ECOM114 Applied Econometrics (Applied Microeconomics) 2020
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ECOM114 Applied Econometrics (Applied Microeconomics)
2020
SECTION A – This section is worth 30 marks in total and consists of 3 questions. Each question is worth 10 marks. Answer ALL questions from this section. Be as formal as possible in all your answers.
1. [10 marks] Regression Discontinuity Design
a. Formally discuss the assumptions that allow a researcher to identify the Local Average Treatment Effect on the Treated using a sharp Regression Discontinuity design (RDD).
b. What additional assumption is needed to identify the Local Average Treatment Effect? Explain using intuition and algebra.
2. [10 marks] Treatment effects
a. Formally define Average Treatment Effect (ATE) and Average Treatment Effect on the Treated (ATT).
b. “With homogenous returns to treatment, ATE and ATT are identical.” Is this statement true or false? Explain.
c. Assume that on average in the population the treatment has a positive effect on outcomes. If agents with higher returns to treatment select into treatment, do you expect the ATT to be larger or smaller than the ATE?
3. [10 marks] Local average Treatment effect
Consider the case when we are interested in the effect of a binary treatment variable D on an outcome variable Y. Suppose that the researcher uses an instrumental variable approach that leverages on variation in D induced by a binary instrument Z.
In practice the researcher runs the following regression:
Yi=a + bDi + ei
where D is instrumented by Z. Assume heterogeneous returns to treatment. Formally discuss the assumptions under which the instrumental variable estimate of bidentifies the Local Average Treatment Effect (LATE) among the compliers. Provide intuition.
SECTION B: This section is worth 40 marks in total and consists of one question. Answer this question. Be as formal as possible in all your answers.
B1. [40 marks] Randomized experiments
Consider a randomised experiment. Z is the variable that is randomly assigned (i.e. " = 1 . if the individual i is randomly assigned to the treatment) while D is the treatment of interest (i.e. " = 1 if the individual i took the treatment). Denote with '(" the potential outcome for an individual if " = 0 (i.e. if she had not been randomly assigned to the treatment), and with * the potential outcome if " = 1 (i.e. if she had been randomly assigned to the treatment). Similarly, denote with '" the potential outcome for an individual if " = 0 (i.e. if she had not been treated), and with *" the potential outcome if " = 1 (i.e. if she had been treated).
a. [10 marks] Formally define the Intention to Treat effect (ITT).
b. [10 marks] Which parameter is identified by the ITT under “perfect compliance”? Explain with algebra.
c. [10 marks] Assume one sided compliance. Consider following Wald estimator:
(" |" = 1) − (" |" = 0)
(" = 1|" = 1)
What parameter does this ratio identify?
d. [10 marks] In the paper entitled “The (perceived) returns to education and the demand for schooling”, The Quarterly Journal of Economics, 2010, which we examined during the lectures, Jensen studies the effect of the perceived returns to education on educational choices. Based on his experimental design and data, he can identify the effect of being assigned to an information campaign regarding the actual returns on subsequent education choices. Is this parameter an ITT, an ATE or ATT? Explain, if possible using formulas.
SECTION C: This section is worth 30 marks and includes two questions. Answer ONLY ONE question from this section. Be as formal as possible in all your answers.
Question C1 – Electoral success and incumbency advantage [30 marks]
In his paper entitled “Randomized experiments from non-random selection in US house elections”, Journal of Econometrics, 2008, that was discussed during the course, Lee estimates the causal effect of incumbency on the probability of winning the next election.
a. [8 marks] Explain the fundamental problem of causal inference in this setting.
b. [8 marks] Describe the RDD approach followed by Lee and how it allows to circumvent the fundamental problem of causal inference described in point a.
c. [8 marks] Discuss the results in column (1) of Table 1 in the Appendix below. What do you learn about the causal effect of incumbency on later electoral outcomes?
d. [6 marks] What do you learn from column (8) of that Table?
Question C2 – Returns to education [30 marks]
Imagine you want to estimate the causal impact of schooling on wages when individual ability is unobserved.
a. [8 marks] Explain the fundamental problem of causal inference in this setting.
b. [8 marks] Describe the solution to this problem proposed by Angrist and Krueger in their paper “Does compulsory school attendance affect schooling and earnings?” Quarterly Journal of Economics (1991). Under what conditions the estimation method proposed by Angrist and Krueger (1991) is valid? Are such conditions testable?
c. [6 marks] How would you expect the OLS and IV estimates for the returns to education to differ – given the problem outlined in point (a)?
d. [8 marks] Look at the results in Table 2 in the Appendix below and comment on the difference between OLS and IV estimates. How can you reconcile such difference with the problem outlined in point (a)?
2022-05-05