Note

Download Jupyter notebook: https://docs.doubleml.org/stable/examples/did/py_rep_cs.ipynb.

Python: Repeated Cross-Sectional Data with Multiple Time Periods

In this example, a detailed guide on Difference-in-Differences with multiple time periods using the DoubleML-package. The implementation is based on Callaway and Sant’Anna(2021).

The notebook requires the following packages:

import seaborn as sns
import matplotlib.pyplot as plt
import pandas as pd
import numpy as np

from lightgbm import LGBMRegressor, LGBMClassifier
from sklearn.linear_model import LinearRegression, LogisticRegression

from doubleml.did import DoubleMLDIDMulti
from doubleml.data import DoubleMLPanelData

from doubleml.did.datasets import make_did_cs_CS2021

Data

We will rely on the make_did_cs_CS2021 DGP, which is inspired by Callaway and Sant’Anna(2021) (Appendix SC) and Sant’Anna and Zhao (2020).

We will observe approximately n_obs units over n_periods. The parameter lambda_t determines the probability of observing a unit i in time period t. The parameter lambda_t is set to 0.5 for all time periods, which means that each unit has a 50% chance of being observed in each time period.

Remark that the dataframe includes observations of the potential outcomes y0 and y1, such that we can use oracle estimates as comparisons.

n_obs = 5000
n_periods = 6

df = make_did_cs_CS2021(n_obs, dgp_type=4, include_never_treated=True, n_periods=n_periods, n_pre_treat_periods=3,
                        lambda_t=0.5, time_type="float")
df["ite"] = df["y1"] - df["y0"]

print(df.shape)
df.head()

(29601, 11)

	id	y	y0	y1	d	t	Z1	Z2	Z3	Z4	ite
0	0	206.290533	206.290533	207.964732	3.0	0	-0.317116	-0.832171	-0.308184	-1.870001	1.674198
1	0	207.450885	207.450885	208.125002	3.0	1	-0.317116	-0.832171	-0.308184	-1.870001	0.674117
2	0	205.392812	205.392812	207.117336	3.0	2	-0.317116	-0.832171	-0.308184	-1.870001	1.724524
3	0	207.727118	205.829388	207.727118	3.0	3	-0.317116	-0.832171	-0.308184	-1.870001	1.897730
5	0	206.798758	203.390777	206.798758	3.0	5	-0.317116	-0.832171	-0.308184	-1.870001	3.407981

Data Details

Here, we slightly abuse the definition of the potential outcomes. :math:`Y_{i,t}(1)` corresponds to the (potential) outcome if unit :math:`i` would have received treatment at time period :math:`mathrm{g}` (where the group :math:`mathrm{g}` is drawn with probabilities based on :math:`Z`).

The data set with repeated cross-sectional data is generated on the basis of a panel data set with the following data generating process (DGP). To obtain repeated cross-sectional data, the number of generated individuals is increased to \(\frac{n_{obs}}{\lambda_t}\), where \(\lambda_t\) denotes the probability to observe a unit at each time period (time constant).

More specifically

\[\begin{split}\begin{align*} Y_{i,t}(0)&:= f_t(Z) + \delta_t + \eta_i + \varepsilon_{i,t,0}\\ Y_{i,t}(1)&:= Y_{i,t}(0) + \theta_{i,t,\mathrm{g}} + \epsilon_{i,t,1} - \epsilon_{i,t,0} \end{align*}\end{split}\]

where

• \(f_t(Z)\) depends on pre-treatment observable covariates \(Z_1,\dots, Z_4\) and time \(t\)

• \(\delta_t\) is a time fixed effect

• \(\eta_i\) is a unit fixed effect

• \(\epsilon_{i,t,\cdot}\) are time varying unobservables (iid. \(N(0,1)\))

• \(\theta_{i,t,\mathrm{g}}\) correponds to the exposure effect of unit \(i\) based on group \(\mathrm{g}\) at time \(t\)

For the pre-treatment periods the exposure effect is set to

\[\theta_{i,t,\mathrm{g}}:= 0 \text{ for } t<\mathrm{g}\]

such that

\[\mathbb{E}[Y_{i,t}(1) - Y_{i,t}(0)] = \mathbb{E}[\epsilon_{i,t,1} - \epsilon_{i,t,0}]=0 \text{ for } t<\mathrm{g}\]

The DoubleML Coverage Repository includes coverage simulations based on this DGP.

Data Description

The data is a balanced panel where each unit is observed over n_periods starting Janary 2025.

df.groupby("t").size()

t
0    4914
1    5000
2    4854
3    5062
4    4887
5    4884
dtype: int64

The treatment column d indicates first treatment period of the corresponding unit, whereas NaT units are never treated.

Generally, never treated units should take either on the value ``np.inf`` or ``pd.NaT`` depending on the data type (``float`` or ``datetime``).

The individual units are roughly uniformly divided between the groups, where treatment assignment depends on the pre-treatment covariates Z1 to Z4.

df.groupby("d", dropna=False).size()

d
3.0    7578
4.0    7186
5.0    7196
inf    7641
dtype: int64

Here, the group indicates the first treated period and NaT units are never treated. To simplify plotting and pands

df.groupby("d", dropna=False).size()

d
3.0    7578
4.0    7186
5.0    7196
inf    7641
dtype: int64

To get a better understanding of the underlying data and true effects, we will compare the unconditional averages and the true effects based on the oracle values of individual effects ite.

