Synthetic Cohort Measures of Fertility & Replacement TFR GRR NRR 1Total Fertility Rate ∑∑−−====49451915xx4915x1000ASFR*51000ASFRTFRx Interpretation Range: ≈1.0 to 9.2 Simple example: 15-19 20-24 25-29 30-34 35-39 40-44 45-49# Women 100 100 100 100 100 100 100# Births 2 11 15 12 7 3 0What is the TFR? 2Comparison of TFR and cohort completed fertility 2.011.972.102.031.983.652.372.002.142.1300.511.522.533.541950 1955 1960 1965 1970Cohort Fertility Period TFR 3Different types of TFR 1) Marital & non-marital 2) By birth order 3) By race, education, religion, etc., etc. 4Decomposition and counterfactuals – an intro. +=+=+=∑−−=txutxutx49451915xtxmtxmtxttxutxutxutxtxmtxmtxmtxtxutxmtxtxPP*ASFRPP*ASFR*5TFR 2)PP*PBPP*PBPBBASFR1) +=′∑−−=nx-tunx-tutx49451915xnx-tmnx-tmtxtPP*ASFRPP*ASFR*5RTF3)=−′−−−tnttntTFRTFRRTFTFR5)contribution of ∆ ASFR 5Decomposition – a hypothetical example ASMR ‰ ASMR ‰ Age group % low edu % high edu low edu high edu A B if edu stayed same if fertility stayed same 15-19 0.6 0.40.1 0.050.06 0.0220-24 0.7 0.30.6 0.30.42 0.0925-29 0.8 0.20.8 0.50.64 0.130-34 0.9 0.10.6 0.40.54 0.0435-39 0.95 0.050.4 0.30.38 0.01540-44 0.95 0.050.2 0.20.1 0.0145-49 0.95 0.050.1 0.10.095 0.00550-54 0.95 0.05 0.01 0.01 0.0095 0.00052.525 ASMR ‰ ASMR ‰ Age group % low edu % high edu low edu high edu A B A* B* A** B**15-19 0.1 0.90.1 0.010.01 0.009 0.06 0.004 0.01 0.04520-24 0.2 0.80.4 0.050.08 0.04 0.28 0.015 0.12 0.2425-29 0.3 0.70.5 0.350.15 0.245 0.4 0.07 0.24 0.3530-34 0.4 0.60.5 0.50.2 0.3 0.45 0.05 0.24 0.2435-39 0.5 0.50.2 0.30.1 0.15 0.19 0.015 0.2 0.1540-44 0.6 0.40.1 0.150.06 0.06 0.095 0.0075 0.12 0.0845-49 0.7 0.30.05 0.050.035 0.015 0.0475 0.0025 0.07 0.0350-54 0.8 0.2 0.01 0.050.008 0.01 0.0095 0.0025 0.008 0.0021.472 1.6985 2.145 TFR 1 2.525 TFR1-TFR2 TFR1-TFR2* TFR1-TFR2** TFR 2 1.472 1.053 0.827 0.380 1.207 TFR 2* 1.699 TFR 2** 2.145 PCT explained by education 0.36 PCT explained by fertility 0.78 1.151980 US 2000 US To what extent is the increase in TFR due to the increase in the representation of Hispanic origin residents in the US population? How can we answer this question? By using counterfactual analysis / decomposition. = By answering the question: What would the US TFR be in 2000 if ethnic composition was the only component of TFR that changed between 1980-200. TFR=1.84 % Hispanic=6.5 TFR=2.06 % Hispanic=12.5OBSERVED DATA Counterfactual Data 1980 US 2000 US 2000 US* Compare 2000 and 2000*US TFR. If TFR 2000> TFR 2000*, composition changes played a role. How big a role? (TFR2000-TFR2000*) ÷ (TFR2000-TFR1980) = % contribution of change in % Hispanic to increase in TFR TFR=1.84 % Hispanic=6.5 TFR=2.06 % Hispanic=12.5 TFR=? if % Hispanic=12.5and ASFRex,t=1980Decomposition and counterfactuals – an intro. ⎟⎟⎠⎞⎜⎜⎝⎛+⎟⎟⎠⎞⎜⎜⎝⎛=⎟⎟⎠⎞⎜⎜⎝⎛+⎟⎟⎠⎞⎜⎜⎝⎛=+=∑−−=txhtxhtx49451915xtxnhtxnhtxttxhtxhtxhtxtxnhtxnhtxnhtxtxhtxnhtxtxPP*ASFRPP*ASFR*TFR 2)PP*PBPP*PBPBBASFR1)5⎟⎟⎠⎞⎜⎜⎝⎛+⎟⎟⎠⎞⎜⎜⎝⎛=′∑−−=2000xh2000xh1970x49451915x2000xnh2000xnh1970x2000PP*ASFRPP*ASFR*RTF3) 50.22αTFRTFRRTFTFR5)1980200020002000=−′− 5) is the contribution of Δ% HispanicGross Reproduction Rate 1) One-sex version of TFR ∑∑−−====49451915xfx4915fx1000ASFR*51000ASFRGRRx 2) 0.4878*TFRBB*TFRGRRf≈= 3) Interpretation 4) GRR=1.0 corresponds approximately to replacement level fertility 6Some examples – 2005 3.723.681.981.521.360.850.690.620.00.51.01.52.02.53.03.54.0NigerMaliCambodiaBangladeshIndiaDenmarkSwitzerlandSpain GRR 7Net Reproduction Rate 1) Modification of GRR to account for mortality 1000/L*ASFRNRR494519150x5fx∑−−==xl where 5Lx is the life table value of number of women in the x-x+5 age interval and l0 is the life table value for initial population (e.g., 1, 1,000) 2) Interpretation 3) Assume ASFRs are the same in two populations. What are implications for NRR of higher mortality in one of the populations? 8Approximation of NRR 1) 0*xll*GRRNRR = where lx* is mean age of childbearing – need both ASFRs and life table to calculate this (see previous notes – also called “mean length of generation”) 2) 0*xll*.49*TFRNRR = 9Relationship betweenNRR and TFRTFR SRB GRRSRBpANRRM=+ =+()*()()*11Replacement level fertilityTFRSRBpAM≈+()()1GRRpAM≈1()NRR=1Some examples – GRR vs. NRR 00.20.40.60.811.21.41.61.821930s 1960s 1985 1930s 1960s 1985GRR and NRRGRR NRR Greece Norway 1011 Summary of Fertility & Reproduction Measures Aspects of age distribution affecting fertility % of total pop. that is RAW Age distribution of RAW CBR Y YGFR N YTFR N NGRR N NNRR N N0123456<50 (≈D/F) <60 (≈C) 60-74 (≈BC) 75-78 (≈B) 79-89 (≈AB) 90-100 (≈A)Mean =