Note

Python: Panel 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:

[1]:

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_CS2021

Data#

We will rely on the make_did_CS2021 DGP, which is inspired by Callaway and Sant’Anna(2021) (Appendix SC) and Sant’Anna and Zhao (2020).

We will observe n_obs units over n_periods. Remark that the dataframe includes observations of the potential outcomes y0 and y1, such that we can use oracle estimates as comparisons.

[2]:

n_obs = 5000
n_periods = 6

df = make_did_CS2021(n_obs, dgp_type=4, n_periods=n_periods, n_pre_treat_periods=3, time_type="datetime")
df["ite"] = df["y1"] - df["y0"]

print(df.shape)
df.head()

(30000, 11)

[2]:
id y y0 y1 d t Z1 Z2 Z3 Z4 ite
0 0 209.834393 209.834393 209.484616 2025-05-01 2025-01-01 2.086558 -0.400637 -2.627901 -0.787781 -0.349777
1 0 211.291834 211.291834 213.805970 2025-05-01 2025-02-01 2.086558 -0.400637 -2.627901 -0.787781 2.514136
2 0 216.193802 216.193802 215.148745 2025-05-01 2025-03-01 2.086558 -0.400637 -2.627901 -0.787781 -1.045056
3 0 217.436498 217.436498 215.108632 2025-05-01 2025-04-01 2.086558 -0.400637 -2.627901 -0.787781 -2.327865
4 0 220.535470 219.069296 220.535470 2025-05-01 2025-05-01 2.086558 -0.400637 -2.627901 -0.787781 1.466174

Data Details#

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

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.

[3]:

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

[3]:

t
2025-01-01    5000
2025-02-01    5000
2025-03-01    5000
2025-04-01    5000
2025-05-01    5000
2025-06-01    5000
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.

[4]:

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

[4]:

d
2025-04-01    7356
2025-05-01    7446
2025-06-01    7242
NaT           7956
dtype: int64

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

[5]:

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

[5]:

d
2025-04-01    7356
2025-05-01    7446
2025-06-01    7242
NaT           7956
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.

[6]:

# rename for plotting
df["First Treated"] = df["d"].dt.strftime("%Y-%m").fillna("Never Treated")

# 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", "First Treated"]).agg(**agg_dictionary).reset_index()
agg_df.head()

[6]:
t First Treated y_mean y_lower_quantile y_upper_quantile ite_mean ite_lower_quantile ite_upper_quantile
0 2025-01-01 2025-04 208.775749 198.348374 219.198271 0.037745 -2.339713 2.380524
1 2025-01-01 2025-05 210.533169 200.534954 220.470757 0.041675 -2.385403 2.282614
2 2025-01-01 2025-06 212.368638 202.069683 222.833765 0.006224 -2.333743 2.343742
3 2025-01-01 Never Treated 214.334565 204.017841 224.103760 0.019119 -2.343730 2.347051
4 2025-02-01 2025-04 208.595832 188.319878 229.209183 0.041360 -2.245479 2.157909 
[7]:

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["First Treated"].nunique()
    color_palette = sns.color_palette("colorblind", n_colors=n_colors)

    sns.lineplot(
        data=df,
        x='t',
        y=f'{col_name}_mean',
        hue='First Treated',
        style='First Treated',
        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='First Treated', 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

[8]:

plot_data(agg_df, col_name='y')
../../_images/examples_did_py_panel_16_0.png

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):

\[ATT(\mathrm{g}, t) = \min(\mathrm{t} - \mathrm{g} + 1, 0) =: e\]
[9]:

plot_data(agg_df, col_name='ite')
../../_images/examples_did_py_panel_18_0.png

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

[10]:

dml_data = DoubleMLPanelData(
    data=df,
    y_col="y",
    d_cols="d",
    id_col="id",
    t_col="t",
    x_cols=["Z1", "Z2", "Z3", "Z4"],
    datetime_unit="M"
)
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: 5000
No. Observations: 30000

------------------ DataFrame info    ------------------
<class 'pandas.core.frame.DataFrame'>
RangeIndex: 30000 entries, 0 to 29999
Columns: 12 entries, id to First Treated
dtypes: datetime64[s](2), float64(8), int64(1), object(1)
memory usage: 2.7+ 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.

