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Efficiency, productivity, and scale economies in the U.S. property-liability insurance industry

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Abstract

The paper examines efficiency, productivity and scale economies in the U.S. property-liability insurance industry. Productivity change is analyzed using Malmquist indices, and efficiency is estimated using data envelopment analysis. The results indicate that the majority of firms below median size in the industry are operating with increasing returns to scale, and the majority of firms above median size are operating with decreasing returns to scale. However, a significant number of firms in each size decile have achieved constant returns to scale. Over the sample period, the industry experienced significant gains in total factor productivity, and there is an upward trend in scale and allocative efficiency. More diversified firms and insurance groups were more likely to achieve efficiency and productivity gains. Higher technology investment is positively related to efficiency and productivity improvements.

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Notes

  1. Previous studies of financial institutions show that although scale economies do exist, the benefits cease to be meaningful beyond a threshold that many companies have already exceeded. Berger and Humphrey (1997) provide a review of the financial institutions efficiency literature, including the literature on scale economies. The insurance efficiency literature is reviewed in Cummins and Weiss (2012).

  2. Studies of scale economies in U.S. P-L insurance using data from 1984 and earlier years include Cho (1988), Weiss (1991), and Johnson et al. (1981).

  3. Cummins and Nini (2002) estimate scale efficiency as part of their study of capital utilization in the P-L industry using data from 1993 to 1998. Choi and Weiss (2005) utilize scale efficiency estimates as regressors in their analysis of market structure in the P-L insurance industry, for the sample period 1992–1998. There also have been several studies that estimate scale economies for P-L insurers in countries other than the U.S. These include Toivanen (1997) (Finland), Fukuyama and Weber (2001) (Japan), Mahlberg and Url (2003) (Austria), Hirao and Inoue (2004) (Japan), Jeng and Lai (2005) (Japan), Cummins and Rubio-Misas (2006) (Spain), and Fenn et al. (2008) (Europe).

  4. Other insurance industry efficiency studies include Berger et al. (1997), Fukuyama (1997), Katrishen and Scordis (1998), Cummins et al. (1999c), Klumpes (2004), Greene and Segal (2004), and Elling and Luhnen (2010).

  5. This is sometimes referred to as the corporate veil rule because creditors cannot proceed against the corporation or brother-sister subsidiaries unless they succeed in “piercing the corporate veil,” which usually requires showing that the corporation has engaged in fraud or other illegal activities.

  6. The alternative to DEA is parametric analysis, which requires the specification of a functional form for the cost and revenue frontiers and also distributional assumptions about the regression error terms. Although there was some debate in the earlier efficiency literature about whether the parametric or non-parametric approach was more appropriate, research by Cummins and Zi (1998), Elling and Luhnen (2010), and others shows that parametric and non-parametric approaches generally produce consistent results.

  7. The tail refers to the length of the loss payout period, as defined by Schedule P of the National Association of Insurance Commissioners (NAIC) regulatory statements.

  8. We utilize constant maturity Treasury yields obtained from the Federal Reserve Economic Data (FRED) database maintained by the Federal Reserve Bank of St. Louis. Yields are obtained by linear interpolation for maturities where constant maturity yields are not published in FRED.

  9. Let \( P_{i} \) denotes the price of insurance output i, \( PE_{i} \) denotes the real premiums earned of insurance output i, and \( LLE_{i} \) denotes the real present value of losses and loss adjustment expenses incurred of insurance output i, then \( P_{i} = [PE_{i} - LLE_{i} ]/LLE_{i} \).

  10. See Cummins and Xie (2008) for the detailed description of the smoothing process.

  11. Some studies (e.g., Cummins and Nini 2002) use home state wage rate for administrative labors, and state-weighted average weekly wage rate for agent labors. Cummins et al. (1999b) conduct a robustness check for alternative types of wages rate for the U.S. life insurance industry and conclude that using the alternative labor price variables do not materially affect the results.

  12. Equity capital is equal to statutory policyholders’ surplus plus reserves required by statutory accounting principles (SAP) but not recognized by generally accepted accounting principles (GAAP). This includes liability items such as the provision for reinsurance, a reserve required by regulators for transactions with non-U.S. regulated reinsurers.

  13. Robustness checks carried out in prior papers show that the results of the analysis generally are not affected by this assumption (e.g., Cummins et al. 1999b, Cummins and Nini 2002, and Cummins and Xie 2008).

  14. Such firms are highly specialized and are not participating in the mainstream property-liability insurance market.

  15. The Department of Justice horizontal merger guidelines define a market as moderately concentrated if the Herfindahl index is between 1,000 and 1,800 and concentrated if the index exceeds 1,800 (U.S. Department of Justice 1997). Choi and Weiss (2005) provide evidence consistent with the efficient structure hypothesis for the U.S. P-L insurance industry, i.e., the hypothesis that efficient firms compete more effectively by charging lower prices. Their results do not support the structure-conduct-performance hypothesis that concentration and larger firm size lead to market power and anti-competitive conditions.

