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 0 205.545000 205.545000 206.800304 2025-06-01 2025-01-01 0.078969 -0.50487 -0.427428 -1.058751 1.255304
1 0 202.458458 202.458458 201.337226 2025-06-01 2025-02-01 0.078969 -0.50487 -0.427428 -1.058751 -1.121232
2 0 199.173479 199.173479 198.659386 2025-06-01 2025-03-01 0.078969 -0.50487 -0.427428 -1.058751 -0.514093
3 0 193.535928 193.535928 194.484784 2025-06-01 2025-04-01 0.078969 -0.50487 -0.427428 -1.058751 0.948856
4 0 189.396871 189.396871 191.392743 2025-06-01 2025-05-01 0.078969 -0.50487 -0.427428 -1.058751 1.995872

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    7428
2025-05-01    7392
2025-06-01    7728
NaT           7452
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    7428
2025-05-01    7392
2025-06-01    7728
NaT           7452
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 2025-04 209.038726 199.025422 218.821333 -0.080941 -2.335878 2.122399
1 2025-01-01 2025-05 210.441994 200.406581 220.837964 -0.009749 -2.439692 2.405100
2 2025-01-01 2025-06 212.275643 202.259758 222.570311 -0.047195 -2.294431 2.179748
3 2025-01-01 Never Treated 214.010358 204.050389 223.951808 -0.046414 -2.431949 2.323493
4 2025-02-01 2025-04 209.041065 189.081809 228.318955 0.026313 -2.299848 2.402820 
[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
Static panel data: False
No. Unique Ids: 5000
No. Observations: 30000
------------------ DataFrame info    ------------------
<class 'pandas.DataFrame'>
RangeIndex: 30000 entries, 0 to 29999
Columns: 12 entries, id to First Treated
dtypes: datetime64[s](2), float64(8), int64(1), str(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]:

np.random.seed(42)
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
Static panel data: False
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: [[1.99783693 1.95559474 1.97705096 2.9341747  4.29438797 2.03639862
  1.94563822 1.98830569 1.92567039 3.00229347 2.01287238 1.93570636
  1.95375694 1.92792647 2.00670088]]
Learner ml_g1 RMSE: [[1.99687082 2.05536632 2.06774347 3.08961517 4.15651259 2.02625079
  2.04514373 2.01223382 1.87295321 2.9143835  2.00364406 1.95454946
  1.94152171 1.95661697 1.88033955]]
Classification:
Learner ml_m Log Loss: [[0.69809183 0.68462555 0.68400496 0.68325631 0.69468899 0.7246079
  0.71054236 0.71022412 0.7060442  0.70394892 0.7291863  0.72942261
  0.73068656 0.72926839 0.72568898]]

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

------------------ Fit summary       ------------------
                                  coef   std err          t         P>|t|  \
ATT(2025-04,2025-01,2025-02)  0.071655  0.142053   0.504426  6.139619e-01
ATT(2025-04,2025-02,2025-03)  0.115669  0.123846   0.933980  3.503144e-01
ATT(2025-04,2025-03,2025-04)  1.170629  0.140908   8.307770  0.000000e+00
ATT(2025-04,2025-03,2025-05)  2.432367  0.315138   7.718426  1.176836e-14
ATT(2025-04,2025-03,2025-06)  3.267878  0.317113  10.305093  0.000000e+00
ATT(2025-05,2025-01,2025-02)  0.054873  0.112810   0.486421  6.266690e-01
ATT(2025-05,2025-02,2025-03) -0.000177  0.113302  -0.001558  9.987565e-01
ATT(2025-05,2025-03,2025-04)  0.067074  0.117999   0.568428  5.697442e-01
ATT(2025-05,2025-04,2025-05)  0.950214  0.114497   8.299055  0.000000e+00
ATT(2025-05,2025-04,2025-06)  2.016258  0.235574   8.558926  0.000000e+00
ATT(2025-06,2025-01,2025-02) -0.121805  0.091006  -1.338431  1.807560e-01
ATT(2025-06,2025-02,2025-03)  0.034326  0.090449   0.379513  7.043072e-01
ATT(2025-06,2025-03,2025-04) -0.109865  0.093832  -1.170864  2.416536e-01
ATT(2025-06,2025-04,2025-05)  0.032421  0.097144   0.333737  7.385782e-01
ATT(2025-06,2025-05,2025-06)  0.836669  0.096834   8.640215  0.000000e+00

