didDML function

Difference-in-Differences in Repeated Cross-Sections for Binary Treatments using Double Machine Learning

This function estimates the average treatment effect on the treated (ATET) in the post-treatment period for a binary treatment using a doubly robust Difference-in-Differences (DiD) approach for repeated cross-sections that is combined with double machine learning. It controls for (possibly time-varying) confounders in a data-driven manner and supports various machine learning methods for estimating nuisance parameters through k-fold cross-fitting.

didDML(
  y,
  d,
  t,
  x,
  MLmethod = "lasso",
  est = "dr",
  trim = 0.05,
  cluster = NULL,
  k = 3
)

Arguments

• y: Outcome variable. Should not contain missing values.
• d: Treatment group indicator (binary). Should not contain missing values.
• t: Time period indicator (binary). Should be 1 for post-treatment period and 0 for pre-treatment period. Should not contain missing values.
• x: Covariates to be controlled for. Should not contain missing values.
• MLmethod: Machine learning method for estimating nuisance parameters using the SuperLearner package. Must be one of "lasso" (default), "randomforest", "xgboost", "svm", "ensemble", or "parametric".
• est: Estimation method. Must be one of "dr" (default) for doubly robust, "ipw" for inverse probability weighting (not doubly robust!), or "reg" for regression (not doubly robust!).
• trim: Trimming threshold (in percentage) for discarding observations with too small propensity scores within any subgroup defined by the treatment group and time. Default is 0.05.
• cluster: Optional clustering variable for calculating cluster-robust standard errors.
• k: Number of folds in k-fold cross-fitting. Default is 3.

Returns

A list with the following components:

ATET: Estimate of the Average Treatment Effect on the Treated (ATET) in the post-treatment period.

se: Standard error of the ATET estimate.

pval: P-value of the ATET estimate.

trimmed: Number of discarded (trimmed) observations.

pscores: Propensity scores of untrimmed observations (4 columns): under treatment in period 1, under treatment in period 0, under control in period 1, under control in period 0.

outcomepred: Conditional outcome predictions of untrimmed observations (3 columns): in treatment group in period 0, in control group in period 1, in control group in period 0.

treat: Treatment status of untrimmed observations.

time: Time period of untrimmed observations.

Details

This function estimates the Average Treatment Effect on the Treated (ATET) in the post-treatment period based on Difference-in-Differences in repeated cross-sections when controlling for confounders in a data-adaptive manner using double machine learning. The function supports different machine learning methods to estimate nuisance parameters (conditional mean outcomes and propensity scores) as well as cross-fitting to mitigate overfitting. Besides double machine learning, the function also provides inverse probability weighting and regression adjustment methods (which are, however, not doubly robust).

Examples

## Not run:

# Example with simulated data
n=4000                            # sample size
t=1*(rnorm(n)>0)                  # time period
u=runif(n,0,1)                    # time constant unobservable
x= 0.25*t+runif(n,0,1)            # time varying covariate
d=1*(x+u+2*rnorm(n)>0)            # treatment
y=d*t+t+x+u+2*rnorm(n)            # outcome
# true effect is equal to 1
results=didDML(y=y, d=d, t=t, x=x)
cat("ATET: ", round(results$ATET, 3), ", Standard error: ", round(results$se, 3))
## End(Not run)

References

Chernozhukov, V., Chetverikov, D., Demirer, M., Duflo, E., Hansen, C., Newey, W., Robins, J. (2018): "Double/debiased machine learning for treatment and structural parameters", The Econometrics Journal, 21, C1-C68.

Zimmert, M. (2020): "Efficient difference-in-differences estimation with high-dimensional common trend confounding", arXiv preprint 1809.01643.