Insurance demand: a historical long-run perspective (1850–2020)

Kohl, Sebastian; Römer, Matthias Article — Published Version Insurance demand: a historical long-run perspective (1850–2020) The Geneva Papers on Risk and Insurance - Issues and Practice Provided in Cooperation with: Springer Nature Suggested Citation: Kohl, Sebastian; Römer, Matthias (2024) : Insurance demand: a historical longrun perspective (1850–2020), The Geneva Papers on Risk and Insurance - Issues and Practice, ISSN 1468-0440, Palgrave Macmillan, London, Vol. 50, Iss. 3, pp. 595-618, https://doi.org/10.1057/s41288-024-00339-8 This Version is available at: https://hdl.handle.net/10419/330560 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/4.0/ Vol.:(0123456789) The Geneva Papers on Risk and Insurance - Issues and Practice (2025) 50:595–618 https://doi.org/10.1057/s41288-024-00339-8 Insurance demand: ahistorical long‑run perspective (1850–2020) SebastianKohl1 · MatthiasRömer1 Received: 22 December 2023 / Accepted: 2 October 2024 / Published online: 31 December 2024 © The Author(s) 2024 Abstract Existing research on how international insurance demand varies with income is largely driven by cross-sectional variation post-1970. Drawing on newly collected historical long-run data on life insurancepremiums starting as early as 1850 to 2020 for 20 OECD countries, we evaluate the ‘S-Curve’ predicting insurance demand as each country transitions through different incomelevels. In contrast to predictions in the literature, we reject the ‘S-curve’, but identify a two-bump curve with two high-elasticity episodes, one driven by amassive expansion of life insurancecontracts at the end of the 19th century to ensure mortality risks and the other in the late 20th century driven by a shift to savings products. This could imply that the longitudinal catching-up process of countries with low insurance density may be steeper than what the cross-sectional ‘S-Curve’ would suggest. Keywords Insurance demand· Life insurance S-curve· Historical-comparative research Introduction Insurance demand has grown over the last two centuries and reached a global maximum in the recent decade. In light of ageing societies, climate change and high inflation, however, it is unclear how insurance demand will evolve in the future. The historic development of insurance markets is often used to predict future insurance demand, but the evidence about past trajectories is mixed. The evolution of The research has been supported by the German Research Council DFG grant KO 6095/1-1. * Sebastian Kohl sebastian.k[email protected] Matthias Römer [email protected] 1 Freie Universität Berlin, Berlin, Germany 596 S.Kohl, M.Römer insurance demand is often assumed to follow a similar pattern across countries.1 A key determinant of insurance demand is income (usually measured by GDP per capita).2 The relation of insurance demand and income is based on the assumption that individuals seek to protect either assets (non-life) or future consumption (life). It is assumed that when income levels are low, individuals tend to spend less on building financial wealth and have limited awareness of financial risk. In addition, the opportunity cost of buying insurance to replace assets (or income in old age) is high. As economies become more affluent and awareness grows, spending on insurance grows faster than income. At higher levels of income the demand for insurance levels off as individuals refrain from expanding their insurance coverage (see Carter and Dickinson 1992). Empirical tests of this proposed relationship between insurance demand and income usually rely on two possible measures of insurance consumption: ‘insurance penetration’ or ‘insurance density’. ‘Insurance penetration’ is the ratio of total (gross) premiums paid each year as percentage of GDP. In contrast, ‘insurance density’ is the amount of (gross) premiums paid per capita. The statistical relationship between either premiums as percent of GDP or premiums per capita is often assumed to follow a common functional form across countries (Enz 2000). Initially, the amount of premiums paid each year relative to GDP is low, as income rises it increases more than proportionally before leveling off as higher levels of income are reached. The relationship between levels of ‘insurance penetration’ and GDP per capita is often referred as the so called ‘S-Curve’. A different measure of this relationship is the income elasticity of insurance. It measures the percentage change in premiums given a change in income. The ‘S-Curve’ implies a hump-shaped income elasticity of insurance for different levels of income, e.g. the percentage change in premiums per capita (or % of GDP) given a change in income is not linear. At lower levels of income, the elasticity is less than 1 or possibly negative. As income grows, elasticity increases as well.3 Life premiums per capita start to grow more than proportionally to income, that is, elasticity now exceeds unity. At a higher levels of income, the income elasticity of income returns to the initial elasticity, according to the predictions of the ‘S-Curve’. In short, a plot of the income elasticity of life insurance and level of income should exhibit a single hump as income elasticity of insurance varies systematically with GDP (per capita). Drawing on newly collected historical long run data of life premiums starting as early as 1850 through 2020 for 20 OECD countries, this article is able to evaluate the ‘S-Curve’ longitudinally, as countries transition through most levels of income instead of comparing highand low-income countries’ insurance demand cross-sectionally. In contrast to predictions in the literature, we reject the ‘S-Curve’ in this longitudinal view, but rather identify a two-bump curve with two high-elasticity 2 See e.g. for Outreville (2013) for an overview. 