Outcome regression DiD estimator for the ATT, with panel data

reg_did_panel computes the outcome regressions estimators for the average treatment effect on the treated in difference-in-differences (DiD) setups with panel data.

reg_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). Please include a constant to serve as intercept.
covariates: An \(n\) x \(k\) matrix of covariates to be used in the regression estimation. Please include a column of constants if you want to include an intercept in the regression model. 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 OR DiD point estimate
se: The OR 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, boot, boot.type, nboot, type="or")

Details

The reg_did_panel function implements outcome regression difference-in-differences (DiD) estimator for the average treatment effect on the treated (ATT) defined in equation (2.2) of Sant'Anna and Zhao (2020) when panel data are available. The estimator follows the same spirit of the nonparametric estimators proposed by Heckman, Ichimura and Todd (1997), though here the the outcome regression models are assumed to be linear in covariates (parametric),

The nuisance parameters (outcome regression coefficients) are estimated via ordinary least squares.

References

Heckman, James J., Ichimura, Hidehiko, and Todd, Petra E. (1997),"Matching as an Econometric Evaluation Estimator: Evidence from Evaluating a Job Training Programme", Review of Economic Studies, vol. 64(4), p. 605–654, doi:10.2307/2971733 .

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$re74))
# Implement OR DiD with panel data
reg_did_panel(y1 = eval_lalonde_cps$re78, y0 = eval_lalonde_cps$re75,
               D = eval_lalonde_cps$experimental,
               covariates = covX)
#>  Call:
#> reg_did_panel(y1 = eval_lalonde_cps$re78, y0 = eval_lalonde_cps$re75, 
#>     D = eval_lalonde_cps$experimental, covariates = covX)
#> ------------------------------------------------------------------
#>  Outcome-Regression DID estimator for the ATT:
#>  
#>    ATT     Std. Error  t value    Pr(>|t|)  [95% Conf. Interval] 
#> -1312.6766  597.2834   -2.1977     0.028    -2483.3521 -142.0011 
#> ------------------------------------------------------------------
#>  Estimator based on panel data.
#>  Outcome regression est. method: OLS.
#>  Analytical standard error.
#> ------------------------------------------------------------------
#>  See Sant'Anna and Zhao (2020) for details.