                                 2.5 %    97.5 %
ATT(2025-04,2025-01,2025-02) -0.206764  0.350075
ATT(2025-04,2025-02,2025-03) -0.127064  0.358402
ATT(2025-04,2025-03,2025-04)  0.894455  1.446802
ATT(2025-04,2025-03,2025-05)  1.814709  3.050026
ATT(2025-04,2025-03,2025-06)  2.646348  3.889408
ATT(2025-05,2025-01,2025-02) -0.166230  0.275976
ATT(2025-05,2025-02,2025-03) -0.222244  0.221891
ATT(2025-05,2025-03,2025-04) -0.164199  0.298347
ATT(2025-05,2025-04,2025-05)  0.725804  1.174623
ATT(2025-05,2025-04,2025-06)  1.554542  2.477974
ATT(2025-06,2025-01,2025-02) -0.300173  0.056563
ATT(2025-06,2025-02,2025-03) -0.142950  0.211603
ATT(2025-06,2025-03,2025-04) -0.293772  0.074043
ATT(2025-06,2025-04,2025-05) -0.157978  0.222819
ATT(2025-06,2025-05,2025-06)  0.646877  1.026461

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) -0.329071 0.472382
ATT(2025-04,2025-02,2025-03) -0.233694 0.465032
ATT(2025-04,2025-03,2025-04) 0.773134 1.568123
ATT(2025-04,2025-03,2025-05) 1.543377 3.321357
ATT(2025-04,2025-03,2025-06) 2.373316 4.162440
ATT(2025-05,2025-01,2025-02) -0.263358 0.373104
ATT(2025-05,2025-02,2025-03) -0.319796 0.319443
ATT(2025-05,2025-03,2025-04) -0.265795 0.399943
ATT(2025-05,2025-04,2025-05) 0.627224 1.273203
ATT(2025-05,2025-04,2025-06) 1.351715 2.680801
ATT(2025-06,2025-01,2025-02) -0.378529 0.134919
ATT(2025-06,2025-02,2025-03) -0.220826 0.289479
ATT(2025-06,2025-03,2025-04) -0.374561 0.154832
ATT(2025-06,2025-04,2025-05) -0.241619 0.306460
ATT(2025-06,2025-05,2025-06) 0.563504 1.109834

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()

[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_1.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) -0.269348    -0.041510  0.071655     0.184821
ATT(2025-04,2025-02,2025-03) -0.207127    -0.006346  0.115669     0.237685
ATT(2025-04,2025-03,2025-04)  0.835966     1.060456  1.170629     1.280801
ATT(2025-04,2025-03,2025-05)  1.778623     2.266250  2.432367     2.598484
ATT(2025-04,2025-03,2025-06)  2.499562     3.014179  3.267878     3.521577
ATT(2025-05,2025-01,2025-02) -0.236015    -0.044897  0.054873     0.154643
ATT(2025-05,2025-02,2025-03) -0.294960    -0.109188 -0.000177     0.108835
ATT(2025-05,2025-03,2025-04) -0.229032    -0.037472  0.067074     0.171619
ATT(2025-05,2025-04,2025-05)  0.671699     0.859149  0.950214     1.041278
ATT(2025-05,2025-04,2025-06)  1.469126     1.850862  2.016258     2.181653
ATT(2025-06,2025-01,2025-02) -0.379883    -0.229711 -0.121805    -0.013899
ATT(2025-06,2025-02,2025-03) -0.222051    -0.073381  0.034326     0.142033
ATT(2025-06,2025-03,2025-04) -0.370474    -0.216445 -0.109865    -0.003284
ATT(2025-06,2025-04,2025-05) -0.230919    -0.072824  0.032421     0.137665
ATT(2025-06,2025-05,2025-06)  0.567256     0.725800  0.836669     0.947538

