Hi-Stat Discussion Paper Series No.248 東京圏における 1990 年代以降の住み替え行動 住宅需要実態調査 を用いた Mixed Logit 分析 小林庸平行武憲史 March 2008 Hitotsubashi University Research Unit
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1 Hi-Stat Discussion Paper Series No.248 東京圏における 1990 年代以降の住み替え行動 住宅需要実態調査 を用いた Logit 分析 小林庸平行武憲史 March 2008 Hitotsubashi University Research Unit for Statistical Analysis in Social Sciences A 21st-Century COE Program Institute of Economic Research Hitotsubashi University Kunitachi, Tokyo, Japan
2 IIA Logit UFJ y.kobayashi@murc.jp HI-STAT COE yukutake@hrf.or.jp i
3 1 *1 Ortalo-Magne and Rady [2006] starter homes (trade-up homes) Clark et al. [2003] Banks et al. [2002] Ortalo-Magne and Rady [2006] IIA Logit Logit 6 5 Logit 7 2 Zorn [1988, 1989] Zorn [1988, 1989] *
4 Hardman and Ioannides [1995] Pickles and Davies [1991] Zorn [1988, 1989] Boehm [1981] Boehm et al. [1991] Boehm [1981] Boehm et al. [1991] Davies and Pickles [1991] Pickles and Davies [1991] [1994, 1995, 2001, 2003] [1995] Zorn [1988, 1989] [1995] Seko and Sumita [2007] KHPS Keio Household Panel Survey Börsch-Supan et al. [2001] Logit Seko and Sumita [2007] Zorn [1988] [1995] U k (h 0 (l 0 ), h 1 (l 1 ),..., h N (l N ), Q, d 0, d 1,..., d n ; z) (1) U k ( ) k h n n (n = 0, 1,..., N) l n Q d n z 2
5 n W t + I t = P q t Q t + [ own n Pt own (l n ) + (1 own n )Pt rent (l n ) ] h n (l n ) + MC n (2) t (t = 0, 1,, T ) W t t I t t P q t t Q own n n P own t (l n ) l n t Pt rent (l n ) l n t MC n n Q t h 1,..., h n own 1,..., own n d 1,..., d n l 1,..., l n d Pt own ctr 23 sub 23 P rent t 1 ( V 1 Wt, I t, Pt own (l n 1 ) or Pt rent (l n 1 ), h n 1, z ) (3) 2 23 V 2 (W t, I t, MC n, P own t ctr(l n ), z) (4) 3 23 V 3 (W t, I t, MC n, P own t sub(l n ), z) (5) 4 23 V 4 ( Wt, I t, MC n, P rent t ctr (l n ), z ) (6) 5 23 V 5 ( Wt, I t, MC n, P rent t sub(l n ), z ) (7) 3
6 3.2 CLOGIT V jk j j k V jk = V jk + ɛ jk = X jk β + ɛ jk (8) ɛ jk k j X jk β X jk ɛ jk 1 k j P j,k = P [V jk V lk, all l j] = exp V jk 5 n=1 exp V nk j = 1, 2, 3, 4, 5 (9) P j,k j β K 5 L = ln L K = y jk ln P j,k k=1 j=1 K y ik j IIA independence of irrelevant alternative Logit 3.3 Logit Error Component Logit j k V jk = V jk + µ D jk + ɛ jk (10) µ µ = (µ 1,..., µ I ) I D jk µ D jk 4
7 j l E ([µ D jk + ɛ jk ][µ D lk + ɛ lk ]) = D jkv (µ)d lk (11) µ V (µ) D j Error Component Djk 1 D2 jk 23 D3 jk µ V (µ) σ i (i = 1, 2, 3) 2 i E ([ µ i Djk i ] [ + ɛ jk µi Dlk i ]) + ɛ lk = E ([µi + ɛ jk ] [µ i + ɛ lk ]) = σ i (12) (10) µ exp(v jk + µ D jk ) L j,k (µ) 5 n=1 exp(v j = 1, 2, 3, 4, 5 (13) nk + µ D nk ) µ (13) µ P j,k = L j,k (µ) f(µ)dµ j = 1, 2, 3, 4, 5 (14) f(µ) µ µ σ i V (µ) closed form f(µ) µ µ r R f(µ) µ r µ r L j,k (µ r ) ˆP j,k = 1 R L j,k (µ r ) (15) R r=1 P j,k K 5 L = y jk ln ˆP j,k k=1 j=1 β σ i 125 *2 *3 *2 Bhat [2001] Train [2003] 100 *3 Kenneth Train Gauss 5
8 * = *5 *6 * *5 Zorn [1988] *6 Zorn [1988] 6
9 1 (m 2 ) 5 ( ) 5 ( ) 5 ( ) ( ) 5 ( /m 2 ) m m m 2 23 ( 9 1m
10
11 ( ) 9
12 ( ) 10
13 ( ) 11
14 5 5.1 Logit IIA 23 IIA Logit Error Component Logit IIA IIA Logit 23 Logit IIA 12
15 *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** ** ** *** *** *** ** *** Hausman value 6.16 (0.9987) (0.0000) 6.20 (0.9986) 4.18 (0.9997) *** *** ** * *** *** *** *** *** ** *** *** *** *** *** ** *** *** *** * ** *** *** * *** *** *** *** *** * *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** Hausman value (0.3807) (0.0000) 6.83 (0.9857) (0.0000) *** *** ** *** *** *** ** ** *** *** *** *** *** *** *** * ( ) ( )Hausman value IIA p SUR ( )*** ** 5 * 10 13
16 IIA IIA Logit Error Component Logit Logit IIA IIA Logit 14
