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Technology and survival in preindustrial England: a Malthusian view

A Malthusian view

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Abstract

This paper contributes to the debate on the evolution of living standards in preindustrial England. It emphasizes the need to depart from the approach of focusing only on the time paths of observables, like income per capita and population size, in order to assess the validity of Malthusian predictions. It first constructs a Malthusian model and then develops a robust algorithm for identifying the latent forces that have shaped aggregate outcomes in the preindustrial era. The analysis suggests the existence of two distinct Malthusian regimes in preindustrial England: a survival-driven regime, where mortality is the main latent force in economic-demographic interactions, and a later technology-driven regime that emerges after the mid-fifteenth century and is characterized by both population and productivity growth but stable mortality and long-run stagnation in per capita income. The paper discusses the role of various historical accidents (e.g., the Black Death, the discovery of the New World, the English Reformation) in triggering the emergence of the technology-driven regime, and it also highlights some mediating mechanisms through which subsequent productivity growth may have been sustained. The existence of long-run stagnation in income per capita in England through the mid-seventeenth century, despite the technological dynamism of the early modern period, is consistent with the predictions of Unified Growth Theory.

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Availability of data and material

Clark’s and Allen’s datasets are available in Clark (2010) and Allen (2010), respectively. The Broadberry et al. (2015) dataset is available at the Bank of England’s “A Millennium of Macroeconomic Data.”

Code Availability

MATLAB scripts and organized data files are available at https://github.com/maattar/Technology-and-Survival-in-Preindustrial-England.

Notes

  1. Reliable and representative demographic statistics for England are available only through the Cambridge Group’s work that covers the period after 1541 (Wrigley and Schofield , 1981; Wrigley et al. , 1997).

  2. Since preindustrial England has a low-pressure demographic system (Lee , 1973; Wrigley and Schofield , 1981; Lee and Loschky , 1987; Møller and Sharp , 2014), shutting down the positive check mechanism is not a major concern for present purposes.

  3. This assumption is essential within a two-generation setup since some adults also face mortality events before the end of their adulthood.

  4. This is very much in line with the well-known practice of decomposing variations in equilibrium quantity and price levels into unobserved demand and supply shocks under the assumption that the laws of supply and demand are true.

  5. Specifically, the point estimate of the correlation coefficient between population and income per capita is negative, but the very small sample size implies a prohibitively large Type-II error probability.

  6. Section 7 demonstrates that the benchmark findings of the paper are robust. For instance, results are not sensitive to the borrowed values of structural parameters, the use of the alternative national income estimate from Clark (2010), and the use of 25-year data on population and income per capita.

  7. Møller and Sharp (2014) estimate various Malthusian models and support the existence of a post-Malthusian regime during which Malthusian and Boserupian forces coexisted. This regime exhibits parameter stability until the late eighteenth century.

  8. Another closely related paper is that of Bouscasse et al. (2021). Estimating a Malthusian model with various types of mortality and technology shocks, they find that perpetual productivity growth in England started in 1600. However, they work with a reduced-form function of population growth, and they also use only the real wage data. As demonstrated and discussed in Section 7.1, the real wage is not an appropriate measure of living standards.

  9. Ashraf and Galor (2011) test the predictions of the Malthusian model using cross-country data. Exploiting exogenous variations in technological advancement and land productivity, they show that technology did not have any causal positive effect on living standards but only increased population density in the long run. In a recent paper, Lagerlöf (2019) complements this evidence with time-series analyses of a Malthusian model implemented for preindustrial Europe. According to the results, a Malthusian model with a realistic demographic structure and with both permanent and transitory shocks to production successfully explains the movements of real GDP per capita in preindustrial times. Similarly, Madsen et al. (2019) extend the Malthusian model with productivity growth and study the convergence properties of the model for several countries. Their results confirm the validity of the Malthusian mechanisms. In a related paper, Attar (2020) shows that a framework with multiple regimes such as UGT is essential in explaining British economic growth in the very long run.

  10. The mortality and fertility statistics for the pre-1541 period are available only through very small samples of particular groups such as the clergy and particular regions and time intervals (e.g., Russell 1948).

  11. There are studies that test the validity of the Malthusian mechanisms for Northern Italy as well. Chiarini (2010) fails to identify the preventive check and finds the positive check to be strong. Fernihough (2013) confirms the validity of both checks and the Malthusian cycle. In a very recent study, Pedersen et al. (2021) identify a reversed preventive check, contradicting the Malthusian postulates and supporting the old age security hypothesis.