                              CI upper
ATT(2025-04,2025-01,2025-02)  0.425439
ATT(2025-04,2025-02,2025-03)  0.445535
ATT(2025-04,2025-03,2025-04)  1.522435
ATT(2025-04,2025-03,2025-05)  3.149313
ATT(2025-04,2025-03,2025-06)  4.052410
ATT(2025-05,2025-01,2025-02)  0.336905
ATT(2025-05,2025-02,2025-03)  0.296599
ATT(2025-05,2025-03,2025-04)  0.369545
ATT(2025-05,2025-04,2025-05)  1.233378
ATT(2025-05,2025-04,2025-06)  2.575667
ATT(2025-06,2025-01,2025-02)  0.136212
ATT(2025-06,2025-02,2025-03)  0.291330
ATT(2025-06,2025-03,2025-04)  0.151751
ATT(2025-06,2025-04,2025-05)  0.299565
ATT(2025-06,2025-05,2025-06)  1.107875

------------------ Robustness Values ------------------
                              H_0     RV (%)    RVa (%)
ATT(2025-04,2025-01,2025-02)  0.0   1.910315   0.000446
ATT(2025-04,2025-02,2025-03)  0.0   2.846290   0.000348
ATT(2025-04,2025-03,2025-04)  0.0  27.548870  22.240583
ATT(2025-04,2025-03,2025-05)  0.0  35.750677  31.075785
ATT(2025-04,2025-03,2025-06)  0.0  32.286293  27.591029
ATT(2025-05,2025-01,2025-02)  0.0   1.661438   0.000593
ATT(2025-05,2025-02,2025-03)  0.0   0.004796   0.000518
ATT(2025-05,2025-03,2025-04)  0.0   1.935359   0.000459
ATT(2025-05,2025-04,2025-05)  0.0  27.131860  20.893105
ATT(2025-05,2025-04,2025-06)  0.0  30.873132  26.076064
ATT(2025-06,2025-01,2025-02)  0.0   3.379841   0.000603
ATT(2025-06,2025-02,2025-03)  0.0   0.966221   0.000516
ATT(2025-06,2025-03,2025-04)  0.0   3.091041   0.000338
ATT(2025-06,2025-04,2025-05)  0.0   0.934083   0.000632
ATT(2025-06,2025-05,2025-06)  0.0  20.496167  16.944610

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()

