Podcast
Questions and Answers
What is the Conditional Independence Assumption (CIA) in the context of causal inference?
What is the Conditional Independence Assumption (CIA) in the context of causal inference?
Y0i, Y1i ⊥ D | Xi, meaning that potential outcomes are independent of treatment status D given the covariates X
What is the goal of pruning in the context of regression adjustment?
What is the goal of pruning in the context of regression adjustment?
To remove control units without similar treatment units, ensuring common support
How is the average treatment effect estimated in regression adjustment?
How is the average treatment effect estimated in regression adjustment?
As a weighted average of cell-specific causal effects
What is the difference between the Average Treatment Effect (ATE) and the Average Treatment Effect on the Treated (ATET)?
What is the difference between the Average Treatment Effect (ATE) and the Average Treatment Effect on the Treated (ATET)?
What is the purpose of subclassification in the context of causal inference?
What is the purpose of subclassification in the context of causal inference?
How are the predictions obtained in the regression Y = α + τD + βX + U?
How are the predictions obtained in the regression Y = α + τD + βX + U?
What is the role of covariates X in the regression adjustment approach?
What is the role of covariates X in the regression adjustment approach?
What is the intuition behind the running example with two covariates, X1 and X2?
What is the intuition behind the running example with two covariates, X1 and X2?
What is the estimate of Ï„j when j is equal to 0, given the provided estimates?
What is the estimate of Ï„j when j is equal to 0, given the provided estimates?
How is the variable x3 defined in the running example?
How is the variable x3 defined in the running example?
What is the resulting subclassification estimate of ATT in the running example?
What is the resulting subclassification estimate of ATT in the running example?
What is the difference between Ï„ATT and Ï„ATE?
What is the difference between Ï„ATT and Ï„ATE?
How are the weights for estimating ATE obtained in the running example?
How are the weights for estimating ATE obtained in the running example?
What is the resulting subclassification estimate of ATE in the running example?
What is the resulting subclassification estimate of ATE in the running example?
What is an alternative approach to estimating the treatment effect, aside from subclassification?
What is an alternative approach to estimating the treatment effect, aside from subclassification?
What is the general form of the regression equation for estimating the treatment effect?
What is the general form of the regression equation for estimating the treatment effect?
What assumption allows us to eliminate selection bias after conditioning on $X$, enabling the estimation of the treatment effect on the treated?
What assumption allows us to eliminate selection bias after conditioning on $X$, enabling the estimation of the treatment effect on the treated?
What is the formula for the average treatment effect on the treated ($Ï„AT T$) in the discrete-only covariate setting?
What is the formula for the average treatment effect on the treated ($Ï„AT T$) in the discrete-only covariate setting?
What is the name of the estimator used to calculate $Ï„AT T$ in the discrete-only covariate setting?
What is the name of the estimator used to calculate $Ï„AT T$ in the discrete-only covariate setting?
What is the purpose of iterating expectations over $X$ in the estimation of $Ï„AT T$?
What is the purpose of iterating expectations over $X$ in the estimation of $Ï„AT T$?
What is the role of $E[Y0i |Xi , Di = 1]$ in the estimation of $Ï„AT T$?
What is the role of $E[Y0i |Xi , Di = 1]$ in the estimation of $Ï„AT T$?
How is the weighted average of $X$-specific differences in $Y$ calculated in the subclassification estimator?
How is the weighted average of $X$-specific differences in $Y$ calculated in the subclassification estimator?
What is the main advantage of using regression adjustment in estimating the treatment effect?
What is the main advantage of using regression adjustment in estimating the treatment effect?
What is the purpose of running separate regressions for each possible value of $X$ in the subclassification estimator?
What is the purpose of running separate regressions for each possible value of $X$ in the subclassification estimator?
What is the purpose of weights w(X) in regression adjustment, and what property do they have?
What is the purpose of weights w(X) in regression adjustment, and what property do they have?
What is the formula to compute AT E using regression adjustment?
What is the formula to compute AT E using regression adjustment?
What is the difference between AT E and AT T in regression adjustment?
What is the difference between AT E and AT T in regression adjustment?
