ipw_did_rc is used to compute inverse probability weighted (IPW) estimators for the ATT in difference-in-differences (DiD) setups with stationary cross-sectional data. IPW weights are not normalized to sum up to one, that is, the estimator is of the Horwitz-Thompson type.

ipw_did_rc(
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. 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.) An $$n$$ x $$1$$ vector of Group indicators (=1 if observation is treated in the post-treatment, =0 otherwise). An $$n$$ x $$k$$ matrix of covariates to be used in the propensity score estimation. If covariates = NULL, this leads to an unconditional DID estimator. An $$n$$ x $$1$$ vector of weights to be used. If NULL, then every observation has the same weights. Logical argument to whether bootstrap should be used for inference. Default is FALSE. Type of bootstrap to be performed (not relevant if boot = FALSE). Options are "weighted" and "multiplier". If boot = TRUE, default is "weighted". Number of bootstrap repetitions (not relevant if boot = FALSE). Default is 999. Logical argument to whether influence function should be returned. Default is FALSE.

## Value

A list containing the following components:

ATT

The IPW DID point estimate.

se

The IPW 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

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, normalized = FALSE, boot, boot.type, nboot, type="ipw")

## References

Abadie, Alberto (2005), "Semiparametric Difference-in-Differences Estimators", Review of Economic Studies, vol. 72(1), p. 1-19, doi: 10.1111/0034-6527.00321

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 unnormalized IPW DID estimator
ipw_did_rc(y = sim_rc$y, post = sim_rc$post, D = sim_rc$d, covariates= covX) #> Call: #> ipw_did_rc(y = sim_rc$y, post = sim_rc$post, D = sim_rc$d, covariates = covX)
#> ------------------------------------------------------------------
#>  IPW DID estimator for the ATT:
#>
#>    ATT     Std. Error  t value    Pr(>|t|)  [95% Conf. Interval]
#>  -19.8933   53.8682    -0.3693     0.7119    -125.475   85.6884
#> ------------------------------------------------------------------
#>  Estimator based on (stationary) repeated cross-sections data.
#>  Horvitz-Thompson-type IPW estimator.
#>  Propensity score est. method: maximum likelihood.
#>  Analytical standard error.
#> ------------------------------------------------------------------
#>  See Sant'Anna and Zhao (2020) for details.