# rename for plotting

# Create aggregation dictionary for means
def agg_dict(col_name):
    return {
        f'{col_name}_mean': (col_name, 'mean'),
        f'{col_name}_lower_quantile': (col_name, lambda x: x.quantile(0.05)),
        f'{col_name}_upper_quantile': (col_name, lambda x: x.quantile(0.95))
    }

# Calculate means and confidence intervals
agg_dictionary = agg_dict("y") | agg_dict("ite")

agg_df = df.groupby(["t", "d"]).agg(**agg_dictionary).reset_index()
agg_df.head()

	t	d	y_mean	y_lower_quantile	y_upper_quantile	ite_mean	ite_lower_quantile	ite_upper_quantile
0	0	3.0	208.711855	199.091900	218.864724	-0.008117	-2.359493	2.310664
1	0	4.0	210.269650	199.849703	220.428055	-0.042078	-2.386611	2.367674
2	0	5.0	212.460444	203.261968	222.618621	-0.017448	-2.285882	2.319843
3	0	inf	214.203281	204.147365	224.192737	-0.005641	-2.298443	2.271431
4	1	3.0	208.757128	188.251340	228.885705	-0.019994	-2.276624	2.293457

def plot_data(df, col_name='y'):
    """
    Create an improved plot with colorblind-friendly features

    Parameters:
    -----------
    df : DataFrame
        The dataframe containing the data
    col_name : str, default='y'
        Column name to plot (will use '{col_name}_mean')
    """
    plt.figure(figsize=(12, 7))
    n_colors = df["d"].nunique()
    color_palette = sns.color_palette("colorblind", n_colors=n_colors)

    sns.lineplot(
        data=df,
        x='t',
        y=f'{col_name}_mean',
        hue='d',
        style='d',
        palette=color_palette,
        markers=True,
        dashes=True,
        linewidth=2.5,
        alpha=0.8
    )

    plt.title(f'Average Values {col_name} by Group Over Time', fontsize=16)
    plt.xlabel('Time', fontsize=14)
    plt.ylabel(f'Average Value {col_name}', fontsize=14)


    plt.legend(title='d', title_fontsize=13, fontsize=12,
               frameon=True, framealpha=0.9, loc='best')

    plt.grid(alpha=0.3, linestyle='-')
    plt.tight_layout()

    plt.show()

So let us take a look at the average values over time

plot_data(agg_df, col_name='y')

/opt/hostedtoolcache/Python/3.12.11/x64/lib/python3.12/site-packages/matplotlib/colors.py:2295: RuntimeWarning: invalid value encountered in divide
  resdat /= (vmax - vmin)

Instead the true average treatment treatment effects can be obtained by averaging (usually unobserved) the ite values.

The true effect just equals the exposure time (in months):

\[ATT(\mathrm{g}, t) = \min(\mathrm{t} - \mathrm{g} + 1, 0) =: e\]

plot_data(agg_df, col_name='ite')

/opt/hostedtoolcache/Python/3.12.11/x64/lib/python3.12/site-packages/matplotlib/colors.py:2295: RuntimeWarning: invalid value encountered in divide
  resdat /= (vmax - vmin)

DoubleMLPanelData

Finally, we can construct our DoubleMLPanelData, specifying

• y_col : the outcome

• d_cols: the group variable indicating the first treated period for each unit

• id_col: the unique identification column for each unit

• t_col : the time column

• x_cols: the additional pre-treatment controls

• datetime_unit: unit required for datetime columns and plotting

dml_data = DoubleMLPanelData(
    data=df,
    y_col="y",
    d_cols="d",
    id_col="id",
    t_col="t",
    x_cols=["Z1", "Z2", "Z3", "Z4"],
)
print(dml_data)

================== DoubleMLPanelData Object ==================

------------------ Data summary      ------------------
Outcome variable: y
Treatment variable(s): ['d']
Covariates: ['Z1', 'Z2', 'Z3', 'Z4']
Instrument variable(s): None
Time variable: t
Id variable: id
No. Unique Ids: 9847
No. Observations: 29601

------------------ DataFrame info    ------------------
<class 'pandas.core.frame.DataFrame'>
RangeIndex: 29601 entries, 0 to 29600
Columns: 11 entries, id to ite
dtypes: float64(9), int64(2)
memory usage: 2.5 MB

ATT Estimation

The DoubleML-package implements estimation of group-time average treatment effect via the DoubleMLDIDMulti class (see model documentation).

Basics

The class basically behaves like other DoubleML classes and requires the specification of two learners (for more details on the regression elements, see score documentation).

The basic arguments of a DoubleMLDIDMulti object include

• ml_g “outcome” regression learner

• ml_m propensity Score learner

• control_group the control group for the parallel trend assumption

• gt_combinations combinations of \((\mathrm{g},t_\text{pre}, t_\text{eval})\)

• anticipation_periods number of anticipation periods

We will construct a dict with “default” arguments.

