PSM

Question 1

What is exact matching?

Answer 1

Comparing individuals for whom the values of x are identical

rarely an option in practice since it’s often difficult to find T and C groups with identical values

Question 2

What is the purpose of matching?

Answer 2

To reproduce the treatment group among the non-treated

Question 3

What two conditions must be met to implement matching estimators?

Answer 3

1. Conditional independence assumption (CIA): There exists a set x of observable covariates such that after controlling for these covariates, the potential outcomes are independent of T status
2. Common support assumption: For each value of x, there is a positive probability of being both treated and untreated (you can find a treated unit to match with an untreated unit)

Question 4

What is the CIA?

Answer 4

Conditional independence assumption (CIA): There exists a set x of observable covariates such that after controlling for these covariates, the potential outcomes are independent of T status

Question 5

What is common support assumption?

Answer 5

Common support assumption: For each value of x, there is a positive probability of being both treated and untreated (you can find a treated unit to match with an untreated unit)

Question 6

How is the CIA used to construct a counterfactual for the treatment group?

Answer 6

It implies that after controlling for x, the assignment of units to T is “as good as random”

Question 7

What assumption does the CIA require?

Answer 7

That all variables relevant to the probability of receiving treatment may be observed and included in x

Question 8

Why is PSM called a “data-hungry” method?

Answer 8

You need a lot of data for this method

Question 9

What is the propensity score?

Answer 9

The probability that a unit in the combined sample of treated and untreated units receives the T, given a set of observed variables

Question 10

What does the propensity score theorem say?

Answer 10

You only need to control for the probability of treatment, because if conditional on x, Ti and (Y1i, Y0i) are independent, then conditional on the propensity score p(xi), Ti and (Y1i, Y01) are independent

Question 11

What is the formula for the ATE conditional on propensity score?

Answer 11

ATE conditional on propensity score=E[Y1i-Y01|p(xi)]

Question 12

Three steps for estimating program impact using PSM?

Answer 12

1. Estimate propensity score
2. Choose matching algorithm
3. Estimates impact of intervention with matched sample

Question 13

True or false: Use flexible functional form to estimate propensity score

Answer 13

True–want to allow for possible nonlinearities in the participation model (i.e., include higher-order terms and interaction terms)

Question 14

With or without replacement-which is better?

Answer 14

Without replacement-can only be matched with one treated unit

Estimators are more stable if a number of comparison cases are considered for each treated case–ie usually should use replacement

Question 15

What is nearest neighbor matching?

Answer 15

Individual from comparison group with closest propensity score is chosen–note that this can be done with or without replacement

Question 16

What is radius matching?

Answer 16

Specify a caliper (maximum propensity score difference)

Question 17

Implication for bias and variance of reducing caliper?

Answer 17

Reduces the bias

Increases variance

Question 18

How do you implement kernel method?

Answer 18

Choose a kernel function, specify bandwidth parameter

Compare each treated unit to a weighted average of the outcomes of all untreated units, with higher weights placed on untreated units with scores closer to that of treated individual

Question 19

Implications for bias and efficiency of choosing only one neighbor for nearest neighbor matching?

Answer 19

Minimize bias by using most similar observation

Ignore information–>reduced efficiency

Question 20

Conventional method for calculating standard errors from PSM estimates?

Answer 20

Bootstrapping-sample from analysis sample with replacement, and replicate multiple times

Question 21

You need to be sure that measures to generate PSM score are not confounded with outcomes or anticipation of treatment–what types of measures should you use?

Answer 21

• stable over time or
• deterministic (ie age) or
• measured before participation

Question 22

How to check specification of your model re CIA?

Answer 22

balancing tests (does the estimated propensity score adequately balance characteristics between T and C group units?)

Question 23

How to check specification of your model re common support?

Answer 23

• visual inspection of densities of propensity scores
• comparison test such as Kolmogrov-Smirnov
• are there big differences between maxima and minima of density distributions?

Question 24

What are we doing when we use propensity score to calculate ATT?

Answer 24

For each propensity score, we calculate the difference in mean outcomes for the treated and untreated with that p(X)

We then take a weighted average of these over the different propensity score values

Question 25

Two advantages of PSM over regression that controls for x?

Answer 25

1. Matching does not require assumptions about functional form (eg linear relationship)
2. Regression runs risk of extrapolating onto a space where there is little common support

Question 26

5 requirements for covariate selection

Answer 26

1. Choose x’s so that unconfoundedness holds
2. Should be correlated with treatment (Di) and outcome
3. Selection should be based on theory
4. x’s should be measured before treatment and not affected by it
5. x;s should not be too good at predicting treatment–we are relying on common support

Question 27

Implications for bias and standard errors of implementing nearest neighbor with replacement?

Answer 27

better matches–> possibly less bias

higher standard errors

Question 28

Implications for bias and standard errors of implementing nearest neighbor without replacement?

Answer 28

worse matches–>possibly more bias

lower standard errors

Question 29

Why would NN matching without replacement lead to lower standard errors?

Answer 29

Using more variation

Question 30

Formula for propensity score matching estimator for ATT?

Answer 30

E[Y(1)|D=1, P(x)] - E[Y(0)|D=0, P(x)]

(treated-untreated)–note that the second term subs in for the unobserved term that we really want to know, which is E[Y(0)|D=1, P(x)]

Question 31

stratification and interval matching

Answer 31

Paritions the common support into intervals (strata) and then calculates mean differences within these strata