Demographic Balancing Equation P1=P0+B-D+IM-OM+e P1=P0+NI+NM+e e=error of closure Example from Japan 2003 P2002=127,435,000, P2003=127,619,000 B2002=1,139,000, D2002=1,023,000, NM2002=68,000 What is error of closure? U.S. exampleCrude rates CBR= (B ÷ P) x 1,000 CDR= (D ÷ P) x 1,000 RNI = [(B – D) ÷ P] x 100 = (CBR – CDR) ÷ 10 CROM = (OM ÷ P) x 1,000, CRIM = (IM ÷ P) x 1,000 CMR = (M ÷ P) x 1,000 = (CRIM-CROM) ÷ 10Rates refer to calendar year – “period” ratesRange of measures 1) CBR: 56 (Niger) to 7 (Hong Kong) 2) CDR: 28 (Botswana, Lesotho) to 1 (UAE), 2 (Kuwait) 3) Why so low in UAE, Kuwait? 4) IMR: 172 (Afghanistan) to 2.4 (Iceland) 5) RNI: 3.4 (Niger) –0.7 (Ukraine)Rates and concept of risk 1) Rates vs. Ratios – what is the difference? 2) Rates vs. Probabilities – what is the difference? 3) How to define “at risk” population? (notion of "person-years")4) Use of mid-year population a. Mean of beginning and end population – assume entries and exits distributed evenly across period 5) Limitations of “crude” rates a. Esp. CBR, CIMRExample of more refined rate 1) Infant mortality rate IMR = (deaths to children under one year of age in year t ÷ live births in year t) x 1,000 2) Advantages 3) What is the problem? 4) Is this really a problem?Growth rates 1) Arithmetic growth a. P1=P0+x b. P2=P1+x c. P2=P0+2x d. Pn=P0+xn e. 000nPxPnP-Pr =÷⎟⎠⎞⎜⎝⎛= f. Growth is constant2) Geometric growth a. P1=P0[1+(CBR0-CDR0)] b. P2=P1[1+(CBR1-CDR1)] c. P2=P0[1+(CBR0-CDR0)][1+(CBR1-CDR1)] d. ∏−−−+=n01n1n0n)CDRCBR(1PP e. Pn=P0(1+r)n f. log(Pn÷P0) ÷ n=log(1+r); 1PPrn0n−= g. Growth is assumed constant over period 0-n h. Compounding takes place at specified intervals3) Exponential growth a. P1=P0er b. P2=P1er c. rn0n0r0nePePP ==∏ d. Growth is constant, but compounding is continuous3) Doubling time a. 2=ern b. ln(2)= .693 = rn c. n ≈ .7 ÷ r 4) ExamplesHuman Population Growth Since 1 A.D. 2000 Bruce Thompson, EcoTracs, 937 E. Browning Ave. Salt Lake City, UT 84105 (801) 467-3240012345671 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000YEAR180019301960197519871999POPULATION (in billions)Sociology 674, 9/14/06, page 9 Some examples 1) Annual growth rate between two censuses a. Pakistan – P1972=65,309,340 P1981=84,253,644 2) Doubling time a. Taiwan – P2000= 22,520,776 P2003= 22,604,550 3) Why not use arithmetic growth? a. Not realistic for longer periods b. Not realistic in high growth contextsSociology 674, 9/14/06, page 10 Population Momentum 1) Why does population continue to grow even after fertility declines to replacement level? 2) When does annual # added to population begin to decline? a. When is Pn+1-Pn < Pn-Pn-1? b. When Pnr* < Pn-1r or rrPP*1-nn<Population Size and Fertility Rates in Italy, 1992-200356,200,00056,400,00056,600,00056,800,00057,000,00057,200,00057,400,00057,600,00057,800,00058,000,00058,200,0001992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003Population11.11.21.31.41.51.61.71.81.92TFRPopulation TFRNatural Increase and TFR in Japan, 1950-2002-2004006008001,0001,2001,4001,600195019521954195619581960196219641966196819701972197419761978198019821984198619881990199219941996199820002002Natural Increase (1,000)0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 TFRNat. Inc.
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