Economics 696, Causal Inference and Program Evaluation
Problem Set 1: due Friday, Feb 10 (in my mail box)
1. Consider the data in Table 1. Assume they arose from a randomized experiment
in which an equal number of units were selected to be given the treat
Economics 696, Causal Inference and Program Evaluation
Lecture Note 9: Instrumental Variables and Control Functions
Based on Heckman (1979), Heckman and Robb (1985), and Newey, Powell, and Vella (1999).
Consider a conventional linear IV model, where the e
Economics 696, Causal Inference and Program Evaluation
Lecture Note 10: Imbens and Newey (2004)
Consider the following model:
T = h ( Z , ),
(1)
Y = g (T , ).
(2)
We interpret Y as the outcome, and T as the (observed) treatment.
The functions h and g are
Economics 696: Lecture Note 11
Partial Identication and Bounds
This is based on the Manski articles; the book Identication Problems in the Social Sciences is
also an excellent source for material on bounds.
Censored Data
Suppose that Y and X are variables
Economics 696, Causal Inference and Program Evaluation
Lecture Note 12: Estimation and Inference for Bounds
1. Estimation of the identied set
Lets continue with the problem of estimating the distribution of a variable subject to missing
data. As before, Y
Economics 696: Lecture Note 13
Differences-in-Differences
Example: Card (1990) Study of the Mariel Boatlift
Q: Do low-skilled immigrants displace low-skilled US citizens in the labor market?
Intervention: Mariel Boatlift, a large-scale migration of Cubans
Economics 696: Lecture Note 14
Regression Discontinuity Design
Examples:
Thistlewaite and Campbell (1960): scholarship and career choice
van der Klaauw (1997): nancial aid and enrollment in college
Angrist and Lavy (1997): class size and test scores
B
Economics 696: Lecture Note 15
Treatment Assignment as a Statistical Decision Problem
Note: this is based on Manski (2004); however, I have changed the notation considerably.
Basic Setup
We imagine a social planner who must assign an individual to one of
Economics 696, Causal Inference
Minipaper Project Instructions
Your minipaper should be a short, focused paper that applies the concepts and methods from
the course to a specic empirical problem.
You may choose the specic topic, and you are encouraged to
Economics 696, Causal Inference and Program Evaluation
Lecture Note 8: Instrumental Variables
1 Wald Estimator
Suppose we are interested in estimating the effect of a treatment T on an outcome Y ,
and we believe the treatment does not satisfy the random a
Economics 696, Causal Inference and Program Evaluation
Lecture Note 7: Multivalued Treatments, Unconfoundedness, and the Generalized Propensity
Score
Multivalued Treatments
Next, suppose that the treatment can take on more than two values:
T T = cfw_t 1 ,
Economics 696F, Causal Inference and Program Evaluation
Problem Set 2: due Friday, March 2 (revised 2/25/11)
1. Revisit the data in ps1b.txt and the setup in HW1, Question 3.
(a) Assume the propensity score has the form
P r (T = 1 | X = x ) =
exp(1 + x 2
Economics 696F, Causal Inference and Program Evaluation
Problem Set 3: due Monday, April 9
Note: you should be working on your mini paper as well.
1. Consider a binary treatment setup, with a binary outcome and binary covariate X . Assume
unconfoundedness
Economics 696F, Causal Inference and Program Evaluation
Lecture Note 1: Econometrics without Error Terms
Read articles: Holland (with discussion), Rubin 1974, Lalonde, Rosenbaum ch.2
T = some treatment
For simplicity, assume binary, so T = 0, 1. (We will
Economics 696F, Causal Inference and Program Evaluation
Lecture Note 2: Potential Outcomes and Randomized Experiments
1 Potential Outcomes Model
Recall: for units i = 1, . . . , n ,
Ti
= 0, 1 treatment
Yi (0) =
potential outcome under control
Yi (1) =
pot
Economics 696, Causal Inference and Program Evaluation
Lecture Note 3: Unconfounded Treatment Assignment and Regression Analysis
1 Causal Model and Unconfoundedness
Next we turn to observational studies, where treatment assignment is not under our control
Economics 696, Causal Inference and Program Evaluation
Lecture Note 4: The Propensity Score
We continue to make the unconfoundedness assumption, and focus on estimating the ATE and
the TT.
Note: in order to simplify the notation a bit, I will sometimes dr
Economics 696, Causal Inference and Program Evaluation
Lecture Note 5: Asymptotics for Weighting Estimators and Efciency of Estimated Weights
Asymptotics for Weighting Estimator
Consider the estimator
=
1 n Ti Yi
(1 Ti )Yi
.
n i =1 p ( X i ) 1 p ( X i )
F
Economics 696, Causal Inference and Program Evaluation
Lecture Note 6: Bootstrap
These notes are based on Politis, Romano, and Wolf (1999), Ch.1. See also Efron (1979) where the
bootstrap was rst introduced.
Sometimes, it is difcult to calculate variance