Demographic Balancing EquationRange of measuresSociology 674, 9/20/05, page 1Demographic Balancing EquationP1=P0+B-D+IM-OM+eP1=P0+NI+NM+ee=error of closureExample from Japan 2003P2002=127,435,000, P2003=127,619,000B2002=1,139,000, D2002=1,023,000, NM2002=68,000What is error of closure?U.S. exampleSociology 674, 9/20/05, page 2Crude ratesCBR= (B ÷ P) x 1,000 CDR= (D ÷ P) x 1,000RNI = [(B – D) ÷ P] x 100 = (CBR – CDR) ÷ 10CMR = (OM ÷ P) x 1,000, (IM ÷ P) x 1,000CMR = (M ÷ P) x 1,000, CDR = (D ÷ P) x 1,000Rates refer to calendar year – “period” ratesSociology 674, 9/20/05, page 3Range of measures1) 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)Sociology 674, 9/20/05, page 4Rates and concept of risk1) Rates vs. Ratios – what is the difference?2) Rates vs. Probabilities – what is the difference? 3) How to define “at risk” population?4) Use of mid-year population a. Mean of beginning and end population – assumeentries and exits distributed evenly across periodb. Census adjustments (April or Oct)5) Limitations of “crude” ratesa. Esp. CBR, CIMRSociology 674, 9/20/05, page 5Example of more refined rate 1) Infant mortality rateIMR = (deaths to children under one year of age ÷live births in year) x 1,0002) Advantages3) What is the problem?4) Is this really a problem?Sociology 674, 9/20/05, page 6Growth rates 1) Geometric growtha. P1=P0[1+(CBR0-CDR0)]b. P2=P1[1+(CBR1-CDR1)]c. P2=P0[1+(CBR0-CDR0)][1+(CBR1-CDR1)]d.n01n1n0n)CDRCBR(1PPe. Pn=P0(1+r)nf. ln(Pn÷P0) ÷ n=ln(1+r) g. Growth is assumed constant over period 0-nh. Compounding takes place at specified intervalsSociology 674, 9/20/05, page 72) Exponential growth a. P1=P0erb. P2=P1erc.rn0n0r0nePePP d. Growth is constant, but compounding is continuousSociology 674, 9/20/05, page 83) Doubling timea. 2=ernb. ln(2)= .693 = rn c. n ≈ .7 ÷ r4) ExamplesSociology 674, 9/20/05, page 9Some examples1) Annual growth rate between two censusesa. Pakistan – P1972=65,309,340 P1981=84,253,6442) Doubling timea. Taiwan – P2000= 22,520,776 P2003= 22,604,5503) Why not use arithmetic growth? a. Not realistic for longer periodsb. Not realistic in high growth contextsSociology 674, 9/20/05, page 10Population Momentum1) 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
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