3 The increase in elasticity reaches a maximum at an inflection point where the second derivative changes sign. 1 We follow the literature in using the term ‘insurance demand’, but insurance consumption depends on both demand and supply. Hence, insurance consumption possibly better describes such an equilibrium outcome. See Millo and Carmeci (2015) on this point. 597 Insurance demand: a historical long-run perspective episodes. We suggest that the first expansion of life contracts is mainly driven by products insuring mortality risks at the end of the 19th century and the other in the late 20th century by products having a saving or investment function. The ‘S-Curve’ does not explain very well past trajectories of life insurance demand of individual countries. This has implications for predicting future life insurance demand. Our finding could imply that the longitudinal catch-up process of low-insured countries may be steeper than what the cross-sectional ‘S-Curve’ would suggest. The remainder of this article is structured as follows: section “Literature: mixed evidence” reviews the empirical evidence on the statistical relationship between insurance demand and income and details how existing evidence on the income elasticity of insurance depends on cross-sectional variation in income.The “Data” section presents newly collected data on life insurance premiums that expands the time coverage by almost 100 years for 20 countries. The time span of 1850 to 2020 allows to observe within-country variation in income rather than relying solely on cross-country variation as in the existing literature. The average (median) starting year in our sample is 1880 (1878). The newly collected data shows how each country arrived at the current life ‘insurance density’ (or ‘penetration’). The“Methods” section uses the observed within-country variation to estimate the country specific income elasticity of life insurance for 20 countries since the 19th century. The income elasticity varies across countries for similar levels of income (seethe “Results” section). However, some common patterns emerge. Insurance consumption seems to rise faster than income at both lower and higher income levels. Section “Two tales of life insurance demand” discusses the varying life insurance product in force across time and income levels. Section “Policy implications” outlines policy implications of our findings for emerging insurance markets. The“Conclusion” section concludes. Literature: mixed evidence Income matters for the purchase of insurance. But it is subject to debate how insurance consumption changes, when income changes. There are two approaches in theliterature addressing this question. A theoretical perspective goes back to Mossin (1968) who considers insurance possibly to be an inferior good. The empirical equivalent is the estimation of income elasticity of insurance. Our analysis contributes tothe latter branch of the literature by adding a time-series perspective to the existing cross-sectional studies. The literature on the relationship between income and life insurance consumption is vast. Studies using household data (Luciano etal. 2016) or country-level data for different regions across the globe find that the effect of income on life insurance consumption is positive(Beck and Webb 2003; Feyen etal. 2013; Giné etal. 2019; Dragotă etal. 2023).4 Other studies additionally provide estimates of income 4 For studies on the effect of insurance on growth see Apergis and Poufinas (2020) for OECD countries, Asongu and Odhiambo (2020) Horvey etal. (2023) for countries in Africa, and Scharner etal. (2023) for a global perspective. 598 S.Kohl, M.Römer elasticity of life insurance. Studies using household data (Lewis 1989) or country level-data (Beenstock etal. 1986; Browne and Kim 1993; Li 2007) find consistently a positive income elasticity of life insurance, but the estimates of income elasticity differ. Studies either characterize life insurance to as a normal or a superior good. Our study contributes to aparticular subset in the literature that analyzes the functional form of the relationship between income and life insurance and considers a possible non-linearity in the relationship between life insurance and income. Table1 presents an overview of different approaches in studies on the relationship of insurance demand and income. First, studies plot income and ‘insurance penetration’ (or ‘density’) for a particular year for a number of countries. Carter and Dickinson (1992) (p.175ff), for instance, suggest that the growth in ‘insurance penetration’ varies with different levels of income. Their empirical analysis is based on 42 countries observed in both 1978 and 1988. In contrast to the ‘S-Curve’ prediction, the authors do not find evidence for a slowing insurance consumption at higher levels of GDP per capita. However, they do find a larger percentage change in ‘insurance penetration’ for middle income countries, a result in line with the ‘S-Curve’ prediction. The descriptive evidence on ‘insurance penetration’ at different levels of income in the literature is based on cross-sectional data at one point in time. For instance, Enz (2000) plots different countries at different levels of income in one year (1998) and cites this as evidence for an ‘S-Curve’ relationship. This snapshot across countries and income levels suggests for both life and non-life a non-linear relationship between ‘insurance penetration’ and GDP per capita. The underlying assumption is that ‘insurance penetration’ is time-invariant given the level of income, that is,the insurance demand evolves in asimilar way in different countries given a particular income levelat different points in time. A second approach, beyond the descriptive evidence, is the estimation of the income elasticity of insurance demand. Enz (2000) (similarly