Package {DIDmultiplegtDYN}

Core function for did_multiplegt_dyn

Description

Estimation of heterogeneity-robust difference-in-differences (DID) event-study estimators, in designs where the treatment may be non-binary and/or non-absorbing, and where past treatments may affect the current outcome.

Usage

did_multiplegt_dyn(
  df,
  outcome,
  group,
  time,
  treatment,
  effects = 1,
  design = NULL,
  normalized = FALSE,
  normalized_weights = FALSE,
  effects_equal = FALSE,
  placebo = 0,
  controls = NULL,
  trends_nonparam = NULL,
  trends_lin = FALSE,
  continuous = NULL,
  weight = NULL,
  cluster = NULL,
  by = NULL,
  by_path = NULL,
  predict_het = NULL,
  predict_het_hc2bm = FALSE,
  date_first_switch = NULL,
  same_switchers = FALSE,
  same_switchers_pl = FALSE,
  switchers = "",
  only_never_switchers = FALSE,
  ci_level = 95,
  graph_off = FALSE,
  save_results = NULL,
  save_sample = FALSE,
  less_conservative_se = FALSE,
  more_granular_demeaning = FALSE,
  bootstrap = NULL,
  dont_drop_larger_lower = FALSE,
  drop_if_d_miss_before_first_switch = FALSE,
  reset = 0,
  avg_time_periods = FALSE,
  ggplot_args = NULL
)

Arguments

Value

A list of class did_multiplegt_dyn containing the arguments used, the results for the estimation requested and a ggplot object with the event-study graph. If the by option is specified, the did_multiplegt_dyn object will contain the arguments, a list with the levels of the by option, a sublist for each of these levels with the results and ggplot objects from these by-estimations and a ggplot object for the combined event-study graph. The class did_multiplegt_dyn is assigned to enable customized print and summary methods.

Overview

did_multiplegt_dyn() computes the heterogeneity-robust DID event-study estimators introduced in de Chaisemartin and D’Haultfoeuille (2026). Like other recently proposed DID estimation commands (did, didimputation, ...), did_multiplegt_dyn() can be used with a binary and staggered (absorbing) treatment. But unlike those other commands, did_multiplegt_dyn() can also be used if the treatment is non-binary (discrete or continuous) and/or non-absorbing (the treatment can increase or decrease multiple times). It is applicable to any “staggered first switch design”, where groups experience their first treatment change at different points in time. Lagged treatments may affect the outcome, and the current and lagged treatments may have heterogeneous effects, across space and/or over time. The event-study estimators computed by the command compare the outcome evolutions of switchers, namely units that experience a change in their treatment, and of not-yet-switchers, namely units whose treatment has not changed yet. Those estimators rely on no-anticipation and parallel-trends assumptions, which can be partly tested by computing pre-trend estimators. The panel may be unbalanced: not all groups have to be observed at every period. The data may also be at a more disaggregated level than the group level (e.g. individual-level wage data to measure the effect of a regional-level minimum-wage on individuals’ wages). See Section 8.3 of “Causal Inference with Differences-in-Differences: Credible Answers to Hard Questions” by Chaisemartin and D’Haultfoeuille for a thorough presentation of the estimators computed by the command.

Further detail

Non-normalized event-study estimators (the default)

Intuitively, those effects compare groups’ outcomes under their actual treatment path to what their outcome would have been under the status-quo path where they would have kept their period-one treatment throughout the panel. Formally, for all “switchers”, namely groups that experience a change of their treatment over the study period, let F_g denote the first time period when g’s treatment changes. The command computes the non-normalized event-study estimators DID_\ell. DID_1 is the average, across all switchers, of DID estimators comparing the F_g-1 to F_g outcome evolution of g to that of groups with the same period-one treatment as g but whose treatment has not changed yet at F_g. More generally, DID_\ell is the average, across all switchers, of DID estimators comparing the F_g-1 to F_g-1+\ell outcome evolution of g to that of groups with the same period-one treatment as g but whose treatment has not changed yet at F_g-1+\ell. Those estimators are unbiased for non-normalized event-study effects, which are average effects of having been exposed to a weakly higher treatment dose for \ell periods. However, the magnitude and timing of the incremental treatment doses received under the actual treatment path relative to the status-quo path can vary across groups, so non-normalized effects can generally not be interpreted as effects of a one unit increase in the treatment.

