`ipwdid`

computes the inverse probability weighted estimators for the average treatment effect
on the treated in difference-in-differences (DiD) setups. It can be used with panel or stationary repeated
cross-sectional data, with or without normalized (stabilized) weights. See Abadie (2005) and Sant'Anna and
Zhao (2020) for details.

```
ipwdid(
yname,
tname,
idname,
dname,
xformla = NULL,
data,
panel = TRUE,
normalized = TRUE,
weightsname = NULL,
boot = FALSE,
boot.type = c("weighted", "multiplier"),
nboot = 999,
inffunc = FALSE
)
```

- yname
The name of the outcome variable.

- tname
The name of the column containing the time periods.

- idname
The name of the column containing the unit id name.

- dname
The name of the column containing the treatment group (=1 if observation is treated in the post-treatment, =0 otherwise)

- xformla
A formula for the covariates to include in the model. It should be of the form

`~ X1 + X2`

(intercept should not be listed as it is always automatically included). Default is NULL which is equivalent to`xformla=~1`

.- data
The name of the data.frame that contains the data.

- panel
Whether or not the data is a panel dataset. The panel dataset should be provided in long format – that is, where each row corresponds to a unit observed at a particular point in time. The default is TRUE. When

`panel = FALSE`

, the data is treated as stationary repeated cross sections.- normalized
Logical argument to whether IPW weights should be normalized to sum up to one. Default is

`TRUE`

.- weightsname
The name of the column containing the sampling weights. 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`

and analytical standard errors are reported.- 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 in the call (panel, normalized, boot, boot.type, nboot, type=="ipw")

The `ipwdid`

function implements the
inverse probability weighted (IPW) difference-in-differences (DiD) estimator for the average treatment effect
on the treated (ATT) proposed by Abadie (2005) (`normalized = FALSE`

) or Hajek-type version
defined in equations (4.1) and (4.2) in Sant'Anna and Zhao (2020), when either panel data or
stationary repeated cross-sectional data are available. This estimator makes use of
a logistic propensity score model for the probability of being in the treated group, and the propensity score
parameters are estimated via maximum likelihood.

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

```
# -----------------------------------------------
# Panel data case
# -----------------------------------------------
# Form the Lalonde sample with CPS comparison group
eval_lalonde_cps <- subset(nsw_long, nsw_long$treated == 0 | nsw_long$sample == 2)
# Further reduce sample to speed example
set.seed(123)
unit_random <- sample(unique(eval_lalonde_cps$id), 5000)
eval_lalonde_cps <- eval_lalonde_cps[eval_lalonde_cps$id %in% unit_random,]
# Implement IPW DiD with panel data (normalized weights)
ipwdid(yname="re", tname = "year", idname = "id", dname = "experimental",
xformla= ~ age+ educ+ black+ married+ nodegree+ hisp+ re74,
data = eval_lalonde_cps, panel = TRUE)
#> Call:
#> ipwdid(yname = "re", tname = "year", idname = "id", dname = "experimental",
#> xformla = ~age + educ + black + married + nodegree + hisp +
#> re74, data = eval_lalonde_cps, panel = TRUE)
#> ------------------------------------------------------------------
#> IPW DID estimator for the ATT:
#>
#> ATT Std. Error t value Pr(>|t|) [95% Conf. Interval]
#> -655.9068 687.8494 -0.9536 0.3403 -2004.0916 692.278
#> ------------------------------------------------------------------
#> Estimator based on panel 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.
# -----------------------------------------------
# Repeated cross section case
# -----------------------------------------------
# use the simulated data provided in the package
#Implement IPW DiD with repeated cross-section data (normalized weights)
# use Bootstrap to make inference with 199 bootstrap draws (just for illustration)
ipwdid(yname="y", tname = "post", idname = "id", dname = "d",
xformla= ~ x1 + x2 + x3 + x4,
data = sim_rc, panel = FALSE,
boot = TRUE, nboot = 199)
#> Call:
#> ipwdid(yname = "y", tname = "post", idname = "id", dname = "d",
#> xformla = ~x1 + x2 + x3 + x4, data = sim_rc, panel = FALSE,
#> boot = TRUE, nboot = 199)
#> ------------------------------------------------------------------
#> IPW DID estimator for the ATT:
#>
#> ATT Std. Error t value Pr(>|t|) [95% Conf. Interval]
#> -15.8033 9.7237 -1.6252 0.1041 -32.7867 1.1801
#> ------------------------------------------------------------------
#> Estimator based on (stationary) repeated cross-sections data.
#> Hajek-type IPW estimator (weights sum up to 1).
#> Propensity score est. method: maximum likelihood.
#> Boostrapped standard error based on 199 bootstrap draws.
#> Bootstrap method: weighted .
#> ------------------------------------------------------------------
#> See Sant'Anna and Zhao (2020) for details.
```