[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_1.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/3.12.13/x64/lib/python3.12/site-packages/sklearn/linear_model/_logistic.py:451: OptimizeWarning: Unknown solver options: iprint
  opt_res = optimize.minimize(
/opt/hostedtoolcache/Python/3.12.13/x64/lib/python3.12/site-packages/sklearn/linear_model/_logistic.py:451: OptimizeWarning: Unknown solver options: iprint
  opt_res = optimize.minimize(
/opt/hostedtoolcache/Python/3.12.13/x64/lib/python3.12/site-packages/sklearn/linear_model/_logistic.py:451: OptimizeWarning: Unknown solver options: iprint
  opt_res = optimize.minimize(
/opt/hostedtoolcache/Python/3.12.13/x64/lib/python3.12/site-packages/sklearn/linear_model/_logistic.py:451: OptimizeWarning: Unknown solver options: iprint
  opt_res = optimize.minimize(
/opt/hostedtoolcache/Python/3.12.13/x64/lib/python3.12/site-packages/sklearn/linear_model/_logistic.py:451: OptimizeWarning: Unknown solver options: iprint
  opt_res = optimize.minimize(
/opt/hostedtoolcache/Python/3.12.13/x64/lib/python3.12/site-packages/sklearn/linear_model/_logistic.py:451: OptimizeWarning: Unknown solver options: iprint
  opt_res = optimize.minimize(
/opt/hostedtoolcache/Python/3.12.13/x64/lib/python3.12/site-packages/sklearn/linear_model/_logistic.py:451: OptimizeWarning: Unknown solver options: iprint
  opt_res = optimize.minimize(
/opt/hostedtoolcache/Python/3.12.13/x64/lib/python3.12/site-packages/sklearn/linear_model/_logistic.py:451: OptimizeWarning: Unknown solver options: iprint
  opt_res = optimize.minimize(
/opt/hostedtoolcache/Python/3.12.13/x64/lib/python3.12/site-packages/sklearn/linear_model/_logistic.py:451: OptimizeWarning: Unknown solver options: iprint
  opt_res = optimize.minimize(
/opt/hostedtoolcache/Python/3.12.13/x64/lib/python3.12/site-packages/sklearn/linear_model/_logistic.py:451: OptimizeWarning: Unknown solver options: iprint
  opt_res = optimize.minimize(
/opt/hostedtoolcache/Python/3.12.13/x64/lib/python3.12/site-packages/sklearn/linear_model/_logistic.py:451: OptimizeWarning: Unknown solver options: iprint
  opt_res = optimize.minimize(
/opt/hostedtoolcache/Python/3.12.13/x64/lib/python3.12/site-packages/sklearn/linear_model/_logistic.py:451: OptimizeWarning: Unknown solver options: iprint
  opt_res = optimize.minimize(
/opt/hostedtoolcache/Python/3.12.13/x64/lib/python3.12/site-packages/sklearn/linear_model/_logistic.py:451: OptimizeWarning: Unknown solver options: iprint
  opt_res = optimize.minimize(
/opt/hostedtoolcache/Python/3.12.13/x64/lib/python3.12/site-packages/sklearn/linear_model/_logistic.py:451: OptimizeWarning: Unknown solver options: iprint
  opt_res = optimize.minimize(
/opt/hostedtoolcache/Python/3.12.13/x64/lib/python3.12/site-packages/sklearn/linear_model/_logistic.py:451: OptimizeWarning: Unknown solver options: iprint
  opt_res = optimize.minimize(
/opt/hostedtoolcache/Python/3.12.13/x64/lib/python3.12/site-packages/sklearn/linear_model/_logistic.py:451: OptimizeWarning: Unknown solver options: iprint
  opt_res = optimize.minimize(
/opt/hostedtoolcache/Python/3.12.13/x64/lib/python3.12/site-packages/sklearn/linear_model/_logistic.py:451: OptimizeWarning: Unknown solver options: iprint
  opt_res = optimize.minimize(
/opt/hostedtoolcache/Python/3.12.13/x64/lib/python3.12/site-packages/sklearn/linear_model/_logistic.py:451: OptimizeWarning: Unknown solver options: iprint
  opt_res = optimize.minimize(
/opt/hostedtoolcache/Python/3.12.13/x64/lib/python3.12/site-packages/sklearn/linear_model/_logistic.py:451: OptimizeWarning: Unknown solver options: iprint
  opt_res = optimize.minimize(
/opt/hostedtoolcache/Python/3.12.13/x64/lib/python3.12/site-packages/sklearn/linear_model/_logistic.py:451: OptimizeWarning: Unknown solver options: iprint
  opt_res = optimize.minimize(
/opt/hostedtoolcache/Python/3.12.13/x64/lib/python3.12/site-packages/sklearn/linear_model/_logistic.py:451: OptimizeWarning: Unknown solver options: iprint
  opt_res = optimize.minimize(
/opt/hostedtoolcache/Python/3.12.13/x64/lib/python3.12/site-packages/sklearn/linear_model/_logistic.py:451: OptimizeWarning: Unknown solver options: iprint
  opt_res = optimize.minimize(
/opt/hostedtoolcache/Python/3.12.13/x64/lib/python3.12/site-packages/sklearn/linear_model/_logistic.py:451: OptimizeWarning: Unknown solver options: iprint
  opt_res = optimize.minimize(
/opt/hostedtoolcache/Python/3.12.13/x64/lib/python3.12/site-packages/sklearn/linear_model/_logistic.py:451: OptimizeWarning: Unknown solver options: iprint
  opt_res = optimize.minimize(
/opt/hostedtoolcache/Python/3.12.13/x64/lib/python3.12/site-packages/sklearn/linear_model/_logistic.py:451: OptimizeWarning: Unknown solver options: iprint
