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Time is Knowledge: What Response Times Reveal

Jean-Michel Benkert, Shuo Liu, Nick Netzer

TL;DR

This paper develops a general framework linking binary choices to latent distributions through a chronometric function $c$, showing that response times encode information about unobserved variables when decisions are faster at larger absolute latent deviations. The key contribution is a complete characterization of which distributional properties of the latent variables are identifiable from data $(p_j,F_j)$ under invariance to monotone transformations, formalized via a representative chronometric function $c^*$ and a transformation class $\boldsymbol{\Psi}$. The authors unify existing results in the literature and extend them to handle multiple chronometric representations, distributional restrictions, and heterogeneity/noise, while illustrating four applications—revealed preferences, optimal nudging, decreasing marginal happiness, and predicting treatment heterogeneity—where RT data yield insights beyond standard binary-data analysis. The practical impact is substantial: researchers can test and bound properties of latent distributions without strong parametric assumptions, enabling more robust inferences and pre-treatment predictions across economic contexts. The framework also opens avenues for broader applications, such as assessing inequality, polarization, and pricing strategies from RT-enabled binary decisions.

Abstract

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.

Time is Knowledge: What Response Times Reveal

TL;DR

This paper develops a general framework linking binary choices to latent distributions through a chronometric function , showing that response times encode information about unobserved variables when decisions are faster at larger absolute latent deviations. The key contribution is a complete characterization of which distributional properties of the latent variables are identifiable from data under invariance to monotone transformations, formalized via a representative chronometric function and a transformation class . The authors unify existing results in the literature and extend them to handle multiple chronometric representations, distributional restrictions, and heterogeneity/noise, while illustrating four applications—revealed preferences, optimal nudging, decreasing marginal happiness, and predicting treatment heterogeneity—where RT data yield insights beyond standard binary-data analysis. The practical impact is substantial: researchers can test and bound properties of latent distributions without strong parametric assumptions, enabling more robust inferences and pre-treatment predictions across economic contexts. The framework also opens avenues for broader applications, such as assessing inequality, polarization, and pricing strategies from RT-enabled binary decisions.

Abstract

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.
Paper Structure (24 sections, 3 theorems, 49 equations, 5 figures, 2 tables)

This paper contains 24 sections, 3 theorems, 49 equations, 5 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Theory
  3. Binary Response Model
  4. Detecting Properties
  5. Generating Chronometric Functions
  6. Main Result
  7. Extensions
  8. Multiple Representative Chronometric Functions
  9. Distributional Assumptions
  10. Heterogeneity and Noise
  11. Applications
  12. Revealed Preference Analysis
  13. Identifying an Optimal Nudge
  14. Testing Decreasing Marginal Happiness
  15. Predicting Treatment Heterogeneity
  16. ...and 9 more sections

Key Result

Theorem 1

Suppose $\mathscr{C}^*$ is generated by $((c^*_j)_j,\Psi)$. If $(H_j)_j$ defined in (defH) satisfies a property $\mathbf{P}$ that is invariant to transformations $\Psi$, then $\mathbf{P}$ is detected.

Figures (5)

  • Figure 1: Examples of chronometric functions.
  • Figure 2: Prediction accuracy with chronometric heterogeneity
  • Figure 3: Shares unvaccinated
  • Figure 4: The relationship between income and reported happiness.
  • Figure 5: Empirical conditions for testing the income-happiness relation.

Theorems & Definitions (9)

  • Definition 1
  • Definition 2
  • Definition 3
  • Theorem 1
  • proof
  • Theorem 2
  • proof
  • Proposition 1
  • proof