The data comes from school records in Florida.
a.Writeout the structural model they have in mind.
b.If they are correct, what does this imply about the coefficients in this model. (You don’t have to write about all the coefficients, only those related to the hypothesis statedabove. You want to write about the signs of the key coefficients you included in your structural model)
c.Writeout the regression commands in Stata that they used to estimate their model assuming that the variables, AB, CHILDAGE, MOMAGE, MOMMARRIED, BOY and SES already exist with MOMMARRIED and BOY already coded as dummy variables.
Here is the result from their paper. Does their hypothesis appear to be correct? Write asentence or two bringing the result shown in this graph, slope -0.075, to life. In the figurethe y axis is the boy minus girl gap in school absences. SES is an index with an overall mean of 0 and a standard deviation of 1.51.
5.(6points) Joshua Angrist is one of this year’s winners of the Nobel Prize in economics.
In 2020 he, David Autor, and Amanda Pallais authored a research paper in which theystudy a true random experiment in which merit scholarships were given to a randomlyselected group of eligible students in Nebraska. Others in the group of eligible studentsdid not receive the scholarship. Eligibility to be in either the control group or thetreatment group was determined both by parental income level being low to moderate and the student having high enough ACT scores. 加拿大经济代考
The size of this one -time scholarship wassubstantial, about $8,200 for a student going from high school directly to college. Theauthors are interested in studying the effect that this scholarship money has on studentoutcomes. One of the student outcomes considered is staying in college. They found thatof all the students who were in the pool to receive money, but did not (the control group),80% are still in school in the spring of their junior year. Let’s think of this as thepopulation parameter of mINSCHOOL_3year. The researchers then report that among thescholarship recipients (the treatment group), 89% are still in school.
a.Assumingthat this statistic from the treatment group (89%) comes from a sample ofsize 100, what is the probability that we would observe a value of 89 or higher even if the true value was 80?
b.Actuallythe size of the treatment was much larger. What would be your answer to part a be if the sample size is 5625 (much closer to the number in the paper)?
6.(6points) All human blood can be “ABO-typed” as one of O, A, B, or AB, but the distribution of the types varies a bit among groups of people. Here is the distribution of blood types for a randomly chosen person in the United States:
| Blood type | O | A | B | AB |
| US probability | 0.45 | 0.40 | 0.11 | 0.04 |
Choose a married couple at random. It is reasonable to assume that the blood types of spouses are independent and follow this distribution.
a.Someonewith type B blood can safely receive transfusions only from persons with type B or type O blood. What is the probability that the spouse of a woman with type B blood is an acceptable blood donor for her?
b.Whatis the probability that spouses share the same blood type?
7.(8points) In the language of government statistics, you are “in the labor force” if you are available for work and either working or actively seeking work. 加拿大经济代考
The unemployment rate is the proportion of the labor force (not of the entire population) who are unemployed. Below are data from the Current Population Survey for the civilian population aged 25 years and over. The table entries are counts in thousands of people.
| Highest education | Total population | In the labor force | Employed |
| Did not finish high school | 27,325 | 12,073 | 11,139 |
| High school but no college | 57,221 | 36,855 | 35,137 |
| Less than BA | 45,471 | 33,331 | 31,975 |
| College grad | 47,371 | 37,281 | 36,259 |
a.Findthe unemployment rate for people with each level of education. Is the level of education independent of being employed? Explain.
b.Youknow that a person is employed. What is the conditional probability that he or she is a college graduate?
8.(6 points) Here are the means, standard deviations, and correlations for the monthly return from two Fidelity mutual funds for a 36 month period.
W=monthly return on Large Cap Fund mW=1.11% sW=4.64%
Y=monthly return on International Fund mY=1.59% sY=6.75%
ρWY=0.54 rWY is the population correlation coefficient ( like the r we learned about in sample statistics). 加拿大经济代考
a.Manyadvisers recommend using roughly 20% foreign stocks to diversity portfolios of US stocks. What is the expected return and standard deviation of a portfoliocontaining 80% Large Cap Fund (which includes only large US companies) and 20% International Fund?
What do you notice about the mean and standard deviation compared to the Large Cap Fund alone?
b.Recalculateyour answers to a if rWY=0. Does it seem reasonable to you that the ρWY would be zero?
9.(16points) Suppose we estimated the following wage equation for the U.S. in 2019 using all individuals between the ages of 25 and 65 with positive earnings and known usual hours worked per week and weeks worked per year. 加拿大经济代考
This is from the ACS data you used in problem set 3.
where lnwagei is hourly wage in dollars, educyrsi is years of education, agei is age measured in years. agesq is age squared, whitei is a dummy variable that is 1 for whitesand 0 for other races, femalei is a dummy variable that is 1 for women and 0 for men.
a.Writethe Stata commands that yielded these results if we began with a data set that contained only the following variables:
Annual earnings last year (incwage) Usual hours worked per week(uhrswork) Weeks worked last year (wkswork1) 加拿大经济代考
age educyrs
race (a categorical variable that took on a 1 if the person was white, 2 if the person was black and 3 if the person was any other race.
sex (a categorical variable that took on a 1 if the person was male and a 2 if the person was female)
b.Interpretthe coefficient on the two dummy variables.
c.Whatis the impact of increasing age by one year for a 30 year old? A 50 year old? Why are they different?
d.Whatwould be the predicted wage of a nonwhite male who is 20 years old and has a twelfth grade education. (Edi = 12)? Please give the answer is dollars, not ln(dollars).
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