ECON7310: Elements of Econometrics
Final Problem Set
Fu Ouyang
June 5, 2023
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Instruction
Answer all questions following a similar format of the answers to your tutorial questions. When
you use R to conduct empirical analysis, you should show your R script(s) and outputs (e.g.,
screenshots for commands, tables, and figures, etc.). You will lose 2 points whenever you fail
to provide R commands and outputs. When you are asked to explain or discuss something,
your response should be brief and compact. To facilitate tutors’ grading work, please clearly
label all your answers. You should upload your answers (in PDF or Word format) via the
“Turnitin” submission link (in the “Final Problem Set” folder under “Assessment”) by 11:59
AM on the due date June 8, 2023. Do not hand in a hard copy. You are allowed to work on this
assignment in groups; that is, you can discuss how to answer these questions with your group
members. However, this is not a group assignment, which means that you must answer all the
questions in your own words and submit your report separately. The marking system will check
the similarity, and UQ’s student integrity and misconduct policies on plagiarism apply.
1. MLR: Sharp RDD (30 points)
The sharp regression discontinuity design (RDD) occurs when the treatment is determined by
a threshold function of X, e.g., D = 1[X ≥ c].1 In most applications, the threshold c is
determined by policy or rule. The covariate X which determines the treatment is typically
called the running variable. The threshold c is often called the cut-off.
Ludwig and Miller (2007)2 used a sharp RDD to evaluate a U.S. federal anti-poverty program
called Head Start (HS). HS was established in 1965 to provide preschool, health, and other
social services to poor children aged three to five and their families. HS funding was awarded to
local municipalities through a competitive grant application. Due to a worry that poor regions
may not apply at the same rate as well-funded regions, during the spring of 1965, the federal
government provided grant-writing assistance (GWA) to the 300 poorest counties in the United
States.
where Y = mort age59 related postHS and X = povrate60. In all the questions below, use
observations satisfying X ∈ [c − 13.8,c + 13.8].
(a) (8 points) Estimate the treatment effect of GWA using model (1) (3 points). Is the
treatment effect statistically significant (2 points). Interpret your result (3 points).
(b) (6 points) RDD estimation is sensitive to the misspecification of the regression function. If
the true regression function is nonlinear in X, then model (1) may mistake the nonlinearity
at X = c for “discontinuity” (i.e., treatment effect) at X = c, leading to biased RDD
estimate of the treatment effect. Add X2 to model (1) and estimate the treatment effect
of GWA (3 points). Test the nonlinearity of the regression function (3 points).
(c) (10 points) Extend model (1) so that the new model allows the regression functions for
treatment and control groups to have different slope coefficients on X (4 points). Estimate
the treatment effect of GWA (3 points) and test if the slope coefficient varies across
treatment and control groups (3 points). Hint: Be careful. Your extended model should
still have the treatment effect at X = c measured by β1.
(d) (6 points) One of your classmates thinks model (1) (and the two extended models studied
in (b) and (c)) may suffer from the omitted variable bias (OVB). She argues that many
other factors, such as income, can affect mortality rate Y and are correlated with X but
are not included in model (1). She suggests adding the county-level Black population
percentage and the county-level urban population percentage to the regression as control
variables, as these variables can be viewed as proxies for income. The addition of these
control variables can help mitigate possible OVB. Do you agree with her (2 point)? Explain
your answer (4 points).
2. IV Regression: Fuzzy RDD (20 points)
The sharp regression discontinuity requires that the cut-off perfectly separates treatment and
control groups. An alternative context is where this separation is imperfect, but the conditional
probability of treatment is discontinuous at the cut-off. This is called fuzzy regression discon-
tinuity. This question asks you to estimate the following fuzzy RDD model using a simulated
data regdisc.csv:
