didweight {causalweight}

Difference-in-differences based on inverse probability weighting

Description

Difference-in-differences-based estimation of the average treatment effect on the treated in the post-treatment period, given a binary treatment with one pre- and one post-treatment period. Permits controlling for differences in observed covariates across treatment groups and/or time periods based on inverse probability weighting.

Usage

didweight(y, d, t, x = NULL, boot = 1999, trim = 0.05, cluster = NULL)

Arguments

y

Dependent variable, must not contain missings.

d

Treatment, must be binary (either 1 or 0), must not contain missings.

t

Time period, must be binary, 0 for pre-treatment and 1 for post-treatment, must not contain missings.

x

Covariates to be controlled for by inverse probability weighting. Default is NULL.

boot

Number of bootstrap replications for estimating standard errors. Default is 1999.

trim

Trimming rule for discarding observations with extreme propensity scores in the 3 reweighting steps, which reweight (1) treated in the pre-treatment period, (2) non-treated in the post-treatment period, and (3) non-treated in the pre-treatment period according to the covariate distribution of the treated in the post-treatment period. Default is 0.05, implying that observations with a probability lower than 5 percent of not being treated in some weighting step are discarded.

cluster

A cluster ID for block or cluster bootstrapping when units are clustered rather than iid. Must be numerical. Default is NULL (standard bootstrap without clustering).

Details

Estimation of the average treatment effect on the treated in the post-treatment period based Difference-in-differences. Inverse probability weighting is used to control for differences in covariates across treatment groups and/or over time. That is, (1) treated observations in the pre-treatment period, (2) non-treated observations in the post-treatment period, and (3) non-treated observations in the pre-treatment period are reweighted according to the covariate distribution of the treated observations in the post-treatment period. The respective propensity scores are obtained by probit regressions.

Value

A didweight object contains 4 components, eff, se, pvalue, and ntrimmed.

eff: estimate of the average treatment effect on the treated in the post-treatment period.

se: standard error obtained by bootstrapping the effect.

pvalue: p-value based on the t-statistic.

ntrimmed: total number of discarded (trimmed) observations in any of the 3 reweighting steps due to extreme propensity score values.

References

Abadie, A. (2005): "Semiparametric Difference-in-Differences Estimators", The Review of Economic Studies, 72, 1-19.

Lechner, M. (2011): "The Estimation of Causal Effects by Difference-in-Difference Methods", Foundations and Trends in Econometrics, 4, 165-224.

Examples

# A little example with simulated data (4000 observations)
## Not run: 
n=4000                            # sample size
t=1*(rnorm(n)>0)                  # time period
u=rnorm(n)                        # time constant unobservable
x=0.5*t+rnorm(n)                  # time varying covariate
d=1*(x+u+rnorm(n)>0)              # treatment
y=d*t+t+x+u+rnorm(n)              # outcome
# The true effect equals 1
didweight(y=y,d=d,t=t,x=x, boot=199)
## End(Not run)