How can you identify both AT E and AT T using regression adjustment?
How can you identify both AT E and AT T using regression adjustment?
What is the purpose of regression adjustment in causal inference?
What is the purpose of regression adjustment in causal inference?
What is the relationship between the least squares regression coefficients and the average treatment effect (AT E)?
What is the relationship between the least squares regression coefficients and the average treatment effect (AT E)?
What is the role of subclassification in regression adjustment?
What is the role of subclassification in regression adjustment?
How does the teffects command in Stata implement regression adjustment?
How does the teffects command in Stata implement regression adjustment?
What is the primary goal of subclassification and matching strategies in causal analysis?
What is the primary goal of subclassification and matching strategies in causal analysis?
What is the conditional independence assumption (CIA) in the context of causal analysis?
What is the conditional independence assumption (CIA) in the context of causal analysis?
What is the purpose of matching in causal analysis, besides generating data for regression analysis?
What is the purpose of matching in causal analysis, besides generating data for regression analysis?
Why is the average treatment effect on the treated (AT T) not equal to the average treatment effect (AT E) in a matching analysis?
Why is the average treatment effect on the treated (AT T) not equal to the average treatment effect (AT E) in a matching analysis?
What is the common support problem in matching, as illustrated in the scatterplot example?
What is the common support problem in matching, as illustrated in the scatterplot example?
What is the purpose of regression adjustment in causal analysis?
What is the purpose of regression adjustment in causal analysis?
What is the role of the propensity score in causal analysis?
What is the role of the propensity score in causal analysis?
What is the advantage of using subclassification and matching strategies together?
What is the advantage of using subclassification and matching strategies together?
Study Notes
Subclassification and Matching
- Subclassification and matching are strategies to control for selection bias, motivated by the conditional independence assumption (CIA).
- CIA states that, within each cell defined by the values of X, treatment is as good as randomly assigned, i.e., no selection effect.
Introduction to Matching
- Matching is a data cleaning process before regression analysis, also known as pruning or pre-processing.
- Matching can be used to generate data that can be analyzed as if it is the result of a randomized experiment, without the need for regression.
- However, in the original non-experimental sample, the covariates are not balanced, and treatment and control groups differ in their characteristics.
Purposes of Matching
- One purpose is to prune the data, removing control units for which there are no similar treatment units.
- Another purpose is to use matching to generate data that can be analyzed as if it is the result of a randomized experiment.
Subclassification and Regression
- Subclassification is a method to do causal analysis in subgroups and aggregate.
- The subclassification estimator (or exact matching estimator) is a weighted average of X-specific differences in Y using the empirical distribution of X among the treated.
Identification under CIA
- The selection bias disappears after conditioning on X, so the treatment effect on the treated can be obtained by iterating expectations over X.
- The treatment effect on the treated (AT T) can be written as the weighted average of X-specific differences in Y.
Average Treatment Effect on the Treated (AT T)
- In the discrete-only covariate setting, AT T can be written as a weighted average of X-specific differences in Y using the empirical distribution of X among the treated.
- The subclassification estimator is a weighted average of X-specific differences in Y using the empirical distribution of X among the treated.
Unconditional Average Treatment Effect (AT E)
- AT E is the average treatment effect for the entire population, whereas AT T is the average effect for the treated.
- The unconditional average treatment effect (AT E) can be written as the expectation of the X-specific differences in Y using the marginal distribution of X.
Running a Regression
- Running a regression of Y on D, X, and their interactions does not identify AT E or AT T unless the effect is constant.
- The least squares regression coefficients do not identify AT E or AT T, and the weights chosen by OLS have no meaningful intuition.
Identifying AT E and AT T with Regression
- One way to identify both AT E and AT T with regression is to:
- Regress Y on X separately in the treatment and control groups.
- Predict YÌ‚1 and YÌ‚0 for each observation.
- Compute AT E and AT T using these predictions.
Regression with teffects
- The teffects command in Stata can be used to implement regression adjustment to identify AT E and AT T.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Related Documents
Description
Learn about subclasses and matching strategies to control for selection bias in data analysis, including the conditional independence assumption (CIA).
