時間割引:双曲割引と弱加法性

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1 Discussion aper No. 666 June 2006 The Institute of Social and Economic Research Osaka University 6-1 Mihogaoka, Ibaraki, Osaka , Japan

2 Time Discounting: Declining Impatience and Interval Effect tsutsui@econ.osaka-u.ac.jp

3 1 T Laibson, A B 1 1 T Uzawa (1968 ) 1

4 T z-tree Fischbacher, T 3 1 Green a 2001b 2 Read Read

5 T Read X t t X s t(>s ) 1 R( 0, s) R(0, t) 1 Richards 1999 ender 1996 Kirby and Marakovic 1995 Myerson and Green 1995 Benzion 1989 Thaler 1981 s t (1) Read T 1+ β (0,18) (1 + β(0,6)) (1 + β(6,12)) (1 + β(12,18)) 2 β ( a, b) a b a A b B β ( a, b) = ( B A) A 2 6 R(a, b) 3 (1 + R (0, 18)) (1 + R(0, 6))(1 + R(6, 12))(1 + R(12, 18)) 3 3 3

6 T Frederick 2002 R( a, b) R( a', b'), if b a b' a' > 0, a, a', b, b' Read T

7 T Benzion 1989 T T 5 T A B 1, 2,

8 3 A A B A B 2 15 A B No No No No No No No No No No No No No No No A A

9 T A B % 50% A B 7 T A 1 B B A B

10 T T T 1 A B A B A 0 B A B s t β ( s, t) β ( s, t) R( s, t) 2 9 T 10 8 T T 3 3 No.1 R(0, 14) No.2 R(0, 28) No.3 R(0, 42) No.4 R(0, 56) % B 625 A R(0, 28) 1+ β (0, 28) 6 1+R(0, 42) 1+ β (0, 42) 3 8

11 T No.5 R(1, 15) No.6 R(7, 21) No.7 R(14, 28) No.8 R(14, 42) No.9 R(14, 56) No.10 R(28, 42) No.11 R(28, 56) No.12 R(42, 56) No.13 R(56, 70) No.14 R(70, 84) No.15 R(84, 98) A B T A B

12 =

13 4 = ** ** ** * * * ** ** ** * ** t- ** * =4 11

14 =6 5 =4 t * * ** * =6 t ** *

15 T T T T T T A A

16 T 12 T T T 16 T T A B

17 T T

18 l ** * a b 16

19 U(a, b) 2 D(n, a, b) n a b Read Read U(0,56) D(4,0,56) D(2,0,56) D(4,0,56) 2 D(2,0,56) (U(0,56)) 17

20 8 4 3 U(0,56) D(4,0,56) U(0,42) D(3,0,42) U(14,56) D(3,4,56) U(0,28) D(2,0,28) U(14,42) D(2,14,42) U(28,56) D(2,28,56) U(0,56) D(2,0,56) ** *

21 T 180 A B 9 X A B 97 X X 8 A B 8 X 19 T ender(1996) A B ** R(2,9) R(90,97) *

22 2 1 6 A B 4 R ~ 4 ( B A) { A( t s) } R R ~ R 4 4 R ~ A B t s,, R R B A R ( B A) { A( t s) } = A ( t s) R 20

23 A 0 B 1 A (1 84 ) A B (4 8 ) A 2 B A 10 A A 21

24 7 R ~ 1 84 A B R ~ 3 7 R ~ 4 8 A A 7 R ~ 2/ Read

25 * * E E A B ** *

26 Read 2001 Loewenstein and relec 1992 Laibson 1997 Read

27 Benzion, U., A. Rapaport and J. Yagil, 1989, Discount Rates Inferred from Decisions: An Experimental Study, Management Science, 35, Fischbacher, U., 1999, z-tree Toolbox for Readymade Economic Experiments, IEW Working paper 21, University of Zurich. Frederick, S., G. Loewenstein and T. O Donoghue, 2002, Time Discounting and Time reference: A Critical Review, Journal of Economic Literature, 40, Green, L., J. Myerson and E. McFadden, 1997, Rate of Temporal Discounting Decreases with Amount of Reward, Memory & Cognition, 25, Kirby, K. N and N. N. Marakovic., 1995, Modeling Myopic Decisions: Evidence for Hyperbolic Delay-Discounting within Subjects and Amounts, Organizational Behavior and Human Decision rocesses, 64, Laibson, D., 1997, Golden Eggs and Hyperbolic Discounting, Quarterly Journal of Economics, 112, Loewenstein, G. and D. relec, 1992, Anomalies in Intertemporal Choice: Evidence and an Interpretation, Quarterly Journal of Economics, 107, McClure, S. M., D. I. Laibson, G. Loewenstein and J. D. Cohen, 2004, Separate Neural Systems Value Immediate and Delayed Monetary Rewards, Science, 306, Myerson, G and L. Green., 1995, Discounting of Delayed Rewards: Models of Individual Choice, Journal of The Experimental Analysis of Behavior, 64,

28 ender, J. L., 1996, Discount Rates and Credit Markets: Theory and Evidence from Rural India, Journal of Development Economics, 50, Read, D., 2001, Is Time-Discounting Hyperbolic or Subadditive?, Journal of Risk and Uncertainty, 23, 5-32 Richards, J. B, L. Zhang, S. H. Mitchell, and Harriet De Wit., 1999, Delay or robability Discounting in a Model of Impulsive Behavior: Effect of Alcohol, Journal of The Experimental Analysis of Behavior, 71, Thaler, R. H., 1981, Some Empirical Evidence on Dynamic Inconsistency, Economic Letters, 8, Uzawa, H., 1968, Time reference, the Consumption Function and Optimum Asset Holdings, in: J.N. Wolfe, ed., Value Capital and Growth: apers In Honour of Sir John Hicks (Chicago: Aldine).,,, 2005,, COE, 74, 1-36, 2001a,,, 26, 6-24, 2001b,, 2001,

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