( 2 65 1995 14.8 2050 33.4 1 2 3 1 7 3 2 1980 3 79
4 ( (1992 1 ( 6069 8 7079 5 80 3 80 1 (1 (Sample selection bias 1 (1 1* 80
1 1 ( (1 0.628897 150.5 0.565148 17.9 0.280527 70.9 0.600129 31.5 0.339812 60.8 0.697020 49.1 0.005994-0.253859-0.043874 87.0-84.9-6.8 0.006592-0.957097-0.227880 5.3-44.5-2.5 0.000897-0.200403 0.002800 49.4-46.0 0.9 0.015719 0.115653-0.230020 27.1 5.9-4.4 0.002668-0.135710-0.021630 48.2-46.2-6.4 0.006424-0.218138-0.059864 20.4-17.9-2.2 109,579 13,467 53,493 4,282 30,296 8,041-16634.9-468.5-2445.2-1490.5-5935.6-2258.0 (2 15 15-5 0.628897 150.5 0.729257 65.4 0.685411 83.5 0.624783 68.4 0.506745 37.8 0.533099 70.4 0.005994-0.253859-0.043874 87.0-84.9-6.8 0.006934-0.294822-0.051828 32.2-32.7-2.5 0.006373-0.257803-0.050176 44.6-42.8-3.4 0.006006-0.238535-0.041236 40.9-37.9-3.1 0.005636-0.269075-0.054896 26.2-27.6-3.8 0.005231-0.238046-0.031584 45.9-46.1-3.1 109,579 18,565 32,041 23,557 8,144 27,272-16634.9-2308.5-4229.6-3498.3-1514.3-4838.4 ( 1 1 0 2 1 0 ( 5054 (2 81
2 27.5 65 34.6 (1994 65 2.6 (3.8 2 ( 1994 20 (2 1 (2 1 3 3* 2 82
2 ( 100 1974 1984 1994 ( 65 ( 95.00 ( 81.15 ( 3.53 ( 89.89 ( 178.70 60-64 ( 105.97 ( 95.02 ( 3.60 ( 103.20 ( 176.82 84.30 80.86 3.14 99.27 177.02 102.10 96.67 3.30 112.79 188.56 76.84 80.12 2.64 108.81 217.11 96.11 97.12 2.97 117.39 187.64 ( 65 ( 89.28 ( 82.78 ( 3.12 ( 102.41 ( 246.71 96.95 84.98 2.73 120.47 255.92 89.02 91.19 2.62 129.47 293.69 60-64 ( ( ( ( 105.85 100.51 3.40 114.11 103.59 89.44 3.02 114.61 ( 186.82 246.46 ( 3 ( 96.74 99.93 2.87 129.53 233.95 ( 1974 6064 65 3 7 4 (3A 3 4 3 1992 83
6 (3B 3A ( 3B ( 84
( (4A 5 (4B 1 (5 60 2 3 4A (1 (2 (2(1 624.7 520 0.83 0.392 538.4 370 0.69 0.472 ( 60 5 85
4B (1 (2 (2(1 731.7 597 0.82 0.391 648.6 489.5 0.75 0.437 245.8 200 0.81 0.409 (1 60 (2 565 86
(6 6 (60 ( ( 300 ( 7 6 ( 6* 87
7 ( (1 60 (2 (3 ( 1995 1.4 200 4 1 7 3 (8 70 7 (1989 (37 (63% 88
8A ( 8B ( 89
8C ( ( 65 6064 34 (9 65 (3 ( 1994 1 65 6064 25 (10 90
9 (6064 1065 91
3 (65 (1 ( (1 ( 38 76 50 154 318 ( 38 76 50 96 260 ( 38 50 140 228 ( 38 50 65 153 (2 ( (1 ( 33 66 48 154 296 ( 33 66 48 89 236 ( 33 48 140 221 ( 33 48 65 146 (1 (2 2 60 70 5 80 3 (11A 60 70 (11B 92
11A (5580 ( 11B ( ( 4 60 93
(1993 4 : 19781981 1984 ( ( : (probit 1978 1% 0.1 1981 1978 2 3 1980 1983 1983 ( : (probit 1% 0.25% 1980 (1994 55 55 ( 69 multinomial logit model ( 4 : ( multi-nominal logit model (1994 ( 1993 ( (5 94
5 1 2-0.925154 * 3 1 5-0.085056 *** -0.268634 *** -0.000051 6-0.006716 *** 7 0.559582 *** 5.994983 *** 2 0.438301 *** 3-0.172419 *** 4-0.375657 *** 5-0.000839 *** 6-0.001981 *** 7 1.594472 *** 11.238710 *** 8,341-7403.77 :1% :5% :10% ( 1 1 2 0 2 1 yes0 no 3-0.04246-0.00674-0.03076 0.00004-0.00119 0.01848 0.52607 0.07914-0.02431-0.04830-0.00014 0.00004 0.23759 1.55956 4 1 yes0 no 5 6 7 ( ( 1993 6 Multi-nominal logit model ( 6 (60 (6070 95
