as well as the level of education and the age dependency ratio, all of which are likely to differ across countries. Indeed, Beenstock, Dickinson and Khajuria (1986) develop a theoretical model for life insurance supply and demand, which is tested with 1970-1981 insurance premium data of 10 industrialized countries from Swiss Re’s Sigma publication. They argue that life insurance demand varies with income because higher income allows to buy more of it, but also because higher income increases the insurable interest, that is the financial loss of the dependents of a deceased income earner. Estimating the parameters of their mathematical model on the data of the 10 countries, they find income elasticity of insurance demand to be positive for all countries but to vary considerably from country to country.

In a longer term perspective, and in line with theorical insights from Kuznets (1955) and Greenwood and Jovanovic (1990), Enz (2000) postulates that “Researchers usually assume a constant income elasticity which, together with an income elasticity greater than one, implies that there are no limits to insurance penetration” (without naming or quoting any particular researcher), and argues that this assumption leads to unreasonable levels of insurance penetration if GDP grows constantly (even at moderate rates). This criticism motivates him to explain the relation between insurance premium and GPD with a logistic function that has additional parameters - minimum and maximum insurance penetration – resulting in variable income elasticity and an inflection point at which the increase in insurance penetration slows. He then introduces the term “S-curve” for this function. His theory proposes to explain non-life insurance as well as life insurance, and he estimates the parameters of the S-curve with 90 countries’ life and non-life premium data from the years 1970 to 1998 (sourced again from Swiss Re’s Sigma publication). As a result, he can quantify the inflection points quoted above and points of maximum income elasticity for life (15,000 USD) and non-life (10,000 USD) insurance and estimate a maximum life insurance penetration parameter of 3.8% (a level surpassed by 16 countries in 2017, including Namibia and Thailand). Enz (2000) does observe that some countries deviate significantly from the international average and points out that “other factors in addition to income must account for the demand of life insurance”, providing some explanations that include changes in age structure, challenges of social security systems, religious considerations and changes in tax treatment (as well as some interesting explanations for non-life). In closing, the paper acknowledges the limitations of the S-curve as a one-factor model that neglects drivers other than income but recommends it for long term forecasting (as done by some large reinsurance companies).

Going beyond GDP per capita, Beck and Webb (2003) look at a considerable number of demographic, economic and institutional variables to explain life insurance consumption in addition to countries’ different per capita income levels. They confirm some earlier researchers’ findings, e.g. Enz’s statement about the role of religious beliefs and Outreville’s findings regarding financial sector development. Their theoretical model is found in the above (and other) publications, but they use much larger data sets to validate it, looking at 68 economies over the period 1961–2000, and are thus able to better control for various geographic and time effects. Their interest in insurance’s role in the financial sector especially as a source of capital market investment guide a more differentiated analysis that yields other results beyond explaining the growth of insurance penetration. They argue that beyond Beenstock’s explanation for the importance of income to life insurance premium, additional reasons are that people can put increasing shares of their increasing income into retirement and investment, and that economies of scale make insurance more cost-efficient and attractive as the sums insured grow. These authors are the first to link institutional determinants such as the rule of law and absence of revolutions to life insurance development, motivations including that excessive fraud dampens the supply of insurance and the inability to enforce consumer rights against insurers dampens the demand for it.

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