Overview of efficiency measurement in the insurance industry

The following overview of 95 papers (63 published articles, 32 working papers) builds upon and significantly extends two earlier surveys of efficiency measurement literature in the financial services industry: One by Berger and Humphrey, which focuses on banks.

The second one by Cummins and Weiss focuses on the insurance industry and covers 21 studies that have been published until the year 1999.

Three studies (Weiss; Bernstein ) that are considered in Cummins and Weiss have been excluded from this overview since they are not efficient frontier based, but focus on productivity (these studies are included in an extended overview that we present in the Appendix).

Table 1 is arranged according to 10 different application areas (first column). Some of these application areas have been selected following Berger and Humphrey’s overview for the banking sector. However, we extended and refined their systematisation to account for the specifics of the insurance sector.

Although many studies make contributions to more than one topic, we tried to focus on the primary field of application. A more detailed table with information, such as input and output factors, types of efficiencies analysed, sample periods, lines of business covered, and main findings, is included in the Appendix.

Econometric approaches

The econometric approaches specify a production, cost, revenue, or profit function with a specific shape and make assumptions about the distributions of the inefficiency and error terms. There are three principal types of econometric frontier approaches.

Although they all specify an efficient frontier form usually translog, but also alternative forms such as generalised translog, Fourier flexible, or composite cost they differ in their distributional assumptions of the inefficiency and random components (see Cummins and Weiss ).

The stochastic frontier approach assumes a composed error model where inefficiencies follow an asymmetric distribution (e.g., half-normal, exponential, or gamma) and the random error term follows a symmetric distribution, usually normal.

The distribution-free approach (DFA) makes fewer specific assumptions, but requires several years of data. Efficiency of each company is assumed to be stable over time, and the random noise averages out to zero.

Finally, the thick frontier approach does not make any distributional assumptions for the random error and inefficiency terms, but assumes that inefficiencies differ between the highest and lowest quartile firms (see, e.g., Kumbhakar and Lovell).

The most commonly used econometric approach is stochastic frontier analysis (SFA), which was first proposed by Aigner et al. SFA is usually applied in two steps: In the first step, a production, cost, revenue, or profit function is estimated, determining the efficient frontier.

In the second step, for individual firms, deviations from the efficient frontier due to inefficiency and a random error are calculated (see Cummins and Weiss).

Mathematical programming approaches

Compared with the econometric approaches, the mathematical programming approaches put significantly less structure on the specification of the efficient frontier and do not decompose the inefficiency and error terms.

The most widespread mathematical programming approach is ‘‘DEA’’, which uses linear programming to measure the relationship of produced goods and services (outputs) to assigned resources (inputs). DEA determines the efficiency score as an optimisation result.

DEA models can be specified under the assumption of constant returns to scale (CRS) or variable returns to scale (VRS) and can be used to decompose cost efficiency into its single components—technical, pure technical, allocative, and scale efficiency.

Total Factor Productivity

The concept of total factor productivity is closely related to efficiency and often used in efficiency studies. Productivity is an index that relates the total amount of outputs produced to the total amount of inputs used in the production process (see Cummins and Weiss (p. 770)).

Total factor productivity growth is thus measured as the change in total outputs net of the change in total input usage. In contrast, the concept of efficiency measures inputs and outputs in relation to a benchmark, that is, the optimal inputoutput usage in an industry.

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