Normalized event-study estimators

The command also computes the normalized event-study estimators DID^n_\ell, that normalize DID_\ell by the average of the sum of the incremental treatment doses received by switchers under their actual path, relative to the doses they would have received under their status-quo path. This normalization ensures that DID^n_\ell estimates a weighted average of the effects of the current treatment and of its \ell-1 first lags on the outcome. Thus, normalized effects can be interpreted as effects of a one unit increase in the treatment. While the effects of the current and lagged treatments cannot be separately estimated, the weight that DID^n_\ell puts on the effect of each lag can be estimated.

Average cumulative (total) effect per dose

The command also computes an estimated average cumulative (total) effect per unit of treatment, where “cumulative effect” refers to the sum of the effects of a treatment dose, at the time when it takes place and at later periods, see Section 3.3 of de Chaisemartin and D’Haultfoeuille (2026) for further details. The command also shows the number of time periods over which the effect of a dose is accumulated, on average across all incremental doses received by switchers over the study period. By dividing the average cumulative effect by the average number of periods across which effects are accumulated, one can get an estimator of the effect of being exposed to one more unit of treatment for one period.

Placebos

The command also computes placebo estimators, that average DIDs comparing the outcome evolution of switcher g and of its control groups, from F_g-1 to F_g-1-\ell, namely before g’s treatment changes for the first time. Those placebos can be used to test the parallel trends and no-anticipation assumptions under which the estimators computed by did_multiplegt_dyn() are unbiased.

Designs compatible with the command

The command can be used in staggered first switch designs, where groups experience their first treatment change at different points in time. Such designs encompass the canonical binary and absorbing treatment case. But they also encompass more complicated designs: groups may have heterogeneous treatments at period one, their treatment may change at different dates, some groups may experience increases in their treatment while other groups experience decreases, some groups may experience more than one change of their treatment, and finally some groups may experience larger treatment changes than others. The command can also be used to separately estimate the effects of several treatment variables, see references in the FAQ section. The only requirement is that not all groups experience their first treatment change at the same date.

Relaxing the parallel-trends assumption

The command allows for many relaxations of the parallel-trends assumption: see the controls option for estimators allowing for time-varying covariates, see the trends_lin option for estimators allowing for group-specific linear trends, and see the trends_nonparam option for estimators allowing to interact time fixed effects with time-invariant variables (e.g. industry\timesyear effect with firm-level panel data).

Contacts

Github repository: chaisemartinPackages/did_multiplegt_dyn

Mail: chaisemartin.packages@gmail.com

FAQ

did_multiplegt_dyn() does not output exactly the same results as did_multiplegt(), is this normal?

Yes, the two commands can sometimes output different results. This is mostly due to different conventions in the way the two commands deal with missing values. See Appendix B of de Chaisemartin et al (2025) for further details.

Do I have to include group and time fixed effects as controls when using did_multiplegt_dyn()?

No, you do not have to. Group and time fixed effects are automatically controlled for.

My group-level panel is unbalanced: some groups (e.g. counties) are not observed in every year. Can I still use the command?

You can. A frequent case of unbalancedness is when some groups are not observed over the full duration of the panel. For instance, your data may be a yearly county-level panel from 1990 to 2000, where some counties appear after 1990 while some exit before 2000. Then, the command just redefines group’s period-one treatment as their treatment at the first period when they are observed.

It may also be that some groups enter and exit the data multiple times. For instance, you observe a county in 1990, 1991, 1994, 1996, and 2000. Then, the command may impute some of that county’s missing treatments. Those imputations are detailed in Appendix A of de Chaisemartin et al (2025). In designs where groups’ treatments can change at most once, all those imputations are justified by the design. In other designs, some of those imputations may be liberal. drop_if_d_miss_before_first_switch can be used to overrule the potentially liberal imputations that are not innocuous for the non-normalized event-study estimators. See Appendix A of de Chaisemartin et al (2025) for further details.

Finally, it may also be the case that the data is fully missing at one or several time periods. For instance, you have data for 1990, 1991, and 1993, but 1992 is missing for every group. Then, it is important to fill the gap in the data, as otherwise the estimation will assume that 1991 and 1993 are as far apart as 1990 and 1991. There are two ways of doing so. First, you can append to your data a data set identical to your 1991 data, but with the year equal to 1992, and the outcome missing for every observation. This is a conservative solution, where no first treatment change occurring between 1991 and 1993 will be used in the estimation, which may be reasonable because the year in which the change occurred is effectively unknown. Second, you can append to your data a data set identical to your 1993 data, with the year equal to 1992, and the outcome missing for every observation. Then, treatment changes occurring between 1991 and 1993 will be used in the estimation, assuming they all took place between 1991 and 1992.