[11]:

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",
    "gt_combinations": "standard",
    "anticipation_periods": 0,
    "n_folds": 5,
    "n_rep": 1,
}

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

[12]:

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: 5000
No. Observations: 30000

------------------ 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_g0 RMSE: [[1.92269763 1.89521715 1.90248195 2.7171236  3.87440456 1.92141246
  1.87394395 1.91285153 1.92189296 2.77207054 1.91052125 1.90057968
  1.92754116 1.86264183 1.89690296]]
Learner ml_g1 RMSE: [[2.0533234  1.96954962 1.94246781 2.98628619 4.15759494 1.95944848
  1.92617326 1.94277186 1.99800655 2.93609912 1.96797058 1.95146424
  1.92958636 1.99831108 1.87082288]]
Classification:
Learner ml_m Log Loss: [[0.6847866  0.69124203 0.68860297 0.69146972 0.6920497  0.70576788
  0.70933631 0.70079106 0.70133042 0.71241791 0.7323105  0.72530759
  0.72592138 0.72518055 0.73706372]]

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

------------------ Fit summary       ------------------
                                  coef   std err          t         P>|t|  \
ATT(2025-04,2025-01,2025-02) -0.125556  0.092593  -1.355995  1.751007e-01
ATT(2025-04,2025-02,2025-03) -0.023540  0.112287  -0.209638  8.339505e-01
ATT(2025-04,2025-03,2025-04)  0.783747  0.099182   7.902152  2.664535e-15
ATT(2025-04,2025-03,2025-05)  1.554008  0.146556  10.603484  0.000000e+00
ATT(2025-04,2025-03,2025-06)  2.496245  0.241582  10.332920  0.000000e+00
ATT(2025-05,2025-01,2025-02) -0.090754  0.091924  -0.987269  3.235107e-01
ATT(2025-05,2025-02,2025-03)  0.105795  0.101881   1.038410  2.990793e-01
ATT(2025-05,2025-03,2025-04) -0.210046  0.097055  -2.164195  3.044940e-02
ATT(2025-05,2025-04,2025-05)  0.931792  0.119133   7.821476  5.329071e-15
ATT(2025-05,2025-04,2025-06)  1.846437  0.149593  12.343041  0.000000e+00
ATT(2025-06,2025-01,2025-02) -0.049208  0.086232  -0.570648  5.682385e-01
ATT(2025-06,2025-02,2025-03)  0.002985  0.087838   0.033983  9.728904e-01
ATT(2025-06,2025-03,2025-04) -0.102654  0.091712  -1.119303  2.630109e-01
ATT(2025-06,2025-04,2025-05) -0.036532  0.086011  -0.424734  6.710308e-01
ATT(2025-06,2025-05,2025-06)  0.963408  0.088396  10.898797  0.000000e+00

                                 2.5 %    97.5 %
ATT(2025-04,2025-01,2025-02) -0.307035  0.055923
ATT(2025-04,2025-02,2025-03) -0.243618  0.196539
ATT(2025-04,2025-03,2025-04)  0.589355  0.978140
ATT(2025-04,2025-03,2025-05)  1.266763  1.841253
ATT(2025-04,2025-03,2025-06)  2.022753  2.969736
ATT(2025-05,2025-01,2025-02) -0.270923  0.089414
ATT(2025-05,2025-02,2025-03) -0.093889  0.305478
ATT(2025-05,2025-03,2025-04) -0.400271 -0.019822
ATT(2025-05,2025-04,2025-05)  0.698297  1.165288
ATT(2025-05,2025-04,2025-06)  1.553239  2.139634
ATT(2025-06,2025-01,2025-02) -0.218221  0.119804
ATT(2025-06,2025-02,2025-03) -0.169175  0.175145
ATT(2025-06,2025-03,2025-04) -0.282407  0.077099
ATT(2025-06,2025-04,2025-05) -0.205111  0.132047
ATT(2025-06,2025-05,2025-06)  0.790155  1.136661

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. \(\widehat{ATT}(g=\text{2025-04}, t_{\text{pre}}=\text{2025-01}, t_{\text{eval}}=\text{2025-02})\) which estimates the pre-trend from January to February even if the actual treatment occured in April.

