The Relationship between Property-Liability Insurance Premiums and Income: An International Analysis

Annual cross-section data for 12 industrialized countries observed over 1970-1981 are pooled in an econometric investigation of the relationship between income and spending on property-liability insurance. A theoretical framework is specified for the supply and demand for insurance in which premiums depend upon income and interest rates. The econometric results are used to measure the short and long run marginal propensities to insure across the 12 countries. The paper concludes with a cross-section analysis of 45 countries in 1981 in which the relationship between economic development (as measured by per capita GNP) and property-liability insurance premiums is investigated. Introduction The literature is well endowed with empirical studies of both the supply and demand for insurance. Most studies have focused on life insurance (e.g., Cummings [7]). Empirical studies of property-liability insurance, however, are less extensive [10]. Typically these studies have been conducted in isolation of each other, having been based on time series data for a given country. The central objective of this paper is two-fold. First, the research uses an international data base, which may not be widely known to the research community and its usefulness for research purposes is investigated. Second, cross-cultural insurance purchase behavior is explored. For example, do relationships for the United States apply to Scandinavia, Australia or Japan? Also, what can be inferred about insurance spending from countries at different stages of economic development? An international data base provides an opportunity for investigating these and other issues. Michael Beenstock is Lady Davis Professor of Economics at Hebrew University of Jerusalem. Gerry Dickinson is Senior Lecturer in Insurance at City University Business School, London. Sajay Khajuria is a Research Assistant at City University Business School, London. This content downloaded from 207.46. 13.113 on Thu, 06 Oct 2016 04:04:24 UTC All use subject to http://about.jstor. org/terms 260 The Journal of Risk and Insurance Source of data The insurance data base used in the study is that constructed by the Swiss Reinsurance Company and summarized annually in the April issue of its publication, Sigma. The data base collates information on annual premiums for a range of countries. The series goes back to the 1960s but the number of countries included increased significantly during the 1970s. Premiums are disaggregated into two broad classes: life and property-liability insurance. The primary data used by the Swiss Reinsurance Company is compiled by governments or insurance associations in individual countries. Recognizing the different valuation bases adopted in different countries, the Swiss Reinsurance Company adjusts the primary data to attain consistency. In particular, an attempt is made to produce premium figures that are gross of reinsurance and gross of commissions. Even though such a valuation basis more closely reflects the demand for insurance rather than the supply, the authors feel that the data are consistent enough to justify the international comparative analysis adopted in this paper. Although the data base affords an opportunity to effect international crosssection analysis, it suffers from the fact that the annual time series is rather short for purposes of econometric investigation. It was therefore necessary to adopt a methodology of pooling cross-section and time series data. While a systematic statistical analysis of this cross-section data has to the authors' knowledge not been carried out, Carter and Dickinson [5] identified the correlation between property-liability premiums and GNP across a wide cross section of the countries, using this same data base. In this paper attention is limited to property-liability insurance. A parallel study deploying the life insurance data has been carried out by Beenstock, Dickinson and Khajuria [3]. A further study on the determinants of ocean marine premiums has also been carried out by Beenstock and Khajuria [2], based on unpublished data supplied by the Swiss Reinsurance Company. Some Theoretical Considerations In this section the empirical analysis is introduced by developing a simple model of how income and property-liability insurance premiums might be linked. Since any observed premiums will reflect both supply and demand considerations, it is essential that the premium model reflect both of these considerations. The following terms will be used in developing the model. W = Level of wealth G = Value of property at risk Q = Sum insured P = Relative price of insurance (premium per $) H = Average probability of loss r = Real rate of interest u = Utility Y = Income per capita D = Country dummy variable This content downloaded from 207.46. 13.113 on Thu, 06 Oct 2016 04:04:24 UTC All use subject to http://about.jstor. org/terms Relationship Between Property-Liability Insurance Premiums and Income 261 V = Real premiums per capita (V = PQ) MPI = Marginal propensity to insure SRMPI = Short-run marginal propensity to insure LRMPI = Long-run marginal propensity to insure Income and the Demand for Insurance In the simple model of the relationship between income and the demand for property-liability insurance outlined below, the following is assumed. An individual possesses insurable assets with a value of G and his or her total wealth is equal to W. For simplicity, it is also assumed that if a loss occurs it produces a total loss of these insurable assets. A two-period framework is adopted. At the end of the period total wealth will be reduced by G if the loss occurs and no insurance has been purchased. Conversely, if insurance has been purchased, the initial wealth is reduced by the premium paid, and if an insured loss takes place end-period wealth is reduced by G Q where Q is the sum insured (or its present value if not paid instantaneously). There are therefore two possible states for end-period wealth. If an accident occurs, wealth will be equal to W, = (W-QP)(1+r)-G+Q where P denotes the relative price of insurance and r is the return on wealth. The model assumes that Q c G. If an accident does not occur wealth will be equal to W2 = (W QP)(1 + r) The expected utility (u) of the individual is equal to E(u) = Hlu(W)+(1-H)u(W2) where HI is the probability of a loss occuring. The authors assume that the individual is risk averse and illustrate their argument with a utility function of the following type: