Recalculating Swedish pre-census demographic data: Was there acceleration in early modern population growth?

Abstract

The world population growth increased in the eighteenth century, which caused real wages to decline in most countries. Eli Heckscher held the view that Swedish population growth was quite low in the seventeenth century, similar to the development in the rest of Europe, and that there was a substantial acceleration after 1720. Recent data for Sweden by Lennart Andersson Palm entail that population growth was stronger in the seventeenth century than in the eighteenth century. However, this is at variance with other types of economic data. For example, Swedish real wages increased during the seventeenth century and fell in the eighteenth century. This study attempts to resolve the anomaly and argues that Palm’s estimates of Swedish population and mortality rates are too low for the seventeenth century. It presents revised annual demographic data for Sweden for the pre-census period, back to 1630. The new data indicate that there was a small acceleration in early modern population growth, due to the decreased occurrence of mortality crises, but the acceleration was not as pronounced as in the rest of the world.

Appendix: Technical details on the adjustment of vital rates

For the period 1736–1748, the present study takes the number of births and deaths from Heckscher (1936b) rather than from Palm. Heckscher derives his series from official statistics and is compatible with the population data from 1749 onwards. Heckscher’s data are used to backproject the population to 1735, which for that year is estimated to be 1.7 million. The size of the population in 1699 is calculated as the geometric average of four conjectures⁸ and set equal to 1.44 million. For the period 1700–1735, no adjustment is made to Palm’s data on births and marriages, since there does not seem to be any underestimation (see below).

Without net migration, the following relation holds:

$${\text{Addition}}\;{\text{to}}\;{\text{population}} = {\text{Births}} - {\text{Deaths}} = {\text{Births}} - {\text{War}}\;{\text{deaths}} - {\text{Civilian}}\;{\text{deaths}}$$

(1)

Equation (1) can be rewritten so that civilian deaths is determined from the number of births, war deaths, the size of population at the end of the period and the size of population in the beginning of the period, i.e.:

$${\text{Civilian}}\;{\text{deaths}} = \,{\text{Births }} - \left( {{\text{Population}}_{{{\text{end}}\,{\text{of}}\,{\text{period}}}} - {\text{Population}}_{{{\text{beginning}}\,{\text{of}}\,{\text{period}}}} } \right) - {\text{War}}\;{\text{deaths}}$$

(2)

In this study, the civilian deaths of the first approximation (Palm’s series for 1700–1720 based on parish records and an average of Palm and Heckscher’s series for 1721–1735) are increased by the same ratio, UCD (upgrading of civilian deaths), for the whole period 1700–1735. This is the ratio of the total number of civilian deaths according to the final approximation and according to the first approximation, determined as (X stands for year; population is end-of-year):

$$\begin{aligned} {\text{UCD}}(1700\;{\text{to}}\;1735) & = \frac{{\sum\nolimits_{X = 1700}^{1735} {{\text{Civilian}}\;{\text{deaths}}_{{{\text{final}}\,{\text{approximation}}}} } (X)}}{{\sum\nolimits_{X = 1700}^{1735} {{\text{Civilian}}\;{\text{deaths}}_{{ 1 {\text{st}}\,{\text{approximation}}}} } (X)}} = \, ({\text{using equation }}2) \\ & = \frac{{\sum\nolimits_{X = 1700}^{1735} {\text{Births}} (X)\; - ({\text{Population}}_{1735} - {\text{Population}}_{1699} ) - \sum\nolimits_{X = 1700}^{1735} {{\text{War}}\;{\text{death}}} s(X)}}{{\sum\nolimits_{X = 1700}^{1735} {{\text{Civilian}}\;{\text{deaths}}_{{ 1 {\text{st}}\,{\text{approximation}}}} } (X)}} \\ \end{aligned}$$

(3)

For the period 1700–1735, the upgrading of civilian deaths (UCD) is calculated to 1.2 and is assumed to be equal for all years. For the 1720s, both Heckscher and Palm probably overestimate population growth. In particular, the crude death rate seems to be underestimated. In 1721, the crude death rate fell to 19.1 per 1,000 inhabitants according to Palm. Heckscher argues that the extremely low mortality in the 1720s was caused by the high death rate during the Great Nordic War, a view that has been criticised by other researchers (Bengtsson and Oeppen 1993, p. 3). The present study increases the crude death rate in 1721 to 20.6 per 1,000 inhabitants.

