The contribution of urbanization to changes in life expectancy in Scotland, 1861–1910

Figures & data

Figure 1 Annual life expectancy at birth in Scotland from 1855 to 2016¹, by period and urban–rural categories² from 1861 to 1910, and best-practice trend³, by sex

¹We include all the values of life expectancy at birth for Scotland available in the Human Mortality Database (HMD), to provide a better idea of the particularities of our study period 1861–1910 (bounded by the black dashed vertical lines in the figure). ²The points show estimates of life expectancy at birth for different urban–rural categories at the middle of each defined subperiod (see ‘Data’ section). The original categories in the sources were regrouped as shown by the legend, thus: Principal and large towns (urban); Small towns (semi-urban); and Rural. Note that before 1871, the Rural category includes the small towns with fewer than 10,000 inhabitants. ³Life expectancy at birth among the best-practice (record-holding) populations, based on the rates of increase reported in Oeppen and Vaupel (2002). Source: 7th to 56th Detailed Annual Reports of the Registrar General for Scotland; the HMD; Oeppen and Vaupel (2002).

Figure 2 (a) Annual estimates of population size at mid-year, 1858–1910, by district type in Scotland¹. (b) Estimates of the proportion of the total population living in cities of 10,000 or more inhabitants, Scotland, 1500–1910²

¹The bars represent annual estimates of mid-year population by urban–rural category, as reported in each Detailed Annual Report (DAR) from 1858 to 1910. The original urban and rural categories in the sources were retained. There was a change in these categories in 1871 (see ‘Data’ section). In an effort to preserve some continuity with the population data before that change, the 17th DAR provided estimates of population size for each one of the new categories for the year 1861 only (see RGS 1875, Table II, p. x). ²The points from the DARs are every tenth year from 1860 to 1910. Source: 4th to 56th Detailed Annual Reports of the Registrar General for Scotland; Whyte (1995).

Table 1 Number of towns with 10,000 or more inhabitants, by period and category,¹ Scotland 1861–70 to 1901–10

Period	Number of towns			Other changes
	Large	Principal	Total
1861–70	–	–	23
1871–74	17	8	25	New categories in the DARs from 1871
1875–80	18	8	26	Changes in the boundaries of the two largest cities, Glasgow and Edinburgh, came into effect in 1875
1881–91	23	10	33	Important boundary changes in some ‘Principal Towns’ came into effect in November 1891
1892–1900	26	11	37
1901–10	27	15	42	The threshold for ‘Principal Towns’ changes from 25,000 to 30,000 inhabitants from 1901

¹Urban categories as reported in the DARs.

Source: 7th to 56th Detailed Annual Reports (DARs) of the Registrar General for Scotland.

Table 2 Notation¹

Sub-indices^2
$a$	Age
$\omega$	Oldest open-ended age category (e.g., 110+)
$i$	Group or subpopulation (e.g., level in the urban–rural hierarchy)
$t$	Time (e.g., year)
$h$	Time interval
$y$	Time interval between 0 and h
Variables
$D$	Number of deaths
$N$	Population at risk or exposure to risk
$N^{\ast }$	Estimated population at risk (using HMD data)
$P$	Population size
$C$	Population proportion
$r$	Mean annualized growth rate
$m$	Central death rate
$\mu$	Instantaneous force of mortality
$q$	Life-table death probability
$e$	Remaining life expectancy
$l$	Life-table survival function
$\theta$	Weighting function
$\dot{v}$	Time derivative of variable $v$, or change in $v$ over time
v̀	Relative derivative of variable $v$ (equivalent to $\dot{v}/v$)
Examples
$m_a$	Death rate at age $a$
$C_{a,i,t}$	Proportion of the population of age $a$ at time $t$ that is in group $i$
$N_{a,i,t}^{\ast }$	Estimated population at risk at age a, in region i and time t, using HMD data
$N_{a,t}^{HMD}$	Population at risk at age a and time t, based on data from the HMD
${\dot{e}}_{0,t}$	Time derivative of life expectancy at birth

¹The notation used follows closely that developed by Vaupel and Canudas-Romo (2003).

²Occasionally, super-indices are used as well in some variables to indicate the data source; see fourth example.

