Demographic measures: birth rate, fertility rate, mortality and dependency ratio

Three kinds of fraction appear. A proportion has the numerator inside the denominator (the share of the population aged 65 and over). A ratio has a numerator that is not part of the denominator (females per 1,000 males; the dependency ratio). A rate is the number of events in a period divided by the population exposed to the risk of the event, usually per 1,000 (births per 1,000 people in a year). The word rate is used loosely in demography, which is why the maternal mortality “rate” of one textbook is the “ratio” of another.

Two ideas organise everything. The base is the population at risk: all people, women of childbearing age, live births. The specific version of a rate restricts it to one group, by age or sex, and a crude rate does not. Specific rates answer the question “how risky is this for this group?”; crude rates answer “how common is this in the population?”, and depend on the group sizes as much as on the risk.

Take a town of 2,000,000 people (we will call it Ashanagar, an invented place used throughout this lesson), where 520,000 women are aged 15 to 49 and 51,508 live births were registered in a year.

Reading them. The CBR is the quickest to compute and the weakest: it falls when the share of women of childbearing age falls even if each woman has as many children as before. The GFR fixes that, but treats a woman of 22 and one of 47 alike. The ASFR is the births to women of one age, per 1,000 of those women; the shape of the ASFRs across ages is the fertility schedule. The TFR adds the ASFRs: with five-year age groups multiply the sum by 5, because each woman spends five years in each group, and divide by 1,000. In Ashanagar the ASFRs of 50, 190, 215, 120, 45, 10 and 2 sum to 632, so TFR = 5 × 632/1,000 = 3.16 births per woman. It is a hypothetical cohort measure: the births a woman would have if she lived through all her childbearing years at today’s age-specific rates.

Replacement. The GRR is the TFR counting daughters only: with about 100 girls born for every 105 boys (100/205 = 48.8% of births), 3.16 × 0.488 = 1.54 daughters per woman. The NRR also allows for the chance that a daughter dies before reaching her mother’s age: it is the number of daughters who will replace the mother. An NRR of 1 means that each generation exactly replaces itself, an NRR above 1 that population will grow in the long run, and below 1 that it will shrink. The “replacement-level” TFR of about 2.1 is the TFR at which the NRR is 1 when mortality is low (it is higher where more daughters die before reaching adulthood).

The crude death rate (CDR) is deaths per 1,000 of the total population: in Ashanagar 16,000/2,000,000 × 1,000 = 8.0. The age-specific death rate is deaths in one age group per 1,000 people of that group. The infant mortality rate (IMR) is deaths of children under one year per 1,000 live births in the same year: 1,700/51,508 × 1,000 = 33.0. The maternal mortality ratio (MMR) is deaths of women from pregnancy-related causes (during pregnancy or within 42 days of its end) per 100,000 live births: 90/51,508 × 100,000 = 174.7. The base is live births, not women, so it is formally a ratio, though some papers, UOH 2017 among them, call it the maternal mortality rate. Life expectancy at birth summarises the age-specific rates in one number: the average years a newborn would live if today’s age-specific death rates stayed unchanged.

The crude death rate depends on age structure. Suppose Country A has 90% of its people under 60 with a death rate of 6 per 1,000 and 10% aged 60 and over with a death rate of 50; its crude rate is 0.9 × 6 + 0.1 × 50 = 10.4. Country B has 60% under 60 with a death rate of 5 and 40% aged 60 and over with a rate of 40: 0.6 × 5 + 0.4 × 40 = 19.0. Every age-specific rate is higher in A, yet its crude rate is far lower, because A is a young country. This is the point of JNU 2019, where country A’s age-specific death rates are all higher and yet its overall rate is lower: possible if A has a younger population than B.

The remedy is standardisation: apply each country’s age-specific rates to the same standard age structure and compare the results, or compare life expectancies. The same distortion affects the CBR: a country whose population is ageing can have a falling birth rate with no change in the number of children per woman.

Every number for Ashanagar is an input. Change the age groups of women, the births, the deaths or the population and each rate is recomputed with its formula. Try these: halve the births to women aged 20–24 and see how little the GFR moves compared with the TFR; double the infant deaths and see that the IMR doubles but the CDR hardly changes; move 100,000 people from the working ages to the 65-and-over group and watch the old-age ratio.

Sex ratio. The Census of India defines it as the number of females per 1,000 males. Ashanagar, with 980,000 females and 1,020,000 males, has 961. The international convention reverses it, as males per 100 females. The child sex ratio is the same ratio for ages 0 to 6. Census of India figures: the sex ratio was 933 in 2001 and 943 in 2011, and the child sex ratio 927 in 2001 and 919 in 2011. The child ratio fell while the overall ratio rose, which is the reason it is watched: it points to sex-selective births and to the higher mortality of girls. (UOH 2015 asked the 2001 figure: 933.)

Dependency ratios. The total dependency ratio is (population aged 0–14 + population aged 65 and over) per 100 people aged 15–64. It is the sum of the young-age ratio (0–14 over 15–64) and the old-age ratio (65 and over over 15–64). The ages are conventions: someone aged 17 may be in school and someone aged 66 working. Ashanagar has 560,000 children, 140,000 elderly and 1,300,000 of working age: young-age ratio 43.1, old-age 10.8, total 53.8. In the data of Lesson 8 India’s total ratio fell from 78 in 1960 to 47 in 2023 (World Bank), while Japan’s rose from 46.7 in 2000 to 70.1 in 2023.

The natural rate of increase is the CBR minus the CDR, divided by 10 to give per cent; migration is not included, so the full growth rate of a population is the natural increase plus net migration. Ashanagar’s is (25.75 − 8.0)/10 = 1.78% a year, which would double its population in about 39 years.

In India, population counts come from the Census, taken every ten years. The first synchronous census, taken on the same date across the country, was in 1881; the 1872 enumeration, done in pieces between 1867 and 1872, was the earlier, non-synchronous one (UOH 2013 asks in which year the first census was held and keys 1881, the first of the synchronous censuses; the offered years 1881, 1891, 1901 and 1911 are all synchronous). Between censuses the rates come from the Sample Registration System (SRS), a continuous survey of births and deaths, and from the National Family Health Survey (NFHS), which reports a total fertility rate of 2.0 for 2019–21, down from 2.2 in 2015–16. Replacement is about 2.1, so India’s fertility is at or just below it on the survey measure.

The practical point for exams: figures from a named source and year (Census 2011, NFHS-5) are facts to learn with their dates; they change, and a question that does not give the year invites a wrong answer. This lesson keeps to definitions and arithmetic, and uses the figures above only with their sources.

Questions on the formulas and bases of the measures, and on calculations from small tables. Those on the stages of the demographic transition and the dividend are in Lesson 8.