  12. Klemp and Møller (2016) confirm the existence of post-Malthusian regimes for Denmark, Norway, and Sweden.

  13. Constructing Malthusian economies with these two exogenous drivers is typical in the related literature since Lee (1973). While exogenous mortality shuts down the positive check mechanism, this is not a concern for preindustrial England because of the prevailing low-pressure demographic system (Lee , 1973; Wrigley and Schofield , 1981; Lee and Loschky , 1987; Møller and Sharp , 2014).

  14. Such a characterization of differential mortality rates for preindustrial England is supported by Bar and Leukhina (2010b).

  15. Note that, as it is typical in the literature, reproduction is assumed to be completed at the exact beginning of a period.

  16. When utility depends on net fertility as in Ashraf and Galor (2011), results do not change provided that the total cost of reproduction is \(\rho b_{t}\). See Section 7.

  17. It is at this point useful to note that (6) for \(z_t\) and (11) for \(n_t\) correspond to equations (2) and (1) of Lee (1993), respectively. Thus, the random disturbances \(\nu _{t}\) and \(\epsilon _{t}\) in Lee (1993) represent \(A_{t}\) and \(s_{t}\) of the present analysis, respectively.

  18. The static equilibrium of the model also satisfies (i) \(\partial b_t/\partial s_t<0\), i.e., lower mortality implying lower gross fertility, and (ii) \(\partial n_t/\partial s_t>0\), i.e., lower mortality implying higher net fertility.

  19. One interesting specification would be the case of perpetual growth in \(A_t\), studied by Madsen et al. (2019). In such a case, population growth and productivity growth are balanced as in \(L_{t+1}/L_t=A_{t+1}/A_t\) for \(t\rightarrow +\infty \). Living standards (\(z^*\) and \(y^*\)) are larger for higher growth rates of productivity, but they are still independent of \(A_t\). This implies that, if we have \(\text {d}y^*<0\) with \(P_t\) and \(A_t\) perpetually growing at fixed rates, then we must have \(\text {d}s^*>0\).

  20. Section 7 implements the analysis for the extended sample that ends at 1800.

  21. \(\text {CBR}_t\), defined as the ratio of the total number of births by surviving adults (\(b_t\times \psi s_t L_t\)) to population (\(P_t\)), simplifies into \((\psi b_t)/(\psi +b_t)\).

  22. As it is typical in the literature that builds on asexual reproduction, \(b_t\) in the model is approximated by the Gross Reproduction Rate in the data.

  23. One other possibility would be to exploit the mapping between \(b_t\) and \(\text {CBR}_t\) and use the \(\text {CBR}_t\) intervals estimated by Foreman-Peck and Zhou (2021) for the pre-1541 period. However, their model has a richer demographic structure, and it is not clear whether this alternative strategy would qualify as an acceptable remedy.

  24. In Bar and Leukhina (2010a), the labor elasticity is denoted by \(\mu \) and corresponds to \((1-\alpha )\) of the present setup. Similarly, \((1-\alpha )\) denotes fertility elasticity in Bar and Leukhina (2010a) and corresponds to \(\gamma \) of this paper.

  25. 50-year average temperature levels for Central England, compiled by Lamb (1965), do not imply a technology-temperature association. This may be due to several factors. Identified technology is an aggregate measure of productivity for all sectors in the economy, and there are other climatic features such as rainfall that may be more decisive.

  26. Lee and Anderson ’s (2002) measure has been reindexed for the base decade 1550 for better visualization.

  27. While the sample size is relatively small with 36 decades, the minimum sample size for \(r=-0.93\) is 12 when the Type-I and Type-II error probabilities are set to 1% (Hulley et al. , 2013).

  28. When the Type-I error probability is 5%, a sample size of 11 increases the Type-II error probability to 50% for \(r=-0.61\) (Hulley et al. , 2013).

  29. The summary trends presented by Broadberry et al. (2015) indicate that the yield averages exhibited sizable improvements. Grain yields in 1650s were about 40% larger than the levels estimated for 1550s. For milk, meat, and wool yields, the associated percentages are 35%, 27%, and 32%, respectively. For the land endowment, the arable area was about 11% larger in 1650s, and the sown area increased by about 30% from 1550s to 1650s.

