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1 5 [ ] Two-Part Model contract decision frequency decision 1st Part nd Part Full Price Model Full Price Elasticity Two-Part Model

2 ed srv.cc.hit-u.ac.jp OECD Iwamoto

3 1985 (2000) (2002) (2002) a (2005) << >> Phelps and Newhouse 1974 Acton 1975 Coffey 1983 Cauley 1987 Gertler et al 1987 Puig-Junoy et al 1998 Bessho and Ohkusa Cauley 1987 time price Coffey 1983 Bessho and Ohkusa Cartwright et al (1992) Hurd and McGarry 1997 Deb and Traveri (1998) 4 Cullis et al 2000 waiting list problem

4 contact analysis frequency analysis << >> 3

5 Full Price Model Zweifel and Manning 2000 Full Price Model H C l U( H, C, l) (1) H Grossman(1972) H = H( M) (2) M U '( i) > 0 U ''( i) < 0 H'( M ) > 0 H''( M ) < 0 cpm + TC + C = Y0 + wh (3) c p M TC Y 0 w h tm + h + l = T (4) t M T Max U ( H ( M ), C, l ) st.. cpm + TC+ C= Y + wt ( l tm) 0 L( M, C, l, λ) = U ( H ( M ), C, l) + λ( Y + w( T l tm ) cpm TC C) (5) 0 4

6 L U H = ( cp wt) 0 M H M λ + = (6) L U = 0 C C λ = (7) L U = λw = 0 (8) l l L = Y 0 + w ( T l tm ) cpm TC C = 0 (9) λ M* M* = M( cp+ wt, TC, w, Y + wt) 10 0 Full Price Full Price = cp + wt + TC (11) Phelps and Newhouse(1974) (1990) (10) Full Price Elasticity ε dm M ε = d( cp+ wt+ TC) ( cp+ wt+ TC) 12 η Mc η Mc dm M dm M d( cp+ wt+ TC) ( cp+ wt+ TC) = = i dc c d( cp + wt + TC) ( cp + wt + TC) dc c cp = ε i ( cp + wt + TC) 13 η Mw η MTC 5

7 dm M wt ηmw = = εi 14 dw w ( cp + wt + TC) dm M TC ηmw = = εi 15 dtc TC ( cp + wt + TC) (10) (12) (15) 6

8 3.1. ( ) (10) M = θ + θ FullPrice + θ Ocost + θ Y + θ LInc + θ X + u (16) i 0 1 i 2 i 3 0,i 4 i 5 1, i i Pohlmeier and Ulrich Two-Part Model 5 Two-Part Model contact decision frequency decision (16) M 1st part 5 Jones 2000 Finite Mixture Model Deb and Trivedi b 7

9 6 2nd Part FullPrice* M (11) * * * * FullPrice = cp + wt +TC (17) cp* w 7 t* TC* 8 Ocost Y 0 LInc X u i

10 3.3 Cauley 1987 marginal value of time Heckman Heckman Regression Equation HLInc =γ +γ Female +γ Age +γ Educ + γ Disease + i 0 1 i 2 i 3 i 4, j i, j j= i Selection Equation Work v if Linc is observed i = δz i + 2, i > 0 i γ Disease * Acute + γ Pref +γ L +γ Mills + v 5, k i, k i, k 6, l i, l 7 8 i 1, i k= 1 l= 1 v1 N(0, σ) v 2 N(0,1) corr( v 1, v 2 ) = ρ (17) HLInc Female Age Educ Disease 12 Acute Pref L 1 Mills Work Z 13 v 1 v

11 << >> << >>

12 4.1 Two-Part Model (15) 3 Unbalanced Panel Data Random Effect 1st part 1 M Count Data 1 st, ij (15) Random Effect Negative Binomial Regression Model RENB M µ Poisson( µ ) ij ij ij µ π gamma( ω, 1/ π ) ij i i ωij = α0 + α1fullpriceij + α2ocosti + α3y0, i + α4linci + α5x1,i + u1, ij exp[ ] 1(1 + π i ) Beta( r, s) (18) u 1 2nd Part M (15) Random Effect Generalized Least Squares REGLS 2 nd, ij M = β + β FullPrice + β Ocost + β Y + β LInc + β X + u (19) u = e + ε 2 nd, ij 0 1 ij 2 i 3 0, i 4 i 5 1,i 2, ij 2,ij i it u 2 e ε 5 << 5 >> st part 2nd Part Model Full Price Model 11

