Propensity Score Matching and Difference-in-Differences Explained: How Researchers Compare Firms Fairly

The Big Problem: Unfair Comparisons

A simple comparison between firms can be misleading.

Imagine we compare firms that adopt a new strategy with firms that do not. The adopting firms may already be larger, more profitable, better governed, and more attractive to investors.

If these firms perform better later, the difference may not be caused by the new strategy. It may simply reflect the fact that they were already stronger from the beginning.

Group	Before the Event	Problem
Strategy Adopters	Larger, more profitable, better governed	Already stronger
Non-Adopters	Smaller, less profitable, weaker governance	Not a fair comparison

Step 1: What Is Propensity Score Matching?

Propensity Score Matching, or PSM, is a method used to find a control group that looks similar to the treatment group before the event happens.

In plain English, PSM asks:

“Which non-treated firms look most similar to the treated firms before treatment?”

Researchers first estimate the probability that each firm receives the treatment based on observable characteristics. This probability is called the propensity score.

Then each treated firm is matched with one or more similar control firms.

What Variables Can Be Used for Matching?

In corporate finance and business research, researchers may match firms based on characteristics such as:

• Firm size
• Return on assets
• Price-to-book ratio
• Leverage
• Cash holdings
• Institutional ownership
• CEO age
• CEO tenure
• Board independence
• CEO gender

The goal is not to make firms identical in every possible way. The goal is to make the treatment and control groups more comparable based on important observable characteristics.

Why Matching Alone Is Not Enough

PSM helps create a more comparable control group, but it does not automatically solve every problem.

Even after matching, both groups may still be affected by market trends, industry shocks, inflation, interest rates, or changes in investor sentiment.

That is why researchers often combine matching with Difference-in-Differences.

Step 2: What Is Difference-in-Differences?

Difference-in-Differences, often called DiD, is a method used to estimate the effect of an event, policy, strategy, or business decision.

Instead of simply comparing firms before and after an event, DiD compares:

• the change in the treatment group
• minus the change in the matched control group

The Clean PSM + DiD Logic

The combined logic is very powerful:

A Simple PSM + DiD Example

Suppose researchers want to know whether firms adopting a new technology improve profitability.

First, they use PSM to match technology-adopting firms with similar non-adopting firms.

After matching, the sample becomes smaller but more comparable:

Sample Stage	Treatment Firms	Control Firms	Meaning
Before Matching	100	1,000	Many firms are not comparable
After Matching	80	80	Unmatched firms are dropped

Then researchers compare performance before and after the event:

This means that the treated firms improved by 2 percentage points more than similar control firms.

That extra improvement is the estimated treatment effect.

Why the After Numbers Do Not Need to Match

A common misunderstanding is thinking that treatment and control outcomes must match after treatment.

They do not.

In PSM, researchers try to make treatment and control firms comparable before treatment. After treatment, the whole point is to see whether the treatment group changes differently.

If the groups were forced to have the same after-treatment outcome, there would be no treatment effect to study.

The DiD Formula

The formula is simple:

In plain English:

Why PSM + DiD Is Better Than a Simple Comparison

Method	What It Does	Main Weakness
Simple Comparison	Compares treated and untreated firms	Groups may be very different
Before-and-After	Compares treated firms before and after	Cannot remove general market trends
PSM	Creates a more comparable control group	Does not fully handle time trends by itself
DiD	Compares changes over time	Requires credible parallel trends
PSM + DiD	Uses comparable firms and compares changes over time	Still requires careful research design

Corporate Finance Example

Suppose researchers want to study whether firms adopting artificial intelligence improve firm performance.

They may first match AI adopters with non-adopters that were similar before adoption in terms of firm size, profitability, leverage, cash holdings, institutional ownership, and governance.

Then they compare the change in performance for both groups:

	ROA Before	ROA After	Change
Matched AI Adopters	5%	9%	+4%
Matched Non-Adopters	5%	7%	+2%

This suggests that AI adoption may be associated with an additional 2 percentage-point improvement in profitability beyond the improvement experienced by similar non-adopting firms.

Why Investors Should Care

Investors constantly hear claims such as:

• AI improves productivity.
• ESG improves firm value.
• Board diversity improves governance.
• Digital transformation increases profitability.
• Innovation creates long-term market value.

Some of these claims may be true. But simple correlations are not enough.

PSM + DiD helps investors and researchers ask a better question:

“Compared with similar firms, did treated firms improve more after the event?”

The Key Assumption: Parallel Trends

The most important assumption behind DiD is called the parallel trends assumption.

This means that, without the treatment, the treatment group and control group would have followed similar trends over time.

If the treatment group was already improving much faster before the event, then DiD may overestimate the treatment effect.

That is why researchers often check pre-treatment trends before trusting DiD results.

Common Applications in Finance and Business

PSM + DiD is widely used in:

• Corporate finance
• Banking research
• Investment research
• Accounting research
• ESG research
• AI adoption research
• Executive leadership studies
• Public policy evaluation
• Mergers and acquisitions
• Capital structure research

Whenever researchers want to understand cause and effect using real-world data, PSM and DiD are often considered together.

PSM + DiD in Regression Form

In academic papers, DiD is often estimated using a regression model after constructing a matched sample.

The most important term is:

This interaction term captures the Difference-in-Differences effect.

Common Mistakes When Using PSM + DiD

• Thinking matched samples should get bigger: They usually get smaller because unmatched observations are dropped.
• Matching on post-treatment variables: Matching should normally use pre-treatment characteristics.
• Choosing a weak control group: The control group should be comparable to the treatment group.
• Ignoring pre-trends: If the groups were already moving differently before the event, DiD may be misleading.
• Assuming causality too quickly: PSM + DiD improves research design, but it does not magically prove causality.
• Using too short a time window: Some corporate effects take time to appear.
• Ignoring other events: Another shock may occur at the same time as the treatment.

PSM + DiD in One Sentence

Final Thoughts

Propensity Score Matching and Difference-in-Differences may sound technical, but their combined intuition is simple.

First, compare treated firms with similar control firms.

Second, compare how both groups change over time.

That simple logic helps researchers move beyond naive comparisons and build stronger evidence about corporate decisions, financial performance, market value, and policy effects.

For investors, students, analysts, and researchers, understanding PSM + DiD can make it much easier to evaluate claims about business strategy, innovation, governance, and financial markets.

---

Recommended Next Step

If you want to understand financial markets more clearly, start with the foundations: valuation, interest rates, risk, market structure, and investor behaviour.