Subjective Time Deformation in Intertemporal Choice: A Functional Data Analysis Approach

2026-05-29

AI Summary

This study addresses a key limitation in traditional intertemporal choice research, which relies on scalar discount rates or prespecified functional forms and thus fails to capture the full trajectory of individuals’ subjective time perception. For the first time, functional data analysis is introduced to this domain: based on discrete intertemporal equivalence judgments, the authors employ monotonic smoothing to reconstruct each individual’s implicit subjective time trajectory. Combining functional principal component analysis with clustering, they systematically uncover substantial heterogeneity in these trajectories. The first two principal components account for 97.44% of total variation, and clustering yields three robust and stable temporal distortion patterns. Although conventional parametric models achieve good fit, they cannot replicate this underlying structure. Notably, implicit time trajectories only partially align with explicit time perception measures, underscoring the unique capacity of functional approaches to reveal complex temporal preferences.

Abstract

Intertemporal choice data are usually summarized through scalar discount-rate parameters or fitted by predetermined parametric discount functions, although relevant information may lie in the shape of the whole discounting trajectory. This paper proposes a Functional Data Analysis framework for reconstructing and analyzing implicit subjective-time trajectories from discrete intertemporal equivalence judgments. Monetary equivalence responses from a multilingual questionnaire are transformed into individual discount curves, regularized by monotone smoothing, and used to recover normalized implicit subjective-time trajectories. The trajectories are examined through derivative summaries, Functional Principal Component Analysis, and clustering on standardized component scores. The empirical application, based on 107 participants, shows that heterogeneity in intertemporal choice is not fully captured by scalar discount-rate variation. The first two functional principal components explain 97.44% of the variability, indicating a low-dimensional structure. Functional clustering identifies three stable profiles of temporal deformation, supported by bootstrap stability analysis and sensitivity checks on components, algorithms, distances, smoothing specifications, and outlier treatment. Parametric benchmarks based on exponential, Weber-Fechner, and Stevens specifications provide accurate fits for many individuals, but do not fully recover the functional clustering structure. The comparison with explicit subjective-time perception measures reveals only partial alignment between implicit trajectories reconstructed from choices and directly reported temporal perception. Functional Data Analysis provides an applied statistical framework for representing intertemporal choice heterogeneity as variation in functional shape, complementing scalar discount-rate and parametric subjective-time models.

Problem

• intertemporal choice
• subjective time
• functional data analysis
• discounting trajectory
• heterogeneity

Innovation

• Functional Data Analysis
• Intertemporal Choice
• Subjective Time
• Functional Principal Component Analysis
• Temporal Deformation