Output Price Indexes for the U.S. Life Insurance Industry
Reece, William S., Journal of Risk and Insurance
For many years analysts have been interested in measuring the cost to consumers of life insurance and in comparing insurance prices across companies.(1) This article focuses on price measurement for the life insurance industry from a different point of view - the price of insurance from the standpoint of the insurance firm. In recent years there have been important advances in the application of index number theory to the financial firm. Barnett (1980) showed how meaningful economic index numbers of monetary aggregates can be constructed using the user cost of each monetary assets as the price of the asset. Hancock (1985) used this user cost concept in developing and testing a theory of the financial firm. Fixler (1988) used modern index number theory and the theory of the financial firm to derive output price indexes for commercial banks. Fixler and Zieschang (1991) used these ideas to measure financial service output for the national income accounts. Weiss (1986) used index number theory to measure total factor productivity for life insurance firms. This article shows how index number theory based on the economic theory of the financial firm can be used to construct meaningful index numbers of output prices for the life insurance industry. It then constructs an index of output prices for the U.S. life insurance industry for 1976 through 1989. Finally, the price index is used to deflate the nominal value of insurance output to get an index of real life insurance output.
The Measurement Issue
The U.S. life insurance industry is large and diverse, with over 2,000 companies providing a wide variety of services. The industry provides traditional whole life insurance, which includes a savings component through the build up of cash value, and term insurance which does not involve saving. In recent years new kinds of policies, such as universal life and variable life, have grown in importance. The industry also provides loans to policyowners whose policies have cash values. Life insurers also sell annuities, health insurance and financial management services. The remainder of the article deals with life insurance products only.
This diversity of activities and mingling of insurance and savings functions calls for a careful treatment of the important issue of constructing output price indexes for the industry. The output of the life insurance industry is the set of real financial services provided by the policies it sells. Smith (1982) argues that a life insurance policy can be viewed as an options package, providing the policyowner with options such as policy loans and guaranteed renewal at fixed premium rates in addition to death benefits. The output of the industry is the entire set of these real financial services or contingent claims on real goods and services. The illustrative application below is based on the assumption that these real financial services are proportional to the level of real insurance in force measured in 1976 dollars. The application constructs an index of the nominal price of this real output from the standpoint of the life insurer.
Index Numbers of Life Insurance Output Prices
Indexes of Output Prices
The modern theory of output price indexes conceptualizes output price differences between the reference and comparison periods as the ratio of the firm's revenue function with the comparison period's output prices to the revenue function with the reference period's output prices. The firm's revenue function is
where p is the Nx1 vector of prices of outputs (to be defined below), x is the Nx1 vector of quantities of outputs, y is the Mx1 vector of inputs, and T is the production possibility or feasible set. In defining the revenue function the levels of inputs are held constant. This revenue maximization process yields the same optimal output results as profit maximization because input levels are fixed. …