Zheng etal. 2008) use cross-sectional descriptive evidence to justify the estimation of ‘insurance penetration’ (both life and non-life) as a logistic function of GDP per capita based on crosssectional time series data. Based on the descriptive evidence, the functional form of the relationship is an assumption. Other functional forms such as a linear trend or a different non-linear function might explain the relationship as well. The imposed nonlinear functional form allows to compute the income elasticity of insurance for different levels of GDP per capita. Enz (2000) finds that income elasticity of insurance reaches a maximum of 2.3 in life and 1.7 in non-life at 12.4000 US$ and 8.900 US$, respectively. Zheng etal. (2008) use the same approach as Enz (2000), but consider a slightly different time span (1980–2006 instead of 1970–1998) and find slightly lower maximum values for the income elasticity of insurance: 1.7 in life (1.4 in non-life). While Enz (2000) and Zheng etal. (2008) predict ‘insurance penetration’, subsequent authors use the (absolute) amount of life and non-life premiums (Lee and Chiu 2012). Millo (2016a) and Millo (2016b) estimate the ‘partial’ income elasticity of insurance, using premiums per capita as a dependent variable. Lee and Chiu (2012) do not assume a functional form a priori, but allow for possible regime-switches. In addition, Lee and Chiu (2012) include panel features such as fixed effects. For life insurance, income elasticity of life insurance is lower compared to previous studies: 0.588 and 0.885 using their threshold model, i.e. much lower 599 Insurance demand: a historical long-run perspective than than the previous estimates.5 In contrast, their estimates of income elasticity of non-life insurance are more in line with the results in the literature, i.e. an elasticity larger than one. Although not imposing a non-linear functional form a priori, Lee and Chiu (2012) find for both life and non-life a non-linear relationship between (absolute) amount of premiums and GDP per capita. Income elasticity of life insurance increases for higher values of GDP per capita. A result at odds with the ‘S-Curve’ prediction. While Lee and Chiu (2012) took into account cross-sectional dependence and country heterogeneity, Millo (2016a) and Millo (2016b) address a number of additional issues previously neglected in the literature such as non-stationarity and common factors such as financial returns, global risk, price of reinsurance, as well as individual time-trends (e.g. urbanisation, agriculture, literacy, income inequality). In contrast to previous studies, Millo (2016a) and Millo (2016b) do not find a nonlinear income elasticity of non-life insurance across different levels of income. This finding is again at odds with the ‘S-Curve’ prediction on income elasticity. In addition, income elasticity of non-life insurance is not different from 1.6 In sum, Millo (2016a) and Millo (2016b) depart from the previous findings (or assumptions) in the literature that the income elasticity of insurance is related to GDP per capita in any systematic way. Rather, non-life premiums and income are co-integrated and estimated average elasticity (across countries) does not differ from 1. Millo concludes that income elasticities of non-life insurance do not follow the shape predicted by the ‘S-Curve’ (p. 620).7 However, the authors assume, although income elasticity could differ across countries, it is constant within each country over time. This seems justified given the relatively short time span of 40 years considered. Table 1 Variation in income and insurance demand studies Variation in income and insurance demand Use of data Time span Examples of studies Cross-section Plot S-curve Various years i.a. Carter and Dickinson (1992), Enz (2000), Millo (2016b) Mainly cross-section Estimate elasticity 1961–2010 i.a. Enz (2000), Zheng etal. (2008), (at most 40 years) Lee and Chiu (2012) Chang and Lee (2012), Millo (2016a), Millo (2016b) Times-series 1850–2020 Our Study 5 Lee and Chiu (2012) also report the income elasticity for life-insurance using a common correlated effects (CCE) estimator controlling for cross-sectional dependence, which are slightly lower: 0.409– 0.590. Non-life: 0.668–0.787 6 Millo (2016a) and Millo (2016b) estimate the elasticity based on individual country time series resulting in one elasticity estimate per country. Subsequently country estimates are grouped by income group (low, mid, high-income) and test whether the difference between coefficients is significant. 7 However, Millo (2016a) notes that individual lines of non-life insurance (such as property) might follow an ‘S-Curve’, but not an aggregated measure such as the entire non-life sector. 600 S.Kohl, M.Römer The findings in the literature are mixed, but what all previously cited studies have in common is the focus on the country level and the fairly late starting point of their sample in the 1970s or 1980s. An exception is Beck and Webb (2003), whose data begin in 1961 but end in 2001.8 The focus on the country level instead of using household data has a number of drawbacks. Using country level data assumes that households within one country are homogeneous compared to other countries. This abstracts from important characteristics such as stratification of insurance demand within a country. Nonetheless, we stick to country levels as a unit of analysis in order to observe countries in the long run for the first time, but we descend intheSection“Two tales of life insurance demand” on the product level in order to accommodate subnational stratification of demand. The late starting point has a number of implications. Most industrialized countries had already reached a certain level of income by 1970. As a consequence, existing studies can not observe a single country transitioning through most