`R/reg_did_rc.R`

`reg_did_rc.Rd`

`reg_did_rc`

computes the outcome regressions estimators for the average treatment effect on the
treated in difference-in-differences (DiD) setups with stationary repeated cross-sectional data.

```
reg_did_rc(
y,
post,
D,
covariates,
i.weights = NULL,
boot = FALSE,
boot.type = "weighted",
nboot = NULL,
inffunc = FALSE
)
```

- 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 regression 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.

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 = FALSE, boot, boot.type, nboot, type="or")

The `reg_did_rc`

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 stationary repeated cross-sectional
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.

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

```
# use the simulated data provided in the package
covX = as.matrix(cbind(1, sim_rc[,5:8]))
# Implement OR DiD estimator
reg_did_rc(y = sim_rc$y, post = sim_rc$post, D = sim_rc$d,
covariates= covX)
#> Call:
#> reg_did_rc(y = sim_rc$y, post = sim_rc$post, D = sim_rc$d, covariates = covX)
#> ------------------------------------------------------------------
#> Outcome-Regression DID estimator for the ATT:
#>
#> ATT Std. Error t value Pr(>|t|) [95% Conf. Interval]
#> -8.791 7.7785 -1.1302 0.2584 -24.0368 6.4548
#> ------------------------------------------------------------------
#> Estimator based on (stationary) repeated cross-sections data.
#> Outcome regression est. method: OLS.
#> Analytical standard error.
#> ------------------------------------------------------------------
#> See Sant'Anna and Zhao (2020) for details.
```