drdid_imp_panel is used to compute the locally efficient doubly robust estimators for the ATT in difference-in-differences (DiD) setups with panel data. The resulting estimator is also doubly robust for inference; see Section 3.1 of Sant'Anna and Zhao (2020).

drdid_imp_panel(
y1,
y0,
D,
covariates,
i.weights = NULL,
boot = FALSE,
boot.type = "weighted",
nboot = NULL,
inffunc = FALSE
)

## Arguments

y1

An $$n$$ x $$1$$ vector of outcomes from the post-treatment period.

y0

An $$n$$ x $$1$$ vector of outcomes from the 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 DID point estimate.

se

The DID standard error.

uci

The upper bound of the 95% CI for the ATT.

lci

The lower bound of the 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 = TRUE, estMethod = "imp", boot, boot.type, nboot, type="dr")

## Details

The drdid_imp_panel function implements the locally efficient doubly robust difference-in-differences (DID) estimator for the average treatment effect on the treated (ATT) defined in equation (3.1) 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 a linear regression model for the outcome evolution among the comparison units.

The nuisance parameters (propensity score and outcome regression parameters) are estimated using the methods described in Sections 3.1 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 locally efficient and doubly robust for the ATT, but it is also doubly robust for inference; 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

# Form the Lalonde sample with CPS comparison group
eval_lalonde_cps <- subset(nsw, nsw$treated == 0 | nsw$sample == 2)
# Further reduce sample to speed example
set.seed(123)
unit_random <- sample(1:nrow(eval_lalonde_cps), 5000)
eval_lalonde_cps <- eval_lalonde_cps[unit_random,]
# Select some covariates
covX = as.matrix(cbind(eval_lalonde_cps$age, eval_lalonde_cps$educ,
eval_lalonde_cps$black, eval_lalonde_cps$married,
eval_lalonde_cps$nodegree, eval_lalonde_cps$hisp,
eval_lalonde_cps$re74)) # Implement improved DR locally efficient DID with panel data drdid_imp_panel(y1 = eval_lalonde_cps$re78, y0 = eval_lalonde_cps$re75, D = eval_lalonde_cps$experimental,
covariates = covX)
#>  Call:
#> drdid_imp_panel(y1 = eval_lalonde_cps$re78, y0 = eval_lalonde_cps$re75,
#>     D = eval_lalonde_cps\$experimental, covariates = covX)
#> ------------------------------------------------------------------
#>  Further improved locally efficient DR DID estimator for the ATT:
#>
#>    ATT     Std. Error  t value    Pr(>|t|)  [95% Conf. Interval]
#> -615.2344   683.2211   -0.9005     0.3679   -1954.3478  723.8791
#> ------------------------------------------------------------------
#>  Estimator based on panel 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.