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

[13]:

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

[13]:
2.5 % 97.5 %
ATT(2025-04,2025-01,2025-02) -0.388683 0.137571
ATT(2025-04,2025-02,2025-03) -0.342630 0.295551
ATT(2025-04,2025-03,2025-04) 0.501899 1.065596
ATT(2025-04,2025-03,2025-05) 1.137532 1.970484
ATT(2025-04,2025-03,2025-06) 1.809730 3.182759
ATT(2025-05,2025-01,2025-02) -0.351980 0.170472
ATT(2025-05,2025-02,2025-03) -0.183726 0.395315
ATT(2025-05,2025-03,2025-04) -0.485853 0.065760
ATT(2025-05,2025-04,2025-05) 0.593248 1.270337
ATT(2025-05,2025-04,2025-06) 1.421330 2.271543
ATT(2025-06,2025-01,2025-02) -0.294259 0.195842
ATT(2025-06,2025-02,2025-03) -0.246629 0.252599
ATT(2025-06,2025-03,2025-04) -0.363277 0.157969
ATT(2025-06,2025-04,2025-05) -0.280954 0.207890
ATT(2025-06,2025-05,2025-06) 0.712209 1.214607

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

Remark that the plot used joint confidence intervals per default.

[14]:

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)

[14]:

(<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'>])
../../_images/examples_did_py_panel_30_2.png

Sensitivity Analysis#

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

[15]:

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  \
ATT(2025-04,2025-01,2025-02) -0.407554    -0.254863 -0.125556     0.003751
ATT(2025-04,2025-02,2025-03) -0.303164    -0.120145 -0.023540     0.073066
ATT(2025-04,2025-03,2025-04)  0.517335     0.678437  0.783747     0.889058
ATT(2025-04,2025-03,2025-05)  1.150065     1.394798  1.554008     1.713219
ATT(2025-04,2025-03,2025-06)  1.899497     2.292502  2.496245     2.699987
ATT(2025-05,2025-01,2025-02) -0.351777    -0.201804 -0.090754     0.020296
ATT(2025-05,2025-02,2025-03) -0.153171     0.008032  0.105795     0.203557
ATT(2025-05,2025-03,2025-04) -0.481067    -0.318824 -0.210046    -0.101268
ATT(2025-05,2025-04,2025-05)  0.658073     0.834802  0.931792     1.028782
ATT(2025-05,2025-04,2025-06)  1.447761     1.690370  1.846437     2.002503
ATT(2025-06,2025-01,2025-02) -0.296954    -0.155005 -0.049208     0.056588
ATT(2025-06,2025-02,2025-03) -0.246013    -0.101630  0.002985     0.107600
ATT(2025-06,2025-03,2025-04) -0.357065    -0.204974 -0.102654    -0.000334
ATT(2025-06,2025-04,2025-05) -0.281671    -0.140790 -0.036532     0.067726
ATT(2025-06,2025-05,2025-06)  0.720532     0.867100  0.963408     1.059716