  30. The growth of the cloth industry is the most prominent example. The productive efficiency in the lighter-weight cloths known as the New Draperies significantly expanded after 1560s (Allen , 2009a).

  31. There is also the causal effect of the printing press on the diffusion of Protestantism. Rubin (2014) confirms the presence of such an effect with a sample of European cities.

  32. Boucekkine et al. (2007) argue that increasing population density in England is the main determinant of these early literacy improvements. From 1550 to 1650, De Pleijt (2018) reports a very modest increase in the average years of schooling as well.

  33. The econometric analysis here is parsimonious in the sense that we do not search for the \(\text {ARIMA}(p,d,q)\) models with best performances in some information criteria such as those of Akaike or Schwarz.

  34. The DGPs for \(A_{t}\) and \(s_{t}\) until 1800 are still nonstationary—integrated of order one—as in the benchmark case, and the first-differences are still characterized by zero-mean processes. However, for both \(\Delta A_{t+1}\) and \(\Delta s_{t+1}\), hypothesis tests return mixed results concerning normality. Additionally, an ARCH structure in \(A_t\) cannot be rejected.

  35. The figure also shows alternative identifications of \(A_t\) and \(s_t\) with 25-year (quadranscentennial) data to see whether the benchmark findings are sensitive to data frequency. It turns out that using decennial versus quadranscentennial data does not imply a vital change in the evolution of technology and survival terms

  36. These patterns are also consistent with recent time-series evidence presented by Crafts and Mills (2017).

  37. There are two minor deviations from the benchmark. First, \(s_{1600}=0.67\) as a calibration target is not sufficiently small to identify \(\{s_{t}\}_{t}\) within the [0, 1] interval for all decades. The level of \(s_{1600}\) that implies \(s_t<1\) for all t is around 0.6, and this has been adopted as a (minimum) plausible benchmark. Second, even though technology and survival are still characterized by pure random walks, structural shocks are not Gaussian.

  38. From 1450 to 1550, literacy exhibits an increase of 8 percentage points according to the compilations presented in Baten and van Zanden (2008, Fig. 2). For industriousness, Humphries and Weisdorf (2019, Fig. 4) estimate that the length of the working year steadily increased from around 125 days in 1450s to nearly 200 days in 1550. Finally, according to Broadberry et al. (2015, Tab. 3.21), relevant agricultural figures exhibit the following percentage increases from 1450s to 1550s: the sown area by 18%, grain yields by 52%, milk yields by 25%, meat yields by 15%, wool yields by 32%.

  39. There exist large literatures devoted to these issues, especially in connection with the origins of capitalism, the Brenner debate, and the timing of agricultural revolutions. These literatures feature Malthusian and Marxian as well as institutionalist views. Relative labor scarcity also resulted in a partial shift from arable to pastoral farming in England (Voigtländer and Voth , 2013a).

  40. Recall that, in the benchmark case, a sample size of 36 implied \(\text {Corr}(P,y)=-0.93\) with very low Type-I and Type-II error probabilities in the survival-driven regime of 1200–1550. With the Broadberry et al. (2015) dataset, the point estimate is \(\text {Corr}(P,y)=-0.95\) for the survival-driven regime of the 1310–1470 period, and the minimum sample size is 10 decades for Type-I and Type-II error probabilities set to 1% (Hulley et al. , 2013). Hence, in both cases, the survival-driven regimes feature a strong Malthusian cycle.

  41. With the Broadberry et al. (2015) dataset, the point estimate is \(\text {Corr}(P,y)=-0.23\) for the technology-driven regime. For this point estimate and a Type-I error probability of 5%, the sample size of 19 implies a Type-II error probability of about 85%.

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Acknowledgements

I am grateful to Oded Galor and three anonymous reviewers for their very helpful comments and suggestions on earlier versions of this paper. I am particularly grateful to Oksana Leukhina; she has generously shared various data files on preindustrial mortality statistics. I also wish to thank Dilek Başar, Osman Küçükşen, Selcen Öztürk, Onur Yeni, symposium participants at the 19th National Economics Symposium of the Turkish Economic Association in Girne, and seminar participants at Hacettepe University, TED University, and Middle East Technical University for their comments and suggestions. All of the remaining errors are my own.

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Attar, M.A. Technology and survival in preindustrial England: a Malthusian view. J Popul Econ 36, 2071–2110 (2023). https://doi.org/10.1007/s00148-023-00952-2

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