For repeated cross-sectional data, we additionally specify the argument

• panel=False

default_args = {
    "ml_g": LGBMRegressor(n_estimators=500, learning_rate=0.01, verbose=-1, random_state=123),
    "ml_m": LGBMClassifier(n_estimators=500, learning_rate=0.01, verbose=-1, random_state=123),
    "control_group": "never_treated",
    "anticipation_periods": 0,
    "n_folds": 5,
    "n_rep": 1,
    "panel": False,
}

The model will be estimated using the fit() method.

dml_obj = DoubleMLDIDMulti(dml_data, **default_args)
dml_obj.fit()
print(dml_obj)

================== DoubleMLDIDMulti Object ==================

------------------ Data summary      ------------------
Outcome variable: y
Treatment variable(s): ['d']
Covariates: ['Z1', 'Z2', 'Z3', 'Z4']
Instrument variable(s): None
Time variable: t
Id variable: id
No. Unique Ids: 9847
No. Observations: 29601

------------------ Score & algorithm ------------------
Score function: observational
Control group: never_treated
Anticipation periods: 0

------------------ Machine learner   ------------------
Learner ml_g: LGBMRegressor(learning_rate=0.01, n_estimators=500, random_state=123,
              verbose=-1)
Learner ml_m: LGBMClassifier(learning_rate=0.01, n_estimators=500, random_state=123,
               verbose=-1)
Out-of-sample Performance:
Regression:
Learner ml_g_d0_t0 RMSE: [[1.98430085 2.92185958 3.96072074 4.01615173 3.99746842 1.94860197
  2.91220897 3.95326435 5.33890777 5.36415913 1.96261388 2.85975739
  3.97859413 5.41113127 6.50649578]]
Learner ml_g_d0_t1 RMSE: [[2.90041844 4.01562045 5.374187   6.47364698 7.88686151 2.97781186
  3.85026247 5.40043967 6.52873332 8.11570692 2.95037883 3.87334694
  5.32207333 6.6825634  7.82987933]]
Learner ml_g_d1_t0 RMSE: [[1.93811241 3.01601231 4.12397944 4.14368631 4.1068965  1.88728285
  2.81496258 3.9901015  4.88683838 4.81874341 1.94094027 3.03267071
  4.01844598 5.25465859 6.30140735]]
Learner ml_g_d1_t1 RMSE: [[3.07358689 4.13338882 5.32536645 6.16452829 7.81141183 2.81327761
  4.04464987 4.68690706 6.34072587 7.41243276 3.03757199 3.99817614
  5.26103716 6.56316397 7.6340788 ]]
Classification:
Learner ml_m Log Loss: [[0.61228405 0.60639433 0.61638235 0.60691978 0.61086846 0.63377629
  0.63142806 0.64685572 0.64520933 0.64537167 0.65369941 0.65833534
  0.6622962  0.66227142 0.65609841]]

------------------ Resampling        ------------------
No. folds: 5
No. repeated sample splits: 1

------------------ Fit summary       ------------------
                  coef   std err         t         P>|t|     2.5 %    97.5 %
ATT(3.0,0,1) -0.111021  0.217438 -0.510588  6.096396e-01 -0.537192  0.315149
ATT(3.0,1,2)  0.195264  0.324272  0.602161  5.470670e-01 -0.440298  0.830826
ATT(3.0,2,3)  1.194680  0.396379  3.013984  2.578410e-03  0.417791  1.971568
ATT(3.0,2,4)  2.078489  0.417198  4.982024  6.292265e-07  1.260797  2.896182
ATT(3.0,2,5)  2.755739  0.541919  5.085153  3.673299e-07  1.693598  3.817880
ATT(4.0,0,1)  0.100516  0.186125  0.540049  5.891635e-01 -0.264281  0.465314
ATT(4.0,1,2)  0.007868  0.243581  0.032303  9.742307e-01 -0.469542  0.485278
ATT(4.0,2,3) -0.260447  0.310786 -0.838028  4.020150e-01 -0.869576  0.348682
ATT(4.0,3,4)  1.466160  0.380038  3.857926  1.143531e-04  0.721298  2.211022
ATT(4.0,3,5)  1.978502  0.477238  4.145737  3.387217e-05  1.043133  2.913870
ATT(5.0,0,1)  0.135144  0.159067  0.849605  3.955447e-01 -0.176622  0.446910
ATT(5.0,1,2)  0.004293  0.217748  0.019716  9.842697e-01 -0.422485  0.431072
ATT(5.0,2,3) -0.470757  0.285231 -1.650440  9.885290e-02 -1.029800  0.088286
ATT(5.0,3,4)  0.117080  0.387465  0.302168  7.625237e-01 -0.642338  0.876498
ATT(5.0,4,5)  0.898292  0.429518  2.091396  3.649257e-02  0.056452  1.740131

The summary displays estimates of the \(ATT(g,t_\text{eval})\) effects for different combinations of \((g,t_\text{eval})\) via \(\widehat{ATT}(\mathrm{g},t_\text{pre},t_\text{eval})\), where

• \(\mathrm{g}\) specifies the group

• \(t_\text{pre}\) specifies the corresponding pre-treatment period

• \(t_\text{eval}\) specifies the evaluation period

The choice gt_combinations="standard", used estimates all possible combinations of \(ATT(g,t_\text{eval})\) via \(\widehat{ATT}(\mathrm{g},t_\text{pre},t_\text{eval})\), where the standard choice is \(t_\text{pre} = \min(\mathrm{g}, t_\text{eval}) - 1\) (without anticipation).

Remark that this includes pre-tests effects if \(\mathrm{g} > t_{eval}\), e.g. \(\widehat{ATT}(g=3, t_{\text{pre}}=0, t_{\text{eval}}=1)\) which estimates the pre-trend from time period \(0\) to \(1\) even if the actual treatment occured in time period \(3\).

