Date: Presenter: Ryan Chen

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Presentation transcript:

Date: 2017.06.27 Presenter: Ryan Chen Treatment effect Date: 2017.06.27 Presenter: Ryan Chen

REF: Introduction to treatment effects in Stata®: Part 1

REF: Introduction to treatment effects in Stata®: Part 1

REF: Introduction to treatment effects in Stata®: Part 1

REF: Introduction to treatment effects in Stata®: Part 1

Treatment-effects estimators: RA: Regression adjustment IPW: Inverse probability weighting IPWRA: Inverse probability weighting with regression adjustment AIPW: Augmented inverse probability weighting NNM: Nearest-neighbor matching PSM: Propensity-score matching REF: Introduction to treatment effects in Stata®: Part 1

Treatment-effects estimators: RA: Regression adjustment IPW: Inverse probability weighting IPWRA: Inverse probability weighting with regression adjustment AIPW: Augmented inverse probability weighting NNM: Nearest-neighbor matching PSM: Propensity-score matching REF: Introduction to treatment effects in Stata®: Part 1

REF: Introduction to treatment effects in Stata®: Part 1

Regression adjustment REF: Introduction to treatment effects in Stata®: Part 1

The counterfactual outcomes are called unobserved potential outcomes. “How would the outcomes have changed had the mothers who smoked chosen not to smoke? “ The counterfactual outcomes are called unobserved potential outcomes. REF: Introduction to treatment effects in Stata®: Part 1

REF: Introduction to treatment effects in Stata®: Part 1

REF: Introduction to treatment effects in Stata®: Part 1

Prepare your dataset.

Which one would you like to estimate? Potential-outcome means (POMs) Average treatment effect (ATE) on the treated (ATET) Syntax examples: teffects ra (bweight mage) (mbsmoke), pomeans teffects ra (bweight mage) (mbsmoke), ate teffects ra (bweight mage) (mbsmoke), atet

Data webuse cattaneo2.dta, clear (Excerpt from Cattaneo (2010) Journal of Econometrics 155: 138-154) To estimate the potential-outcome means (POMs), we type teffects ra (bweight mage) (mbsmoke), pomeans REF: Introduction to treatment effects in Stata®: Part 1

To estimate the average treatment effect (ATE), we type teffects ra (bweight mage) (mbsmoke), ate REF: Introduction to treatment effects in Stata®: Part 1

IPW: The inverse probability weighting estimator REF: Introduction to treatment effects in Stata®: Part 1

“We wish we had more upper-age green points and lower-age red points.” Some researchers prefer to model the treatment assignment process and not specify a model for the outcome. “We wish we had more upper-age green points and lower-age red points.” REF: Introduction to treatment effects in Stata®: Part 1

weight smokers in the lower-age range and nonsmokers in the upper-age range more heavily, and weight smokers in the upper-age range and nonsmokers in the lower-age range less heavily. REF: Introduction to treatment effects in Stata®: Part 1

We will fit a probit or logit model of the form Pr(woman smokes) = F(a + b*age) REF: Introduction to treatment effects in Stata®: Part 1

use probabilities to weight prediction Pr(woman smokes) for each observation in the data on smokers by 1/pi so that weights will be large when the probability of being a smoker is small. on nonsmokers by 1/(1-pi) so that weights will be large when the probability of being a nonsmoker is small.

The first set of parentheses specifies the outcome model. The second set of parentheses specifies the treatment model, which includes the outcome variable (mbsmoke) followed by covariates (in this case, just mage) and the kind of model (probit). REF: Introduction to treatment effects in Stata®: Part 1

IPWRA: Inverse probability weighting with regression adjustment

RA estimators model the outcome to account for the nonrandom treatment assignment. IPW estimators model the treatment to account for the nonrandom treatment assignment. IPWRA estimators model both the outcome and the treatment to account for the nonrandom treatment assignment IPWRA uses IPW weights to estimate corrected regression coefficients that are subsequently used to perform regression adjustment

The outcome model will include mage: the mother’s age prenatal1: an indicator for prenatal visit during the first trimester mmarried: an indicator for marital status of the mother fbaby: an indicator for being first born The treatment model will include all the covariates of the outcome model mage^2 medu: years of maternal education We will also specify the aequations option to report the coefficients of the outcome and treatment models.

(continue) The OME0 and OME1 sections display the RA coefficients for the untreated and treated groups, respectively. The TME1 section of the output displays the coefficients for the probit treatment model. Just as in the two previous cases, if we wanted the ATE with standard errors, etc., we would specify the ate option. If we wanted ATET, we would specify the atet option.

AIPW: The augmented IPW estimator

AIPW IPWRA estimators model both the outcome and the treatment to account for the nonrandom treatment assignment. So do AIPW estimators. The AIPW estimator adds a bias-correction term to the IPW estimator. If the treatment model is correctly specified, the bias-correction term is 0 and the model is reduced to the IPW estimator. If the treatment model is misspecified but the outcome model is correctly specified, the bias-correction term corrects the estimator. Thus, the bias-correction term gives the AIPW estimator the same double-robust property as the IPWRA estimator.

The ATE is 3172.366 – 3403.355 = -230.989.