Electronic copy available at: http://ssrn.com/abstract=1627366 Non-linear time perception and time inconsistency (draft version) Kan Takeuchi * Graduate School of Economics Hitotsubashi University Email: kan@econ.hit-u.ac.jp. May 10th, 2010 When a man sits with a pretty girl for an hour, it seems like a minute. But let him sit on a hot stove for a minute and it’s longer than any hour. That’s relativity. — Albert Einstein 1 Abstract This brief paper proposes a framework that interprets time inconsistent behavior being caused by nonlinear time perception of individuals. I assume that individuals have their own internal clock, on which they make consistent intertemporal choices. If the conversion from the physical time t into the psychological time τ is not linear, it naturally causes time inconsistent behavior. Indeed, any time inconsistent behavior can be solely attributed to the nonlinear transformation of time. In the prospect theory, the irregular risk taking behavior is attributed to the inverse S- shaped probability weighting function. Similarly, the inverse S-shaped time perception function is consistent with the present bias (hyperbolic discounting) and the future bias. I estimate such a time perception function from the data of my recent experiment. Keywords: intertemporal choice, time preference, hyperbolic discounting, time perception JEL Classifications: C91, D81, D99 1 Introduction This paper applies the prospect theory of Kahneman and Tversky (1979) to the intertemporal choice framework. I assume that an intertemporal choice consists of two parts. First, subjects perceive time t according to their internal clocks: t → τ (t). Second, they make time consistent decisions based on the perceived τ . In this way, any time inconsistent behavior can be attributed solely to the * I thank Yan Chen, Yusufcan Masatlioglu, Scott Page, Taiki Takahashi and seminar participants at Michigan, Cal- tech, Amsterdam, Gifu Shotoku Gakuen, and the ESA meetings (Osaka, Shanghai and Tucson) for helpful comments and discussions. All errors are mine. Comments are very welcomed. 1 This famous quotation is collected in Calaprice (2005) as Einstein’s explanation of relativity which he gave to his secretary Helen Dukas. 1