Charles Gauthier - RP Series

Revealed Preference, Explained

About This Series

My research spans several areas in economics — including econometrics, computational economics, and applied microeconomic theory. While diverse in method and scope, one common thread ties much of it together: revealed preference analysis.

Revealed preference is a powerful and elegant way to learn from behavior without making strong assumptions about what agents want. But despite its importance, it is often seen as too abstract to apply or too rigid to handle real-world data.

This series aims to change that.
It offers a clear and approachable introduction to revealed preference theory, how it works, and why it matters — both in theory and in practice. Each part walks through a different aspect of the framework, using intuitive explanations to make the key ideas accessible.

I hope this series shows the depth, flexibility, and practical relevance of revealed preference theory — and why it continues to shape how we think about choice, rationality, and economic inference

Part 1: What Do Your Choices Say About You?

Imagine watching someone shop at a grocery store.

They pick the red apples over the green ones. They skip the fancy yogurt, grab the mid-range one, and go with the off-brand cereal over the big-name box.

They never say a word, but if you observe them long enough, you can start to piece together their values: what they like, what they’re willing to pay for, what matters more and what matters less.

This is the core idea behind revealed preference theory:

People’s choices reveal their preferences.

Why Ask People When You Can Just Watch Them?

Revealed preference was introduced by economist Paul Samuelson in 1938. He proposed a simple but radical idea: rather than asking people what they prefer (which can be unreliable or biased), we can infer their preferences from what they actually do.

If someone chooses bundle A over bundle B when both are affordable, we say:

“They prefer A to B.”

No surveys. No hypotheticals. Just behavior.

A Scientific Way to Study Behavior

The beauty of revealed preference theory is that it provides a testable framework.

Economists like Afriat and Varian showed that we can take observed choices and ask:

Are these consistent with some rational underlying preference?

This gives us the ability to:

Check if someone is behaving rationally
Recover a utility function even if we don’t observe it directly
Detect behavioral patterns like inconsistencies, self-control problems, or biases

In short: it gives us tools to analyze choice behavior without needing strong assumptions.

Real-World Impact

Revealed preference tools are now used in:

Consumer analysis: How do people respond to price changes, subsidies, or taxes?
Transportation: How do people choose between speed and cost?
Health & education: How do patients and students respond to limited options?
Behavioral economics: Can we detect internal conflicts or irrationalities?

They’re especially useful when what people say isn’t as reliable as what they do—something economists often confront.

Because behind every choice lies a story—and with the right tools, we can begin to understand it.

Part 2: The Power of Nonparametrics

Imagine trying to understand someone’s preferences—what they value, what matters most—just by watching their behavior.

Now imagine doing that without assuming anything about their preferences upfront.
That’s the heart of nonparametric economics.

What Are Nonparametric Methods?

In economics, a nonparametric approach means you’re not assuming a specific functional form for preferences.
You’re not saying:

“Let’s assume utility = income⁰⋅⁵.”

You’re saying:

“Let’s check whether their choices are consistent with some utility function—even if we don’t know what it is.”

It's about letting the data speak, not forcing it into a predefined model.

Why This Matters

Nonparametric revealed preference methods help us:

Test for rationality in choices
Recover preferences without imposing a specific model
Allow for complex behavior, including behavioral biases
Avoid misspecification, a major risk with parametric models
Work with messy, real-world data, where assumptions often fail

This flexibility is what makes the approach so powerful.

In My Research

In my work, I use nonparametric tools to:

Identify whether behavior is dynamically consistent
Recover the impacts of parental inputs on children's human capital
Analyze choices with measurement error or price search behavior

All of this is possible without assuming any specific utility shape—making the conclusions more robust and more broadly applicable.

The Trade-Off

Of course, nonparametrics come with trade-offs:

You often need more data
Results can be harder to interpret
The math can be more involved

But if you care about drawing conclusions that aren’t just artifacts of your assumptions, it’s a trade-off worth making.

Part 3: Afriat’s Theorem — Rationality, Proven with Math and Modesty

How do you know if someone is behaving rationally?

In everyday life, it’s easy to say someone is being irrational. But in economics, we need something more precise. Something we can test.

That’s where Afriat’s Theorem comes in—one of the most elegant results in revealed preference theory. It gives us a simple way to ask:

Are these observed choices consistent with some utility maximization?

What’s the Setup?

Let’s say we observe someone’s choices over a few decision settings:

In each case, they face prices and have a budget.
We observe which bundle of goods they choose.

Now we ask:

Could all these choices come from someone maximizing a stable utility function under a budget constraint?

Afriat showed that the answer is yes if and only if a certain set of inequalities holds—known as the Generalized Axiom of Revealed Preference (GARP).

GARP in Plain Terms

If someone prefers bundle A to bundle B (either directly or through a chain of other revealed preferences), then they should not also choose B when A is affordable.

In everyday words:

Don’t say you prefer tea over coffee, and then pick coffee when both are available.

Violating this logic is what makes behavior irrational in this framework.

A visual illustration of a GARP violation with two budgets and two choices.

Afriat’s Theorem: What It Says

Afriat’s Theorem tells us that if a finite set of observed choices satisfies GARP, then there exists a utility function that is:

Monotonic (more is better),
Concave (diminishing returns), and
Rationalizing those choices exactly.

Not only does the theorem say a utility function exists—it even shows how to construct it.

Why It’s So Beautiful

Afriat’s Theorem is:

Constructive – It doesn’t just say "there exists" a utility function, it builds one.
Nonparametric – It doesn’t assume a specific shape for preferences.
Testable – You can actually apply this to real-world datasets.

It’s one of those results in economics that is both practically useful and intellectually elegant.

In My Work

I build on this logic to:

Test rationality when people face uncertainty or search frictions
Recover time preferences and production technologies
Handle measurement error in choice data while preserving the rationality structure

Afriat's logic is the bedrock—even in far more complex models.

Part 4 – Making Revealed Preference Practical

Revealed preference theory has long been celebrated for its clean logic, but applying it to real data presents challenges. In this final section, I develop tools to make revealed preference usable — both to test for irrationality and to recover economically meaningful objects like preferences or production functions.

Measuring and Testing Irrationality

Real data is messy — measurement error, rounding, behavioral noise. Observed choices often violate rationality, but not all violations are equal.

My research builds statistical tools that help distinguish:

Systematic violations that point to real inconsistencies in behavior
Non-systematic violations that can be explained by noise or error

I also show how to:

Measure the “distance from rationality” — how close are the data to satisfying rational choice?
Quantify the severity of violations using test statistics grounded in economic theory
Build confidence sets and hypothesis tests to formally evaluate rationality assumptions

These methods bring discipline to revealed preference analysis. They allow researchers and policymakers to judge whether behavior is “rational enough” to trust — or whether inconsistencies are too large to ignore.

Learning from Behavior: Preferences, Production & Counterfactuals

Revealed preference isn't just about detecting irrationality — it’s also about recovering structure from behavior. In my research, I also show how to use rationality conditions as powerful restrictions to:

Estimate demand and preferences nonparametrically
Characterize production technologies in household models
Compute welfare bounds without estimating utility functions
Evaluate counterfactuals while respecting observed behavior

The core idea is that if choices are rational, then they reveal information about the agent’s preferences or technology — even if we don’t specify a functional form. My work builds algorithms and statistical techniques to make this information computable and testable.

In doing so, I show that revealed preference theory can be a constructive tool. It doesn't just rule models out — it builds models up, enabling researchers to estimate, simulate, and make predictions grounded directly in observed behavior.

Google Sites

Report abuse