Quantitative Demography Flashcards

Includes both definitions and formulas

Annualized growth rate

The rate of growth in a population per year; [B - D +/- migration]/1000

Observed Rate of Natural Increase

[Births - Deaths]/1000

Natural Growth Population Prediction Equation

Pop(t) = Pop(0) * e^rt

Growth Rate Equation (real population)

r = ln(B - D +/- migration] / 1000

Lotka's r

the instrinic rate of natural increase; r = ln(NRR)/MAC

Period Person-Years Lived (PPYL)

The area under the curve of the population size K over time t; must use a mid-year estimation

Crude death rate

Deaths per 1,000 population during a time period; using a life table it can be estimated with 1/e₀

Crude birth rate

Live births per 1,000 population

l_x

Refers to the number of survivors to age x

_nd_x

Refers to the number of deaths between age x and age x+n; = l_x - l_x+n

_nq_x

Refers to the probability of death between x and age x+n; calculated as deaths(_nd^_x) / survivors(l_x); or 1 - _np_x

_np_x

Refers to the probability of survival between age x and age x+n; = 1 - _nq_x or = l_x+n/l_x

l₀

The radix of the lifestyle; the number of members of the cohort alive at age 0

_na_x

The average number of person-years lived by individuals who die between the exact age of x and exact x+n; to estimate, use half of the interval (e.g. 2 or 2.5), except for the first year which is usually 0.3

_nL_x

The total number of person-years lived by individuals between age x and exact x+n; = n * l_x+n + _nd_x * _na_x

T_x

The sum of all person-years lived beyond age x; e.g. used for computing life expectancy; = _nL_x + _2nL_x+n …

e_x

Life expectancy at age x; ex = T_x/l_x

_nM_x

Observed age-specific death rate (ASDR); the number of deaths during a certain age interval per person in the population at risk; = _nD_x / P_x, where P_x is a mid-year population

_nm_x

Assumed age-specific death rates using a life table (i.e. a synthetic cohort); = _nd_x / _nL_x

Greville-Chang Conversion

Used to calculate _nq_x from the _nM_x; _nq_x = (n * _nM_x) / 1 + (n-_na_x)*_nM_x

Synthetic Cohort

The computed cohort using age-specific mortality rates from the current period without waiting for the members of the cohort to die

Standardization

Allows for fair comparisons between populations by adjusting for differences in age distribution; using a given population, calculate the proportion of each age-group, multiple these proportions by the other population's ASMR/ASFR and sum to reveal the new comparable rates

MAC (Mean age at childbirth) or μ

Σ(ASFR * _nmindpoint_x)/Σ(ASFR); where _nmindpoint_x represents x+n/2

l_m

This represents the proportion of the original cohort that survives to the midpoint of an age-group, usually provided in the life table or can be calculated by = _nL_x / (n*l₀)

Cohort Measures

Based on the data specific cohorts as they proceed through life

Period Measures

Based on the period data referring to a particular calendar year, representing a cross-section of the population at a specific time

TFR from ASFR

[Σ(ASFR) * n]/1000; where n is the width of the age interval

_nF_x

Age-specific fertility rate, or ASFR; can be used to calculate TFR

Sex Ratio at Birth (SRB) or fab

[Female births / total number of births] * 100; expected 0.49 or 100 female births per 205 total births

Gross Replacement Rate (GRR)

the average number of daughters a woman would have over her lifetime, assuming she experiences current fertility rates and there is no mortality; = 0.49 * TFR

Net Replacement Rate (NRR)

The average number of daughters female members of the cohort will bear during their reproductive life were they subject to the same ASFR and nMx; = SUM(l_m *ASFR) * 0.49 * n

Cohort Component Method

Used to predict future population sizes based on current survivorship rates; multiply _2nS_x+n with the population at age x to project into the future

Survivorship ratio (_nS_x)

Number of person years lived in one cohort over the previous cohort; represents the proportion of surviving into the cohort; for the first cohort, divide by n * 100,000; for the rest: = _2nL_x+n / _nL_x

Dependency ratio

Represents the ratio of dependents onto the working age population; [age 0-14 + age 65+]/age 15-64

Potential support ratio

represents the ratio of working age population on pensioners; age 15-64 / age 65+