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
)

## Arguments

yname The name of the outcome variable. The name of the column containing the time periods. The name of the column containing the unit id name. The name of the column containing the treatment group (=1 if observation is treated in the post-treatment, =0 otherwise) 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. The name of the data.frame that contains the data. 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 = TRUE, the variable idname must be set. When panel = FALSE, the data is treated as stationary repeated cross sections. Logical argument to whether IPW weights should be normalized to sum up to one. Default is TRUE. The name of the column containing the sampling weights. If NULL, then every observation has the same weights. Logical argument to whether bootstrap should be used for inference. Default is FALSE and analytical standard errors are reported. 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 in the call (panel, normalized, boot, boot.type, nboot, type=="ipw")

## Details

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.

## 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

# -----------------------------------------------
# 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   687.8493   -0.9536     0.3403   -2004.0914  692.2778
#> ------------------------------------------------------------------
#>  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.