Difference-in-Differences Estimator in Stata

How do researchers measure the real impact of a big event—like a policy change or natural disaster—on a specific group? Enter the Differences-in-Differences (DID) regression, It is a powerful tool for isolating causal effects by comparing changes between two groups over time.

Imagine two groups: one affected by an event (treatment group) and another that remains unchanged (control group). If no event occurred, the gap between these groups would stay consistent. DID checks whether that gap shifts after the event—if it does, that suggests a causal impact.

Think of it as a before-and-after snapshot with a twist. Instead of just analyzing the treatment group’s outcome, DID also tracks changes in the control group to separate true effects from pre-existing differences.

Below, we present an example from the Stata Manual. It demonstrates how to use the commands didregress and xtdidregress.

‏‏‎ To see if the new process worked, the health provider will use a method called DID regression. They will compare patient satisfaction scores in hospitals that used the new process to those that didn’t. Patient satisfaction (“satis”) is measured on a scale of 0 to 10 (0 = very unsatisfied, 10 = very satisfied). A variable called “procedure” will be used: it’s marked as 1 if a patient used the new process after March, and 0 if not. This will help them estimate the impact of the new procedure on patient satisfaction. To get the ATET on the outcome satis, we type

didregress (satis) (procedure), group(hospital) time(month)

The second parentheses are for the “procedure” variable – this tells the command which hospitals used the new process.

The words group() and time() tell the command to include “fixed effects.” Think of these as extra checks in your model for hospital groups and time periods. group() is also important because it tells the computer to group the data by hospital when it calculates the standard errors, making sure the results are reliable even if data within the same hospital are related. This is called clustering at the hospital level.

 * Load hospdd data

use https://www.stata-press.com/data/r18/hospdd

‏‏‎ ‎

 didregress (satis) (procedure), group(hospital) time(month)

Treatment and time information
Time variable: month

Control:       procedure = 0

Treatment:     procedure = 1

-----------------------------------

             |   Control  Treatment

-------------+---------------------

Group        |

    hospital |        28         18

-------------+---------------------

Time         |

     Minimum |         1          4

     Maximum |         1          4

-----------------------------------
Difference-in-differences regression                     Number of obs = 7,368

Data type: Repeated cross-sectional
                               (Std. err. adjusted for 46 clusters in hospital)

-------------------------------------------------------------------------------

              |               Robust

        satis | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
--------------+----------------------------------------------------------------

ATET          |

    procedure |

(New vs Old)  |   .8479879   .0321121    26.41   0.000     .7833108     .912665

-------------------------------------------------------------------------------

Note: ATET estimate adjusted for group effects and time effects.

The first table in the results tells you about the groups and when the new procedure started. The “Group” part shows you how many hospitals are in each group: 28 used the old procedure (control group) and 18 used the new one (treated group).

The next part of the table shows you when the control group hospitals are first seen in the data, and when the treated hospitals started using the new procedure. In this example, all hospitals that used the new procedure started in April (time period 4). If some hospitals had started later, these times would be different.

The “ATET” number is 0.85. This means that, on average, patient satisfaction increased by almost 1 point because of the new procedure. Another way to think about it is: if those 18 hospitals hadn’t used the new procedure, their patient satisfaction would likely be almost 1 point lower.

Now, we need to check if the patient satisfaction scores were changing in a similar way for both groups before the new procedure started. This is called checking the “parallel trends” assumption, which is important for DID to work correctly. We can visually check this by plotting the average satisfaction scores over time for both groups.

. estat ptrends

Parallel-trends test (pretreatment time period)

H0: Linear trends are parallel

F(1, 45) = 0.55

Prob > F = 0.4615

You can find more examples and uses in the Stata Manual.

The drdid package implements the locally efficient, doubly robust difference-in-differences (DiD) estimators for the average treatment effect as proposed by Sant’Anna and Zhao (2020). It also includes inverse probability weighting (IPW) and outcome regression estimators for the DiD average treatment effect on the treated (ATT).

These doubly robust estimators combine IPW and outcome regression to yield more reliable statistical properties. In particular, the estimator remains valid as long as either the treatment propensity model or the outcome regression model is correctly specified.

Note that the panel data estimators assume you are working with time-invariant variables. Even if some variables vary over time, only their pre-treatment values are used when estimating the outcome or probability models.

In contrast, when using repeated cross-section data, you can incorporate time-varying controls. However, the underlying assumption is that the control variables should be time constant—a condition Sant’Anna and Zhao (2020) refer to as the stationarity assumption.

While it is possible to add time-varying covariates to panel data estimators by including changes in covariates as additional controls alongside the pre-treatment values, this approach may lead to inconsistent results unless the controls are strictly exogenous (which is a strong assumption). Otherwise, the effects that should be captured by the ATT might be absorbed by the varying covariates.

Model Specification Options