As usual for the DoubleML-package, you can obtain joint confidence intervals via bootstrap.

level = 0.95

ci = dml_obj.confint(level=level)
dml_obj.bootstrap(n_rep_boot=5000)
ci_joint = dml_obj.confint(level=level, joint=True)
ci_joint

	2.5 %	97.5 %
ATT(3.0,0,1)	-0.742576	0.520533
ATT(3.0,1,2)	-0.746594	1.137122
ATT(3.0,2,3)	0.043387	2.345972
ATT(3.0,2,4)	0.866728	3.290251
ATT(3.0,2,5)	1.181722	4.329756
ATT(4.0,0,1)	-0.440088	0.641121
ATT(4.0,1,2)	-0.699619	0.715356
ATT(4.0,2,3)	-1.163133	0.642238
ATT(4.0,3,4)	0.362329	2.569991
ATT(4.0,3,5)	0.592353	3.364651
ATT(5.0,0,1)	-0.326870	0.597159
ATT(5.0,1,2)	-0.628162	0.636748
ATT(5.0,2,3)	-1.299219	0.357704
ATT(5.0,3,4)	-1.008324	1.242483
ATT(5.0,4,5)	-0.349254	2.145838

A visualization of the effects can be obtained via the plot_effects() method.

Remark that the plot used joint confidence intervals per default.

dml_obj.plot_effects()

/opt/hostedtoolcache/Python/3.12.11/x64/lib/python3.12/site-packages/matplotlib/cbook.py:1719: FutureWarning: Calling float on a single element Series is deprecated and will raise a TypeError in the future. Use float(ser.iloc[0]) instead
  return math.isfinite(val)

(<Figure size 1200x800 with 4 Axes>,
 [<Axes: title={'center': 'First Treated: 3.0'}, ylabel='Effect'>,
  <Axes: title={'center': 'First Treated: 4.0'}, ylabel='Effect'>,
  <Axes: title={'center': 'First Treated: 5.0'}, xlabel='Evaluation Period', ylabel='Effect'>])

Sensitivity Analysis

As descripted in the Sensitivity Guide, robustness checks on omitted confounding/parallel trend violations are available, via the standard sensitivity_analysis() method.

dml_obj.sensitivity_analysis()
print(dml_obj.sensitivity_summary)

================== Sensitivity Analysis ==================

------------------ Scenario          ------------------
Significance Level: level=0.95
Sensitivity parameters: cf_y=0.03; cf_d=0.03, rho=1.0

------------------ Bounds with CI    ------------------
              CI lower  theta lower     theta  theta upper  CI upper
ATT(3.0,0,1) -0.818764    -0.458395 -0.111021     0.236352  0.593280
ATT(3.0,1,2) -0.858645    -0.325634  0.195264     0.716162  1.252033
ATT(3.0,2,3) -0.128834     0.515808  1.194680     1.873552  2.535848
ATT(3.0,2,4)  0.632813     1.320627  2.078489     2.836352  3.525724
ATT(3.0,2,5)  0.964192     1.851576  2.755739     3.659903  4.558834
ATT(4.0,0,1) -0.539144    -0.234324  0.100516     0.435357  0.743780
ATT(4.0,1,2) -0.880782    -0.477338  0.007868     0.493075  0.892826
ATT(4.0,2,3) -1.390373    -0.878496 -0.260447     0.357601  0.869695
ATT(4.0,3,4)  0.070589     0.692491  1.466160     2.239829  2.870595
ATT(4.0,3,5)  0.296190     1.078591  1.978502     2.878412  3.668259
ATT(5.0,0,1) -0.459971    -0.197916  0.135144     0.468204  0.730141
ATT(5.0,1,2) -0.801110    -0.442732  0.004293     0.451318  0.810448
ATT(5.0,2,3) -1.548992    -1.080603 -0.470757     0.139088  0.610499
ATT(5.0,3,4) -1.291787    -0.656763  0.117080     0.890922  1.532429
ATT(5.0,4,5) -0.746335    -0.037688  0.898292     1.834272  2.540801

------------------ Robustness Values ------------------
              H_0    RV (%)   RVa (%)
ATT(3.0,0,1)  0.0  0.968935  0.000389
ATT(3.0,1,2)  0.0  1.135473  0.000393
ATT(3.0,2,3)  0.0  5.218702  2.432460
ATT(3.0,2,4)  0.0  8.012316  5.416995
ATT(3.0,2,5)  0.0  8.862832  6.100256
ATT(4.0,0,1)  0.0  0.910369  0.000381
ATT(4.0,1,2)  0.0  0.049243  0.000664
ATT(4.0,2,3)  0.0  1.275524  0.000636
ATT(4.0,3,4)  0.0  5.608286  3.269934
ATT(4.0,3,5)  0.0  6.476406  3.968677
ATT(5.0,0,1)  0.0  1.228492  0.000646
ATT(5.0,1,2)  0.0  0.029110  0.000619
ATT(5.0,2,3)  0.0  2.323931  0.007919
ATT(5.0,3,4)  0.0  0.459629  0.000583
ATT(5.0,4,5)  0.0  2.881040  0.621311

In this example one can clearly, distinguish the robustness of the non-zero effects vs. the pre-treatment periods.

Control Groups

The current implementation support the following control groups

• "never_treated"

• "not_yet_treated"

Remark that the ``”not_yet_treated” depends on anticipation.