13 15 << 6 >> 1st Part LR test RENB Model Full Price Model Model 2nd Part Model Full Price 1st part Model Model Model 15 2nd Part Model

14 << >> 12 1st Part nd Part Newhouse et al st Part nd Part st Part nd Part st Part nd Part

15 contract decision frequency decision 1st Part nd Part st Part nd Part st Part nd Part

16 15

17 References Vol ( ) Vol.10, No.2, , Vol.4, No.1, Vol.38 No a count data Vol.40 No b Finite Mixture Model Vol.14, No Vol.38 No DP1044 Acton, J.P. (1975) "Nonmonetary factors in the demand for medical services: some empirical evidence", Journal of Political Economy, Vol.83, No.3, pp Bessho, S. and Y. Ohkusa 2003 "What are the determinants of hospital choice time, costs, option demands and communication", mimeo. Cartwright, W.S., Hu, T-W., and Huang, L-F. (1992) "Impact of varying medigap insurance coverage on the use of medical services of the elderly", Applied Economics, vol.24, No., pp

18 Cauley, S.D. (1987) "The time price of medical care", Review of Economics and Statistics, Vol.69, No.1, pp Coffey, R.M. (1983) "The effect of time price on the demand for medical-care services", Journal of Human Resources, Vol.18, No.3, pp Cullis, J.G., P.R. Jones, and C.Propper (2000) "Waiting lists and medical treatment: analysis and policies", in A.J. Culyer and J.P. Newhouse eds., Handbook of Health Economics, Vol.1B, pp Deb, P. and P.K., Trivedi 1997 "Demand for medical care by the elderly: a finite mixture approach", Journal of Applied Econometrics, Vol.12, No.3, pp Deb, P. and P.K., Trivedi (2002) "The structure of demand for health care: latent class versus two-part model", Journal of Health Economics, Vol.21, pp Gertler, P., L.Locay, and W.Sanderson (1987) "Are user fees regressive? the welfare implications of health care financing proposals in Peru", Journal of Econometrics, Vol.36, No.1-2, pp Greene, W.H. (2003) Econometric Analysis, 5th edition, Prentice Hall. Grossman, M. (1972) "On the Concept of Health Capital and the Demand for Health", Journal of Political Economy, Vol.80, No.2, pp Heckman, J.J. (1974) "Shadow prices, market wages, and labor supply", Econometrica, Vol.42, pp Heckman, J.J. (1979) "Sample selection bais as a specification error", Econometrica, Vol.47, pp Hurd, M.D. and K.McGarry (1997) "Medical insurance and the use of health care services by the elderly", Journal of Health Economics, Vol.16, pp Iwamoto, Y. (2004) "Issues in Japanese health policy and medical expenditure", in T.Tachibanaki eds., The Economics of Social Security in Japan, pp Jones, A.M. (2000) "Health econometrics", in A.J. Culyer and J.P. Newhouse eds., Handbook of Health Economics, Vol.1A, pp Long, J.S. and Freese, J. (2003) Regression Models for Categorical Dependent Variables Using Stata, Revised edition, Stata Press. Newhouse, J.P. and the Insurance Experiment Group (1993) Free for all? Lessons from the RAND Health Insurance Experiment, Harvard University Press. Phelps, C.E. and J.P. Newhouse (1974) "Coinsurance, the price of time, and the demand for medical services", Review of Economics and Statistics, vol.56, No.3, pp Pohlmeier, W. and V. Ulrich (1995) "An econometric model of the two-part decisionmaking process in the demand for health care", Journal of Human Resources, Vol.30, No.2, pp Puig-Junoy, J., M.Saez, and E.Martines-Garcia (1998) "Why do patients prefer hospital emergency 17

19 visits? a nested multinominal logit analysis for patient-initiated contracts", Health Care Management Science, Vol.1, No.1, pp Winkelmann, R. (2003) Econometric Analysis of Count Data, 4th edition, Springer. Wooldridge, J. M. (2002) Econometric Analysis Cross Section and Panel Data, MIT Press. Zweifel, P. and Manning, W.G. (2000) Moral hazard and consumer incentives in health care, in A.J. Culyer and J.P. Newhouse eds., Handbook of Health Economics, Vol.1A, pp

20 Linear (OLS) (2) (2000) 1 Linear (RE) Linear (RE), OLS (2002) Two-Part Model (2nd) GLS (2002) Linear (FE) (3) Two-Part Model (1st) Probit Model (RE) ** Two-Part Model (2nd) Median Reression *** Two-Part Model (2nd) Median Reression *** Two-Part Model (2nd) Median Reression *** Two-Part Model (2nd) Median Reression *** 2004a Finite Mixture Negative Binomial Finite Mixture Negative Binomial Two-Part Model (1st) Probit Model Two-Part Model (2nd) Negative Binomial (2005) Two-Part Model (1st) Negative Binomial (RE) Two-Part Model (2nd) GLS (RE) (1) RE=Random Effect Model FE=Fixed Effect Model (2) (3) (4) (5) *** 19

21 2 Phelps and Newhouse (1974) OLS Time Price Acton (1975) Simultaneous Equations system 0.14*** 0.029*** using 2sls 0.23*** Coffey (1983) Logit Model time price *** ( ) 0.23*** 0.20** Logit Model time Price ** time Price *** 0.04 Tobit Model time Price time Price time Price *** 0.05 Cauley (1987) Poisson Regression *** *** Gertler et al (1987) Multinominal Logit model ( ) (##)-2.05*** Puig-Junoy et al (1998) Nested Multinominal Logit model ( ) Emergency 0.618**, GP:0.397** Specialist: 0.288** ( ) Emergency 0.066, GP:0.394** Specialist: 0.537** Bessho and Ohkusa (2004) Logit model ( ) (#) *** *** (#) *** *** ( ) (#) *** *** (#) *** *** ( ) (#) 0.010*** *** (#) *** *** ( ) (#) (2) *** (3) Time Price= 20

22 (1) ( ( ( ( ( ( ( ( ( ( ( (

23 *** ** *** ** * ** ** ** *** * * * ** * *** ( ( ( ( ** ( ( ( *** ( *** ( ( ( *** ( (3) ** *** Censored observations Uncensored observations ρ Wald test (zero slope) chi2(121) = *** (1) Heckman 2 (2) *** ** 5 * 10 22

24 (1) 5 ( ) First Part Second Part Number of observations Number of individuals

25 6 First Part Second Part Model 1 (RENB) Model 2 (REGLS) Model 1 (RENB) Model 2 (REGLS) Full Price *** *** *** ** *** ** *** *** ** ** ** *** *** * ** *** *** *** * * ** ** ** * ** * * *** *** *** *** * * r s σe σε Log Likelihood R-Squared (overall) Wald test(zero slope) chi2(74) = *** chi2(77) = *** chi2(74) = *** chi2(76) = *** LR test (Ho: Poisson Model) chibar2(01) = *** chibar2(01) = *** LR test (Ho: pooled regression) chibar2(01) = 92.05*** chibar2(01) = 94.64*** (1) *** ** 5 * 0 (2) (1) 1st part 2nd Part Full Price ε η Mc η Mw η MTC (2) 24

26 First Part Second Part Model 1 (RENB) Model 2 (REGLS) Model 1 (RENB) Model 2 (REGLS) Full Price *** *** *** ** * ** ** *** ** * ** ** *** *** * ** *** * * *** *** ** ** * * r s σe σε Log Likelihood R-Squared (overall) Wald test(zero slope) chi2(64) = *** chi2(67) = *** chi2(64) = *** chi2(66) = LR test (Ho: Poisson Model) chibar2(01) = *** chibar2(01) = *** LR test (Ho: pooled regression) chibar2(01) = 95.92*** chibar2(01) = 99.65*** (1) *** ** 5 * 0 (2) (1) 1st part 2nd Part Full Price ε η Mc η Mw η MTC (2) 25

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