A Student’s Guide: How to Run a Difference-in-Differences (DiD) Analysis in Stata

A Student's Guide: How to Run a Difference-in-Differences (DiD) Analysis in Stata

Navigating the world of econometrics can be challenging, especially when you encounter methods like Difference-in-Differences (DiD). It’s a powerful and popular technique for estimating the causal effect of a specific intervention, but it’s also one where students often get stuck. You might be asking yourself, “How do I even set up the data?” or “What does this interaction term actually mean?”

You’re in the right place.

At QuantThesis, we help students with econometrics every single day. This guide will walk you through the entire process of running a Difference-in-Differences in Stata, from the core intuition to the practical code and interpretation.

What is Difference-in-Differences, Anyway?

Before we type a single command in Stata, let’s understand the logic.

DiD analysis is used to measure the effect of a policy or event (the “treatment”) on an outcome. To do this, it compares the change in the outcome over time for a group that received the treatment (the treatment group) to the change in the outcome over time for a group that did not (the control group).

Imagine a city introduces a new training program to boost wages, but only for residents in one specific area (the treatment group). All other areas are the control group.

  1. First Difference (Time): We look at how wages changed for the treatment group before and after the program.

  2. Second Difference (Treatment vs. Control): We also look at how wages changed for the control group over the same period. This captures general economic trends that have nothing to do with the program.

The “Difference-in-Differences” is the crucial step: we subtract the control group’s change from the treatment group’s change. The result is our estimate of the program’s true causal effect, stripped of any background trends.

Before Program (Time=0)

After Program (Time=1)

Change over Time

Treatment Group

Avg. Wage (Treat, Before)

Avg. Wage (Treat, After)

Δ Treat

Control Group

Avg. Wage (Control, Before)

Avg. Wage (Control, After)

Δ Control

Difference

DiD Effect = Δ Treat – Δ Control

The DiD Regression Model

In practice, we don’t just subtract averages. We use a regression model, which allows us to control for other variables. The standard DiD regression equation looks like this:

Y = β₀ + β₁[Time] + β₂[Treated] + β₃[Time * Treated] + ε

Where:

  • Y is your outcome variable (e.g., wages, test scores).

  • Time is a dummy variable (0 for the pre-period, 1 for the post-period).

  • Treated is a dummy variable (0 for the control group, 1 for the treatment group).

  • Time * Treated is the interaction term. This is the magic ingredient!

  • β₃ is your Difference-in-Differences estimator. It captures the additional change in Y experienced by the treatment group in the post-period. This is the coefficient you care about most.

A Step-by-Step Guide to Difference-in-Differences in Stata

Let’s use a practical example. Imagine we want to see if a new teaching method (method) improves student test_score. The method was introduced in some schools (treated = 1) but not others (treated = 0). We have data from before the change (time = 0) and after (time = 1).

Step 1: Set Up Your Data

Your data needs to be in a “long” format. This means each observational unit (e.g., a school) will have two rows: one for the pre-period and one for the post-period.

Here’s how to interpret each key coefficient:

  • _cons (β₀): The intercept is 72. This is the average test score for the control group in the pre-period. It’s our baseline.

  • time (β₁): The coefficient is 3. This means the control group’s scores increased by 3 points from the pre- to the post-period. This captures the general trend.

  • treated (β₂): The coefficient is 2. This means that in the pre-period, the treatment group’s scores were, on average, 2 points higher than the control group’s. This is the baseline difference between the groups.

  • did_estimator (β₃): The coefficient is 7. This is our DiD effect! It means the new teaching method caused an additional increase of 7 points for the treated schools, on top of the general trend. This is the causal effect we were looking for.

A Crucial Assumption: Parallel Trends

The single most important assumption for DiD is parallel trends. It assumes that the treatment and control groups’ outcomes would have followed the same trend over time in the absence of the treatment.

While you can never prove this (it’s a counterfactual), you can find evidence for it by plotting the average outcomes for both groups in the periods before the treatment. If the lines are roughly parallel, your assumption is more credible.

Need More Help With Your Analysis?

The Difference-in-Differences in Stata is a foundational tool for any budding econometrician. But getting it right, checking assumptions, and dealing with more complex scenarios (like multiple time periods or staggered adoption) can be tough.

If you’re feeling overwhelmed with your coursework, thesis, or dissertation, you don’t have to do it alone.

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