Difference in Difference in Python

The csdid package contains tools for computing average treatment effect parameters in a Difference-in-Differences setup allowing for

• More than two time periods

• Variation in treatment timing (i.e., units can become treated at different points in time)

• Treatment effect heterogeneity (i.e, the effect of participating in the treatment can vary across units and exhibit potentially complex dynamics, selection into treatment, or time effects)

• The parallel trends assumption holds only after conditioning on covariates

The main parameters are group-time average treatment effects. These are the average treatment effect for a particular group (group is defined by treatment timing) in a particular time period. These parameters are a natural generalization of the average treatment effect on the treated (ATT) which is identified in the textbook case with two periods and two groups to the case with multiple periods.

Group-time average treatment effects are also natural building blocks for more aggregated treatment effect parameters such as overall treatment effects or event-study-type estimands.

Getting Started

There has been some recent work on DiD with multiple time periods. The csdid package implements the framework put forward in

• Callaway, Brantly and Pedro H.C. Sant’Anna. “Difference-in-Differences with Multiple Time Periods.” Journal of Econometrics, Vol. 225, No. 2, pp. 200-230, 2021. or [arXiv](https://arxiv.org/abs/1803.09015

This project is based on the original did R package.

Instalation

You can install csdid from pypi with:

pip install csdid

or via github:

pip install git+https://github.com/d2cml-ai/csdid/

Dependencies

Additionally, I have created an additional library called drdid, which can be installed via GitHub.

pip install git+https://github.com/d2cml-ai/DRDID

Basic Example

The following is a simplified example of the effect of states increasing their minimum wages on county-level teen employment rates which comes from Callaway and Sant’Anna (2021).

• More detailed examples are also available

A subset of the data is available in the package and can be loaded by

from csdid.att_gt import ATTgt
import pandas as pd
data = pd.read_csv("https://raw.githubusercontent.com/d2cml-ai/csdid/function-aggte/data/mpdta.csv")

The dataset contains 500 observations of county-level teen employment rates from 2003-2007. Some states are first treated in 2004, some in 2006, and some in 2007 (see the paper for more details). The important variables in the dataset are

• lemp This is the log of county-level teen employment. It is the outcome variable

• first.treat This is the period when a state first increases its minimum wage. It can be 2004, 2006, or 2007. It is the variable that defines group in this application

• year This is the year and is the time variable

• countyreal This is an id number for each county and provides the individual identifier in this panel data context

To estimate group-time average treatment effects, use the ATTgt().fit() method

out = ATTgt(yname = "lemp",
              gname = "first.treat",
              idname = "countyreal",
              tname = "year",
              xformla = f"lemp~1",
              data = data,
              ).fit(est_method = 'dr')

Summary table

out.summ_attgt().summary2

In the graphs, a semicolon ; should be added to prevent printing the class and the graph information.

out.plot_attgt();

/home/runner/work/csdid/csdid/csdid/plots/gplot.py:19: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise in a future error of pandas. Value '['2004' '2005' '2006' '2007']' has dtype incompatible with int64, please explicitly cast to a compatible dtype first.
  ssresults.loc[:, 'year'] = ssresults['year'].astype(int).astype(str)
/home/runner/work/csdid/csdid/csdid/plots/gplot.py:19: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise in a future error of pandas. Value '['2004' '2005' '2006' '2007']' has dtype incompatible with int64, please explicitly cast to a compatible dtype first.
  ssresults.loc[:, 'year'] = ssresults['year'].astype(int).astype(str)
/home/runner/work/csdid/csdid/csdid/plots/gplot.py:19: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise in a future error of pandas. Value '['2004' '2005' '2006' '2007']' has dtype incompatible with int64, please explicitly cast to a compatible dtype first.
  ssresults.loc[:, 'year'] = ssresults['year'].astype(int).astype(str)

out.aggte(typec='calendar');

Overall summary of ATT's based on calendar time aggregation:
    ATT Std. Error  [95.0%  Conf. Int.]  
-0.0417     0.0169 -0.0748      -0.0086 *


Time Effects (calendar):
   Time  Estimate  Std. Error  [95.0% Simult.   Conf. Band   
0  2004   -0.0105      0.0244          -0.0584      0.0374   
1  2005   -0.0704      0.0307          -0.1305     -0.0103  *
2  2006   -0.0488      0.0210          -0.0900     -0.0076  *
3  2007   -0.0371      0.0136          -0.0637     -0.0105  *
---
Signif. codes: `*' confidence band does not cover 0
Control Group:  Never Treated , 
Anticipation Periods:  0
Estimation Method:  Doubly Robust

out.plot_aggte();

