First Marriage Trajectories – Japan 2000Survival curvesMarriage and Divorce – Basic Measures Crude rates General rates Age-specific rates Duration-specific rates Synthetic cohort measures Total first marriage rate / Total remarriage rate Total divorce rate Synthetic cohort trajectories 1Crude rates• The denominator includes people who are – Too young– Already married• Also influenced by population age structure000,1*PMCMR =000,1*PDCDR =Crude marriage rateCrude divorce rateNote on general marriage/divorce rates f4915fPMGMR-= 1) Can specify with greater accuracy if marital status distributions are available 2) Not everyone is at risk of marriage/remarriage/divorce 3) e.g., uf,4915fPMGMR-= or nf,4915ffPFMGFMR-= where FMf=# first marriages to women and n references the never married population 2Measures of marriage timing 1) Mean age at (first) marriage 2) Median age at (first) marriage 3) Marital status distributions (stock vs. flow) 4) Singulate Mean Age at Marriage – SMAM a. Rationale – limited data b. Calculation 3Mean age at marriage• Mean age at marriage for females• Can calculate from information on number of marriages by age (often not available)∑∑+++⋅=5515fx5515fxM(f)M)2n(xMAMedian age at marriage• Median age at marriage for females• As on p.92 of text. – l is lower limit of age group w/middle marriage– N is total number of marriages– F is cumulative frequency up to l– f is number of marriages in age group containing middle marriage– I is the width of age group containing middle marriage (e.g., 5 yrs)⎟⎟⎠⎞⎜⎜⎝⎛⎟⎠⎞⎜⎝⎛−+=ffffMed(f)fi*F2NlAComparison of A-S % Never Married 010203040506070809010015-19 20-24 25-29 30-34 35-39 40-44 45-49Indonesia -97 Italy -91 4SMAM - Three components 1) ⎟⎟⎠⎞⎜⎜⎝⎛+∑−−=5*PN*100150049451915xxx# years lived single thru age 50 among group of 100 2) ⎥⎦⎤⎢⎣⎡⎟⎟⎠⎞⎜⎜⎝⎛÷÷−−−−/2PNPN*1005450545049454945Pct. never marrying by age 50 3) ⎥⎦⎤⎢⎣⎡⎟⎟⎠⎞⎜⎜⎝⎛÷÷−−−−/2PNPN*100*505450545049454945 # years lived single thru age 50 among those who never married⎥⎥⎦⎤⎢⎢⎣⎡⎥⎦⎤⎢⎣⎡⎟⎟⎠⎞⎜⎜⎝⎛÷÷−⎥⎦⎤⎢⎣⎡⎟⎟⎠⎞⎜⎜⎝⎛÷÷−⎟⎟⎠⎞⎜⎜⎝⎛+=−−−−−−−−−−=∑/2PNPN*100100/2PNPN*100*505*PN*1001500SMAM5450545049454945545054504945494549451915xxx Intuitively = the number of years lived single among those who ever married by age 50Mean age at marriage/divorce/remarriage 1) Two methods for calculation a. Simple average if enumerated by single years of age b. Weighted average if enumerated by age group c. Same is true for median 7Comparison of SMAM and Mean age at first marriage – Japanese Men 202224262830321920192519301935194019501955196019651970197519801985199019952000AgeSMAM mean age 8Age specific marriage rate• If data about age at marriage are provided:• Usually calculated for women and men separately, because timing of marriage is different000,1*PMASFMRnf,fxftx,x=First Marriage Trajectories – Japan 2000 02040608010012014015 to1920 to2425 to2930 to3435 to3940 to4445 to4950 to54Rate (per 1,000)men women 10Synthetic Cohort Measures 1) Total First Marriage Rate ∑−−==49451915xii5*ASFMRTFMR where i indexes sex. 2) Analogous measures for remarriage, divorce 3) Can also use age-specific rates to represent marriage behavior in other ways a. Trajectories b. Cumulative failure/survival curves 9Construct cumulative experience trajectories 5*)ASFMR*(NMEMx5x1-n1915xxn +−=∑= 5*]ASFMR*)EM-[(100EMx5x1-n1915xxn +−=∑= for example, EM20=(100*ASFMR15-19)*5, EM25=[(100*ASFMR15-19)+(NM20*ASFMR20-24)]*5 etc. Survival curves 5*)ASFMR*(NM100EM100NMx5x1-n1915xxnn +−=∑−=−= 11Cumulative first marriage trajectories - Japan 010203040506070809010015 to1920 to2425 to2930 to3435 to3940 to4445 to4950 to54 percentmen women 1213 010203040506070809010015 to1920 to2425 to2930 to3435 to3940 to4445 to4950 to54percentmen women Cumulative survival curves for first
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