  opt_res = optimize.minimize(
/opt/hostedtoolcache/Python/3.12.13/x64/lib/python3.12/site-packages/sklearn/linear_model/_logistic.py:451: OptimizeWarning: Unknown solver options: iprint
  opt_res = optimize.minimize(
/opt/hostedtoolcache/Python/3.12.13/x64/lib/python3.12/site-packages/sklearn/linear_model/_logistic.py:451: OptimizeWarning: Unknown solver options: iprint
  opt_res = optimize.minimize(
/opt/hostedtoolcache/Python/3.12.13/x64/lib/python3.12/site-packages/sklearn/linear_model/_logistic.py:451: OptimizeWarning: Unknown solver options: iprint
  opt_res = optimize.minimize(
/opt/hostedtoolcache/Python/3.12.13/x64/lib/python3.12/site-packages/sklearn/linear_model/_logistic.py:451: OptimizeWarning: Unknown solver options: iprint
  opt_res = optimize.minimize(
/opt/hostedtoolcache/Python/3.12.13/x64/lib/python3.12/site-packages/sklearn/linear_model/_logistic.py:451: OptimizeWarning: Unknown solver options: iprint
  opt_res = optimize.minimize(
/opt/hostedtoolcache/Python/3.12.13/x64/lib/python3.12/site-packages/sklearn/linear_model/_logistic.py:451: OptimizeWarning: Unknown solver options: iprint
  opt_res = optimize.minimize(
/opt/hostedtoolcache/Python/3.12.13/x64/lib/python3.12/site-packages/sklearn/linear_model/_logistic.py:451: OptimizeWarning: Unknown solver options: iprint
  opt_res = optimize.minimize(
/opt/hostedtoolcache/Python/3.12.13/x64/lib/python3.12/site-packages/sklearn/linear_model/_logistic.py:451: OptimizeWarning: Unknown solver options: iprint
  opt_res = optimize.minimize(
/opt/hostedtoolcache/Python/3.12.13/x64/lib/python3.12/site-packages/sklearn/linear_model/_logistic.py:451: OptimizeWarning: Unknown solver options: iprint
  opt_res = optimize.minimize(
/opt/hostedtoolcache/Python/3.12.13/x64/lib/python3.12/site-packages/sklearn/linear_model/_logistic.py:451: OptimizeWarning: Unknown solver options: iprint
  opt_res = optimize.minimize(
/opt/hostedtoolcache/Python/3.12.13/x64/lib/python3.12/site-packages/sklearn/linear_model/_logistic.py:451: OptimizeWarning: Unknown solver options: iprint
  opt_res = optimize.minimize(
/opt/hostedtoolcache/Python/3.12.13/x64/lib/python3.12/site-packages/sklearn/linear_model/_logistic.py:451: OptimizeWarning: Unknown solver options: iprint
  opt_res = optimize.minimize(
/opt/hostedtoolcache/Python/3.12.13/x64/lib/python3.12/site-packages/sklearn/linear_model/_logistic.py:451: OptimizeWarning: Unknown solver options: iprint
  opt_res = optimize.minimize(
/opt/hostedtoolcache/Python/3.12.13/x64/lib/python3.12/site-packages/sklearn/linear_model/_logistic.py:451: OptimizeWarning: Unknown solver options: iprint
  opt_res = optimize.minimize(
/opt/hostedtoolcache/Python/3.12.13/x64/lib/python3.12/site-packages/sklearn/linear_model/_logistic.py:451: OptimizeWarning: Unknown solver options: iprint
  opt_res = optimize.minimize(
/opt/hostedtoolcache/Python/3.12.13/x64/lib/python3.12/site-packages/sklearn/linear_model/_logistic.py:451: OptimizeWarning: Unknown solver options: iprint
  opt_res = optimize.minimize(
/opt/hostedtoolcache/Python/3.12.13/x64/lib/python3.12/site-packages/sklearn/linear_model/_logistic.py:451: OptimizeWarning: Unknown solver options: iprint
  opt_res = optimize.minimize(
/opt/hostedtoolcache/Python/3.12.13/x64/lib/python3.12/site-packages/sklearn/linear_model/_logistic.py:451: OptimizeWarning: Unknown solver options: iprint
  opt_res = optimize.minimize(
/opt/hostedtoolcache/Python/3.12.13/x64/lib/python3.12/site-packages/sklearn/linear_model/_logistic.py:451: OptimizeWarning: Unknown solver options: iprint
  opt_res = optimize.minimize(
/opt/hostedtoolcache/Python/3.12.13/x64/lib/python3.12/site-packages/sklearn/linear_model/_logistic.py:451: OptimizeWarning: Unknown solver options: iprint
  opt_res = optimize.minimize(
/opt/hostedtoolcache/Python/3.12.13/x64/lib/python3.12/site-packages/sklearn/linear_model/_logistic.py:451: OptimizeWarning: Unknown solver options: iprint
  opt_res = optimize.minimize(
/opt/hostedtoolcache/Python/3.12.13/x64/lib/python3.12/site-packages/sklearn/linear_model/_logistic.py:451: OptimizeWarning: Unknown solver options: iprint
  opt_res = optimize.minimize(
/opt/hostedtoolcache/Python/3.12.13/x64/lib/python3.12/site-packages/sklearn/linear_model/_logistic.py:451: OptimizeWarning: Unknown solver options: iprint
  opt_res = optimize.minimize(
/opt/hostedtoolcache/Python/3.12.13/x64/lib/python3.12/site-packages/sklearn/linear_model/_logistic.py:451: OptimizeWarning: Unknown solver options: iprint
  opt_res = optimize.minimize(
/opt/hostedtoolcache/Python/3.12.13/x64/lib/python3.12/site-packages/sklearn/linear_model/_logistic.py:451: OptimizeWarning: Unknown solver options: iprint