Table 3 Changes in life expectancy at birth between selected periods, and total contributions of changes in mortality and in urban–rural population composition, by sex, Scotland 1861–65 to 1906–10

Periods compared,^1 by sex	Percentage urban^2	Life expectancy at birth (e0)	Annual change in percentage urban (percentage points)^3	Annual change in e0 (years)^3	Annual contributions (years)^3
					Change in mortality	Change in population composition^4
Females
1861–65	38.64	43.14	0.37	0.13	0.19	−0.06
1866–70	40.51	43.78
1875–77	43.51	44.42	0.26	0.36	0.41	−0.03
1878–80	44.29	45.51
1881–85	49.30	46.40	0.32	0.16	0.20	−0.03
1886–90	50.88	47.22
1893–96	52.82	47.88	0.38	0.03	0.07	−0.04
1897–1900	54.34	48.00
1901–05	56.98	49.88	0.01	0.31	0.32	−0.01
1906–10	57.05	51.44
Males
1861–65	37.21	40.50	0.45	0.10	0.16	−0.06
1866–70	39.44	41.02
1875–77	42.70	41.59	0.25	0.44	0.48	−0.03
1878–80	43.46	42.91
1881–85	48.42	43.85	0.31	0.21	0.25	−0.04
1886–90	49.95	44.92
1893–96	52.13	45.30	0.38	−0.08	−0.04	−0.04
1897–1900	53.63	44.99
1901–05	56.26	46.88	−0.02	0.35	0.35	0.00
1906–10	56.16	48.61

¹The comparable subperiods identified in the ‘Data’ section.

²Proportion of the population living in cities of 10,000 or more inhabitants.

³The columns showing annual changes between two periods were obtained by dividing the total changes by the number of years between the mid-years of each period (e.g., 1 July 1863 and 1 July 1868 are the dates that correspond to the middle of the periods 1861–65 and 1866–70, respectively, thus we divide the total changes by five, which is the number of years between those dates). The examples in units of months per year presented in the text (e.g., annual gains in life expectancy at birth of x months per year during a given period) were obtained by multiplying the corresponding values in this table by twelve.

⁴The values in the last column, which correspond to the annual contribution of changes in the composition of the population, can be interpreted as the average number of years lost per annum in terms of life expectancy because of population redistribution between rural and urban categories.

Source: Detailed Annual Reports of the Registrar General for Scotland and authors’ decomposition results.

Figure 3 Levels of life expectancy at birth in Scotland, based on rates of change with (‘observed’) and without (‘hypothetical’) the urbanization penalty, by sex, 1861–65 to 1906–10¹

¹Points located at the middle of each time interval as defined in Table A4 (supplementary material). Source: Computed life tables based on data from the Detailed Annual Reports (DARs) of the Registrar General for Scotland (7th to 56th DARs) and the Human Mortality Database; authors’ decomposition results; and Appendix 4 in the supplementary material (Table A4).

Table 4 Annual contribution (in years) of changes in mortality and in population composition to the total changes in life expectancy at birth in Scotland between selected periods, by sex, urban population

	Annual contribution to total change in life expectancy
Periods compared, by sex	Urban, all ages			Urban, ages 0–4
	Total	Change in mortality	Change in population composition	Change in mortality	Change in population composition
Females
1861–65 to 1866–70	−0.02	0.12	−0.14	0.13	−0.07
1875–77 to 1878–80	0.13	0.21	−0.08	0.05	−0.04
1881–85 to 1886–90	0.10	0.20	−0.09	0.07	−0.04
1893–96 to 1897–1900	−0.03	0.07	−0.10	0.01	−0.05
1901–05 to 1906–10	0.20	0.21	−0.01	0.09	0.00
Males
1861–65 to 1866–70	−0.03	0.12	−0.15	0.11	−0.07
1875–77 to 1878–80	0.16	0.24	−0.08	0.07	−0.04
1881–85 to 1886–90	0.12	0.21	−0.09	0.08	−0.04
1893–96 to 1897–1900	−0.11	0.00	−0.10	−0.01	−0.05
1901–05 to 1906–10	0.25	0.25	0.00	0.10	0.00

Source: Authors’ decomposition results based on data from the Detailed Annual Reports of the Registrar General for Scotland.

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