levels of income. Instead, existing studies rely on emerging countries’ transition through lower levels of income since 1970. If it were safe to assume that each country would move through different income levels in a similar way in terms of‘insurance penetration’, this would not be an issue.Put differently, the existing literature implicitly assumes that the insurance-income level nexus is independent of time-variant effects. However, this assumption is challenged by Pearson (1999) (p.232) who argues, for the case of Britain, that ‘insurance penetration’ was much lower for Britain in 1840 compared to India, Pakistan or the Philippines in the year 1970 at similar levels of income. This paper addresses this short-coming by expanding the time-period covered considerably by about 100 years. Changing the perspective from cross-sectional variation to a historical long run perspective allows to observe individual (by now industrialized) countries to transition through different levels of income. Data The newly collected data covers the longest currently available historyof life premiums development in 20 advanced economies for (on average) 120 years, starting as early as 1850.9 We focus on life insurance which covers biometric risks such as death, long life or invalidity. Our data contain collected (gross) life premiums paid each year to domestically operating insurers. We collected premiums for the sums of three types of life policies: term, cash-value and annuities.10 The data allow 9 The data on aggregated life premiums can potentially even be extended further back in time if firmlevel data are collected and aggregated. For our country-level data sources, see the Appendix. 10 Browne and Kim (1993) (p.620) point out that premiums are not necessarily a good measure for cross-country comparisons in insurance coverage as premiums vary between countries due to different types of life policies sold as well as differences in costs, regulation and competition. Since our focus lies primarily on within country variation, we use premiums as measure of insurance consumption. However, 8 An exception is Pearson etal. (2023) who compare insurance development during the 19th and 20th century in China, Middle East and sub-Sahara Africa over time. However, they do not estimate an income elasticity of insurance. 601 Insurance demand: a historical long-run perspective to observe each country to transition through different levels of income. The data hence span most levels of income within a country not just across different countries. Our earliest observations start in 1850. The data collected are an unbalanced panel. Earliest observations for each country are forAustralia (1850), Austria (1875), Belgium (1930), Canada (1870), Denmark (1892), Finland (1890), France (1869), Germany (1855), Ireland (1923), Italy (1861), Japan (1881), Netherlands (1884), Norway (1892), New Zealand (1870), Portugal (1918), Spain (1912), Sweden (1855), Switzerland (1887), the United Kingdom (1870) and the United States of America (1854). In many countries private domestic or foreign life insurance companies were present before these dates.11 To compute ‘insurance penetration’ we divide nominal premiums by nominal GDP of the same currency, drawing on Jordà etal. (2017) for 18 countries and adding Austria and New Zealand.12 As an alternative to ‘insurance penetration’, we also compute ‘insurance density’. For that purpose, life insurance premiums are deflated by the CPI for each country using Jordà etal. (2017) for 18 countries and the New Zealand Long Term Data Series of the statistical office as well as Hubmann etal. (2020) for Austria. Population data for computing ‘insurance density’ are from the Maddison Project (Update 2024, see Bolt and van Zanden 2024). Our time span covered is long enough to observe the complete transition of each country through several levels of income. According to the Maddison Project, in the year 1855 the United States had a GDP per capita of $ 4200 (2011 international $). Hence, the United States were back then almost a middle income country by today’s standards. In contrast, in 1855 Germany had a GDP per capita of $ 2300 and Sweden a GDP per capita of $ 1800, for instance.13 Hence, our sample allows many countries to transition through most income levels. Figure1 contrasts our newly collected data with the data used in the existing literature. It shows the relationship of ‘insurance penetration’ and GDP per capita (PPP) since 1850 and afterwards. The observations are coloured differently depending on which time period they stem from. Our earliest observations from the years between 1850 and 1910 are coloured black, observations between 1910 and 1940 are coloured red, while observations from the time period between 1940 and 1970 are blue. Finally, the most recent observations between 1970 and 2020 are green. The vertical line demarcates the year 1970 which 11 First private domestic (foreign) life insurance companies in Australia 1836, Austria 1831, Belgium 1819, Canada 1847 (foreign:1833), Switzerland 1857, Germany 1776, Denmark 1842, Spain 1856, Finland 1874 (foreign: 1834), France 1787, United Kingdom 1721, Ireland 1773, Italy 1821, Japan 1881, Netherlands 1807, Norway 1844, New Zealand 1869, Portugal 1819, Sweden 1855 (foreign: 1831) and United States 1759. 