  opt_res = optimize.minimize(
/opt/hostedtoolcache/Python/3.12.13/x64/lib/python3.12/site-packages/sklearn/linear_model/_logistic.py:451: OptimizeWarning: Unknown solver options: iprint
  opt_res = optimize.minimize(
/opt/hostedtoolcache/Python/3.12.13/x64/lib/python3.12/site-packages/sklearn/linear_model/_logistic.py:451: OptimizeWarning: Unknown solver options: iprint
  opt_res = optimize.minimize(
/opt/hostedtoolcache/Python/3.12.13/x64/lib/python3.12/site-packages/sklearn/linear_model/_logistic.py:451: OptimizeWarning: Unknown solver options: iprint
  opt_res = optimize.minimize(
/opt/hostedtoolcache/Python/3.12.13/x64/lib/python3.12/site-packages/sklearn/linear_model/_logistic.py:451: OptimizeWarning: Unknown solver options: iprint
  opt_res = optimize.minimize(
/opt/hostedtoolcache/Python/3.12.13/x64/lib/python3.12/site-packages/sklearn/linear_model/_logistic.py:451: OptimizeWarning: Unknown solver options: iprint
  opt_res = optimize.minimize(
/opt/hostedtoolcache/Python/3.12.13/x64/lib/python3.12/site-packages/sklearn/linear_model/_logistic.py:451: OptimizeWarning: Unknown solver options: iprint
  opt_res = optimize.minimize(
/opt/hostedtoolcache/Python/3.12.13/x64/lib/python3.12/site-packages/sklearn/linear_model/_logistic.py:451: OptimizeWarning: Unknown solver options: iprint
  opt_res = optimize.minimize(
/opt/hostedtoolcache/Python/3.12.13/x64/lib/python3.12/site-packages/sklearn/linear_model/_logistic.py:451: OptimizeWarning: Unknown solver options: iprint
  opt_res = optimize.minimize(
/opt/hostedtoolcache/Python/3.12.13/x64/lib/python3.12/site-packages/sklearn/linear_model/_logistic.py:451: OptimizeWarning: Unknown solver options: iprint
  opt_res = optimize.minimize(
/opt/hostedtoolcache/Python/3.12.13/x64/lib/python3.12/site-packages/sklearn/linear_model/_logistic.py:451: OptimizeWarning: Unknown solver options: iprint
  opt_res = optimize.minimize(
/opt/hostedtoolcache/Python/3.12.13/x64/lib/python3.12/site-packages/sklearn/linear_model/_logistic.py:451: OptimizeWarning: Unknown solver options: iprint
  opt_res = optimize.minimize(
/opt/hostedtoolcache/Python/3.12.13/x64/lib/python3.12/site-packages/sklearn/linear_model/_logistic.py:451: OptimizeWarning: Unknown solver options: iprint
  opt_res = optimize.minimize(
/opt/hostedtoolcache/Python/3.12.13/x64/lib/python3.12/site-packages/sklearn/linear_model/_logistic.py:451: OptimizeWarning: Unknown solver options: iprint
  opt_res = optimize.minimize(
/opt/hostedtoolcache/Python/3.12.13/x64/lib/python3.12/site-packages/sklearn/linear_model/_logistic.py:451: OptimizeWarning: Unknown solver options: iprint
  opt_res = optimize.minimize(
/opt/hostedtoolcache/Python/3.12.13/x64/lib/python3.12/site-packages/sklearn/linear_model/_logistic.py:451: OptimizeWarning: Unknown solver options: iprint
  opt_res = optimize.minimize(
/opt/hostedtoolcache/Python/3.12.13/x64/lib/python3.12/site-packages/sklearn/linear_model/_logistic.py:451: OptimizeWarning: Unknown solver options: iprint
  opt_res = optimize.minimize(
/opt/hostedtoolcache/Python/3.12.13/x64/lib/python3.12/site-packages/sklearn/linear_model/_logistic.py:451: OptimizeWarning: Unknown solver options: iprint
  opt_res = optimize.minimize(
/opt/hostedtoolcache/Python/3.12.13/x64/lib/python3.12/site-packages/sklearn/linear_model/_logistic.py:451: OptimizeWarning: Unknown solver options: iprint
  opt_res = optimize.minimize(
/opt/hostedtoolcache/Python/3.12.13/x64/lib/python3.12/site-packages/sklearn/linear_model/_logistic.py:451: OptimizeWarning: Unknown solver options: iprint
  opt_res = optimize.minimize(
/opt/hostedtoolcache/Python/3.12.13/x64/lib/python3.12/site-packages/sklearn/linear_model/_logistic.py:451: OptimizeWarning: Unknown solver options: iprint
  opt_res = optimize.minimize(
/opt/hostedtoolcache/Python/3.12.13/x64/lib/python3.12/site-packages/sklearn/linear_model/_logistic.py:451: OptimizeWarning: Unknown solver options: iprint
  opt_res = optimize.minimize(
/opt/hostedtoolcache/Python/3.12.13/x64/lib/python3.12/site-packages/sklearn/linear_model/_logistic.py:451: OptimizeWarning: Unknown solver options: iprint
  opt_res = optimize.minimize(
/opt/hostedtoolcache/Python/3.12.13/x64/lib/python3.12/site-packages/sklearn/linear_model/_logistic.py:451: OptimizeWarning: Unknown solver options: iprint
  opt_res = optimize.minimize(
/opt/hostedtoolcache/Python/3.12.13/x64/lib/python3.12/site-packages/sklearn/linear_model/_logistic.py:451: OptimizeWarning: Unknown solver options: iprint
  opt_res = optimize.minimize(
/opt/hostedtoolcache/Python/3.12.13/x64/lib/python3.12/site-packages/sklearn/linear_model/_logistic.py:451: OptimizeWarning: Unknown solver options: iprint
  opt_res = optimize.minimize(

