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Analyzing Firm Performance in the Insurance Industry Using Frontier Efficiency and Productivity Methods

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Handbook of Insurance

Abstract

This chapter reviews the modern frontier efficiency and productivity methodologies that have been developed to analyze firm performance, emphasizing applications to the insurance industry. The focus is on the two most prominent methodologies—stochastic frontier analysis using econometrics and non-parametric frontier analysis using mathematical programming. The chapter considers the underlying theory of the methodologies as well as estimation techniques and the definition of inputs, outputs, and prices. Seventy-four insurance efficiency studies are identified from 1983 to 2011, and 37 chapters published in upper tier journals from 2000 to 2011 are reviewed in detail. Of the 74 total studies, 59.5% utilize data envelopment analysis as the primary methodology. There is growing consensus among researches on the definitions of inputs, outputs, and prices.

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Notes

  1. 1.

    In developing his efficiency concepts, Farrell drew upon earlier work by Debreu (1951). It took nearly 20 years following Farrell’s initial theoretical contribution for empiricists to develop methodologies to estimate efficiency. The most important contributions were the development of stochastic frontier analysis by Aigner et al. (1977), Battese and Corra (1977), and Meeusen and van den Broeck (1977) and the development of non-parametric mathematical programming frontiers by Charnes et al. (1978). Since that time, the growth in efficiency research has been explosive.

  2. 2.

    This definition applies to an input-oriented frontier. It is also possible to estimate output-oriented measures of efficiency by maximizing outputs produced conditional on inputs used. Most efficiency analyses in insurance and other financial industries are input oriented, and most of the discussion in this chapter assumes an input-orientation.

  3. 3.

    This discussion applies to standard cost, revenue, and profit efficiency analysis. Non-standard functions also are used for purposes such as studying revenue or profit scope economies (see Berger et al. 1997). Although frontier analysis is typically conducted under the assumption that the industry is competitive, efficiency also can be measured for non-competitive industries, public utilities, or government entities (Cooper et al. 2004).

  4. 4.

    In Fig. 28.1, lines are labeled using capital letters. Firm operating points are represented by dots ( •).

  5. 5.

    Single factor productivity indices are considered to be uninformative by economists because they take into account only one input, such as labor, and omit other important inputs, such as capital.

  6. 6.

    Profit frontiers pose a somewhat different problem than the other types of DEA frontiers (Färe et al. 1994c, pp. 212–217).

  7. 7.

    The Malmquist method is credited to Caves et al. (1982), for the theory, and to Färe et al. (1994a), for the empirical methodology. See also Färe et al. (1994b).

  8. 8.

    For more details, see R-D (1997), Simar and Wilson (1998), and Cummins and Rubio-Misas (2006).

  9. 9.

    Hicks neutrality means that the ratio of the marginal products of captial and labor for any ratio of capital and labor input is independent of time.

  10. 10.

    For simplicity, we use only one output. However, the Divisia index can be defined for multiple outputs.

  11. 11.

    The orthogonality is perfect only if the data are evenly distributed over the [0, 2π] interval, but in most applications to date, the Fourier terms lead to a significant improvement in the fit of the model.

  12. 12.

    The recommended number of parameters is N (2∕3)where Nis the number of observations. For example, Berger et al. (1997) had 4,720 observations and 492 parameters including translog and first, second, and third-order Fourier terms. For relatively large data sets such as theirs and the even larger data sets used in many banking studies, the number of parameters is not a serious problem because the number of parameters as a proportion of the total number of observations is declining in N.

  13. 13.

    For specificity, this discussion focuses on the translog, but a similar approach would apply for the other functional forms discussed above.

  14. 14.

    The choice of distributional assumptions can be avoided by using the distribution free approach, but it is not clear that this approach yields efficiency estimates that are as accurate as the fully specified SFA approach or DEA.

  15. 15.

    For example, if many insurance lines are lumped together in a broad category such as non-life insurance, firms concentrating on lines of insurance with relatively high operating expenses will appear inefficient, whereas they would likely be measured as more efficient if compared against other firms specializing in high expense lines.

  16. 16.

    Some recent chapters in the insurance literature have claimed to utilize the “intermediation approach” in defining outputs (e.g., Brocket et al. 2005). However, as discussed further below, their approach is actually not the intermediation approach but rather utilizes arbitrary and ad hoc sets of output variables.

  17. 17.

    Efforts to apply the user–cost method in banking found that the classifications of inputs and outputs were not robust to the choice of opportunity cost estimates nor were they robust over time (see Berger and Humphrey 1992).

  18. 18.

    Cummins (1990) generalizes the model to incorporate taxes.

  19. 19.

    In the NAIC life insurer annual statements, incurred benefits plus additions to reserves is line 20 in the Analysis of Operations by Lines of Business.

  20. 20.

    Insurers are required to allocate investment income by line in their regulatory annual reports, and we use the reported allocations in defining output prices. Premiums plus investment income appears as line 9 in the Analysis of Operations by Line of Business in the NAIC annual regulatory statement.

  21. 21.

    Using this approach assumes that insurers have equity portfolios with a beta coefficient of 1.0.

  22. 22.

    In fact, paying claims following adverse loss fluctuations from catastrophic events and unusual accumulations of non-catastrophe claims is an important function of insurance and should be counted as output. An insurer’s reputation for paying catastrophic claims will lead to higher prices and profits in normal periods, compensating investors for paying catastrophic losses.