12 For Austria, we combine the Maddison Project data with a reflated series of Schulze (1997) and for New Zealand, we use the New Zealand Long Term Data Series of the statistical office combined with current Worldbank data. 13 The long time span considered raises the question of the role of PPP as it raises GDP per capita of countries relying on non-traded goods to a greater extent. The data on GDP per capita used here are from Bolt and van Zanden (2024). we will discuss within country variation in types of life policies sold. Seethe "Two tales of life insurance demand" section. Footnote 10 (Continued) 602 S.Kohl, M.Römer is usually the starting point for any (unbalanced) data set used in the literature.14 Put differently, any data left of the vertical line have not been used previously to estimate the income elasticity of life insurance. The green data points in Figure1 represent the data for high-income countries currently used in the literature to estimate the income elasticity of insurance demand. The newly collected data show for the first time how each country arrived at the currently observed ‘insurance penetration’. Cross-sectional evidence of a particular year does not reveal anything about the evolution of ‘insurance penetration’ for different levels of income for each country.15 Different countries potentially arrived in a similar spot via differing trajectories (not necessarily via an ‘S-Curve’) and the newly collected data show that the past trajectories do not follow the predictions of the ‘S-Curve’. The latter would predict a single growth episodes of life insurance premiums as incomes rises. Many, but not all, countries experienced a growth in life premiums at higher levels of income. This is in line with previous findings in the literature (e.g. Lee and Chiu 2012 for the case of life insurance). However, a century of data prior to 1970 shows that the same industrialized countries had already experienced an increase in ‘insurance penetration’ at lower levels of income (see again Figure1). We will discuss the role of changing types of life insurance policies in these two growth episodes inthe "Two tales of life insurance demand" section. First, however, we test the related prediction by the ‘S-Curve’ of a single ‘hump’ in income elasticity of life insurance demand. While the descriptive evidence in Figure1 is suggestive, the estimation of income elasticity requires a model. This is what we turn to next. Methods An estimation of the relationship between income and life insurance consumption requires an underlying model. The model choice is subject to debate. The descriptive evidence shown in Figure1 suggests a non-linear relationship of ‘insurance penetration’ and GDP per capita. The long time-span considered does not justify the assumption that the income elasticity of life insurance is necessarily constant within a country over more than a century. However, imposing a functional form upfront such as in Enz (2000) or Zheng etal. (2008) to estimate the elasticity is not justified either. Hence, the estimation of income elasticity of insurance has to allow for a non-linear relationship, but we will not impose non-linearity a priori. Lee and Chiu (2012) use a model that allows for a linear, hyberbolic or logistical functional form. We will allow for a possibly more complex relationship by using a General 14 See e.g. Enz (2000) and Millo (2016a). Their (unbalanced) panel of countries starts in 1970 taken from the Sigma database by Swiss Re. The panel size increases with time. There are 35 countries in 1970, 56 countries in 1980, 68 countries in 1990 and 93 countries in 2000. 15 The estimates of income elasticity of insurance in the literature do not rely on cross-sectional data only, but use cross-sectional time series data. However, the variation in income is largely cross-sectional. 609 Insurance demand: a historical long-run perspective density’ (or ‘penetration’) was largely driven by insuring the risk of mortality, while the second half of the 20th century saw a shift towards savings and living benefits (see Figure1 for theinitial growth period between 1870 and 1910.). Similar to the German case, in Switzerland initially the bulk of individual life insurance was also insuring mortality risks.26 Figure5 shows that at lower levels of income - similar to Germany - insurance products insuring mortality dominate, while at higher levels of income endowment products offering both death and living benefitsprevailed.27 The growth in sum assured in each case resembles the two-fold surge in premiums as percentage of GDP shown earlier (see Figure1). What sets the Swiss experience apart is the rise of group insurance addressing mortality after World War II. Such products are often cheaper than individual insurance products. Similar to Germany, the two episodes of growth in life insurance demand were driven by the demand for different products. In contrast to Germany, the growth oflife insurance premiums at higher levels of income is more pronounced. In the United States (1870–2000) the initial surge in insurance demand in the 19th century is driven by whole life policies, which offer a death benefit while accumulating a cash value at the same time(see Figure6).28 Endowment insurance plays a much smaller role in terms of amount insurance in force. In addition, the late 19th century saw the introduction of industrial life insurance. Initially offered in the United Kingdom in the 1850s, it subsequently spread to both other Anglophone and Continental European countries. Industrial (or ‘small’) life insurances offer a smaller sum assured than all other life insurances, used for burial expenses, dowries, etc. (see Eriksson 2015). However, the amount of insurance in force remained comparatively low and ceased to be of relevance in the mid 20th century.29 Starting in 1911, group insurance consists largely of term insurance and increased in the 1950 as industrial insurance (mostly whole life plans) continuously declined. The late 20th century saw a rise in products focusing on savingsproducts offering saving such asuniversal life, variable life insurance or universal-variable life. Similar to Switzerland, group insurance in the US saw a large rise in amount of insurance in force. The increase is largely due to group term insurance (see Figure6). In sum, the decomposition by type of life insurance policy shows that the type of policy varies tremendously across time within countries. While insuring mortality risks matters initially and not endowment products, policies offering a saving (or investment) function gain in importance at higher levels of income. This finding raises doubts aboutwhy an aggregate measure such as life insurance premiums should follow a single ‘S-Curve’. Cross-sectionally an S-Curve is unlikely as the type of life-insurance policy in demand differs by income level, i.e. the growth in life 26 Sources: Bericht des Eidgenössischen Versicherungsamtes (various issues). In particular, TableA18 (1947), Table1.2 (1975), Table2.1.1.3 (1990), Table AL16 C (2007). All data: (Direktes) Schweizergeschaeft. 27 The data for insurance products offering death benefits include small life insurances (’industrials’). 28 Data for the years 1870 to 1872 are from Hoffman (1911). 1873–1925 from the Spectator Life Insurance Yearbook (various issues). 1946–2000 Life Insurance Fact book (various issues). Private pension plans not administered by life insurance companies are not included. 29 The data used for Switzerland do not separately show the amount (or number) of industrial policies in force 610 S.Kohl, M.Römer premiums at higher levels of income already shown in Enz (2000) is at odds with the ‘S-Curve’ as new types of life insurance dominate at such levels of income. For the same reason, a single ‘S-Curve’ is unlikely in the longitudinal within-country perspective. The emergence of new life insurance products leads to multiple growth accelerations in life insurance premiums. Hence, the ‘S-Curve’ abstracts from product innovation over time and income levels. Our decomposition focused on broad categories offering mortality risks vs. products with a saving (or investment function). A more fine-grained analysis could focus on more specific product features 0% 25% 50% 75% 100% 1900 1950 2000 Year % of Total Insurance in Force by Policy Type (%) Type of Life Policy Endowment Group Industrial Insurance payable at deathPrivate Pension Insurance Germany − Life Insurance Products (1860 − 1995) Fig. 4 Germany-life insurance products 0% 25% 50% 75% 100% 1890 1920 1950 1980 2010 Year % of Total Insurance in Force by Policy Type Type of Life Policy Endowment (both living and death benefits) Endowment (living benefits) Endowment (payable at death) Group Private Pension Insurance Term Swiss − Life Insurance Products (1870 − 2000) Fig. 5 Swiss-life insurance policies 611 Insurance demand: a historical long-run perspective such as interest rate guarantees, which could lead to higher demand for particular life insurance policies, for instance (see Swiss Re 2018a). Overall, we argue that the absence ofa single ‘S-Curve’ is due to the changing types of life insurance policies in demand across income levels. A single ‘S-Curve’ might possibly be observed for a particular type of life insurance policy (e.g. term), but not in aggregate as the composition of policies in demand shifts as income varies. Each type of life insurance policy might experience its very own ‘S-Curve’. This has implications for emerging insurance markets. Policy implications The ‘S-Curve’ would predict that insurance demand is a function of income only. At a certain (unspecified) level of income, insurance demand picks up, before it levels off. Our long run data suggest that there is no such single surge in life insurance demand, but possibly multiple periods of larger-than-income growth in life premiums. This has a number of policy implications. If life insurance demand is not just a function of income growth, policy can potentially address the insurance gap. This is an opportunity for policy. At the same time, as already pointed out by Giné etal. (2019), this implies that income growth alone will not close an insurance gap.30 Our results show that the demand for life insurance differs by type of life insurance depending on the income level. At lower levels of income life insurance products addressing mortality risks, as observed in Germany, Switzerland and the United 0% 25% 50% 75% 100% 1900 1950 2000 Year % of Total Insurance in Force by Policy Type Type of Life Policy Credit Endowment Group Industrial Other Term Universal Variable Whole Life USA − Life Insurance Products (1870 − 2000) Fig. 6 USA-life insurance policies 30 Giné etal. (2019) show that other factors such as level of governance and accountability do matter as well for a thriving insurance market. 612 S.Kohl, M.Römer States, are in demand. This means that thedemand for life insurance could possibly very well exceed the demand predicted by an ‘S-Curve’ if suitableand affordable products are available. Historical experience shows that theinsurance market goes through several episodesof growth driven by different insurance products, i.e. catch-up processes - at least in terms of diffusion, if not in terms ofvolume of life premiums-might occur earlier as insuring mortality precedes insuring longevity. At higher levels of income life insurance products offering a savings function become more important. Providing tax relief for premiums paid can be an important incentive. However, this is just one tax incentive. Others include the tax treatment of dividends, cash values, annuities and death proceeds (see OECD 1996). Overall, the absence of an ‘S-Curve’ is both a curse and a blessing. While income growth will not necessarily close the insurance gap, policy and product innovation has potentially a larger role to play to close an insurance gap. Conclusion How does the demand for lifeinsurance vary with income? Estimating the demand for lifeinsurance requires observations across differentincome levels. Existing evidence relies on cross-country differences in income. Newly collected historical - long run data on life insurancepremiums offer the possibility to use