Time is Knowledge: What Response Times Reveal

Response times contain information about economically relevant but unobserved variables like willingness to pay, preference intensity, quality, or happiness. We provide a general characterization of the properties of latent variables that can be detected using response time data. Our theoretical framework unifies and generalizes results in the literature and gives rise to many new applications. We illustrate the rich insights that the method can deliver through several empirical applications: revealed preference analysis, identifying an optimal nudge, testing decreasing marginal happiness of income, and predicting treatment heterogeneity.

💡 Research Summary

The paper develops a general theoretical framework for exploiting response‑time data to identify distributional features of unobserved latent variables in binary choice settings. The authors start from the canonical binary response model where a latent continuous variable x determines the observed choice: i = 0 if x ≤ 0 and i = 1 if x > 0. The distribution of x is described by a continuous cumulative distribution function G, but without additional information only G(0) (the choice probability) is identified.

The key innovation is to introduce a “chronometric function” c(·) that maps the realized value of x to a response time t. The function is monotone in the sense that larger absolute values of x lead to faster decisions; formally c is strictly increasing on the negative half‑line, strictly decreasing on the positive half‑line, and satisfies c(0)=t_min and lim_{|x|→∞}c(x)=t_max. By separating c into its left‑hand and right‑hand branches c₀ and c₁, the authors obtain inverse functions c₀⁻¹ and c₁⁻¹ that translate observed response‑time thresholds into quantiles of G. Consequently, the joint distribution of choices and response times identifies the composition G∘c⁻¹, and if the chronometric function were known exactly the entire latent distribution could be recovered.

Because c is typically unknown, the authors ask which properties of G can still be detected under various assumptions about c. Their main theorem shows that any property that is invariant under the class of transformations allowed for c can be identified. For example, if only monotonicity of c is assumed, properties preserved under monotone transformations—such as the sign of the mean, ordering of means across groups, or stochastic dominance—are identifiable. If c is further assumed to be symmetric (i.e., c₀(x)=c₁(−x)), stronger statements become possible, including identification of absolute mean differences and certain variance ratios. The theorem also provides a constructive recipe: pick a plausible representative c, construct an empirical candidate distribution Ĝ using the observed joint data, and test whether the property holds for Ĝ. If it does, the property holds for all admissible c within the specified transformation class.

The paper then applies this general result to four distinct empirical contexts, demonstrating how response‑time information resolves identification problems that plague standard approaches.

1. Revealed Preference Analysis – Building on Alós‑Ferrer, Fahr, and Netzer (2021), the authors show that the condition “the mean of the latent distribution is positive” follows directly from monotonicity of c, without needing any distributional assumptions. They extend the analysis to allow heterogeneous chronometric effects across tasks and verify that out‑of‑sample predictions improve when their robustness test classifies datasets as “heterogeneity‑robust.”

2. Optimal Nudging – When a policy maker can choose between two framing devices that symmetrically distort choices, response‑time data can uncover the true underlying preference shares, provided the two frames induce equally fast decisions. Using data from Serra‑Garcia and Szech (2023), the authors recover the unbiased preference distribution and show that the optimal nudge derived from this information outperforms existing benchmarks both in the original sample and in synthetic subsamples designed to stress‑test the method.

3. Decreasing Marginal Happiness of Income – The authors translate the hypothesis of diminishing marginal utility of income into a testable ordering of means across income groups. By exploiting the fact that faster responses imply larger latent effects, they construct a rank‑ordering test that requires only monotonicity (and in one version a mild additional condition). Applying the test to Liu and Netzer (2023) survey data, they find strong evidence for decreasing marginal happiness and robustly reject the opposite hypothesis of increasing marginal happiness.

4. Heterogeneous Treatment Effects – The paper introduces the concept of “near‑indifferent mass”: the proportion of agents whose latent utility difference lies close to zero. A larger near‑indifferent mass leads to shorter response times and, consequently, to stronger observed treatment effects. Using the Krefeld‑Schwalb, Sugerman, and Johnson (2024) dataset, the authors predict which sub‑populations will exhibit larger treatment responses before the treatment is administered, achieving substantially higher predictive accuracy than standard pre‑treatment covariate‑based methods.

Beyond these applications, the authors discuss extensions that incorporate individual‑specific chronometric functions and stochastic noise, providing necessary and sufficient conditions for the rationalizability of observed (choice, response‑time) pairs. They also compile an appendix of common distributional properties (e.g., stochastic dominance, mean‑variance trade‑offs) together with the corresponding response‑time identification conditions.

In sum, the paper establishes that response‑time data are a powerful, under‑utilized source of information for uncovering latent economic variables. By formalizing the link between latent magnitude and decision speed, and by characterizing the invariance properties required for identification, the authors offer a versatile toolkit that can be deployed across a wide range of empirical settings, from consumer choice and policy nudging to happiness economics and treatment effect heterogeneity. The work opens avenues for future research on multi‑alternative choices, dynamic decision environments, and networked interactions where response‑time information may similarly enrich identification strategies.