What hypothetical choices can reveal about real decisions

If someone says poor health would make them stop working, how much does that tell us about what they would actually do? Taking the answer literally risks confusing intentions with behavior. Ignoring it entirely might discard useful information.

In an arXiv preprint, Romuald Meango, Marc Henry, Ismael Mourifie and Ju Hyun Oh propose a different use for hypothetical answers: treat them as evidence about otherwise hidden differences between people. Their framework combines those answers with observed choices, including when the two come from samples whose individuals cannot be linked.

Answers as controls, not predictions

Economists call hypothetical answers “stated preferences” and actual choices “revealed preferences.” Each has a weakness. Hypothetical answers can differ systematically from behavior. Actual choices, meanwhile, do not automatically reveal cause and effect.

Consider health and employment. People who develop poor health may already differ in their attachment to work. Those underlying differences can influence both health and employment, making a simple comparison misleading. This is the problem of endogeneity: the attribute being studied is entangled with other influences on the outcome.

The paper asks whether responses across hypothetical scenarios can capture those influences. Someone who reports nearly the same willingness to work under every health scenario differs from someone whose answer changes sharply. Those patterns might reveal relevant differences even if neither person's reported probabilities accurately predict their actions.

When survey answers and actual outcomes belong to the same individuals, the method estimates actual choices while controlling for the answers. It then averages across the population to estimate what would happen if everyone faced a specified attribute, such as good or poor health.

That interpretation requires substantial assumptions. The answers must distinguish all the hidden characteristics needed to remove the confounding, and those characteristics must remain stable between reporting and acting. Relevant answer patterns must also be represented across the attribute groups being compared. Hypothetical bias is allowed; answers that conceal important differences are not.

When the people cannot be matched

Separate datasets create another problem: researchers know the distribution of answers and the distribution of decisions, but not which answers go with which decisions.

Instead of inventing those missing connections, the authors calculate the smallest and largest counterfactual choice probabilities compatible with the observed distributions and maintained assumptions. These are “sharp bounds”: narrower limits would exclude possibilities the framework still permits.

The calculation uses optimal transport, a mathematical approach that here considers possible ways of joining the two distributions. For the baseline problem, the authors reduce the calculation to optimization over a single number. Both samples must represent the same underlying population.

They also develop a specialized bootstrap procedure—repeatedly resampling the data—to quantify statistical uncertainty under additional conditions. Simulations support its performance in the designs tested, not universally. Restrictions on how answers predict choices, or on which variables can affect outcomes, can provide further information, but require their own justification.

A retirement illustration

The application uses the US Health and Retirement Study. In 2016, a survey module asked about the chance of working for pay two years later under different hypothetical health conditions. The 2018 wave recorded actual health and employment.

The starting sample contained 6,982 respondents aged 50–65 who were attached to the labor force in 2016; 1,090 completed the hypothetical-choice module. Final estimation samples were smaller because of missing information. Importantly, the outcome analyzed was being out of work, not necessarily retirement.

Taking hypothetical answers literally implied that fair or poor health increased the probability of being out of work by 24.2 percentage points. An actual-choice estimate controlling for gender, but not the stated probabilities, gave 15.8 points. Combining actual choices with the survey-answer controls gave 13.8 points.

Under the assumption that the answers capture the relevant hidden differences, this comparison suggests hypothetical bias matters more here than the correction for unobserved selection. Similar estimates do not themselves prove that assumption. The combined estimates were also less precise for respondents aged 60–65.

What remains uncertain

Health was self-reported and measured alongside employment. Employment shocks could themselves affect reported health, threatening the causal interpretation. Follow-up information was missing for about one-fifth of the starting sample, and hypothetical health categories did not perfectly match the observed categories.

The unmatched application carries further qualifications: results using auxiliary restrictions are exploratory because the inference theory covers only the baseline bounds. Its density assumptions are also maintained rather than established.

Finally, the theory shows that coarse answers can destroy much of the identifying information unless stronger restrictions are added. The preprint therefore offers neither a cure for unreliable surveys nor automatic causal inference. Its contribution is a conditional one: hypothetical answers can help explain real behavior without being reliable forecasts of it.