Selection on Observables

Question 1

assignment mechanism

Answer 1

the mechanism by which individuals came to receive the
treatment they actually received.

Question 2

problem with RCTS

Answer 2

expensive, unfeasible and unethical

Question 3

assumption behind assignment mechanism of selection on observables

Answer 3

that assignment to treatment
was based on observables.

Question 4

selection on observables

Answer 4

the treatment is randomly assigned within each stratum of X

Question 5

what is the ‘random’ part of SOO mean?

Answer 5

within strata defined by X, the remaining variation in the treatment D is
completely random and hence the process that generates this remaining variation is
labeled “ignorable.”

Question 6

equation

Answer 6

τAT E =
Sum of E[Y | X, D = 1] − E[Y | X, D = 0] x dP(X)

Question 7

what does treatment have to be

Answer 7

probabilistic - not that some certainly do and some certainly do not receive treatment

Question 8

Is SOO controlling on observables?

Answer 8

NO! Selection on observables does not just mean “controlling” for
observable stuff! It only works if we condition on ALL variables that we KNOW
cause the treatment

Question 9

Three covariates for SOO

Answer 9

• Subclassification
• Matching
• Regression

Question 10

Subclassification

Answer 10

Construct weighted averages of these differences in means estimates using
▶ the proportion of units in each bin to recover the ATE
▶ the proportion of treated units in each bin to recover the ATT
▶ the proportion of untreated units in each bin to recover the ATC

Question 11

SOO regressions

Answer 11

▶ The interpretation of βs changes slightly in the multivariate setting.
▶ Bivariate setting: Y = β0 + β1X1 + u
▶ In the bivariate setting, we interpret β1 as the average change in Y for a one unit
change in X1
▶ Multivariate setting: Y = β0 + β1X1 + β2X2 + u
▶ In the multivariate setting we interpret β1 as the average change in Y for a one unit
change in X1 holding X2 constant.
▶ Holding Xi constant means that we fix the value of Xi to a certain value such as 0 or
the mean of Xi
, etc.

Question 12

Matching

Answer 12

Fill in missing potential outcomes using the observed outcomes of units that resemble
treated and/or untreated units on key covariates.
▶ Match treated units to untreated units with the same characteristics to estimate τAT T .
▶ Match untreated units to treated units with the same characteristics to estimate τAT C.

Question 13

Can also match on more than one variable - need a distance metric

Answer 13

Can be done through a propensity score