6 (1991 1974 1977 30 44 ( (probit (probit (1994 1984 60 (1996 multinomial logit model( : 2 (7 96
1. 2 7 1-0.000087 3-0.244101 *** 4 0.031226 *** -0.235802 * 5 0.001022-1.917775 *** 2. 2-0.000325 *** 3-0.402790 *** 4-0.013532 *** -0.487615 *** 5 0.166209 ** 1.065789 *** 6,093-6210.81 1 5 10 0.00001-0.00560 0.00567 0.00209-0.01251-0.36612-0.00007-0.07950-0.00567-0.10078 0.04040 0.40557 ( 1 (60 1 2 0 2 3 6 4 5 60 70 ( ( (1996 (8 (1996 97
98 2 1 2 (9 8 (1986 1974 1979 ( ( (1994 1986 3 4 ( ( (1996 1989 ( 9 1 2 3 4 5 6 7 8 1% :5% :10% ( 1 2 1 yes0 no 3 1 0 4 1 yes0 no 5 1 0 6 500 1 yes0 no 7 60 1 yes0 no 8 (60
99 3 (60 (1993 ( (82 ( 12
12 (65 ( ( (13 (65 (60 65 5 3 ( 75 (57 ( 100
13 ( ( 387 796 2 226 167 (14 1 101
14 2 (Kotlikoff and Morris 1988 1993 3 93 84 9 5 102
(10 (11A1 ( 2 (11B 3 2 10 1974 1979 1. (1986 ( 2. (1991 1986 ( ( (1994 (1994 1986 1989 ( (47 1990 ( 56 ( 1994 (1994 ( 1989 1. (1996 ( 2 (1 (2 103
(11C (11D 11A 1 2 3 4 5 6 7 8 9 10 11 R2 0.35805 0.10941 0.01253-0.24100 0.31465 0.00242 0.12885-0.00242-0.00020 0.60552-1.49240 20,168 0.1568 1 5 10 0.12404 0.03924 0.00457-0.08718 0.10662 0.00088 0.47960-0.00088-0.00007 0.20650 ( 1 60 ( =1 0 2 =1 yes0 no 3 =1 yes1 no 4 5 =1 0 6 =1 yes0 no 7 ( =10.0 8 =1 0 9 10 11 =1 0 11B 1 2 0.5717144 3 0.2101434 4 0.0369532 5-0.1636400 6 0.3870963 7 0.0035851 8 0.4293855 9-0.0030970 10-0.0004580 11 0.7545467-4.4278000 15,411 R2 0.3199 1 5 10 0.21810 0.08241 0.01467-0.06479 0.14771 0.00142 0.16955-0.00123-0.00018 0.28600 ( 1 60 ( =1 0 11A ( 104
11C 1 2 0.518495 *** 3 0.165846 *** 4 0.037390 *** 5 0.148031 *** 6 0.400747 *** 7 0.003769 *** 8 0.344577 *** 9-0.002780 *** 10-0.000445 *** 11 0.414092 * -4.449100 *** 15,411 R2 0.3332 ***:1 **5 *10 0.19898 0.06527 0.01484 0.05877 0.15265 0.00150 0.17581-0.00110-0.00018 0.16152 ( 1 60 ( =1 0 2 1 yes0 no 4 5 =1 0 6 =1 yes0 no 7 ( =10.0 8 =1 0 9 10 11 =1 0 11D 1 2 0.766347 *** 3 0.397353 *** 4 0.034333 *** 5 0.088723 *** 6 0.378103 *** 7 0.003423 *** 8 0.397536 *** 9 0.275577 *** 10 0.690321 *** -4.831300 *** 15,411 R2 0.3199 ***1 **5 *10 0.28555 0.15306 0.01363 0.03523 0.14451 0.00136 0.15727 0.10948 0.26335 ( 1811C 9 =1 0 10 =1 0 4 105
106 Ohtake (1993
