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A copula regression model for estimating firm efficiency in the insurance industry

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  • Peng Shi
  • Wei Zhang

Abstract

This article considers the estimation of insurers' cost-efficiency in a longitudinal context. The current practice ignores the tails of the cost distribution, where the most and least efficient insurers belong to. To address this issue, we propose a copula regression model to estimate insurers' cost frontier. Both time-invariant and time-varying efficiency are adapted to this framework and various temporal patterns are considered. In our method, flexible distributions are allowed for the marginals, and the subject heterogeneity is accommodated through an association matrix. Specifically, when fitting to the insurance data, we perform a GB2 regression on insurers total cost and employ a t-copula to capture their intertemporal dependencies. In doing so, we provide a nonlinear formulation of the stochastic panel frontier and the parameters are easily estimated by likelihood-based method. Based on a translog cost function, the X-efficiency is estimated for US property-casualty insurers. An economic analysis provides evidences of economies of scale and the consistency between the cost-efficiency and other performance measures.

Suggested Citation

  • Peng Shi & Wei Zhang, 2011. "A copula regression model for estimating firm efficiency in the insurance industry," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(10), pages 2271-2287.
    • Handle: RePEc:taf:japsta:v:38:y:2011:i:10:p:2271-2287
    DOI: 10.1080/02664763.2010.545376
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    5. Huang, Tai-Hsin & Chen, Kuan-Chen & Lin, Chung-I, 2018. "An extension from network DEA to copula-based network SFA: Evidence from the U.S. commercial banks in 2009," The Quarterly Review of Economics and Finance, Elsevier, vol. 67(C), pages 51-62.
    6. Huang, Tai-Hsin & Hu, Chu-Nan & Chang, Bao-Guang, 2018. "Competition, efficiency, and innovation in Taiwan’s banking industry — An application of copula methods," The Quarterly Review of Economics and Finance, Elsevier, vol. 67(C), pages 362-375.
    7. Wondmagegn Tirkaso & Atakelty Hailu, 2022. "Does neighborhood matter? Spatial proximity and farmers’ technical efficiency," Agricultural Economics, International Association of Agricultural Economists, vol. 53(3), pages 374-386, May.
    8. Tai-Hsin Huang & Nan-Hung Liu & Subal C. Kumbhakar, 2018. "Joint estimation of the Lerner index and cost efficiency using copula methods," Empirical Economics, Springer, vol. 54(2), pages 799-822, March.
    9. Hung-pin Lai & Cliff Huang, 2013. "Maximum likelihood estimation of seemingly unrelated stochastic frontier regressions," Journal of Productivity Analysis, Springer, vol. 40(1), pages 1-14, August.

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