APPLIED ECON 440.606 — Econometrics Midterm Exam

Problem 1 (25 Points)

In a Master’s Program in Applied Economics, a professor has observed the following final grade and attendance of his students in Microeconomics:

Considering this information, answer the following questions:

a)   Draw a graph to illustrate this relationship between Attendance (X) and Grade (Y). What kind of association (positive, negative, or neutral) do you find in the graph? Explain why (5 points).

b)   Show one formula (either matrix or sum) to obtain the linear relationship between grade and attendance. Then, calculate the intercept and the slope using the formula presented. Interpret your eventual answer (10 points).

c)   Show the formula for the R-square and calculate it using the formula proposed. How can you interpret this outcome? (5 points).

d)   If you are willing to take this course and you want to finish with a grade B+ (88 or 89), what should your attendance be? Interpret your result (5 points).

Problem 2 (25 Points)

A researcher is interested to understand what affects the time spent sleeping among students from the master’s program at John Hopkins University. She believes that sleeping time is a linear function of the total daily time spent working, individual’s age and individual’s weight. Having this information, please answer the following questions:

a)   If you write down the econometric specification for this investigation, provide at least one example of what could be in the error term (affects time spent sleeping but it is NOT one of these three variables and it is difficult to measure) (3 points).

b)   After running the regression with the referred variables, the estimated equation is

ŝleep = 2 − 0.3 totwoTk + 0.01age + 0.05weigℎt

Where the total  number of students in the sample  is 706. What  happens  if someone decides  to  work  one  extra  hour?  What  is  the  expected  sleeping  time  if  someone weights 98.4 kg, is 28 years old and works 4 hours daily? Interpret your answers (7 points).

c)   Among these 706 students, the average age is 25, average weight is 79 kg, and the average time spent sleeping is 8. Based on that, what can you say about the average time working? Interpret your answer (5 points).

d)   After collecting the data from the students, another researcher suggested to include the number of years of education, but she observed that all students have the same number of  years  studying.  Discuss  the  pros  and  cons  of  introducing  the  number  of  years  of education as an independent variable in this regression (10 points).

Problem 3 (25 Points)

A researcher collected Covid death rates across 300 municipalities in a particular country from 2021. He wants to understand whether the percentage of people vaccinated can explain the death rates, but he knows that other factors might also affect it. In summary, he has estimated the model and got the following outcome

deâtℎTate = 20 − 2 VaCPeTC + 3.2 RiSkPeTC + 4 0ldPeTC + 1.5 AtℎletPeTC

(4.5)        (0.5)                    (0.8)                   (1.2)                  (2.0)

Where deathrate is the percentage of people who died of covid, VacPerc is the percentage of people vaccinated,  RiskPerc  is the  percentage of people with  high  health  risk, OldPerc  is the percentage of people older than 60 and AthletPerc is the percentage of people who are athletes in the city. Based on this information (SE is below the estimated parameter), answer the following questions below.

a)   Evaluate whether all the parameters are statistically significant to explain the percentage of people who died of covid (Hint: do not forget to draw the graphs) . (10 points)

b)   If the researcher has used the number of deaths and the number of vaccinated people, both in logs, how would you interpret this new parameter estimated. (5 points)

c)   Someone says that you should eliminate any parameter that is not statistically significant. After doing that, your unrestricted model has SSR = 183 and R-squared = 0.6, while your restricted model has SSR = 198 and R-squared = 0.5. What do you conclude after doing an F-test for this? Why should (or should not) you compare the R-squared to decide to include or not the variables with non-significant parameters? (10 points)

Problem 4 (25 Points)

A  professor of  Economics wants to evaluate whether  he  has any gender  bias on grading the students as well as whether students perform worst when taking online courses. After collecting data from the last two years, he obtained the following outcome when regressing the grade on two dummies: gender (male=1, female=0), online (online=1, in-person=0).

ĝrade = 90  − 1. 98 gender − 13. 45 Online

(3.60)      (2.56)            (3.60)

n=178, R-squared = 0.07

a)   Based on the rule of thumb, how do you interpret this outcome? (5 points)

b)   Someone told this professor that he needs to consider the efforts made by his students. Then, this  professor decided to  run another  regression  including the grades from the Problem Sets and the Midterm. After adding these new variables, he found the following:

Interpret this new outcome  [gender, online, problem sets (ps), and mdexam (midterm exam grade)], stressing the differences that you have found in letter a. (10 points)

c)   He showed his outcome to a gender specialist, and this person said: “You should know that the  pandemic  has affected  much  more women than  men, so your outcome  might  be influenced  by the  grades  obtained  by woman  attending  in  person without  any  home obligation. Their performance might have offset the bad outcomes of those suffering doing their home tasks while attending your classes. Everyone knows that women perform much better  than  men  in  any  course  when  they  have  the  same  opportunities .”  Then,  this professor ran another regression creating other dummies for gender and online, and he found the following outcome.