For the seventeenth century, a first approximation of the annual population is computed by using Palm’s series of population growth to interpolate between the population estimates of the present study for the two benchmarks of 1629 and 1699. In the final approximation, the death and birth rates are adjusted as well, which renders a new series of the population growth rate between the benchmark years.

Over time, it may be assumed that there was a lower floor to the civilian death rate, which was only occasionally broken. This boundary was largely determined by the living conditions in agrarian society, which probably varied positively with the rate of urbanisation (i.e. a higher rate of urbanisation implied a higher death rate⁹). Mortality crises could also temporarily decrease the lower boundary for the subsequent years. Since the rate of urbanisation was quite low in Sweden in the second half of the eighteenth century, it may be assumed that the lower boundary did not change substantially before the first census in 1749.

The civilian death rate of the first approximation in year X is computed as the ratio between the number of civilian deaths according to Palm based on parish records (i.e. excluding recorded war deaths and without his further additions grounded on his judgement of the underestimation in the primary sources) and the adjusted size of the population of the first approximation according to the present study:

$${\text{CIVDR}}_{{ 1 {\text{st}}\,{\text{approximation}}}} (X) = \frac{{{\text{Civilian}}\;{\text{deaths}}_{{{\text{parish}}\,{\text{records}}}} (X)}}{{{\text{Population}}_{{ 1 {\text{st}}\,{\text{approximation}}}} (X)}}$$

(4)

To evaluate the lower boundary of the civilian death rate, its 9-year moving minimum (CIVDR9MIN_{1st approximation}(X)) is first calculated. Subsequently an HP-filter is estimated for this 9-year moving minimum (CIVDR9MIN_{1st approximation, HP-filter}(X)). λ is set very high. Even if the common value for λ in business cycles research is often set to 6.25 or 100 for annual data, for this study such values would be too low, since the lower boundary for death rates could be assumed to change very slowly over time. Furthermore, a higher λ increases the correlation for annual fluctuations with Palm’s data. For the period 1631–1679, the correlation is maximised when λ = 32,937, which is also the value set for the HP-filter. Furthermore, the correlation between the logarithmic annual changes in the silver price of grain and deaths is maximised when λ is around that value as well. For the period 1749–1820, a HP-filter for the 9-year moving minimum of the civilian death rate with λ = 32,937 entails a coefficient of variation of only 0.004, while at λ = 6.25 it is 0.032 and at λ = 100 it is 0.022.

A ratio, R _{CIVDR, 1st approximation}(X), is computed as the average level of the 9-year moving minimum in 1749–1820 (i.e. before the secular decline in death rates) to this filter for a year X, i.e.;

$$R_{{{\text{CIVDR,1st}}\,{\text{approximation}}}} (X) = \frac{{\frac{1}{72}\sum\nolimits_{k = 1749}^{1820} {{\text{CIVDR9MIN}}_{{ 1 {\text{st}}\,{\text{approximation}}}} (k)} }}{{{\text{CIVDR9MIN}}_{{ 1 {\text{st}}\,{\text{approximation, HP-filter}}}} (X)}}$$

(5)

Assuming that the lower boundary for the civil death rate did not change much during the early modern period, the ratio should be around one for the whole period. A ratio higher than one is an indicator that the civil death rate is underestimated. For the period 1681–1735, R _{CIVDR, 1st approximation}(X) is quite stable, and for the period 1681–1699, the number of civilian deaths is increased by the same rate as in 1700–1735 [UCD (1700–1735)]. Going backward from 1681, R _{CIVDR, 1st approximation}(X) increases substantially. For a year X before 1681, the number of civilian deaths in the second and final approximation is calculated as:¹⁰

$$\begin{aligned} & {\text{Civilian}}\;{\text{deaths}}_{{{\text{final}}\,{\text{approximation}}}} (X) = {\text{Civilian}}\;{\text{deaths}}_{{{\text{parish}}\;{\text{records}}}} (X){\text{UCD}}(X) \\ & = {\text{Civilian}}\;{\text{deaths}}_{{{\text{parish}}\,{\text{records}}}} (X)\frac{{R_{{{\text{CIVDR,1st}}\,{\text{approximation}}}} (X)}}{{R_{{{\text{CIVDR,1st}}\,{\text{approximation}}}} (1731)}}{\text{UCD}}(1700\;{\text{to}}\;1735) \\ \end{aligned}$$

