Final Exam-100 points
DS-UA 201
Causal Inference
Instructor: Parijat Dube
August 15, 2023
Wi1 by considering the scenario in which all non-blue-collar voters in precinct i vote for the Nazis.
Express this value as a function of Xi and Yi. Similarly, what is the largest possible value for Wi1
? Calculate these bounds, keeping in mind that the value for Wi1 cannot be negative or greate
than 1. Finally, compute the bounds for the nationwide proportion of blue-collar voters who voted
for the Nazis (i.e., combining the blue-collar voters from all precincts by computing their weighted
average based on the number of blue-collar voters). Give a
ief substantive interpretation of the
esults.
Problem 5 (20 points)
In this problem we are interested in the question of whether an extra year of education causes
increased wages. We will use wage2.csv data used in the following paper:
M. Blackburn and D. Neumark (1992), Unobserved Ability, E�ciency Wages, and Interindustry
Wage Di↵erentials, Quarterly Journal of Economics 107, XXXXXXXXXXhttps:
doi.org/10.3386/w3857
This dataset includes a bunch of di↵erent variables. These are the variables we care about for this
question:
Variable name Description
wage Monthly wage (1980 dollars)
educ Years of education
feduc Years of education for fathe
meduc Years of education for mothe
Question A (4 points)
1. (2 points) First create a naive model of the relationship between years of education and
wage, by treating wage as a dependent variable. What is the e↵ect of education on wage as
predicted by the model?
2. (2 points) Does this naive model co
ectly estimates the e↵ect of education on wages? Why
or why not?
Question B (6 points)
We next want to apply 2SLS (two-stage least squares) approach to account for unobservable con-
founders. For this we need to identify an instrument variable (IV). Remember, for an instrument
to be valid, it should meet these criteria:
1. Relevance: Instrument is co
elated with policy variable
2. Exclusion: Instrument is co
elated with outcome only through the policy variable
3. Exogeneity: Instrument isn’t co
elated with anything else in the model (i.e. omitted variables)
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https:
doi.org/10.3386/w3857
Final Exam-100 points
DS-UA 201
Causal Inference
Instructor: Parijat Dube
August 15, 2023
We have two choices for the instrument variable: years of education of father and years of education
of mother. Select one of them and show using the data that it satisfies all the three criteria to be
an instrument variable.
Question C (5 points)
Using the IV identified in Question B, you will next perform 2SLS manually.
1. (2 points) In the first stage, predict education using the IV.
2. (3 points) In the second stage, use the predicted education to estimate the exogenous e↵ect of
education on wages. What is the causal e↵ect of education on wage using this 2SLS analysis?
Question D (5 points)
Now using iv robust() perform 2SLS in a single step.
1. (2 points) Compare the exogenous e↵ect of education on wages predicted by the manual 2SLS
from Question C with the e↵ect obtained using iv robust(). Are they same or di↵erent?
2. (3 points) Next compare the standard e
ors of the e↵ect estimate from the two approaches.
Which approach co
ectly estimates the standard e
or and why?
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