Computed Variables

For replicability, data processing scripts for computed variables are hosted on github.

NRR: the net reproduction rate is a measure of fertility alternative to the more commonly reported total fertility rate TFR. Whereas the TFR measures the number of born-alive children a woman is expected to have over a fertile lifetime on average, the NRR measures only the number of surviving daughters a woman is expected to have over a fertile lifetime on average.
I believe the NRR is more informative than the TFR. Why? Because I am interested in which populations have above-replacement fertility and which populations have below-replacement fertility. The replacement-level TFR (RLTFR) is typically said to be 2.1 but this is not a universal. The RLTFR is dependent on local mortality rates and on the local sex ratio at birth. In contrast, the replacement-level NRR is independent of the local sex ratio at birth. For the purpose of making coherent comparisons between populations with respect to replacement-level fertility, using the NRR sidesteps the possibility of misevaluating a population that has an atypical sex ratio at birth.

CRR: the crude reproduction rate approximates the NRR similarly to how the crude fertility rate CFR approximates the TFR. In all cases, I compute CRR as the ratio of the size of the youngest cohort of girls to the average size of cohorts of women aged 15-44 (see [1]).
Unlike the NRR, the CRR does not account for mortality rates. In the Anglosphere countries, which all have low mortality rates, CRR > 1.03 indicates that above-replacement reproduction is taking place, CRR = 1.03 indicates that at-replacement reproduction is taking place, and CRR < 1.03 indicates that below-replacement reproduction is taking place, in general.

ACE is a variable I've defined called annual cohort exchange, which is the difference between the (approximate) number of daughters born in a year and the (approximate) number of women who leave the oldest fertile cohort in a year. The ACE gives an indication of which regions are acting as population sources (positive ACE) and which regions are acting as population sinks (negative ACE).

Racial Designations

In all cases, and in all cohorts, I have partitioned the "EVERYONE" group into racial groups such that a person of mixed ancestry from racial groups A and B is counted as half of a person from racial group A and half of a person from racial group B. For example, by this partitioning, Barack Obama counts as 1 person in the "EVERYONE" group, and he also counts for 0.5 people in the "WHITE" group and 0.5 people in the "BLACK" group.

The designations for racial groups are as follows:

GroupDesignation
EVERYONEEveryone
WHITEEuropeans
BLACKSub-Saharan Africans
REDMestizos, North Americans, and South Americans
YELLOWEast Asians, Micronesians, and Polynesians
BROWNSouth Asians, West Asians, and North Africans
BRONZEAborigines, Australoids, and Melanesians

Data Sources for population by age, sex, race, and region:

(This section is under construction. Some sources may be outdated.)
USA:

The geographies were chosen as the sets of counties constituting the Primary Statistical Areas defined by the Office of Management and Budget. The delineations of PSAs are defined at census.gov

The population data comes from the Census Bureau's county characteristics dataset of population by age, sex, race, and Hispanic origin, estimates for 2011.

Canada:

The geographies were chosen as the relevant Census Metropolitan Areas. The population data is derived from a synthesis of the Visible Minority tables and the Aboriginal Identity tables.

statcan.gc.ca -> English -> Census Program -> Census Datasets -> (2001 Census/2006 Census/2011 NHS/2016 Census Part B) -> Variable: (Visible minority/Aboriginal Identity)

Ireland and the UK: The geographies were chosen as the European Union NUTS regions.

The population data for Ireland were got from the Central Statistics Office index of interactive tables: People and Society -> Census of Population -> 2011 Census Results -> Profile 7 - Religion, Ethnicity and Irish Travellers -> CD795 Population Usually Resident and Present in the State by Sex, Regional Authority, Age Group, CensusYear and Ethnic or Cultural Background.

It was assumed that whites and nonwhites gave the "not stated" response to the ethnic background question at equal rates.

The population data for England and Wales were got from the www.nomisweb.co.uk data query tool for table DC2101EW - Ethnic group by sex by age - queried at the level of local authorities composing each Functional Urban Area.

The population data for Northern Ireland in 2011 were got from www.ninis2.nisra.gov.uk. Search for DC2101NI to find the relevant table.

The population data for Northern Ireland in 2001 were got from www.nisra.gov.uk -> Census -> 2001 Census -> Results -> Commissioned Output -> Demography -> Sex and Ethnic Group by Age (Table Ext20050509)

The population data for Scotland were got from scotlandscensus.gov.uk -> Census Data Explorer -> Standard Outputs -> 2011 -> Ethnicity, Identity, Language and Religion -> DC2101SC Ethnic group by sex by age -> Council Area 2011, and selecting the relevant council areas composing each Functional Urban Area

New Zealand:

The geographies were chosen as the Regional Council Areas of New Zealand. The population data comes from nzdotstat.stats.govt.nz -> 2018 Census -> Ethnicity, culture, and identity -> Ethnic group (detailed total response - level 4), by age group and sex, 2006, 2013, and 2018 Censuses

Australia:

The geographies were chosen as the sets of Local Government Areas that are at least partially contained in the Greater Capital City Statistical Areas of the relevant city, except for Canberra, for which the encompassing Significant Urban Area + Australian Capital Territory was selected.

The population data comes from the Expanded Community Profile for each region, table X07f, Ancestry of Dependent children by age. To interpret the data from that table, three assumptions were made: 1) that whites and nonwhites gave the "ancestry not stated" response at equal rates. 2) that 50% of the "Other" responses were nonwhite ethnicities (to minimize the maximum error). And 3) that each single response for a nonwhite ethnicity counted for one nonwhite child (since nonwhites don't often racemix with other kinds of nonwhites and so a mixed child is not likely to have two different nonwhite ancestries).

Footnotes

  1. ^ In all cases, I compute CRR as the ratio of the size of the youngest cohort of girls to the average (mean) size of cohorts of women aged 15-44, or in other words, women in the age range [15,45). However, when the size of the youngest cohort is measured over an age range of length Δt, then women who are currently in the age ranges [15,15+Δt) and [45,45+Δt) will have, on average, spent half of the past Δt being in the relevant age range [15,45). So when computing the average size of cohorts of women aged 15-44, the cohorts of women in the age ranges [15,15+Δt) and [45,45+Δt) are included and weighted by 0.5.
    For example, in the USA County Characteristics dataset, the youngest cohort is girls aged 0-4, or in other words, girls in the age range [0,5), so Δt = 5 years. So cohorts of women in the age ranges [15,20) and [45,50), or in other words, women aged 15-19 and women aged 45-49, are included in the mean and weighted by 0.5, and cohorts of women in the age range [20,45), or in other words, women aged 20-44, are included and weighted by 1.0. If P(a,b) is the population of women in the age range [a,b), then CRR is computed as CRR = P(0,5) / ( ( (P(15,20)+P(45,50))/2 + P(20,45) ) / 6 ).
    In general, CRR is computed as CRR = P(0,Δt) / ( ( (P(15,15+Δt)+P(45,45+Δt))/2 + P(15+Δt,45) ) * (Δt/30) )