ECOM30002/90002 ECONOMETRICS 2

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ECOM30002/90002 ECONOMETRICS 2

SEMESTER 2, 2021

ASSIGNMENT 1

Information and instructions

● This assignment contributes 7.5% to the overall assessment. There are 15 questions, each worth 5 marks.

● An assignment can be submitted individually or by a group of up to four students. Students form their own groups. Members of a group need not be enrolled in the same tutorial. All group members will receive the same mark for the assignment.

● Assignment groups must be registered through LMS by Tuesday, 9am, 17 August (students working individually need not register). Assignments have to be submitted electronically via LMS. Further instructions for group registration and assignment submission to follow.

● List all group members and their student ID number on the first page.

● Assignments must be submitted as a Portable Document File (pdf). Assignments should not exceed 600 words in total. Be short, precise and clear in your answers. Do not present unnecessary graphs, tables or numbers, and do not discuss irrelevant matters. However, show your work and intuition: marks are given for explanations and not just for having the correct answer. Give precise numerical answers when possible and explain what units your answers are in. Raw R output or screenshots are not acceptable. Regression output must be presented in clearly labelled equation or table form.

● Extension Policy

Late assignments will not be accepted. Students with a genuine and documented reason for not completing an assignment, such as illness, can apply for special consideration to have the marks for that assignment re-weighted to the exam.

Special Consideration

Students who have been significantly affected by illness or other serious circumstances during the semester may be eligible to apply for Special Consideration. The following website contains detailed information relating to who can apply for Special Consideration and the process for making an application: http://students.unimelb.edu.au/admin/special

Section 1

Consider the following causal model that links an individual i’s years of schooling (s = 10, 11, . . . , 20) to that individual’s life expectancy at 40 years for (Ysi):

Ysi = fi(s) = 65 + s + Ui.

1. If the model is true, is it possible for someone with 10 years of education to live to the age of 80? Explain.

2. If the model is true, what is the effect of an additional year of education on life expectancy for an individual with s=12? What about for s=16? Can there be a difference between the average treatment effect and the average treatment effect on the treated in this model? Explain.

3. Based on the causal model, we can write the observed outcome (Yi) for actual years of schooling (Si) as

Yi = 65 + Si + Ui.

Consider this statement: “Because (2) is based on the true causal model (1), it holds that Cov(Si , Ui)=0.” True or false? Explain.

4. A researcher collects data on life expectancy, schooling and income, and runs the regression of life expectancy on schooling and income. Can you see an argument against including income in the regression in this case? Explain.

Section 2

In the U.S., black students obtain lower scores on school exams, and are less likely to graduate from high school and attend college. Differences in school exam scores are observed as early as at age 8 years. Differences in school performance may be due to (i) black children being less able on a genetic basis (i.e., at birth), (ii) due to poorer parental care and assistance, or (iii) due to black children being enrolled in lower quality schools.

        To understand if black children are less able genetically, researchers collected information on the mental ability of infants aged 8 to 12 months. These infants were tested by specialists on a range of mental abilities, and each infant was given a score of overall mental ability on a range of zero to 100.

        If differences in mental ability are observed across races at such an early age, it suggests that there may be potential genetic differences in ability. If not, it suggests that other environmental factors during childhood (parents and schools) are the main cause of early differences in school performance.

        The file infants.csv contains information on a sample of 4,321 infants who were tested for mental ability when aged 8 to 12 months. These tests were undertaken between 1959 and 1965 as part of the US Collaborative Perinatal Project (CPP). The table below contains a description of the variables included in infants.csv.

Reference

RG Fryer, SD Levitt (2013), “Testing for Racial Differences in the Mental Ability of Young Children,” American Economic Review, 103(2), 981–1005.

Consider the following short and long regression models:

where Xi = (siblingsi , age_motheri , birth_weighti , age_childi)' and  is a conformable vector of coefficients.

5. Provide a table called “descriptive statistics" with means, standard deviations, minima and maxima of the variables in the data set.

6. What is the relation between  and ?

7. Estimate regressions (3) and (4). Using the estimated coefficients and those from any nec-essary auxiliary regressions show that the relation you gave in question 6 holds for the estimated coefficients, too.

8. Interpret the estimated  and .

9. Do the results support the hypothesis that black infants’ scores are lower due to genetic differences? Explain.

Section 3

Angrist (1990) studied the effect of Vietnam-era military service on the earnings of veterans. He used the Wald estimator, β = [E(Yi|Zi = 1) − E(Yi|Zi = 0)]/[E(Xi|Zi = 1) − E(Xi|Zi = 0)], to estimate the causal effect of military service on earnings using the draft lottery as an instrument for military service. The draft lottery was used to determine priority in conscription: In each year 1970-1972, every 19-year-old man in the U.S. was randomly assigned a lottery number. Men with numbers below a cutoff value were eligible for the draft (i.e. they could be forced to serve in the army). In practice, many draft-eligible men were still exempted from service, while many men who were draft-exempt nevertheless volunteered.

        This table presents some statistics from the data on white men born in 1951 used by the study:

Reference

JD Angrist (1990), “Lifetime earnings and the Vietnam era draft lottery: evidence from social security administrative records,” American Economic Review, 80(3), 313–336.

10. Replace Yi, Xi, Zi by appropriate variable names for this study and write down the equation for (i) the causal model, (ii) the first stage model, (iii) the reduced form model.

11. Why is OLS estimation of the causal model problematic? Give a specific example.

12. Calculate the reduced form effect from the table and interpret it.

13. What is the exogeneity assumption for the instrument here? Do you think the instrument satisfies it?

14. Calculate the first stage effect and interpret it.

15. Calculate the causal effect and interpret it.