Main function of the DIDHAD package

Description

Estimates the effect of a treatment on an outcome in a heterogeneous adoption design with no untreated, but some quasi-untreated groups (see de Chaisemartin et. al. (2025)).

Usage

did_had(
  df,
  outcome,
  group,
  time,
  treatment,
  effects = 1,
  placebo = 0,
  level = 0.05,
  kernel = "epa",
  bw_method = "mse-dpi",
  trends_lin = FALSE,
  dynamic = FALSE,
  yatchew = FALSE,
  graph_off = FALSE
)

Arguments

Value

An list object of did_had class. The object contains the estimation results, as well as the selected arguments of the function and a ggplot graph with the event study estimates.

Overview

did_had() estimates the effect of a treatment on an outcome in a heterogeneous adoption design (HAD) with no untreated, but some quasi-untreated groups. HADs are designs where all groups are untreated in the first period, and then some groups receive a strictly positive treatment dose at a period F, which has to be the same for all treated groups (with variation in treatment timing, the did_multiplegt_dyn package may be used). Therefore, there is variation in treatment intensity, but no variation in treatment timing.

HADs without untreated groups are designs where all groups receive a strictly positive treatment dose at period F. Then, one cannot use untreated units to recover the counterfactual outcome evolution that treated groups would have experienced from before to after F, without treatment. To circumvent this, did_had() implements the estimator from de Chaisemartin et. al. (2025) which uses so-called "quasi-untreated groups" as the control group. Quasi-untreated groups are groups that receive a "small enough" treatment dose at F to be regarded as "as good as untreated". Therefore, did_had() can only be used if there are groups with a treatment dose "close to zero". Formally, the command checks the presence of quasi untreated groups via the test proposed in section 3.3 of de Chaisemartin et al. (2025). This test is automatically performed once for each event-study effect and results are reported in the output table. If the results are the same for each event-study effect, this indicates that the treatment changes only once.

The command makes use of the lprobust command by Calonico, Cattaneo and Farrell (2019) to determine an optimal bandwidth, i.e. a treatment dose below which groups can be considered as quasi-untreated. To estimate the treatment's effect, the command starts by computing the difference between the change in outcome of all groups and the intercept in a local linear regression of the outcome change on the treatment dose among quasi-untreated groups. Then, that difference is scaled by groups' average treatment dose at period two. Standard errors and confidence intervals are also computed leveraging lprobust. We recommend that users of did_had() cite de Chaisemartin et. al. (2025), Calonico, Cattaneo and Farrell (2019), and Calonico, Cattaneo and Farrell (2018).

Interpreting the results from the yatchew option

Following Theorem 5 of de Chaisemartin et. al. (2025), in designs where there are untreated or quasi-untreated groups, under a parallel trends assumption the treatment coefficient from a regression of groups' F-1 to F-1+\ell outcome evolution on their the treatment at F-1+\ell is unbiased for the WAS if and only if the conditional expectation of the outcome evolution from F-1 to F-1+\ell given the treatment at F-1+\ell is linear. As a result, if the linearity hypothesis cannot be rejected, then one can unbiasedly estimate the WAS at period F-1+\ell using the simple OLS regression described above, rather than resorting to the non-parametric estimator computed by did_had().

Contacts

Github repository: chaisemartinPackages/did_had

Mail: chaisemartin.packages@gmail.com

References

de Chaisemartin, C., Ciccia, D., D'Haultfoeuille, X. and Knau, F. (2025). Difference-in-Differences Estimators When No Unit Remains Untreated.

Calonico, S., M. D. Cattaneo, and M. H. Farrell. (2019). nprobust: Nonparametric Kernel-Based Estimation and Robust Bias-Corrected Inference.

Calonico, S., M. D. Cattaneo, and M. H. Farrell. (2018). On the Effect of Bias Estimation on Coverage Accuracy in Nonparametric Inference.

Yatchew, A. (1997). An elementary estimator of the partial linear model, doi:10.1016/S0165-1765(97)00218-8.

Examples

# The sample data for this example can be downloaded by running:
repo <-"https://raw.githubusercontent.com/chaisemartinPackages/did_had/" 
data <- haven::read_dta(paste0(repo,"main/tutorial_data.dta"))

# Estimating the effects over five periods and placebos for four pre-treatment periods, 
# suppressing the graph and with a triagular kernel:

summary(did_had(df = data, 
                outcome = "y",
                group = "g",
                time = "t",
                treatment = "d",
                effects = 5,
                placebo = 4,
                kernel = "tri",
                graph_off = TRUE))