                              CI upper
ATT(2025-04,2025-01,2025-02)  0.156720
ATT(2025-04,2025-02,2025-03)  0.262619
ATT(2025-04,2025-03,2025-04)  1.056741
ATT(2025-04,2025-03,2025-05)  1.953620
ATT(2025-04,2025-03,2025-06)  3.108963
ATT(2025-05,2025-01,2025-02)  0.173584
ATT(2025-05,2025-02,2025-03)  0.379535
ATT(2025-05,2025-03,2025-04)  0.056855
ATT(2025-05,2025-04,2025-05)  1.248252
ATT(2025-05,2025-04,2025-06)  2.253161
ATT(2025-06,2025-01,2025-02)  0.198726
ATT(2025-06,2025-02,2025-03)  0.252598
ATT(2025-06,2025-03,2025-04)  0.149804
ATT(2025-06,2025-04,2025-05)  0.210298
ATT(2025-06,2025-05,2025-06)  1.204479

------------------ Robustness Values ------------------
                              H_0     RV (%)    RVa (%)
ATT(2025-04,2025-01,2025-02)  0.0   2.914338   0.000604
ATT(2025-04,2025-02,2025-03)  0.0   0.739625   0.000500
ATT(2025-04,2025-03,2025-04)  0.0  20.245042  15.892026
ATT(2025-04,2025-03,2025-05)  0.0  25.638379  20.824841
ATT(2025-04,2025-03,2025-06)  0.0  31.000133  24.657721
ATT(2025-05,2025-01,2025-02)  0.0   2.458633   0.000643
ATT(2025-05,2025-02,2025-03)  0.0   3.242475   0.000449
ATT(2025-05,2025-03,2025-04)  0.0   5.711374   1.425081
ATT(2025-05,2025-04,2025-05)  0.0  25.293401  20.088342
ATT(2025-05,2025-04,2025-06)  0.0  30.124641  26.444081
ATT(2025-06,2025-01,2025-02)  0.0   1.406902   0.000557
ATT(2025-06,2025-02,2025-03)  0.0   0.086733   0.000569
ATT(2025-06,2025-03,2025-04)  0.0   3.009697   0.000367
ATT(2025-06,2025-04,2025-05)  0.0   1.061783   0.000386
ATT(2025-06,2025-05,2025-06)  0.0  26.179979  22.160397

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).

[16]:

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)

[16]:

(<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'>])
../../_images/examples_did_py_panel_35_2.png

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

[17]:

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)

[17]:

(<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'>])
../../_images/examples_did_py_panel_37_2.png

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 \(\mathrm{g}\).

[18]:

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

[18]:

d
2025-04-01    1.933297
2025-05-01    1.478893
2025-06-01    1.048899
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.

[19]:

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 %
1.323413 0.087245 15.168875    0.0 1.152415 1.494411
------------------ Aggregated Effects         ------------------
             coef   std err          t  P>|t|     2.5 %    97.5 %
2025-04  1.611333  0.144573  11.145444    0.0  1.327975  1.894692
2025-05  1.389114  0.118084  11.763752    0.0  1.157673  1.620555
2025-06  0.963408  0.088396  10.898797    0.0  0.790155  1.136661
------------------ Additional Information     ------------------
Score function: observational
Control group: never_treated
Anticipation periods: 0


/home/runner/work/doubleml-docs/doubleml-docs/doubleml-for-py/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(
../../_images/examples_did_py_panel_42_2.png

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

[20]:

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

[20]:

t
2025-04-01    0.929986
2025-05-01    1.461868
2025-06-01    1.987128
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".

[21]:

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 %
1.265978 0.093417 13.551859    0.0 1.082884 1.449073
------------------ Aggregated Effects         ------------------
             coef   std err          t         P>|t|     2.5 %    97.5 %
2025-04  0.783747  0.099182   7.902152  2.664535e-15  0.589355  0.978140
2025-05  1.241009  0.107732  11.519388  0.000000e+00  1.029857  1.452160
2025-06  1.773178  0.126519  14.015139  0.000000e+00  1.525206  2.021151
------------------ Additional Information     ------------------
Score function: observational
Control group: never_treated
Anticipation periods: 0


/home/runner/work/doubleml-docs/doubleml-docs/doubleml-for-py/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(
../../_images/examples_did_py_panel_47_2.png

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

[22]:

df["e"] = pd.to_datetime(df["t"]).values.astype("datetime64[M]") - \
    pd.to_datetime(df["d"]).values.astype("datetime64[M]")
df.groupby("e")["ite"].mean()[1:]

[22]:

e
-122 days    0.023103
-92 days     0.026339
-61 days     0.034840
-31 days     0.015622
0 days       0.985383
31 days      1.965469
59 days      2.918589
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).