Related to imbalanced panels, my outcomes (and potentially the control variables) are measured less frequently than the treatment. For instance, the outcome is measured every two years, but I know the treatment of every group in every year. How should I proceed?

To fix ideas, let us first assume that the outcome is measured every two years, but you know the treatment of every group in every year. Then, you should split the sample into two subsamples, and run the command twice, one time on each of the subsamples. In the first estimation, you should include all group \times time cells (g,t) such that at t, g’s treatment has never changed since the start of the panel, and all (g,t)s such that i) g’s treatment has changed at least once at t and ii) the change occurred at a period where the outcome is observed. Since the outcome is measured every two years, in that subsample the first event-study effect (denoted effect_1) is the effect of being exposed to a higher treatment for one period, the second effect (effect_2) is the effect of being exposed to a higher treatment for three periods, etc. In the second estimation, you should include all group \times time cells (g,t) such that at t, g’s treatment has never changed since the start of the panel, and all (g,t)s such that i) g’s treatment has changed at least once at t and ii) the change occurred at a period where the outcome is not observed. In that subsample, the first event-study effect (denoted effect_1) is the effect of being exposed to a higher treatment for two periods, the second effect (effect_2) is the effect of being exposed to a higher treatment for four periods, etc. You may then combine the two sets of estimated effects into one event-study graph, with the only caveat that the “odd” and “even” effects are estimated on different subsamples. Importantly, the two estimations have to be run on a dataset at the same bi-yearly level as the outcome variable: the yearly level treatment information should only be used to select the relevant subsamples.

If the treatment is observed three times more often than the treatment, you can follow the same logic, splitting the sample into three subsamples and running the command three times, etc.

A short do file with a simple example where the treatment status is observed in each period while the outcome is only observed every second period can be found here.

What is the maximum number of event-study effects I can estimate?

With a balanced panel of groups, the maximum number of event-study effects one can estimate can be determined as follows. For each value of the period-one treatment d, start by computing the difference between the last period at which at least one group has had treatment d since period 1, and the first period at which a group with treatment d at period 1 changed its treatment. Add one to this difference. Then, the maximum number of event-study effects is equal to the maximum of the obtained values, across all values of the period-one treatment. With an unbalanced panel, this method can still be used to derive an upper bound of the maximum number of event-study effects one can estimate.

How many control variables can I include in the estimation?

Estimators with control variables are similar to those without controls, except that the first-difference of the outcome is replaced by residuals from regressions of the first-difference of the outcome on the first-differences of the controls and time fixed effects. Those regressions are estimated in the sample of control (g,t)s: (g,t)s such that group g’s treatment has not changed yet at period t. Those regressions are also estimated separately for each value of the period-one treatment. If at period one, treatment takes values 0, 1, 2, 3, and 4, one regression is estimated for control (g,t)s with a period-one treatment equal to 0, one regression is estimated for control (g,t)s with a period-one treatment equal to 1, etc. The number of control variables needs to be significantly smaller than the number of control (g,t)s in each of those regressions. Otherwise, those regressions will overfit and produce noisy estimates. If the number of observations is lower than the number of variables in one of those regressions, the command will run but will not take into account all the controls for all values of the period-one treatment. An error message will let the user know that they are encountering this situation, and may thus want to reduce their number of control variables.

My design is such that treatment is binary, and groups can enter the treatment, and then leave it once. Can I use the command to separately estimate the effect of joining and leaving the treatment?

Yes you can. See Section 1.6 of the Web Appendix of de Chaisemartin and D’Haultfoeuille (2026) for further details.

My design has several treatments. Can I use the command to estimate the event-study effects of a treatment controlling for other treatments?

Yes. See Section 3.2 of the Web Appendix of de Chaisemartin and D’Haultfoeuille (2023) for further details, keeping in mind that the did_multiplegt command referenced at the time is now superseded by this command.

Can I perform triple difference-in-differences with the command?

Yes. Suppose for instance your third difference is across men and women in the same (g,t) cell. Then, for each (g,t) cell, you just need to compute the difference between the average outcome of men and women in cell (g,t). Then, you simply run the command with this new outcome. The triple difference-in-differences should be used to relax the identifying assumption, not to estimate heterogeneous treatment effects between men and women. To estimate heterogeneous effects, you can use the predict_het or by option.

Is it possible to compute switchers’ average counterfactual outcome at periods F_g, F_{g+1}, ..., so as to then express the event-study effects in percentage points of the counterfactual outcome level?