(6)

Since R _{CIVDR, 1st approximation}(1731) ≈ 1.326, this implies that the upward revision of total deaths (for 1731 UCD is 1.2, see above) is still too low compared with an assumption that the moving 9-year minimum of the civilian death rate would be at the same level as that in 1749–1820. However, the further upward revision of deaths implies too high population estimates for the seventeenth century. It may also be assumed that the severe mortality crises in the period 1630–1748 decreased the lower boundary for the civilian death rate somewhat compared with that in the period 1749–1820.

Since birth and marriages seem to follow each other, their adjustment is made together. Adjusting birth and marriage rates is more difficult since there could be some substantial long-term trends. An HP-filter of the crude birth rate (CBR) and marriage rate (MR) according to the first approximation is estimated for the period up to 1735, for year X designated as CBR_{1st approximation, HP-filter}(X) and MR_{1st approximation, HP-filter}(X), respectively. For the years before 1700, the number of births is recalculated as (i.e. births according to Palm are multiplied by the geometric average of the upgrading indicated by the birth and marriage rates, respectively):

$${\text{Births}}_{{{\text{final}}\,{\text{approximation}}}} (X) = {\text{Births}}_{\text{Palm}} (X)\sqrt {\frac{{{\text{CBR}}_{{ 1 {\text{st}}\,{\text{approximation,}}\,{\text{HP-filter}}}} (1700)}}{{{\text{CBR}}_{{ 1 {\text{st}}\,{\text{approximation,}}\,{\text{HP-filter}}}} (X)}}\frac{{{\text{MR}}_{{ 1 {\text{st}}\,{\text{approximation,}}\;{\text{HP-filter}}}} (1700)}}{{{\text{MR}}_{{ 1 {\text{st}}\,{\text{approximation,}}\;{\text{HP-filter}}}} (X)}}}$$

(7)

The number of marriages in year X (before 1700) is similarly determined as:

$${\text{Marriages}}_{{{\text{final}}\,{\text{approximation}}}} (X) = {\text{Marriages}}_{\text{Palm}} (X)\sqrt {\frac{{{\text{CBR}}_{{ 1 {\text{st}}\,{\text{approximation,}}\,{\text{HP-filter}}}} (1700)}}{{{\text{CBR}}_{{ 1 {\text{st}}\,{\text{approximation,}}\,{\text{HP-filter}}}} (X)}}\frac{{{\text{MR}}_{{ 1 {\text{st}}\,{\text{approximation,}}\,{\text{HP-filter}}}} (1700)}}{{{\text{MR}}_{{ 1 {\text{st}}\,{\text{approximation,}}\,{\text{HP-filter}}}} (X)}}}$$

(8)

Since no net migration is assumed, the annual population can then be calculated by back projection from the estimated birth and deaths rates from the benchmark of 1699 (end-of-year). Through such back projection, the estimated population in 1629 (end-of-year) comes very close to the estimate described above, and it depends on the λ for CBR_{1st approximation, HP-filter}(X) and MR_{1st approximation, HP-filter}(X), which in itself is an indication that the method used produces sound results. Setting λ = 3430, which has been computed iteratively, implies that the population estimate for 1629 is the same as that according to the calculations above. A lower λ for CBR_{1st approximation, HP–filter}(X) and MR_{1st approximation, HP-filter}(X) than for the filter of the moving 9-year minimum of the civilian death rate is reasonable, considering that the lower boundary of the death rate may be assumed more stable than the trends for the birth and marriage rates. Henceforth, no further adjustments are necessary. The revised data are presented in Tables 3, 4, 5, and 6.

Table 3 Population in Sweden within present borders, 1000s, end-of-year, 1620–1759

Table 4 The crude death rate in Sweden, number of deaths per 1,000 end-of-year inhabitants, 1630–1759

Table 5 The crude birth rate in Sweden, number of births per 1,000 end-of-year inhabitants, 1630–1759

Table 6 The marriage rate in Sweden, number of marriages per 1,000 end-of-year inhabitants, 1630–1759