MATCHING METHODS
Matching covariates treated control groups
to make them
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two types 1 outcome not available Matching followup
cost saving
2 outcome Available Matching I bias
treatment
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outcome values not used in MAKING
Can be done multiple times and most
balanced
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4 key steps for Marlena
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Implementing it
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SUTVA: Stable Unit Treatment Value Assumption. Outcome of one individual is not a ected by
treatment assignment of another individual.
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defined
Effects of causes us
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Improving water quality and its impact on hospitilization. SUTVA violation because
Hand Washing Practices to Reduce the risk of getting diarrhea.
SUTVA isnt the worst thing. Just a better design. Explicitly incorporate that into your research design.
Use an interaction term or smth to that nature.
E ects of Causes vs Causes of E ects (Next lecture)
Intro to Matching:
Non-Experimental Research Design.
Example: What is the e ect of a windmill on farmland values. Nick Pates, Mark.
Windmill are not randomly assigned across states
Using a Matching Estimator: Why?
Matching Estimator usually makes sense when there are a lot more potential control units/observations
than treatment units/observations.
You only want the controls that are similar to the treatment cases.
In Economics: You have a better chance of nding a good match.
Other good thing about matching is: Permits pre-outcome analysis.
Balance Table in RCT:
We have the treatment and control Means:
List all the covariates and their means. In RCTs you want them both to be similar to one another.
With pre outcome analysis, you can select a sample and construct a balance table. And just look if
both look similar.
RCTs assess balance in covariate means between treatment and control units/groups
Matching estimators require us to assess likeness of covariate distribution between treatment and
control.
Show a balance table. in RCTs
Matching show a table but show p-value/t-test
xx
k
Same mean but di erent distribution.
k
Examples of Matching Estimators:
1. Exact Matching on X1, X2, X3 .. Xn
2. One to One Matching based on a distance metric
3. 1 to n matching based on a distance metric
Distance Metric: Euclidean Distance. Pick the variable, say age, pick the groups that are closest in age.
Can also de ne them in terms of age and experience.
Propensity Score Matching can also do this
Mahalanobis Distance: Takes into account weights which down-weights potential control units when
distance is farther in one or more dimensions.
1 to n: Composite control unit. Becomes like a weighted average.
Control
treats
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Economic Signi cance: Subject/real world signi cance
Statistical Signi cance: *** p-value
Homework: bysort miss: sum names of variables that you want to summarize
will not include summarize that has a missing value*
another way: sum apgar if miss == 1
sum apgar if miss == 0
For variables you observe, compare the characteristics of missing values vs non-missing values.
Just generate a summary stats table for which you have observations on all the participants. Compare
the characteristics.
*** Approach for assessing a paper/ writing a referee report: Prepare and structure
• Provide a summary
• Note to self:
• Main empirical objective
• E ective defense of research design
• E ective implementation entation of research design
• Presentation of results
• Writing quality
Comments on Introduction, motivation, research design, results
Summary: Impact of remittances on Welfare in a particular region of Nepal
Dataset size?
Main objective: Causal impact of remittances on welfare
ATE, ATOT.
ALWAYS DO PRE OUTCOME ANALYSIS WHEN DOING MATCHING/PROPENSITY SCORE
Dont start a sub section with a table. Always start with text before a table.
If two samples are not the same, then we can assume that they are going to be di erent across
unobservables which we can not control for thereby leading OLS to be biased.
Laxmi's Paper:
Objective
Pre outcome analysis: Highlights that we are trying to approximate an experiment (i.e an RCT)
Unconfoundedness Assumption:
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Assumption:
variation
error term of the second equation is unrelated to the error term of the mDi
rst equation.
if this were not hold, then there is something in treatment group that is making them getting the
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treatment.
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That something will go to the error term of the rst equation.
2nd Assumption in the imbens paper: Overlap Assumption
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Overlap assumption
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Treatment group has prob from 0.2 to 1
Control group has prob from 0 to 1
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The predicted probabilities are gonna lie between 0 and 1
ATE, ATT, ATC
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Lhs is an estimate of the probability of being in treatment based on observable characteristics
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The Ols estimator is called the linear probability model
Discussion of LPM:
Di Rot Fini t É
prob Diii
Gedn y
Because LPM generates negative or greater than 1 probabilities, we often prefer to estimate the
propensity score using a logit or probit estimator (both of which arex non-linear estimator).
Predicted probability is not going to vary linearly with the covariates.
propensity score is just a predicted probability (can use both linear and non-linear probability models)
Matching: To recover causal e ects. Embedded within the procedure is a predictive objective.
time
Prediction excercise: We don't care about the right hand side of the equation. Or biasedness. All we
care about is do we get predictive values that are close to the true value.
NOA models to predict hurricanes.
If linear model gives better prediction,
How to assess Balance:
to look at the treatment and control group for all the covariates:
pairwise comparison
2nd way: Look at each one of covariates and their distribution
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