Appendix 1 5 0.1590 0.3658 0.1275 0.3336 0.2020 0.4016 71.7469 7.6387 67.5041 6.0355 64.9253 4.8360 0.4598 0.4984 0.3621 0.4807 0.3221 0.4674 515.0128 432.0377 479.0319 476.6378 429.2209 404.0846 154.1477 112.3147 80.6021 89.9048 118.6627 122.2889 0.2589 0.3792 0.3280 0.3977 0.4034 0.3528 4,156 2,071 2,114 7 829.3768 629.2301 801.7201 697.2429 730.4315 438.6916 0.5805 0.8343 0.3702 0.7129 0.3810 0.7159 42.2573 9.8459 45.2259 8.3903 41.7651 8.2026 0.1046 0.3061 0.0930 0.2906 0.0666 0.2493 0.2444 0.4298 0.1940 0.3956 0.2866 0.4523 2,410 1,129 2,554 9 11 0.5137 0.3322 0.3618 0.2326 548.1338 442.6423 0.1489 50.7579 14.6948 0.3212 2792.2920 1530.7070 70.7171 1.5788 1.0280 0.5795 3.5492 4.2299 0.0430 0.5171 0.3218 416.9957 0.3709 0.3624 0.9057 0.6181 0.4859 80.1966 0.6807 0.4662 95.9250 0.1908 0.3929 0.3144 0.0215 0.1450 15,656 0.1360 0.3430 0.6140 0.8160 0.2133 0.4096 27,689 0.4998 0.4225 0.3560 0.4669 7.7316 0.4937 0.2028 205.3680 0.2922 94.0164 332.2344 0.4643 ( 107
Appendix 2 1 (1 *1 0.392 0.496 0.782 60 10.472 0.694 0.483 65 *2 0.489 0.757 0.419 (2 0.392 0.447 0.351 0.329 0.426 60 0.472 0.467 0.383 0.391 0.410 65 0.489 0.472 0.391 0.401 0.407 2 (1 0.698 0.771 0.915 60 0.632 0.902 0.609 65 0.624 0.944 *3 0.559 (260 0.673 0.949 0.445 0.489 0.880 0.412 0.552 0.926 0.452 0.728 0.789 (365 0.664 0.961 0.426 0.490 0.924 0.381 0.542 0.930 0.443 0.542 0.929 3 ( (1 0.586 0.673 0.907 60 0.514 0.840 0.517 65 0.524 0.908 0.454 (260 0.651 0.914 0.407 0.415 0.841 0.324 0.504 0.886 0.395 0.518 0.619 (365 0.662 0.939 0.385 0.425 0.898 0.293 0.495 0.890 0.385 0.641 0.828 (46064 0.564 0.787 0.511 0.390 0.733 0.380 0.599 0.821 0.490 0.499 0.594 108
1 2 65 365 109
Appendix 3 (1Multinomial Logit Model( (1996,Amemiya(1985 3 i Y i = 0 Y i = 1 Y i = 2 U, U, U iy i = 0 U U, U U i 0 i1 i 0 i2 iiy i = 1 U > U, U U i1 i0 i1 i2 iiiy i = 2 U > U, U > U i2 i0 i2 i1 i j Uij = µ + ε ij ij µ ij εij Multinomial Logit Model ε I ( ij U > > i 2 Ui1, Ui2 Ui0 I exp( (exp( z P(Y = 2 = P(U > U, U > U i = ( ε + µ - = f ( ε - = exp i 2 j = 0 i2 ( ε exp ( µ = i 2 i2 exp ( µ 1j = 2 exp ( µ µ + µ µ i 1 > ε µ exp [ exp ( ε exp [ exp ( ε i2 { i 2 i1 1j i 0 2 exp ( µ j = 0 ij µ i 0 ε ij i 21 i2 i 1 i 1 f ( ε i2 i0, ε i1 i 2 dε i2 µ + µ + µ µ µ > ε ] exp [ exp ( ε i2 i 1 }{ i 2 i0 ε + µ i 2 i 0 i 2 ] dε i2 i 1 i 0 f ( ε i2 i 0 i0 dε µ i 0 i2 i1 } dε + µ i2 i 2 i1 ] 110
β ' µ i2 µ i0 = xi2βj, µ i1 µ i0 = xi 1 ' exp xi 1β1 P Y i = 2= (1 ' ' 1+ exp x β + exp x β i1 1 j i2 2 P Y i 1 = 0= (2 ' ' 1+ exp x β + exp x β i1 1 i2 2 xij i (j=0 j(0 βj Multinomial Logit Model L ( β1, β2 = Yi= 0 Pi 0 Yi = 1 Pi 0 Yi= 2 Pi 2 β1 β 2 (1 P1 X i P1 X 1 i 2 = Pβ 1 = Pβ 2 1 2 2 j= 0 2 j = 0 P β ij P β ij j j β, β 1 2 P1 P1, X (2Bivariate Probit Model (Greene(1997 X i1 i 2 * * y = x β + ε, y = 1 if y > 1 1 1 1 1 1 y 0, * = x β + ε, y = 1 if y 0, * 2 2 2 2 2 2 > 0 0 111
Eε = Eε 0 = 1 2 Varε = Varε = 1 1 2 Covε 1, ε 2 = ρ 112