[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    1.960505
2025-05-01    1.525345
2025-06-01    0.883017
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 %
1.527503 0.130943 11.66542    0.0 1.27086 1.784146
------------------ Aggregated Effects         ------------------
             coef   std err         t  P>|t|     2.5 %    97.5 %
2025-04  2.290291  0.233159  9.822854    0.0  1.833307  2.747275
2025-05  1.483236  0.165159  8.980648    0.0  1.159530  1.806941
2025-06  0.836669  0.096834  8.640215    0.0  0.646877  1.026461
------------------ Additional Information     ------------------
Score function: observational
Control group: never_treated
Anticipation periods: 0


/opt/hostedtoolcache/Python/3.12.13/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(
../../_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    1.003831
2025-05-01    1.512257
2025-06-01    1.915667
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 %
1.629337 0.152908 10.655679    0.0 1.329643 1.929031
------------------ Aggregated Effects         ------------------
             coef   std err          t  P>|t|     2.5 %    97.5 %
2025-04  1.170629  0.140908   8.307770    0.0  0.894455  1.446802
2025-05  1.693090  0.191124   8.858579    0.0  1.318494  2.067687
2025-06  2.024293  0.174991  11.567979    0.0  1.681317  2.367269
------------------ Additional Information     ------------------
Score function: observational
Control group: never_treated
Anticipation periods: 0