17 *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** ** *** *** Hausman value (0.7724) (0.0000) 2.66 (1.0000) (0.0161) *** *** * *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** ** *** *** ** *** *** ** *** *** *** *** *** * *** * *** *** *** *** *** Hausman value (0.0000) (0.0000) (0.0000) (0.0000) *** *** ** *** *** ** *** *** * *** *** *** *** *** * *** *** *** *** *** *** ( ) ( )Hausman value IIA p SUR ( )*** ** 5 * 10 15
18 Hausman IIA Logit Error Component Logit Logit Logit IIA IIA Logit IIA Logit Logit Error Component
19 *** *** *** *** *** *** *** ** *** * *** ** *** *** * *** * *** *** *** Hausman value (0.0000) 0.10 (1.0000) (0.7641) (0.0000) *** *** *** *** *** *** * ** *** *** *** *** *** ** ** *** *** *** *** *** *** *** *** *** *** *** ** *** *** *** *** *** *** *** *** *** *** *** * ** *** *** Hausman value (0.0000) (0.0000) (0.0000) (0.0000) *** *** *** *** * ** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** ( ) ( )Hausman value IIA p SUR ( )*** ** 5 * 10 17
20 5.2 Logit APE Average Partial Effect *7 Logit Logit m * *7 Logit s (15) x js n = j ˆP j,k x ns n j ˆP j,k x ns = 1 R = 1 R RX ˆLj,k (µ r k ) L j,k(µ r )2 k (β is + µ r k r ) r=1 RX ˆ Lj,k (µ r )2 k (β is + µ r k r ) r=1 * m m m 2 18
21
22 9 CLOGIT LOGIT CLOGIT LOGIT CLOGIT LOGIT CLOGIT LOGIT
23
24 10 CLOGIT LOGIT CLOGIT LOGIT CLOGIT LOGIT CLOGIT LOGIT
25 6 Logit Logit Logit
26 ( ) CLOGIT LOGIT ( ) CLOGIT LOGIT ( ) CLOGIT LOGIT
27
28 ( ) CLOGIT LOGIT ( ) CLOGIT LOGIT ( ) CLOGIT LOGIT
29 7 IIA IIA IIA Logit
30 IIA Logit Error Component Logit Random Coefficient Banks, J., R. Blundell, and J. Smith [2002] Wealth Portfolios in the UK and the US, NBER Working Paper Series. Bhat, C.R. [2001] Quasi-random maximum simulated likelihood estimation of the mixed multinomial logit model, Transportation Research Part B, Vol. 35, No. 7, pp Boehm, T.P. [1981] Tenure Choice and Expected Mobility: A Synthesis, Journal of Urban Economics, Vol. 10, No. 3, pp Boehm, T.P., H.W. Herzog Jr, and A.M. Schlottmann [1991] Intra-Urban Mobility, Migration, and Tenure Choice, The Review of Economics and Statistics, Vol. 73, No. 1, pp Börsch-Supan, A., F. Heiss, and M. Seko [2001] Housing Demand in Germany and Japan, Journal of Housing Economics, Vol. 10, No. 3, pp Clark, W. A., M. C. Deurloo, and F. M. Dieleman [2003] Housing Careers in the United States, : Modelling the Sequencing of Housing States, Urban Studies, Vol. 40, No. 1, pp Davies, RB and AR Pickles [1991] An analysis of housing careers in Cardiff, Environment and Planning A, Vol. 23, pp Hardman, A.M. and Y.M. Ioannides [1995] Moving behavior and the housing market, Regional Science and Urban Economics, Vol. 25, No. 1, pp Ortalo-Magne, F. and S. Rady [2006] Housing Market Dynamics: On the Contribution of Income Shocks and Credit Constraints, Review of Economic Studies, Vol. 73, No. 2, pp Pickles, A.R. and RB Davies [1991] The empirical analysis of housing careers: a review and a general statistical modelling framework, Environment and Planning A, Vol. 23, No. 4, pp Seko, M. and K. Sumita [2007] Effects of government policies on residential mobility in Japan: Income tax deduction system and the Rental Act, Journal of Housing Economics, Vol. 16, No. 2, pp Train, K. [2003] Discrete Choice Methods with Simulation: Cambridge University Press. 28
31 Zorn, P.M. [1988] An Analysis of Household Mobility and Tenure Choice: An Empirical Study of Korea, Journal of Urban Economics, Vol. 24, No. 2, pp [1989] Mobility-Tenure Decisions and Financial Credit: Do Mortgage Qualification Requirements Constrain Homeownership?, Real Estate Economics, Vol. 17, No. 1, pp [1994] [1995] [2001] [2003]
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