[23]:

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 %
1.696711 0.129587 13.09318    0.0 1.442724 1.950698
------------------ Aggregated Effects         ------------------
               coef   std err          t     P>|t|     2.5 %    97.5 %
-4 months -0.049208  0.086232  -0.570648  0.568239 -0.218221  0.119804
-3 months -0.044536  0.067211  -0.662624  0.507571 -0.176266  0.087195
-2 months -0.039887  0.060365  -0.660760  0.508766 -0.158200  0.078426
-1 months -0.090806  0.062626  -1.449972  0.147066 -0.213551  0.031939
0 months   0.892777  0.065431  13.644606  0.000000  0.764535  1.021019
1 months   1.701111  0.122839  13.848291  0.000000  1.460351  1.941872
2 months   2.496245  0.241582  10.332920  0.000000  2.022753  2.969736
------------------ Additional Information     ------------------
Score function: observational
Control group: never_treated
Anticipation periods: 0


/home/runner/work/doubleml-docs/doubleml-docs/doubleml-for-py/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(

[23]:

(<Figure size 1200x600 with 1 Axes>,
 <Axes: title={'center': 'Aggregated Treatment Effects'}, ylabel='Effect'>)
../../_images/examples_did_py_panel_51_3.png

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

[24]:

print(aggregated_eventstudy)

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

------------------ Overall Aggregated Effects ------------------
    coef  std err        t  P>|t|    2.5 %   97.5 %
1.696711 0.129587 13.09318    0.0 1.442724 1.950698
------------------ Aggregated Effects         ------------------
               coef   std err          t     P>|t|     2.5 %    97.5 %
-4 months -0.049208  0.086232  -0.570648  0.568239 -0.218221  0.119804
-3 months -0.044536  0.067211  -0.662624  0.507571 -0.176266  0.087195
-2 months -0.039887  0.060365  -0.660760  0.508766 -0.158200  0.078426
-1 months -0.090806  0.062626  -1.449972  0.147066 -0.213551  0.031939
0 months   0.892777  0.065431  13.644606  0.000000  0.764535  1.021019
1 months   1.701111  0.122839  13.848291  0.000000  1.460351  1.941872
2 months   2.496245  0.241582  10.332920  0.000000  2.022753  2.969736
------------------ Additional Information     ------------------
Score function: observational
Control group: never_treated
Anticipation periods: 0

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

[25]:

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

[26]:

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

[26]:

array([0.        , 0.        , 0.33369624, 0.        , 0.        ,
       0.        , 0.        , 0.        , 0.33777899, 0.        ,
       0.        , 0.        , 0.        , 0.        , 0.32852477])

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

  • \(\widehat{ATT}(04,03,04)\)

  • \(\widehat{ATT}(05,04,05)\)

  • \(\widehat{ATT}(06,05,06)\)

[27]:

print(dml_obj.summary["coef"])

ATT(2025-04,2025-01,2025-02)   -0.125556
ATT(2025-04,2025-02,2025-03)   -0.023540
ATT(2025-04,2025-03,2025-04)    0.783747
ATT(2025-04,2025-03,2025-05)    1.554008
ATT(2025-04,2025-03,2025-06)    2.496245
ATT(2025-05,2025-01,2025-02)   -0.090754
ATT(2025-05,2025-02,2025-03)    0.105795
ATT(2025-05,2025-03,2025-04)   -0.210046
ATT(2025-05,2025-04,2025-05)    0.931792
ATT(2025-05,2025-04,2025-06)    1.846437
ATT(2025-06,2025-01,2025-02)   -0.049208
ATT(2025-06,2025-02,2025-03)    0.002985
ATT(2025-06,2025-03,2025-04)   -0.102654
ATT(2025-06,2025-04,2025-05)   -0.036532
ATT(2025-06,2025-05,2025-06)    0.963408
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.

