A Logical Economist's Argument Against Hyperbolic Discounting

摘要: Although there is a large and growing literature in psychology economics that uses experimental evidence to support the hyperbolic discounting hypothesis, this note first address question "Can we detect by offering choices between various monetary amounts at dates future people who also participate markets?" If answer "yes," I show marketplace will exploit discounters point where their wealth zero. "no", then interpretations of results psychologists some economists are illogical. M This addresses Hyperbolic exponential defined Section I. II outlines typical experiment can be found literatures interpreted several as for discounting. distinguish two types III maximizers nonwealth former should respond experiments exactly same way "exponential" populate literature. IV shows maximizing exploited marketplace. Working Definitions Exponential Discount Preferences adopt working definitions Laibson (1994). Consider following preferences date t consumer deterministic consumption sequences beginning continuing into (potentially infinite) future: For discounter, < 1 while = discounter. The populates huge number economic models including Samuelson (1937), Barro (1974), Lucas (1990), has “time consistent preferences” sense his marginal rates substitution do not change with passage time. Consider, example, MRS t+1 t+2 Against Discounting 2 other formulations discounting, see Strotz (1955), Pollak (1968), Peleg Yaari (1973), Thaler Shefrin (1981), Simon (1990). it common modeling allow discount vary over time, but does lead preference reversals. time variable rate models, Koopmans (1960), Uzawa or Becker Mulligan consumption. from view t+1: discounter's changes time: Because MRSs said exhibit As t, very urgent them (relative consumption), when arrives. There “exponential” “hyperbolic” , presence lack “preference reversals” important distinction any formulation. II. A Typical Monetary Experiment "time preference" literature: Question Would you like $10 today $15 tomorrow? 100 days $14 101 days? Actual money corresponding above often paid respondents questions. Examples such have been cited include Kurz et al Kirby Herrnstein (1995), 3 Respondents take usually assumed (and reasonably my opinion reasonableness idea doesn't matter argument) they would if were reasked days. posed "Does say anything about preferences?" III. Do Discounters Maximize Wealth? At point, pose simple proponents "Do your maximize wealth?" only require either yes no question, "maybe." trade market, Questions order wealth. interest (inclusive all relevant transactions costs) greater than 50%, maximizer chooses because can, interest, produce more tomorrow. less Note agents so many discounter; us discounter he maximizing. IV. Nonwealth discounters? markets wealth, let's suppose (as does) consume cash flows receive rather trading away might. market participants selfish hyperbolically, loose reversals these leave open "Dutch books." To how create own money-making Dutch book, offer sequence deals answered suggested. Deal Ask promise pay exchange He 4 and, according 2, prefers After passed, collect $10. Offer (the 100th day) tomorrow 101st day). deal 1, now. Pay When day arrives, promised 1. You'll make $1 every time! Notice promises made broken. limit size books which participate. Moreover, "shop around" cheaper booker". In words, one booker compete another attention Exchange exploitation latter.