drdid_imp_rc1 is used to compute the doubly robust estimators for the ATT in difference-in-differences (DiD) setups with stationary repeated cross-sectional data. The resulting estimator is also doubly robust for inference, though it is not locally efficient; see Section 3.2 of Sant'Anna and Zhao (2020).

drdid_imp_rc1(
y,
post,
D,
covariates,
i.weights = NULL,
boot = FALSE,
boot.type = "weighted",
nboot = NULL,
inffunc = FALSE
)

Arguments

y

An $$n$$ x $$1$$ vector of outcomes from the both pre and post-treatment periods.

post

An $$n$$ x $$1$$ vector of Post-Treatment dummies (post = 1 if observation belongs to post-treatment period, and post = 0 if observation belongs to pre-treatment period.)

D

An $$n$$ x $$1$$ vector of Group indicators (=1 if observation is treated in the post-treatment, =0 otherwise).

covariates

An $$n$$ x $$k$$ matrix of covariates to be used in the propensity score and regression estimation. If covariates = NULL, this leads to an unconditional DID estimator.

i.weights

An $$n$$ x $$1$$ vector of weights to be used. If NULL, then every observation has the same weights.

boot

Logical argument to whether bootstrap should be used for inference. Default is FALSE.

boot.type

Type of bootstrap to be performed (not relevant if boot = FALSE). Options are "weighted" and "multiplier". If boot = TRUE, default is "weighted".

nboot

Number of bootstrap repetitions (not relevant if boot = FALSE). Default is 999.

inffunc

Logical argument to whether influence function should be returned. Default is FALSE.

Value

A list containing the following components:

ATT

The DR DID point estimate

se

The DR DID standard error

uci

Estimate of the upper bound of a 95% CI for the ATT

lci

Estimate of the lower bound of a 95% CI for the ATT

boots

All Bootstrap draws of the ATT, in case bootstrap was used to conduct inference. Default is NULL

ps.flag

Convergence Flag for the propensity score estimation: =0 if trust algorithm converged, =1 if IPW algorithm converged (in case it was used), =2 if GLM logit estimator was used (i.e., if both trust and IPT did not converged).

att.inf.func

Estimate of the influence function. Default is NULL

call.param

The matched call.

argu

Some arguments used (explicitly or not) in the call (panel = FALSE, estMethod = "imp2", boot, boot.type, nboot, type="dr")

Details

The drdid_imp_rc1 function implements the doubly robust difference-in-differences (DID) estimator for the average treatment effect on the treated (ATT) defined in equation (3.3) in Sant'Anna and Zhao (2020). This estimator makes use of a logistic propensity score model for the probability of being in the treated group, and of (separate) linear regression models for the outcome among the comparison units in both pre and post-treatment time periods. Importantly, this estimator is not locally efficient for the ATT.

The nuisance parameters (propensity score and outcome regression parameters) are estimated using the methods described in Sections 3.2 of Sant'Anna and Zhao (2020). In short, the propensity score parameters are estimated using the inverse probability tilting estimator proposed by Graham, Pinto and Pinto (2012), and the outcome regression coefficients are estimated using weighted least squares,where the weights depend on the propensity score estimates; see Sant'Anna and Zhao (2020) for details.

The resulting estimator is not only doubly robust for the ATT, but it is also doubly robust for inference. However, we stress that it is not locally efficient; see Sant'Anna and Zhao (2020) for details.

References

Graham, Bryan, Pinto, Cristine, and Egel, Daniel (2012), "Inverse Probability Tilting for Moment Condition Models with Missing Data." Review of Economic Studies, vol. 79 (3), pp. 1053-1079, doi:10.1093/restud/rdr047

Sant'Anna, Pedro H. C. and Zhao, Jun. (2020), "Doubly Robust Difference-in-Differences Estimators." Journal of Econometrics, Vol. 219 (1), pp. 101-122, doi:10.1016/j.jeconom.2020.06.003

Examples

# use the simulated data provided in the package
covX = as.matrix(sim_rc[,5:8])
# Implement the improved DR DID estimator (but not locally efficient!)
drdid_imp_rc1(y = sim_rc$y, post = sim_rc$post, D = sim_rc$d, covariates= covX) #> Call: #> drdid_imp_rc1(y = sim_rc$y, post = sim_rc$post, D = sim_rc$d,
#>     covariates = covX)
#> ------------------------------------------------------------------
#>  Further improved DR (but not locally efficient) DID estimator for the ATT:
#>
#>    ATT     Std. Error  t value    Pr(>|t|)  [95% Conf. Interval]
#>  -3.6837     3.1145    -1.1828     0.2369    -9.7881     2.4207
#> ------------------------------------------------------------------
#>  Estimator based on (stationary) repeated cross-sections data.
#>  Outcome regression est. method: weighted least squares.
#>  Propensity score est. method: inverse prob. tilting.
#>  Analytical standard error.
#> ------------------------------------------------------------------
#>  See Sant'Anna and Zhao (2020) for details.