For differences and recommendations, we refer to Callaway and Sant’Anna(2021).

dml_obj_nyt = DoubleMLDIDMulti(dml_data, **(default_args | {"control_group": "not_yet_treated"}))
dml_obj_nyt.fit()
dml_obj_nyt.bootstrap(n_rep_boot=5000)
dml_obj_nyt.plot_effects()

/opt/hostedtoolcache/Python/3.12.11/x64/lib/python3.12/site-packages/matplotlib/cbook.py:1719: FutureWarning: Calling float on a single element Series is deprecated and will raise a TypeError in the future. Use float(ser.iloc[0]) instead
  return math.isfinite(val)

(<Figure size 1200x800 with 4 Axes>,
 [<Axes: title={'center': 'First Treated: 3.0'}, ylabel='Effect'>,
  <Axes: title={'center': 'First Treated: 4.0'}, ylabel='Effect'>,
  <Axes: title={'center': 'First Treated: 5.0'}, xlabel='Evaluation Period', ylabel='Effect'>])

Linear Covariate Adjustment

Remark that we relied on boosted trees to adjust for conditional parallel trends which allow for a nonlinear adjustment. In comparison to linear adjustment, we could rely on linear learners.

Remark that the DGP (``dgp_type=4``) is based on nonlinear conditional expectations such that the estimates will be biased

linear_learners = {
    "ml_g": LinearRegression(),
    "ml_m": LogisticRegression(),
}

dml_obj_linear = DoubleMLDIDMulti(dml_data, **(default_args | linear_learners))
dml_obj_linear.fit()
dml_obj_linear.bootstrap(n_rep_boot=5000)
dml_obj_linear.plot_effects()

/opt/hostedtoolcache/Python/3.12.11/x64/lib/python3.12/site-packages/matplotlib/cbook.py:1719: FutureWarning: Calling float on a single element Series is deprecated and will raise a TypeError in the future. Use float(ser.iloc[0]) instead
  return math.isfinite(val)

(<Figure size 1200x800 with 4 Axes>,
 [<Axes: title={'center': 'First Treated: 3.0'}, ylabel='Effect'>,
  <Axes: title={'center': 'First Treated: 4.0'}, ylabel='Effect'>,
  <Axes: title={'center': 'First Treated: 5.0'}, xlabel='Evaluation Period', ylabel='Effect'>])

Aggregated Effects

As the did-R-package, the \(ATT\)’s can be aggregated to summarize multiple effects. For details on different aggregations and details on their interpretations see Callaway and Sant’Anna(2021).

The aggregations are implemented via the aggregate() method.

Group Aggregation

To obtain group-specific effects one can would like to average \(ATT(\mathrm{g}, t_\text{eval})\) over \(t_\text{eval}\). As a sample oracle we will combine all ite’s based on group \(\mathrm{g}\).

df_post_treatment = df[df["t"] >= df["d"]]
df_post_treatment.groupby("d")["ite"].mean()

d
3.0    1.935077
4.0    1.511858
5.0    0.958206
Name: ite, dtype: float64

To obtain group-specific effects it is possible to aggregate several \(\widehat{ATT}(\mathrm{g},t_\text{pre},t_\text{eval})\) values based on the group \(\mathrm{g}\) by setting the aggregation="group" argument.

aggregated_group = dml_obj.aggregate(aggregation="group")
print(aggregated_group)
_ = aggregated_group.plot_effects()

================== DoubleMLDIDAggregation Object ==================
 Group Aggregation

------------------ Overall Aggregated Effects ------------------
    coef  std err        t        P>|t|    2.5 %   97.5 %
1.551448  0.23123 6.709534 1.952460e-11 1.098245 2.004651
------------------ Aggregated Effects         ------------------
         coef   std err         t         P>|t|     2.5 %    97.5 %
3.0  2.009636  0.305576  6.576548  4.814948e-11  1.410718  2.608554
4.0  1.722331  0.341061  5.049922  4.419900e-07  1.053864  2.390798
5.0  0.898292  0.429518  2.091396  3.649257e-02  0.056452  1.740131
------------------ Additional Information     ------------------
Score function: observational
Control group: never_treated
Anticipation periods: 0

/opt/hostedtoolcache/Python/3.12.11/x64/lib/python3.12/site-packages/doubleml/did/did_aggregation.py:368: UserWarning: Joint confidence intervals require bootstrapping which hasn't been performed yet. Automatically applying '.aggregated_frameworks.bootstrap(method="normal", n_rep_boot=500)' with default values. For different bootstrap settings, call bootstrap() explicitly before plotting.
  warnings.warn(

The output is a DoubleMLDIDAggregation object which includes an overall aggregation summary based on group size.

Time Aggregation

To obtain time-specific effects one can would like to average \(ATT(\mathrm{g}, t_\text{eval})\) over \(\mathrm{g}\) (respecting group size). As a sample oracle we will combine all ite’s based on group \(\mathrm{g}\). As oracle values, we obtain

df_post_treatment.groupby("t")["ite"].mean()

t
3    0.932968
4    1.478475
5    2.005921
Name: ite, dtype: float64

To aggregate \(\widehat{ATT}(\mathrm{g},t_\text{pre},t_\text{eval})\), based on \(t_\text{eval}\), but weighted with respect to group size. Corresponds to Calendar Time Effects from the did-R-package.