incomedifferences within countries over time and trace the path by whichcountries arrived attheir current amount of ‘life insurance penetration’ (or ‘density’). Initially, the demand for insurance was assumed to be non-linear (‘S-Curve’). The demand forinsurance increases with income, but aftera certain income levelit starts to increase more rapidly, before leveling off at higher incomes. The underlying assumption is that the relationship between insurance demand and GDP per capita is time-invariant given income. Subsequent studies havemade less sweeping assumptions andhavefocused less on finding particular functional forms, but more ontesting whether the income elasticity of insurance is indeed different from 1 (i.e. any non-linearity present). Almost all of the existing studies have in common that the data used start no earlier than in 1970. This has several implications. Most industrialized countries had already reached a certain level of income by the 1970. In turn, existing studies can not follow a single country transitioning through all income levels. Given our longrun data, our descriptive and estimation approach exploits time variability rather thancross-country variability in income and ‘insurance penetration’. Our analysis contributes to the literature in two ways. First, we extend the time span by at least 100 years (1850-2020) for 20 countries. Second, our estimates show that the ‘S-Curve’ is not supported by the data. Life premiums per capita or aspercentage of GDP do not level off at higher incomelevels, but haveactually accelerated twice in the history of industrialized countries for different reasons. Our longterm historical perspective has further implications forthe futureof life insurance demand in emerging markets. The type of life-insurance policies in demand varies considerably across income levels within-countries. This suggests that countries may experienceseveral episodes of growth in life insurance demand,as type of life insurance policies in demand differ by income level. Thus, the catching-up process 613 Insurance demand: a historical long-run perspective of emergingmarkets may be steeper than previously thought. A number of questions remain for future research. Our study does not fully explain the differents paths and volatility of the elasticity across countries. Therefore, future research should consider more micro-level evidence such as tax treatment and the regulatory framework in the long run. Appendix Insurance data sources In the following, we report chronologically for every country which sources we used to collect the total life premium numbers. Our base definition is to include all life insurance gross premiums collected by (1) all type of entities (stock companies, public or mutual insurance), (2) the complete domestic market (including foreign companies’ firm in the domestic market, but excluding exports of domestic companies) and (3) including different product lines (ordinary, industrial, other). While a number of countries diverge from this base definition, we try to maintain an overtime consistency, as the cross-sectional dimension is less important to our argument. We draw on sources which themselves report statistics from supervision authorities or business associations. The sources are mostly country-specific before 1980 and, if necessary, we draw on the Swiss Re Sigma database for the more recent time period up to 2020. Australia: Gray, A. C. (1977): Life Insurance in Australia. McCarron Bird, Melbourne; Statistical Yearbook of Australia (various editions); SwissRe. 2021. Sigma Database. All Rights Reserved. Note: New Zealand life insurance business excluded in data before 1901, interpolated between 1902–1905. Austria: Hollmayer, Angelika. 2000. "Makrodaten der Österreichischen Assekuranz, 1875–2000." In An der Schwelle zum 3. Jahrtausend, edited by Wolfgang Rohrbach, 1377-. Wien: Holzhausen. SwissRe. 2021. Sigma Database. All Rights Reserved. Note: Gaps in hyperinflation and war-time years; Austria-Hungary prior to 1919; net premiums. Belgium: Rapport sur l’exécution de la Loi du 25 juin 1930 relative au contrôle des entreprises d’assurances sur la vie.; Annuaire statistique de la Belgique Office central de statistique (various years); Assuralia-Principaux résultats de l’assurance belge (various years). SwissRe. 2021. Sigma Database. All Rights Reserved. Canada: Urquhart, M. C. (1965): Canada Historical Statistics. Cambridge University Press; Statistical Yearbooks of Canada (various editions); Canadian Life and Health Insurance Facts published by Canadian Life and Health Insurance Association Inc. (various editions). Note: Net premiums throughout; fraternal societies are not included. Denmark: Finanstilsynet (Hg.). Forsikringsselskaber. Statistisk materiale; Finanstilsynet (Hg.). Livsforsikringsselskabernes regnskaber (various years). Statistical Yearbook (various years), Copenhagen, Danmarks Statistik. Note: Gap year in 1982. 614 S.Kohl, M.Römer Finland: "The Insurance Companies" (various years), Helsinki, Official Statistics of Finland; Statistical Yearbook of Finland (various years), Helsinki, Statistical Office. Note: Missing years 1891–1892. France: Annuaire statistique de la France (various years), Paris, Institut national de la statistique et des études économiques. SwissRe. 2020. "Sigma Database. All Rights Reserved. Note: Coverage gaps prior to 1907 and in post-WWII. Germany: Borscheid, Peter, and Anette Drees. 1988. Versicherungsstatistik Deutschlands, 1750–1985. Quellen und Forschungen zur historischen Statistik von Deutschland. St. Katharinen: Scripta Mercaturae Verlag; GdV. various. Gesamtverband der deutschen Versicherungswirtschaft. Statistisches Taschenbuch der Versicherungswirtschaft. Karlsruhe: Verl. Versicherungswirtschaft. Note: Gaps in hyperinflation and war years; interwar excludes public insurers. Ireland: Statistical Abstract of Ireland (various years), Central Statistical Office. SwissRe. 