多维家庭人口预测模型的建立及应用

5619985(68)曾毅金沃泊王正联=本文建立了多维的家庭人口预测模型该模型可用于同时预测家庭户以及人口的规模结构特征及分布,并保证人口事件(如结婚离婚再婚子女离家等)的发生在男性人口与女性人口之间的一致性以及在父母辈与子女辈之间的一致性与国外学者近年提出的多维宏观家庭户预测模型相比,本文建立的模型的一个明显优点是无需从专项家庭抽样调查得到的家庭户类型转换概率数据,只需通常的生育死亡婚姻等人口数据与传统的户主率方法不同,本文模型将家庭户预测与未来生育死亡婚姻等人口事件发生率紧密地联系起来,可同时预测核心与三代家庭户,既可用于中国等发展中国家,又可用于西方发达国家=曾毅北京大学人口研究所,教授;金沃泊(JamesW1Vaupel)德国马普研究院人口研究所,所长;王正联德国马普研究院人口研究所,研究人员11,,,,,,,,10%,,21:,,#1#,,(Hammelet1al11976;Wachter,1987;Smith,1987;Nelissen,1991),,,1%1200260,,,Hammel,Wachter()(19801990)(19401950),,,,,,,/0,,,,,,,,,:()(MasonandRacelis,1992;Spiceretal1,1992),,,,,,,,VanImholfKeilman(1992)LIPRO,,/0/0(),,Bongaarts(1987)Bongaarts,,Bongaarts,,Bongaarts80,,#2#80,,,,,31,,,()Brass1983(Brass,1983),,:¹,(1)1xx=0,1,2,3,W,Wss=1,;21mm=1,;21;31;41;51kk=1,;21;31,;41,pp=0,1,2,,,Pcc=0,1,2,,,P1(c[p)rr=1,;21tt1=;t2=;t1t2:,(),41Brass/0(Brass,1983)/0,,,,;,,;,,C,2+C;,()1+C;,,C(),1+C;,,i,2+2+C1+2+C;,1;,C#3#¹/0,,60,/0,2+1+C1+1+C,/022/0/0skmpc131,3,4\001G1a(t)=Ex=0,,,wEm=1,3,4Ep=0,,pN3,m,p.o(x,t,1)231,3,4\001G1b(t)=Ex=0,,,wEm=1,3,4Ep=0,,pN3,m,p.o(x,t,2)132,5\002G1c(t)=Ex=0,,,wEm=2,5Ep=0,,pN3,m,p.o(x,t,1)132,5002+cG2a(t)=Ex=0,,,wEm=2,5Ep=1,,,pN3,m,p.c(x,t,1)-Ta131,3,4001+cG2b(t)=Ex=0,,,wEm=1,3,4Ep=1,,,pN3,m,p.c(x,t,1)-Tb231,3,4001+cG2c(t)=Ex=0,,,wEm=1,3,4Ep=1,,,pN3,m,p.c(x,t,2)-Tc2++112,5002+2+cG3a(t)=Ex=0,,,wEm=2,5Ep=1,,,pN1,m,p.c(x,t,1)1++122,5001+2+cG3b(t)=Ex=0,,,wEm=2,5Ep=1,,,pN2,m,p.c(x,t,1)2++111,3,4002+1+cG3c(t)=Ex=0,,,wEm=1,3,4Ep=1,,,pN1,m,p.c(x,t,1)1++121,3,4001+1+cG3d(t)=Ex=0,,,wEm=1,3,4Ep=1,,,pN2,m,p.c(x,t,1)2++211,3,4002+1+cG3e(t)=Ex=0,,,wEm=1,3,4Ep=1,,,pN1,m,p.c(x,t,2)1++221,3,4001+1+cG3f(t)=Ex=0,,,wEm=1,3,4Ep=1,,,pN2,m,p.c(x,t,2):(1)s,k,m,p,c,W,P1,Nk,m,p,c(x,t,s)t,x,s,k,m,p,c(2)(,),,K=3,c0,,,,G2a(t)G2b(t)G2c(t),Ta=G3a(t)+G3c(t)+G3e(t);Tb=[G3b(t)+G3d(t)+G3f(t)]#R;Tc=[G3b(t)+G3d(t)+G3f(t)]#(1-R)#R49,(k=3)c049K=3,c049K=3,c0(3)19901j23434/01x,s,m,k,p,c,r,t,2/0,,#4#3#%#%202547202493540103010694010697-010003-0143193416193376400102010662010666-010004-01601981961197737045910123016768016806-010019-0128542496531983105131198011858011831010027114729204202905222151980152110000110000//:#()=-:%()=100(-)/4#%#%1202547202493540103010694010697-010003-01432~310180341038631-20597-1198013486013575-01008921494~51326508124803678472612901454201429601024651746+373331416062-42731-10127011278011432-010154-1017429204202005222151980152110000110000//:3/0/03/0/0,1%/0/0,115%~2%2222,,,,3,2~3/0/0-2%,-2%4~56%,6-1015%/0/0,(P)5,5:Zc(i,t)=a(i,t)#Z(i,t)Z(i,t)Zc(i,t)tia(i,t)t/0,iia(i,t)a(i,t)6,,(P),#5#,