Yes. You just need to define a new outcome variable Y’ = -Y \cdot 1\lbrace t < F_g \rbrace, where F_g is the first date at which g’s treatment has changed. Essentially, you replace the outcome by 0 after the treatment change, and by -Y before the treatment change. Then, you compute non-normalized event-study estimators with Y’ as the outcome.

Can the command be used in fuzzy designs, where the treatment varies within group \times time cells?

Yes it can, see Section 1.7 of the Web Appendix of de Chaisemartin and D’Haultfoeuille (2026) for further details.

My data is at a more disaggregated level than the group level (e.g., observations are at the individual level while groups are municipalities). How can I control for individual-level covariates?

One possibility is to include those variables in the controls option. In that case, the command does not control for the individual-level covariates themselves, but for their averages within each (g,t) cell. Specifically, the controls option works by regressing the first difference of the average outcome in each (g,t) cell on the first differences of the average controls in that cell, and replacing the first-differenced outcome with the resulting residuals. Accordingly, the estimator allows for differential trends across groups experiencing different changes in the average values of their covariates.

If instead you wish to control for the individual-level covariates themselves, rather than for their (g,t)-level averages, you can first regress the individual-level outcome on those covariates, compute the residuals from that regression, and then run the command using those residuals as the outcome variable.

Authors

• Clément de Chaisemartin, Economics Department, Sciences Po, France.

• Xavier D’Haultfoeuille, CREST-ENSAE, France.

• Diego Ciccia, Northwestern University, USA.

• Felix Knau, LMU Munich, Germany.

• Mélitine Malézieux, Stockholm School of Economics, Sweden.

• Doulo Sow, Princeton University, USA.

• David Arboleda, Stanford University, USA.

• Romain Angotti, Stanford University, USA.

• Henri Fabre, LSE, UK.

• Bingxue Li, UIUC, USA.

• Anzoni Quispe, Brown University, USA.

References

Bell, R. M., McCaffrey, D. F. (2002). Bias reduction in standard errors for linear regression with multi-stage samples. Survey Methodology.

de Chaisemartin, C, D’Haultfoeuille, X (2026). Difference-in-Differences Estimators of Intertemporal Treatment Effects doi:10.2139/ssrn.3731856. Review of Economics and Statistics.

de Chaisemartin, C, D’Haultfoeuille, X (2023). Two-way fixed effects regressions with several treatments doi:10.2139/ssrn.3751060. Journal of Econometrics.

de Chaisemartin, C., Ciccia, D., Knau, F., Malézieux, M., Sow, D., Arboleda, D., Angotti, R., D’Haultfoeuille, X., Li, B., Fabre, H., Quispe, A. (2025). Using did_multiplegt_dyn to Estimate Event-Study Effects in Complex Designs: Overview, and Four Examples Based on Real Datasets doi:10.2139/ssrn.5337463.

Examples

# See the did_multiplegt_dyn GitHub page for examples and details.

Favara and Imbs (2015)

Description

Favara and Imbs (2015) use 1994-to-2005 county-level data to estimate the effect of the number of regulations lifted on the growth of mortgages originated by banks, and on the growth of houses prices. Their findings are revisited in de Chaisemartin and D'Haultfoeuille (2024a). This dataset includes only the first 10 states. The full dataset is available on GitHub.

Usage

data(favara_imbs)

Format

An object of class tbl_df (inherits from tbl, data.frame) with 1157 rows and 7 columns.

References

Favara and Imbs (2015) (AER)

A print method for did_multiplegt_dyn

Description

A customized printed display for did_multiplegt_dyn output

Usage

## S3 method for class 'did_multiplegt_dyn'
print(x, ...)

Arguments

Value

No return, custom print method for did_multiplegt_dyn objects. Estimation tables are fetched from the object and displayed in the same style as the Stata did_multiplegt_dyn command.

rnames method for did_multiplegt_dyn

Description

A customized rnames method for did_multiplegt_dyn output

Usage

## S3 method for class 'did_multiplegt_dyn'
rnames(obj, ignore = c("plot", "args"), ...)

Arguments

Value

The same output as rnames.

A summary method for did_multiplegt_dyn

Description

A customized summary display for did_multiplegt_dyn output

Usage

## S3 method for class 'did_multiplegt_dyn'
summary(object, ...)

Arguments

Value

No return, custom summary method for did_multiplegt_dyn objects. Estimation tables are fetched from the object and displayed in the same style as the Stata did_multiplegt_dyn command.