For calendar time effects set aggregation="time".

aggregated_time = dml_obj.aggregate("time")
print(aggregated_time)
fig, ax = aggregated_time.plot_effects()

================== DoubleMLDIDAggregation Object ==================
 Time Aggregation

------------------ Overall Aggregated Effects ------------------
    coef  std err        t        P>|t|    2.5 %   97.5 %
1.622625 0.208521 7.781601 7.105427e-15 1.213932 2.031318
------------------ Aggregated Effects         ------------------
       coef   std err         t         P>|t|     2.5 %    97.5 %
3  1.194680  0.396379  3.013984  2.578410e-03  0.417791  1.971568
4  1.780454  0.321475  5.538381  3.052803e-08  1.150373  2.410534
5  1.892742  0.375189  5.044763  4.540839e-07  1.157384  2.628100
------------------ Additional Information     ------------------
Score function: observational
Control group: never_treated
Anticipation periods: 0

/opt/hostedtoolcache/Python/3.12.11/x64/lib/python3.12/site-packages/doubleml/did/did_aggregation.py:368: UserWarning: Joint confidence intervals require bootstrapping which hasn't been performed yet. Automatically applying '.aggregated_frameworks.bootstrap(method="normal", n_rep_boot=500)' with default values. For different bootstrap settings, call bootstrap() explicitly before plotting.
  warnings.warn(

Event Study Aggregation

To obtain event-study-type effects one can would like to aggregate \(ATT(\mathrm{g}, t_\text{eval})\) over \(e = t_\text{eval} - \mathrm{g}\) (respecting group size). As a sample oracle we will combine all ite’s based on group \(\mathrm{g}\). As oracle values, we obtain

df_treated = df[df["d"] != np.inf].copy()
df_treated["e"] = df_treated["t"] - df_treated["d"]
df_treated.groupby("e")["ite"].mean().iloc[1:]

e
-4.0   -0.031310
-3.0   -0.011711
-2.0   -0.018675
-1.0    0.011166
 0.0    0.949051
 1.0    2.007699
 2.0    2.929263
Name: ite, dtype: float64

Analogously, aggregation="eventstudy" aggregates \(\widehat{ATT}(\mathrm{g},t_\text{pre},t_\text{eval})\) based on exposure time \(e = t_\text{eval} - \mathrm{g}\) (respecting group size).

aggregated_eventstudy = dml_obj.aggregate("eventstudy")
print(aggregated_eventstudy)
aggregated_eventstudy.plot_effects()

================== DoubleMLDIDAggregation Object ==================
 Event Study Aggregation

------------------ Overall Aggregated Effects ------------------
    coef  std err        t        P>|t|    2.5 %   97.5 %
1.990652  0.27966 7.118121 1.094014e-12 1.442529 2.538775
------------------ Aggregated Effects         ------------------
          coef   std err         t         P>|t|     2.5 %    97.5 %
-4.0  0.135144  0.159067  0.849605  3.955447e-01 -0.176622  0.446910
-3.0  0.052371  0.128468  0.407662  6.835221e-01 -0.199421  0.304163
-2.0 -0.189998  0.121834 -1.559477  1.188835e-01 -0.428788  0.048793
-1.0  0.020521  0.166128  0.123526  9.016905e-01 -0.305084  0.346126
0.0   1.186394  0.190961  6.212758  5.206264e-10  0.812118  1.560671
1.0   2.029823  0.315928  6.424960  1.319043e-10  1.410616  2.649030
2.0   2.755739  0.541919  5.085153  3.673299e-07  1.693598  3.817880
------------------ Additional Information     ------------------
Score function: observational
Control group: never_treated
Anticipation periods: 0

/opt/hostedtoolcache/Python/3.12.11/x64/lib/python3.12/site-packages/doubleml/did/did_aggregation.py:368: UserWarning: Joint confidence intervals require bootstrapping which hasn't been performed yet. Automatically applying '.aggregated_frameworks.bootstrap(method="normal", n_rep_boot=500)' with default values. For different bootstrap settings, call bootstrap() explicitly before plotting.
  warnings.warn(

(<Figure size 1200x600 with 1 Axes>,
 <Axes: title={'center': 'Aggregated Treatment Effects'}, ylabel='Effect'>)

Aggregation Details

The DoubleMLDIDAggregation objects include several DoubleMLFrameworks which support methods like bootstrap() or confint(). Further, the weights can be accessed via the properties

• overall_aggregation_weights: weights for the overall aggregation

• aggregation_weights: weights for the aggregation

To clarify, e.g. for the eventstudy aggregation

print(aggregated_eventstudy)

================== DoubleMLDIDAggregation Object ==================
 Event Study Aggregation

------------------ Overall Aggregated Effects ------------------
    coef  std err        t        P>|t|    2.5 %   97.5 %
1.990652  0.27966 7.118121 1.094014e-12 1.442529 2.538775
------------------ Aggregated Effects         ------------------
          coef   std err         t         P>|t|     2.5 %    97.5 %
-4.0  0.135144  0.159067  0.849605  3.955447e-01 -0.176622  0.446910
-3.0  0.052371  0.128468  0.407662  6.835221e-01 -0.199421  0.304163
-2.0 -0.189998  0.121834 -1.559477  1.188835e-01 -0.428788  0.048793
-1.0  0.020521  0.166128  0.123526  9.016905e-01 -0.305084  0.346126
0.0   1.186394  0.190961  6.212758  5.206264e-10  0.812118  1.560671
1.0   2.029823  0.315928  6.424960  1.319043e-10  1.410616  2.649030
2.0   2.755739  0.541919  5.085153  3.673299e-07  1.693598  3.817880
------------------ Additional Information     ------------------
Score function: observational
Control group: never_treated
Anticipation periods: 0

Here, the overall effect aggregation aggregates each effect with positive exposure

print(aggregated_eventstudy.overall_aggregation_weights)

[0.         0.         0.         0.         0.33333333 0.33333333
 0.33333333]

