推定モデル

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あいねいさし
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1 kohara@osipp.osaka-u.ac.jp ** *** 1

2 % % Machin and Manning (1999) Duration Dependence Turon (2003) Bover, Arellano and Betolila (2002) 2

3 Katz and Meyer (1990), Meyer (1990) Carling (1996) van den Berg and van Ours (1996)Abbring, van den Berg and van Ours (2002) 2002b 3

5 A

7 a 2002a C a 4 7

8 Cox (1972) Proportional Hazard Proportional Hazard 8

9 T T t T 0 F ( t) = f ( s) ds = prob( T t) f (t) T prob ( T t) = 1 F( t) = S( t) t t +1 λ( t) lim = t 0 prob( t T t + t T t) F(t + t) F(t) = t ts( t) = f ( t) S( t) X (t) β Cox Proportional Hazard λ( t ) = λ0 ( t)e X β λ Baseline 0 Hazard Proportional Hazard T, T, 1 2 L,T K T i Ri exp( X ( t) β ) j R i i exp( X j ( t) β ) Partial Likelihood L( β ) = K i 1 exp( X j ( t) β ) j i = exp( X ( t) β ) K l( β ) = X i ( t) β exp( X i ( t) β ) βˆ i= 1 j Ri X i (t) 1 9

10 40 40 Baseline Hazard Hazard m i (t) e 2 X iβ λm l( β ) = l ( β ) m = m m=

12 Cox and Snell Residual deviance residual B

13 40 Kaplan-Meier k h = i S( T k ) 1 hi T k n i T k i= 1 ni 14 Kaplan-Meier Proportional Hazard Proportionality Proportional Hazard β β (t) = β Grambsch and Therneau (1994) Global Test of proportionality over all covariates exp(0.352) 13

14 10 10 Baseline Hazard %5%

15 b 2002b

16 % %

18 Abbring, Jan, Gerard van den Berg and Jan van Ours (2002), The Anatomy of Unemployment Dynamics, European Economic Review 46(10): Bover, Olympia, Manuel Arellano and Samuel Betolila (2002), Unemployment Duration, Benefit Duration and the Business Cycle, The Economic Journal 112: Carling, Kenneth, Per-Anders Edin, Anders Harkman and Bertil Holmlund (1996), "Unemployment Duration, Unemployment Benefits and Labor Market Programs in Sweden", Journal of Public Economics 59(3): Cox, David (1972), Regression Models and Life Tables, Journal of the Royal Statistical Society Series B 34(2): Grambsch, Patricia and Terry Therneau (1994), Proportional Hazards Tests and Diagnostics Based on Weighted Residuals, Biometrika 81(3): Katz, Lawrence and Bruce Meyer (1990), "The Impact of the Potential Duration of Unemployment Benefits on the Duration of Unemployment", Journal of Public Economics 41(1): Machin, Stephen and Alan Manning 1999), The Causes and Consequences of Longterm Unemployment in Europe, in Orley Ashenfelter, and David Card, Handbook of Labor Economics Vol.3C (Elsevier, Amsterdam). Meyer, Bruce (1990), "Unemployment Insurance and Unemployment Spells", Econometrica 58(4): Turon, Hélène(2003), Inflow Composition, Duration Dependence and their Impact on the Unemployment Outflow Rate, Oxford Bulletin of Economics and Statistics 65(1): van den Berg, Gerard and Jan van Ours (1996), Unemployment Dynamics and Duration Dependence, Journal of Labor Economics 14(1): ( ) (2002a)

19 (2002b) ( ) ( ) 19

26 p y

DP

KEIO UNIVERSITY MARKET QUALITY RESEARCH PROJECT (A 21 st Century Center of Excellence Project) DP2004-13 * ** * ** Graduate School of Economics and Graduate School of Business and Commerce, Keio University