Inverse probability weighted DiD estimator, with panel data

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

ipw_did_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 estimation. Please add a vector of constants if you want to include an intercept in the models. 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.

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 = TRUE, 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

# 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(1, 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$re74))
# Implement (unnormalized) IPW DiD with panel data
ipw_did_panel(y1 = eval_lalonde_cps$re78, y0 = eval_lalonde_cps$re75,
                D = eval_lalonde_cps$experimental,
                covariates = covX)
#>  Call:
#> ipw_did_panel(y1 = eval_lalonde_cps$re78, y0 = eval_lalonde_cps$re75, 
#>     D = eval_lalonde_cps$experimental, covariates = covX)
#> ------------------------------------------------------------------
#>  IPW DID estimator for the ATT:
#>  
#>    ATT     Std. Error  t value    Pr(>|t|)  [95% Conf. Interval] 
#> -724.1929   692.1639   -1.0463     0.2954   -2080.8342  632.4484 
#> ------------------------------------------------------------------
#>  Estimator based on panel data.
#>  Horvitz-Thompson-type IPW estimator.
#>  Propensity score est. method: maximum likelihood.
#>  Analytical standard error.
#> ------------------------------------------------------------------
#>  See Sant'Anna and Zhao (2020) for details.