If one would like to consider how the aggregated effect with \(e=0\) is computed, one would have to look at the corresponding set of weights within the aggregation_weights property

# the weights for e=0 correspond to the fifth element of the aggregation weights
aggregated_eventstudy.aggregation_weights[4]

array([0.        , 0.        , 0.34508197, 0.        , 0.        ,
       0.        , 0.        , 0.        , 0.32723133, 0.        ,
       0.        , 0.        , 0.        , 0.        , 0.3276867 ])

Taking a look at the original dml_obj, one can see that this combines the following estimates (only show month):

• \(\widehat{ATT}(04,03,04)\)

• \(\widehat{ATT}(05,04,05)\)

• \(\widehat{ATT}(06,05,06)\)

print(dml_obj.summary["coef"])

ATT(3.0,0,1)   -0.111021
ATT(3.0,1,2)    0.195264
ATT(3.0,2,3)    1.194680
ATT(3.0,2,4)    2.078489
ATT(3.0,2,5)    2.755739
ATT(4.0,0,1)    0.100516
ATT(4.0,1,2)    0.007868
ATT(4.0,2,3)   -0.260447
ATT(4.0,3,4)    1.466160
ATT(4.0,3,5)    1.978502
ATT(5.0,0,1)    0.135144
ATT(5.0,1,2)    0.004293
ATT(5.0,2,3)   -0.470757
ATT(5.0,3,4)    0.117080
ATT(5.0,4,5)    0.898292
Name: coef, dtype: float64

Anticipation

As described in the Model Guide, one can include anticipation periods \(\delta>0\) by setting the anticipation_periods parameter.

Data with Anticipation

The DGP allows to include anticipation periods via the anticipation_periods parameter. In this case the observations will be “shifted” such that units anticipate the effect earlier and the exposure effect is increased by the number of periods where the effect is anticipated.

n_obs = 4000
n_periods = 6

df_anticipation = make_did_cs_CS2021(n_obs, dgp_type=4, n_periods=n_periods, n_pre_treat_periods=3, time_type="datetime", anticipation_periods=1)

print(df_anticipation.shape)
df_anticipation.head()

(19046, 10)

	id	y	y0	y1	d	t	Z1	Z2	Z3	Z4
1	0	209.943892	209.943892	206.488123	2025-05-01	2025-01-01	0.295609	-0.260085	-0.736988	-0.638664
6	0	205.309536	201.959006	205.309536	2025-05-01	2025-06-01	0.295609	-0.260085	-0.736988	-0.638664
8	1	222.862644	222.862644	221.543711	2025-06-01	2025-01-01	0.674337	-0.172129	0.316567	0.243262
10	1	234.222429	234.222429	234.788618	2025-06-01	2025-03-01	0.674337	-0.172129	0.316567	0.243262
12	1	247.298166	246.590073	247.298166	2025-06-01	2025-05-01	0.674337	-0.172129	0.316567	0.243262

To visualize the anticipation, we will again plot the “oracle” values

df_anticipation["ite"] = df_anticipation["y1"] - df_anticipation["y0"]
agg_df_anticipation = df_anticipation.groupby(["t", "d"]).agg(**agg_dictionary).reset_index()
agg_df_anticipation.head()

	t	d	y_mean	y_lower_quantile	y_upper_quantile	ite_mean	ite_lower_quantile	ite_upper_quantile
0	2025-01-01	2025-04-01	208.157834	191.445418	225.238046	0.053598	-2.240579	2.526612
1	2025-01-01	2025-05-01	210.667238	193.058954	227.275186	0.059441	-2.387472	2.331671
2	2025-01-01	2025-06-01	212.951414	196.611318	229.209814	-0.022312	-2.427173	2.313213
3	2025-02-01	2025-04-01	208.204619	184.353255	232.589209	0.021270	-2.227462	2.383587
4	2025-02-01	2025-05-01	210.865913	187.348219	236.274644	-0.063757	-2.505044	2.174914

One can see that the effect is already anticipated one period before the actual treatment assignment.

plot_data(agg_df_anticipation, col_name='ite')

Initialize a corresponding DoubleMLPanelData object.

dml_data_anticipation = DoubleMLPanelData(
    data=df_anticipation,
    y_col="y",
    d_cols="d",
    id_col="id",
    t_col="t",
    x_cols=["Z1", "Z2", "Z3", "Z4"],
    datetime_unit="M"
)

ATT Estimation

Let us take a look at the estimation without anticipation.

dml_obj_anticipation = DoubleMLDIDMulti(dml_data_anticipation, **default_args)
dml_obj_anticipation.fit()
dml_obj_anticipation.bootstrap(n_rep_boot=5000)
dml_obj_anticipation.plot_effects()

/opt/hostedtoolcache/Python/3.12.11/x64/lib/python3.12/site-packages/matplotlib/cbook.py:1719: FutureWarning: Calling float on a single element Series is deprecated and will raise a TypeError in the future. Use float(ser.iloc[0]) instead
  return math.isfinite(val)

(<Figure size 1200x800 with 4 Axes>,
 [<Axes: title={'center': 'First Treated: 2025-04'}, ylabel='Effect'>,
  <Axes: title={'center': 'First Treated: 2025-05'}, ylabel='Effect'>,
  <Axes: title={'center': 'First Treated: 2025-06'}, xlabel='Evaluation Period', ylabel='Effect'>])

The effects are obviously biased. To include anticipation periods, one can adjust the anticipation_periods parameter. Correspondingly, the outcome regression (and not yet treated units) are adjusted.