  23. 23.

    Some earlier chapters utilized book value measures of the cost of capital, e.g., the average book return on equity (ROE) (net income divided by policyholders surplus) for the 3 or 5 years prior to the year of analysis. One problem with this approach is that it reduces the number of years for which efficiencies can be calculated by requiring at least 3 years prior to the start of the first year of efficiency analysis to compute average ROE. Another problem is that realized ROE can be negative, whereas the ex ante ROE must be positive. An alternative approach to ROE estimation is to estimate a regression equation with realized ROE as the dependent variable and variables such as leverage, business mix, and asset mix as independent variables. The cost of capital for a given firm is then estimated by inputting the firm’s values of the regressors into the estimated regression equation.

  24. 24.

    Using this approach implicitly assumes that insurers have equity portfolios with market betas of 1.0. This is reasonable given that insurers are conservative investors.

  25. 25.

    More specifically, the firms in the sample are first ranked by size decile based on book values of equity capital. Firms are then placed into the following four categories, following Ibbotson Associates (2011): large-cap = deciles 1 and 2 (the largest size deciles), mid-cap = deciles 3 through 5, small-cap = deciles 6 through 8, and micro-cap = deciles 9 and 10. The cost of capital is then calculated as: \(R_{it} = R_{f,t-1}\)+ Risk Premium \(_{t-1}+\) Size Premium i, t−1, where R i t = cost of capital for firm iin year t and Size Premium i, t−1 = the size premium for firm ibased on the capitalization category of the firm. Researchers also have estimated efficiencies omitting the size premium and assigning the same cost of capital to each firm in a given year. It is important to run sensitivity analysis to see if using the size premium produces results that yield different conclusions.

  26. 26.

    Some researchers have used inappropriate measures of the cost of equity capital. For example, Jeng et al. (2007) utilize the debt-to-equity ratio as the cost of capital. Even though the debt-to-equity ratio is likely to be correlated with the cost of capital, it is not a price variable. Using this variable is likely to distort the efficiency estimates and is difficult to rationalize given that much better proxies are readily available.

  27. 27.

    The sum of the non-equity expenditures, i.e., labor and materials, is measured so that it will equal total insurer operating costs as reported on the expense statement.

  28. 28.

    This is based on the argument that investors will not supply capital to an insurer unless they receive a market return equal to the amount they could receive by investing in an asset portfolio that replicates the insurer’s portfolio plus a risk premium for any additional costs associated with committing capital to the insurance business.

  29. 29.

    For books and working chapters, the classification was based on the authors’ evaluation of the studies themselves.

  30. 30.

    Unlike standard DEA, RAM is non-radial in the sense that it does not preserve the mix between inputs in movements toward the frontier. RAM was introduced by Cooper et al. (1999). For a general discussion of non-radial measures, see Fried et al. (2008).

  31. 31.

    In thick frontier analysis (TFA), a frontier is estimated for the lowest cost quartile of firms. This lowest cost quartile is considered a “thick frontier,” in which it may be reasonably assumed that the firms are of greater than average efficiency (Berger and Humphrey 1991). A cost function is also estimated for the highest average cost quartile, in which it may be reasonably assumed that the firms are of less than average efficiency. The differences between these two cost functions are separated into “market factors,” which are explained by differences in the available exogenous variables, and an “inefficiency residual,” which cannot be explained. The inefficiency residual is then decomposed among several types of inefficiencies. The exact maintained assumptions necessary to yield the thick frontier approach are that the error terms within the lowest and highest cost quartiles reflect only random measurement error and luck, while the differences between the lowest and highest cost quartiles reflect only inefficiencies and market factors. TFA analysis has gone out of fashion. It places heavy demands on the data and is difficult to use for small samples because half of the observations are not used.

  32. 32.

    Berger et al. (2000) develop an alternative to the traditional scope economy measures. They estimate separate functions for joint producers and specialists in order to allow for differences in technology between joint producing and specializing firms. For their data, scope estimates are significantly different using the alternative approach.

  33. 33.

    The appropriate SIC and NAICS categories for wages are discussed above in Sect. 28.4.2.

  34. 34.

    For property–liability insurance, the expense page is the Underwriting and Investment Exhibit: Part 3— Expenses; and for life insurers, it is Exhibit 2—General Expenses.

  35. 35.

    A few studies have utilized inappropriate measures of the cost of equity capital such as the debt-to- equity ratio (Jeng et al. 2007). Such mistakes are rare but inexcusable given the widespread availability of more appropriate cost of capital measures.

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Authors and Affiliations

  1. Temple University, 617 Alter Hall, 1801 Liacouris Walk, Philadelphia, PA, 19122, USA

    J. David Cummins

  2. Temple University, 624 Alter Hall, 1801 Liacouris Walk, Philadelphia, PA, 19122, USA

    Mary A. Weiss

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  1. Finance, HEC Montreal, Montreal, Québec, Canada

    Georges Dionne

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Cummins, J.D., Weiss, M.A. (2013). Analyzing Firm Performance in the Insurance Industry Using Frontier Efficiency and Productivity Methods. In: Dionne, G. (eds) Handbook of Insurance. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-0155-1_28

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