/home/runner/work/csdid/csdid/csdid/plots/gplot.py:19: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise in a future error of pandas. Value '['2004' '2005' '2006' '2007']' has dtype incompatible with int64, please explicitly cast to a compatible dtype first.
  ssresults.loc[:, 'year'] = ssresults['year'].astype(int).astype(str)

Event Studies

Although in the current example it is pretty easy to directly interpret the group-time average treatment effects, there are many cases where it is convenient to aggregate the group-time average treatment effects into a small number of parameters. A main type of aggregation is into an event study plot.

To make an event study plot in the csdid package, one can use the aggte function with dynamic option

out.aggte(typec='dynamic');

Overall summary of ATT's based on event-study/dynamic aggregation:
ATT Std. Error  [95.0%  Conf. Int.]  
-0.0772     0.0207 -0.1179      -0.0366 *


Dynamic Effects:
  Event time  Estimate  Std. Error  [95.0% Simult.   Conf. Band   
0          -3    0.0305      0.0146           0.0019      0.0591  *
1          -2   -0.0006      0.0129          -0.0259      0.0248   
2          -1   -0.0245      0.0141          -0.0521      0.0032   
3           0   -0.0199      0.0117          -0.0428      0.0030   
4           1   -0.0510      0.0154          -0.0811     -0.0208  *
5           2   -0.1373      0.0366          -0.2091     -0.0655  *
6           3   -0.1008      0.0337          -0.1669     -0.0347  *
---
Signif. codes: `*' confidence band does not cover 0
Control Group:  Never Treated , 
Anticipation Periods:  0
Estimation Method:  Doubly Robust

The column event time is for each group relative to when they first participate in the treatment. To give some examples, event time=0 corresponds to the on impact effect, and event time=-1 is the effect in the period before a unit becomes treated (checking that this is equal to 0 is potentially useful as a pre-test).

To plot the event study, use plot_aggte method

out.plot_aggte();

/home/runner/work/csdid/csdid/csdid/plots/gplot.py:19: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise in a future error of pandas. Value '['2004' '2005' '2006' '2007']' has dtype incompatible with int64, please explicitly cast to a compatible dtype first.
  ssresults.loc[:, 'year'] = ssresults['year'].astype(int).astype(str)

The figure here is very similar to the group-time average treatment effects. Red dots are pre-treatment periods, blue dots are post-treatment periods. The difference is that the x-axis is in event time.

Overall Effect of Participating in the Treatment

The event study above reported an overall effect of participating in the treatment. This was computed by averaging the average effects computed at each length of exposure.

In many cases, a more general purpose overall treatment effect parameter is give by computing the average treatment effect for each group, and then averaging across groups. This sort of procedure provides an average treatment effect parameter with a very similar interpretation to the Average Treatment Effect on the Treated (ATT) in the two period and two group case.

To compute this overall average treatment effect parameter, use

out.aggte(typec='group');

Overall summary of ATT's based on group/cohort aggregation:
ATT Std. Error  [95.0%  Conf. Int.]  
-0.031     0.0124 -0.0553      -0.0067 *


Group Effects:
  Group  Estimate  Std. Error  [95.0% Simult.   Conf. Band   
0   2004   -0.0797      0.0301          -0.1387     -0.0208  *
1   2006   -0.0229      0.0172          -0.0567      0.0109   
2   2007   -0.0261      0.0174          -0.0601      0.0080   
---
Signif. codes: `*' confidence band does not cover 0
Control Group:  Never Treated , 
Anticipation Periods:  0
Estimation Method:  Doubly Robust

Of particular interest is the Overall ATT in the results. Here, we estimate that increasing the minimum wage decreased teen employment by 3.1% and the effect is marginally statistically significant.

How to cite

If you want to cite CSDID, you can use the following BibTeX entry:

@software{csdid,
  author  = {Callaway, Brantly and Sant'Anna, Pedro HC and Quispe, Alexander and Guevara, Carlos},
  title   = {{csdid: Difference-in-Differences with Multiple Time Periods in Python}},
  year    = {2024},
  url     = {https://github.com/d2cml-ai/csdid}
}