dml_obj_anticipation = DoubleMLDIDMulti(dml_data_anticipation, **(default_args| {"anticipation_periods": 1}))
dml_obj_anticipation.fit()
dml_obj_anticipation.bootstrap(n_rep_boot=5000)
dml_obj_anticipation.plot_effects()

/opt/hostedtoolcache/Python/3.12.11/x64/lib/python3.12/site-packages/matplotlib/cbook.py:1719: FutureWarning: Calling float on a single element Series is deprecated and will raise a TypeError in the future. Use float(ser.iloc[0]) instead
  return math.isfinite(val)
/opt/hostedtoolcache/Python/3.12.11/x64/lib/python3.12/site-packages/matplotlib/cbook.py:1719: FutureWarning: Calling float on a single element Series is deprecated and will raise a TypeError in the future. Use float(ser.iloc[0]) instead
  return math.isfinite(val)
/opt/hostedtoolcache/Python/3.12.11/x64/lib/python3.12/site-packages/matplotlib/cbook.py:1719: FutureWarning: Calling float on a single element Series is deprecated and will raise a TypeError in the future. Use float(ser.iloc[0]) instead
  return math.isfinite(val)
/opt/hostedtoolcache/Python/3.12.11/x64/lib/python3.12/site-packages/matplotlib/cbook.py:1719: FutureWarning: Calling float on a single element Series is deprecated and will raise a TypeError in the future. Use float(ser.iloc[0]) instead
  return math.isfinite(val)
/opt/hostedtoolcache/Python/3.12.11/x64/lib/python3.12/site-packages/matplotlib/cbook.py:1719: FutureWarning: Calling float on a single element Series is deprecated and will raise a TypeError in the future. Use float(ser.iloc[0]) instead
  return math.isfinite(val)

(<Figure size 1200x800 with 4 Axes>,
 [<Axes: title={'center': 'First Treated: 2025-04'}, ylabel='Effect'>,
  <Axes: title={'center': 'First Treated: 2025-05'}, ylabel='Effect'>,
  <Axes: title={'center': 'First Treated: 2025-06'}, xlabel='Evaluation Period', ylabel='Effect'>])

Group-Time Combinations

The default option gt_combinations="standard" includes all group time values with the specific choice of \(t_\text{pre} = \min(\mathrm{g}, t_\text{eval}) - 1\) (without anticipation) which is the weakest possible parallel trend assumption.

Other options are possible or only specific combinations of \((\mathrm{g},t_\text{pre},t_\text{eval})\).

All combinations

The option gt_combinations="all" includes all relevant group time values with \(t_\text{pre} < \min(\mathrm{g}, t_\text{eval})\), including longer parallel trend assumptions. This can result in multiple estimates for the same \(ATT(\mathrm{g},t)\), which have slightly different assumptions (length of parallel trends).

dml_obj_all = DoubleMLDIDMulti(dml_data, **(default_args| {"gt_combinations": "all"}))
dml_obj_all.fit()
dml_obj_all.bootstrap(n_rep_boot=5000)
dml_obj_all.plot_effects()

(<Figure size 1200x800 with 4 Axes>,
 [<Axes: title={'center': 'First Treated: 3.0'}, ylabel='Effect'>,
  <Axes: title={'center': 'First Treated: 4.0'}, ylabel='Effect'>,
  <Axes: title={'center': 'First Treated: 5.0'}, xlabel='Evaluation Period', ylabel='Effect'>])

Universal Base Period

The option gt_combinations="universal" set \(t_\text{pre} = \mathrm{g} - \delta - 1\), corresponding to a universal/constant comparison or base period.

Remark that this implies \(t_\text{pre} > t_\text{eval}\) for all pre-treatment periods (accounting for anticipation). Therefore these effects do not have the same straightforward interpretation as ATT’s.

dml_obj_universal = DoubleMLDIDMulti(dml_data, **(default_args| {"gt_combinations": "universal"}))
dml_obj_universal.fit()
dml_obj_universal.bootstrap(n_rep_boot=5000)
dml_obj_universal.plot_effects()

/opt/hostedtoolcache/Python/3.12.11/x64/lib/python3.12/site-packages/matplotlib/cbook.py:1719: FutureWarning: Calling float on a single element Series is deprecated and will raise a TypeError in the future. Use float(ser.iloc[0]) instead
  return math.isfinite(val)

(<Figure size 1200x800 with 4 Axes>,
 [<Axes: title={'center': 'First Treated: 3.0'}, ylabel='Effect'>,
  <Axes: title={'center': 'First Treated: 4.0'}, ylabel='Effect'>,
  <Axes: title={'center': 'First Treated: 5.0'}, xlabel='Evaluation Period', ylabel='Effect'>])

Selected Combinations

Instead it is also possible to just submit a list of tuples containing \((\mathrm{g}, t_\text{pre}, t_\text{eval})\) combinations. E.g. only two combinations

gt_dict = {
    "gt_combinations": [
        (4.0, 1, 2),
        (4.0, 1, 3),
        ]
}

dml_obj_all = DoubleMLDIDMulti(dml_data, **(default_args| gt_dict))
dml_obj_all.fit()
dml_obj_all.bootstrap(n_rep_boot=5000)
dml_obj_all.plot_effects()

(<Figure size 1200x800 with 2 Axes>,
 [<Axes: title={'center': 'First Treated: 4.0'}, xlabel='Evaluation Period', ylabel='Effect'>])