Standardized inverse probability weighted DiD estimator, with repeated cross-section data

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
)

Arguments

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.

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 = TRUE, 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(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.