`R/std_ipw_did_rc.R`

`std_ipw_did_rc.Rd`

`std_ipw_did_rc`

is used to compute inverse probability weighted (IPW) estimators for the ATT
in DID setups with stationary repeated cross-sectional data. IPW weights are normalized to sum up to one, that is,
the estimator is of the Hajek type.

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

- 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 estimation. Please add a column of ones if you want to include an intercept. 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. The weights are normalized and therefore enforced to have mean 1 across all observations.

- 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.

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 = TRUE, boot, boot.type, nboot, type="ipw")

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

```
# use the simulated data provided in the package
covX = as.matrix(cbind(1, sim_rc[,5:8]))
# Implement normalized IPW DID estimator
std_ipw_did_rc(y = sim_rc$y, post = sim_rc$post, D = sim_rc$d,
covariates= covX)
#> Call:
#> std_ipw_did_rc(y = sim_rc$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]
#> -15.8033 9.0879 -1.7389 0.082 -33.6156 2.009
#> ------------------------------------------------------------------
#> Estimator based on (stationary) repeated cross-sections data.
#> Hajek-type IPW estimator (weights sum up to 1).
#> Propensity score est. method: maximum likelihood.
#> Analytical standard error.
#> ------------------------------------------------------------------
#> See Sant'Anna and Zhao (2020) for details.
```