Academic journal article Journal of Risk and Insurance

Multivariate Analysis of Premium Dynamics in P&L Insurance

Academic journal article Journal of Risk and Insurance

Multivariate Analysis of Premium Dynamics in P&L Insurance

Article excerpt


This article studies the dynamic relationship between premiums and losses on the U.S. property-casualty insurance market, accounting for the external impacts of GDP and interest rate. Compared to the existing literature, the present work innovates in that the dynamic relationships between premiums, losses, GDP, and interest rate are studied in a cointegration framework, single-equation and vector approach, involving the long- and short-run dynamics. The results suggest a stable long-run equilibrium between premiums, losses, and general economy. On short term, the premiums adjust quickly and significantly to the long-term disequilibrium and have a strong autoregressive behavior. External factors contribute to explain the dynamics of premiums.


The present study aims to provide a multivariate time-series analysis of the dynamics of nonlife insurance premiums. Such an analysis allows to understand, at least partially, the long- and short-run determinants of the property-liability insurance premiums.

Most empirical and theoretical studies on this topic focus on the causes of underwriting cycles and are conducted on loss ratio, combined loss ratio, unit price, or underwriting profit ratio (and few studies on nominal premiums). Our article focuses on the dynamics of insurance real premiums. In a perfect market framework, premiums contain information about expected losses, claim settlement costs, discount rates, economic environment, and other information available at the time of pricing.

In the framework of a demand and supply premium model, Weiss (2007) points out that a number of economic factors may play a role in premium determination (e.g., demand, losses, interest rates). As the author suggests, the cointegration procedures can be used to analyze if premiums are indeed related to these factors. Cummins and Outreville (1987) postulate that premium is a function of a set of lagged variables, including past claim experience, interest rates, or inflation rates, but these relationships were not explicitly modeled in a multivariate framework. Since Cummins and Outreville, most empirical studies retain an autoregressive process of second order to study the cyclical behavior of insurance results. As suggested by Meier (2006), there are nevertheless theoretical and empirical reasons to extend this model, including exogenous variables. The regulation can also affect insurance pricing (Berry-Stolzle and Born, 2010).

The present article studies the dynamics of nonlife insurance premiums. The empirical analysis is conducted on U.S. property--liability insurance data. Variables involved in our analysis are real premiums, real losses, real GDP, and real interest rates. In an efficient market with rational expectations, the insurance premium is equal to the expected present value of losses, settlement costs, and underwriting expenses. The extrapolative ratemaking practice described in Venezian (1985) links current premiums with lagged losses. More precisely, Venezian (1985) considers that prices are determined mainly by the insurance industry, past losses being used as a basis for forecasting future losses. Therefore, past losses can contribute to explain current premiums. In this article, we use the annual time series for net premiums earned and net losses incurred available from Best's Aggregates and Average over the period 1951-2007.

In addition to real losses, macroeconomic variables are introduced in the model. These variables (possibly lagged) may help to explain the premium dynamics. The macroeconomic time series involved in this study is the annual gross domestic product (GDP) (1) and the mid-term interest rate. (2) It is well documented that booms or recessions of an economic (or business) cycle appear almost at the same time in many economic activities. Therefore, we expect the insurance business to follow the aggregate economic cycles, being affected, positively or negatively, by significant growth or by crises in the economy. …

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