1990-113%511,(t)(x),(s),(m),(k),(p),(c)(r)m,k,p,c,t,ri5,4,5,2(),,:T=2@5@4@E5p=0(p+1)=1680,T=1680(i=1,2,3,,,T)li(x,t,s)tx,s,i,pij(x,t,s)tx,s,i(t,t+1)(x,x+1)j,:lj(x+1,t+1,s)=ETi=1li(x,t,s)#Pij(x,t,s)(i,j=1,2,3,,T)pij(x,t,s)T@TT=1680,2822400(=1680@1680),(),,,,Bongaarts(1987)(1988):(x,x+1),,(,),:(1)(2),61,,611男女两性婚姻状态变化的一致性/0,,()(),,,,()(#6#)612父母子女相关状态变化的一致性:C1:K=12()K=3();C2:K=1K=2K=3;C3:,S1=C1+C2+C3S1,C1,C2,C3,:P1:()c()¹;P2:()c;P3=Epc=1(tc#c+oc#c),tcc,occ,pS2=P1+P2+P3,,S1S2,,S1S2,,/0,:c1#a1+c2#a2+c3#a3=[2#s1#s2/(s1+s2)]#r1(1)p1#b1+p2#b2+p3#b3=[2#s1#s2/(s1+s2)]#r2(2)a1,a2,a3,b1,b2,b3r1=2#R/(R+1);r2=2/(R+1);r1/r2=R;r1+r2=2;R(k=1,2)CR,c,(,),K=1,2,,,R1,(1)(2)r1r2,s1s2RºC2,C3,P2,P3,,C2#a2=P3#b3C3#a3=P2#b2,C3P3,,C2P2,,,-,,C3P3,a3=110;b3=110,,a2=P3/C2;b2=C3/P2;a1=[(2#s1#s2/(s1+s2))#r1-c2#a2-c3#a3]/c1(3)a2=[(2#s1#s2/(s1+s2))#r1-p2#b2-p3#b3]/p1(4)613按照育龄女性与育龄男性计算的出生数之间的一致性,ii,i#7#¹º1990R11025,r1=11012,r2=01988Ci,CC-i,i,i,,,,614男女双方离婚(或同居结束)前后一起居住子女数的一致性(),,,,,615男女双方再婚(或同居)前后一起居住子女数的一致性()()()()()i(i=0,1,2,,p)()¹71:t+1,x+1i=[t,xi]+[(t,t+1)i,t+1x+1]-[(t,t+1)i,t+1x+1](x,x+1)(t,t+1)k,m,pc:(x,s,m,k,p,c,t1,r,r=1,;r=2,)1:pcNk,m,0,0(x+015,t+015,s)=Nk,m,010(x,t,s)(1-1/2bo,m(x,t,s))(5)p0Nk,m,p,c(x+015,t+015,s)=Nk,m,p,c(x,t,s)(1-1/2bp,m(x,t,s))+Nk,m,p-1,c-1(x,t,s)1/2bp-1,m(x,t,s)(6)Nk,m,p,c(x,t,s)txsk,m,p,c,Nk,m,p,c(x+015,t+015,s)tx+015sk,m,p,c,1/2bp,m(x,t,s)xsmptp+12:():()t,,,,,t-t+1t,-,#8#¹-,,(,,,)(\18),pcpc(18)Wij(x,t,s,m)txsmit+1x+1j,Wij(x,t,s,m)(t,t+1),(x,x+1)(k,1):,,k,Ndi,m,p,c(x+015,t+015,s)=E4j=1Nci,m,p,c(x+015,t+015,s)wji(x,t,s,m)(7)Ncj,m,p,c(x+015,t+015,s)Ndi,m,p,c(x+015,t+015,s)k(),,,,S1(x,t),S2(x,t),S3(x,t)t123x+1t+1,123;d1(x,t),d2(x,t),d3(x,t)x,t123,x+1t+1,123,1230;d12(x,t)xt2,x+1t+12;d13(x,t),d23(x,t)xt3,x+1t+1312,,S1(x,t),S2(x,t),S3(x,t),d1(x,t),d2(x,t),d3(x,t),d12(x,t),d13(x,t),d23(x,t),(c):NÊk,m,0,0(x+015,t+015,s)=Ndk,m,0,0(x+015,t+015,s)(8)p0p\c,NÊk,m,p,0(x+015,t+015,s)=Ndk,m,p,0(x+015,t+015,s)+Ndk,m,p,1(x+015,t+015,s)d1(t)+Ndk,m,p,2(x+015,t+015,s)d2(t)+Ndk,m,p,3(x+015,t+015,s)d3(t)(9)NÊk,m,p,1(x+015,t+015,s)=Ndk,m,p,1(x+015,t+015,s)s1(t)+Ndk,m,p,2(x+015,t+015,s)d12(t)+Ndk,m,p,3(x+015,t+015,s)d23(t)(10)NÊk,m,p,2(x+015,t+015,s)=Ndk,m,p,2(x+015,t+015,s)s2(t)+Ndk,m,p,3(x+015,t+015,s)d13(t)(11)#9#NÊk,m,p,3(x+015,t+015,s)=Ndk,m,p,3(x+015,t+015,s)s3(t)(12)NÊk,m,p,c(x+015,t+015,s)tk,m,p,c,s,()/0,,,(8)~(12),/c0,85+90+99+,,3:pcNk,m,0,0(x+1,t+1,s)=NÊk,m,0,0(x+015,t+015,s)(1-1/2b0,m(x+015,t+015,s))(13)P0Nk,m,p,c(x+1,t+1,s)=NÊk,m,p,c(x+015,t+015,s)(1-1/2bp,m(x+015,t