/opt/hostedtoolcache/Python/3.12.13/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(
../../_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   -0.017912
-92 days     0.003451
-61 days     0.008799
-31 days    -0.006125
0 days       0.983733
31 days      1.967663
59 days      2.924150
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 %
2.158868  0.19623 11.001709    0.0 1.774264 2.543473
------------------ Aggregated Effects         ------------------
               coef   std err          t     P>|t|     2.5 %    97.5 %
-4 months -0.121805  0.091006  -1.338431  0.180756 -0.300173  0.056563
-3 months  0.044371  0.077053   0.575853  0.564714 -0.106650  0.195393
-2 months -0.014107  0.085234  -0.165508  0.868545 -0.181162  0.152949
-1 months  0.071206  0.082564   0.862426  0.388453 -0.090618  0.233029
0 months   0.983909  0.081666  12.047898  0.000000  0.823846  1.143973
1 months   2.224818  0.245254   9.071474  0.000000  1.744128  2.705507
2 months   3.267878  0.317113  10.305093  0.000000  2.646348  3.889408
------------------ Additional Information     ------------------
Score function: observational
Control group: never_treated
Anticipation periods: 0


/opt/hostedtoolcache/Python/3.12.13/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(

[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 %
2.158868  0.19623 11.001709    0.0 1.774264 2.543473
------------------ Aggregated Effects         ------------------
               coef   std err          t     P>|t|     2.5 %    97.5 %
-4 months -0.121805  0.091006  -1.338431  0.180756 -0.300173  0.056563
-3 months  0.044371  0.077053   0.575853  0.564714 -0.106650  0.195393
-2 months -0.014107  0.085234  -0.165508  0.868545 -0.181162  0.152949
-1 months  0.071206  0.082564   0.862426  0.388453 -0.090618  0.233029
0 months   0.983909  0.081666  12.047898  0.000000  0.823846  1.143973
1 months   2.224818  0.245254   9.071474  0.000000  1.744128  2.705507
2 months   3.267878  0.317113  10.305093  0.000000  2.646348  3.889408
------------------ 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.        , 0.32943055, 0.        , 0.        ,
       0.        , 0.        , 0.        , 0.32783395, 0.        ,
       0.        , 0.        , 0.        , 0.        , 0.3427355 ])

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)    0.071655
ATT(2025-04,2025-02,2025-03)    0.115669
ATT(2025-04,2025-03,2025-04)    1.170629
ATT(2025-04,2025-03,2025-05)    2.432367
ATT(2025-04,2025-03,2025-06)    3.267878
ATT(2025-05,2025-01,2025-02)    0.054873
ATT(2025-05,2025-02,2025-03)   -0.000177
ATT(2025-05,2025-03,2025-04)    0.067074
ATT(2025-05,2025-04,2025-05)    0.950214
ATT(2025-05,2025-04,2025-06)    2.016258
ATT(2025-06,2025-01,2025-02)   -0.121805
ATT(2025-06,2025-02,2025-03)    0.034326
ATT(2025-06,2025-03,2025-04)   -0.109865
ATT(2025-06,2025-04,2025-05)    0.032421
ATT(2025-06,2025-05,2025-06)    0.836669
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()

(19044, 10)

[28]:
id y y0 y1 d t Z1 Z2 Z3 Z4
8 1 213.103046 213.103046 214.236987 2025-04-01 2025-01-01 0.142936 0.760454 -0.547813 0.597645
9 1 215.220461 215.220461 214.852432 2025-04-01 2025-02-01 0.142936 0.760454 -0.547813 0.597645
10 1 217.774389 218.174382 217.774389 2025-04-01 2025-03-01 0.142936 0.760454 -0.547813 0.597645
11 1 222.633611 218.941946 222.633611 2025-04-01 2025-04-01 0.142936 0.760454 -0.547813 0.597645
12 1 223.394685 220.681601 223.394685 2025-04-01 2025-05-01 0.142936 0.760454 -0.547813 0.597645

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 2025-04 209.493216 193.039383 226.430229 0.073816 -2.221312 2.474106
1 2025-01-01 2025-05 210.624922 194.211557 227.980492 0.048725 -2.164466 2.433486
2 2025-01-01 2025-06 212.496091 194.922874 229.425009 0.100002 -2.465654 2.375147
3 2025-01-01 Never Treated 217.530968 200.308472 234.165844 0.056374 -2.343018 2.280556
4 2025-02-01 2025-04 209.695077 185.130656 235.122434 -0.002373 -2.405460 2.361630

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()

[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_1.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()

[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_1.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()

[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_1.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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