  16. The adjacent-year comparisons provide more complete information about the industry as a whole than the three endpoint to endpoint comparisons (1993-to-2009, 1993-to-2006, and 2006-to-2009). Firms had to be present only in the two adjacent comparison years in order to be included in the adjacent-year analysis, whereas firms in the endpoint comparisons had to be present both in the beginning and the ending year of the period. Thus, firms entering or exiting the industry during the comparison period were not included in the endpoint indices. Thus, there is a degree of survivor bias in the endpoint comparisons.

  17. The multiplicative calculation simply multiplies the sixteen adjacent year indices, whereas the additive calculation sums the sixteen indices and subtracts sixteen. Taking the sixteenth root of the multiplicative number gives the geometric mean, and dividing the additive number by 16 gives an arithmetic mean. These calculations are meant to be summary statistics because technically Malmquist indices do not “chain.” Nevertheless, these calculations provide useful information about average productivity growth for the sample period.

  18. These decompositions are exact for individual firms but do not hold exactly for the averages shown in the table.

  19. The magnitudes of efficiency scores in this study are consistent with prior research (Cummins and Weiss 1993; Cummins et al. 1999c; Cummins and Xie 2008, 2009).

  20. Ours is the first property-liability insurance efficiency study to present the results by size decile. Size decile results for life insurers are presented in Cummins and Zi (1998) and Cummins (1999). Figure on efficiencies by size decile is available from the authors.

  21. Two sub-period comparisons were conducted—(1) splitting the overall period roughly in half (1993–2000 vs. 2001–2009), and (2) comparing the pre and post-financial crisis periods (1993–2006 vs. 2007–2009).

  22. Similar results are found for the other years and for the entire sample period of 1993–2009.

  23. The pattern shown in Fig. 1 is consistent with results for the U.S. life insurance industry in Cummins (1999) and for the Spanish insurance industry in Cummins and Rubio-Misas (2006).

  24. To be consistent with the Malmquist approach, we measure cost, scale and revenue efficiency change using ratios as well, i.e. cost efficiency change (t, t + 1) = cost efficiency (t + 1)/cost efficiency (t), and analogously for other types of efficiency. This approach is also used in Cummins et al. (1999b) and Cummins and Xie (2008).

  25. The Breusch-Pagan Lagrange multiplier test showed that unit effects are present in our data so that either fixed or random effects estimation should be used (Greene 2003). Hausman tests clearly reject the null hypothesis that the unit effects are orthogonal with the regressors, implying that random effects estimation would be inconsistent. Accordingly, the regressions are based on two-way fixed effects, with dummy variables for firms and years included in the models. Ordinary least squares estimation produces consistent estimators when used with two-way fixed effects in a panel data model (Greene 2003). Regressions omitting the fixed effects support the same conclusions.

  26. The quantity of equity capital is an input in our efficiency analysis. However, the ratio of premiums-to-equity capital does not measure the quantity of equity but rather its relationship with the amount of premium revenues generated by the insurer. Hence, we do not believe that using equity in both contexts is likely to bias the results. As a robustness test, we also conducted the regressions excluding the premiums-to-equity ratio. The signs and significances of the other variables in the regressions remained unchanged.

  27. The signs and significances of the other variables in the regressions were not materially affected by the omission of the squared size variable.

  28. Specifically, we utilize the sum of admitted and non-admitted electronic data processing (EDP) assets plus furniture and equipment divided by total assets. This variable is suggested in Garven and Grace (2001).

  29. As an alternative technology variable, we tested the ratio of technology expenses to non-commission expenses. This variable is positively related to productivity and efficiency change but is statistically significant only for total factor productivity and revenue efficiency.

  30. The marginal effects are estimated as: \( \frac{{\partial p_{ki} }}{{\partial x_{ji} }} = p_{ki} \left( {\beta_{kj} - \sum\nolimits_{k = 0}^{K} {p_{ki} \beta_{kj} } } \right) \), for k = 0, 1, 2, where \( p_{ki} \) represents the multinomial logit model right hand side and \( \beta_{kj} \) is the coefficient of variable \( x_{j} \) for returns to scale type \( k \). The marginal effects depend on the point of valuation, and their sign can differ from that of the coefficients \( \beta_{kj} \).

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Authors and Affiliations

  1. Joseph E. Boettner Professor, Temple University, 617 Alter Hall, 1801 Liacouras Walk, Philadelphia, PA, 19122, USA

    J. David Cummins

  2. California State University, Fullerton, Steven G. Mihaylo Hall 5113, 800 N. State College Blvd., Fullerton, CA, 92834, USA

    Xiaoying Xie

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Correspondence to J. David Cummins.

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Cummins, J.D., Xie, X. Efficiency, productivity, and scale economies in the U.S. property-liability insurance industry. J Prod Anal 39, 141–164 (2013). https://doi.org/10.1007/s11123-012-0302-2

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