2021. "Sigma Database. All Rights Reserved." Italy: Del Chiaro, Adolfo. 1968. Alcuni aspetti delle assicurazioni private in Italia nel periodo 1861–1961(Private Insurances in Italy from 1861 to 1961). Roma: Istituto di statistica economica. Istat (2011). L’Italia in 150 anni. Sommario di statistiche storiche 1861–2010. Roma. SwissRe. 2021. Sigma Database. All Rights Reserved. Note: Data include the National Institute of Insurance; break in the Istat source in the 1930s and 1945. Japan: Historical Statistics of Japan, Japan Historical Association; Life Insurance Factbook (various years), Life Insurance Association of Japan; The Japan Year Book (various years), Japan Statistical Yearbook, Statistics Bureau (various years). Note: Excluding postal insurance. Netherlands: Vijfennegentig jaren statistiek in tijdreeksen, 1899–1994, Centraal Bureau voor de Statistiek, Amsterdam. Jaarcijfers voor Nederland, Centraal Bureau voor de Statistiek (various years). Sigma Database. All Rights Reserved. Note: Missing years 1933–1934. Norway: Statistical Yearbook (various years), Oslo, Central Bureau of Statistics. New Zealand: The New Zealand Official Yearbook (various years), Department of Statistics, Wellington. SwissRe. 2021. Sigma Database. All Rights Reserved. Note: Missing year 1979, pre-1898 numbers estimated with numbers of the N.Z. Government Life Insurance Office. Portugal: Anuário estatístico (various years), Lisboa, Instituto nacional de estatística; OECD Insurance Statistics Database. SwissRe. 2021. Sigma Database. All Rights Reserved. Note: Certain gaps in the post-WWII period. Spain: Casares GT etal. 2014: Historia del seguro en España. Fundación Mapfre; 2014. López, C. B., A. Carreras and X. Tafunell (2005). Estadísticas históricas de España: siglos XIX–XX. Bilbao Fundacion BBVA. European Insurance Industry Database, March 2022. Note: Civil War years and most pre-1912 years missing; jump in 1988 due to introduction of unit-linked products. Sweden: Bergander (1967). Försäkringsväsendet i Sverige 1814–1914. Stockholm, Eget förlag. Historical Statistics of Sweden, Statistical Survey, 1960, Stockholm. Statistisk Årsbok, Statistiska Centralbyrån, Stockholm (various years). 615 Insurance demand: a historical long-run perspective Switzerland: Bericht des Eidgenössischen Versicherungsamtes über die privaten Versicherungs-Unternehmungen in der Schweiz, Bern, Commissionsverlag Schmid, Francke & Comp.; Die privaten Versicherungseinrichtungen in der Schweiz, Schweiz Bundesamt für Privatversicherungen (various years), FINMA (various years); Historische Statistik der Schweiz, Schweizerische Gesellschaft für Wirtschaftsund Sozialgeschichte. United Kingdom: Annual Abstract of Statistics (various years), London, Central Statistical Office; Sheppard (1971); SwissRe. 2021. Sigma Database. All Rights Reserved. Note: Excludes reinsurance and the UK business of foreign firms before 1980. Missing years 1913, 1978–1979. United States: Census, United States. Bureau of the. 1975. Historical Statistics of the United States, Colonial Times to 1970: US Department of Commerce, Bureau of the Census; Factbook. various. Life Insurance Fact Book. Washington: American Council of Life Insurance, SwissRe. 2021. Sigma Database. All Rights Reserved. Note: Net premiums throughout; fraternal societies are not included. Country‑by‑country income elasticity Figure2 plots the estimated income elasticity of life insurance for each country in one graph. Figure7 shows the estimated income elasticity of life insurance for each country individually. The elasticity plots for Spain and Italy show quite volatile elasticity estimates. For the case of Italy, frequent changes in sources are a possible reason. In the case of Spain, the introduction of products in 1988 and 2000 explain a surge in demand (see Casares GT etal. 2014: Historia del seguro en España. Fundación Mapfre; 2014. López, C. B. p. 495). In the case of ‘insurance penetration’ an fluctuations in GDP and potential differences in overall inflation and inflation in life premiumsare additional factors. We also estimate for each country an estimate of income elasticity of life insurance based on ’insurance density’, that is, based on real (gross) life premiums per capita (see Figure7 and Table2). 616 S.Kohl, M.Römer Funding Open Access funding enabled and organized by Projekt DEAL. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long NOR NZL PRTSWE USA GBR IRLITA JPN NLD DEU DNK ESP FI NF RA AUSAUT BEL CA NC HE 8910 11 8910 8910 8910 91 01 1 8.59.0 9.510.010.5 8910 11 8910 8910 910 8910 8910 8910 8910 8910 8910 11 8910 8910 8910 8910 11 −5 0 5 10 −5 0 5 10 −5 0 5 10 −5 0 5 10 −5 0 5 10 −5 0 5 10 −5 0 5 10 −5 0 5 10 −5 0 5 10 −5 0 5 10 −5 0 5 10 −5 0 5 10 −5 0 5 10 −5 0 5 10 −5 0 5 10 −5 0 5 10 −5 0 5 10 −5 0 5 10 −5 0 5 10 −5 0 5 10 GDP per capita (PPP, log) Elasticity Legend Elasticity based on insurance density Elasticity based on insurance penetration Income Elasticity Life (1850−2020) Fig. 7 Income elasticity of life insurance Table 2 Overview of main variables and sources used Variables Description Sources & notes Total life premia ‘Life insurance penetration’ Own collection 1850-2020 see Appendix (Total gross premiums of domestic life insurance activity per GDP in % ) GDP (Nominal) Nominal GDP Jordà etal. (2017) plus additional sources (cf. footnote) in local currency CPI Consumer price index Jordà etal. (2017) plus additional sources (cf. footnote) 1990 = 100 Interest Long term bond interests Jordà etal. (2017), Jobst (2022) and additional sources 617 Insurance demand: a historical long-run perspective as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/ licenses/by/4.0/. References Alborn, Timothy. 2009. 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