[28]:

n_obs = 4000
n_periods = 6

df_anticipation = make_did_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()

(19224, 10)

[28]:
id y y0 y1 d t Z1 Z2 Z3 Z4
1 0 214.361389 214.361389 214.613240 NaT 2025-01-01 -0.664241 0.506813 -1.159897 -0.560357
2 0 214.110524 214.110524 216.149195 NaT 2025-02-01 -0.664241 0.506813 -1.159897 -0.560357
3 0 215.669066 215.669066 216.213941 NaT 2025-03-01 -0.664241 0.506813 -1.159897 -0.560357
4 0 217.636602 217.636602 215.144016 NaT 2025-04-01 -0.664241 0.506813 -1.159897 -0.560357
5 0 218.276018 218.276018 218.025551 NaT 2025-05-01 -0.664241 0.506813 -1.159897 -0.560357

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

[29]:

df_anticipation["ite"] = df_anticipation["y1"] - df_anticipation["y0"]
df_anticipation["First Treated"] = df_anticipation["d"].dt.strftime("%Y-%m").fillna("Never Treated")
agg_df_anticipation = df_anticipation.groupby(["t", "First Treated"]).agg(**agg_dictionary).reset_index()
agg_df_anticipation.head()

[29]:
t First Treated y_mean y_lower_quantile y_upper_quantile ite_mean ite_lower_quantile ite_upper_quantile
0 2025-01-01 2025-04 208.969085 193.019851 225.595729 0.041509 -2.214455 2.391724
1 2025-01-01 2025-05 210.478955 194.195254 227.566796 -0.065063 -2.490558 2.396774
2 2025-01-01 2025-06 212.319284 195.561561 228.548760 -0.041493 -2.422167 2.384281
3 2025-01-01 Never Treated 217.353168 200.263305 233.480668 0.067892 -2.289238 2.509938
4 2025-02-01 2025-04 208.998796 184.709580 234.336423 -0.002723 -2.286180 2.372940

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

[30]:

plot_data(agg_df_anticipation, col_name='ite')
../../_images/examples_did_py_panel_66_0.png

Initialize a corresponding DoubleMLPanelData object.

[31]:

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.

[32]:

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()

/home/runner/work/doubleml-docs/doubleml-docs/doubleml-for-py/doubleml/double_ml.py:1479: UserWarning: The estimated nu2 for d is not positive. Re-estimation based on riesz representer (non-orthogonal).
  warnings.warn(msg, UserWarning)
/home/runner/work/doubleml-docs/doubleml-docs/doubleml-for-py/doubleml/double_ml.py:1479: UserWarning: The estimated nu2 for d is not positive. Re-estimation based on riesz representer (non-orthogonal).
  warnings.warn(msg, UserWarning)
/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)

[32]:

(<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'>])
../../_images/examples_did_py_panel_70_2.png

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.

[33]:

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)

[33]:

(<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'>])
../../_images/examples_did_py_panel_72_2.png

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).

[34]:

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()

[34]:

(<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'>])
../../_images/examples_did_py_panel_75_1.png

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.

[35]:

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)

[35]:

(<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'>])
../../_images/examples_did_py_panel_77_2.png

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

[36]:

gt_dict = {
    "gt_combinations": [
        (np.datetime64('2025-04'),
         np.datetime64('2025-01'),
         np.datetime64('2025-02')),
        (np.datetime64('2025-04'),
         np.datetime64('2025-02'),
         np.datetime64('2025-03')),
    ]
}

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()

[36]:

(<Figure size 1200x800 with 2 Axes>,
 [<Axes: title={'center': 'First Treated: 2025-04'}, xlabel='Evaluation Period', ylabel='Effect'>])
../../_images/examples_did_py_panel_79_1.png
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