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Identification of Insurance Models with Multidimensional Screening

  • Gaurab Aryal

    ()

  • Isabelle Perrigne

    ()

  • Quang Vuong

We study the identification of an insurance model with multidimensional screening, where insurees are characterized by risk and risk aversion. The model is solved using the concept of certainty equivalence under constant absolute risk aversion and an unspecified joint distribution of risk and risk aversion. The paper then analyzes how data availability constraints identification under four data scenarios from the ideal situation to a more realistic one. The observed number of accidents for each insuree plays a key role to identify the model. In a first part, we consider the case of a continuum of coverages offered to each insuree whether the damage distribution is fully observed or truncated. Truncation arises from that an insuree files a claim only when the accident involves a damage above the deductible. Despite bunching due to multidimensional screening, we show that the joint distribution of risk and risk aversion is identified. In a second part, we consider the case of a finite number of coverages offered to each insuree. When the full damage distribution is observed, we show that despite additional pooling due to the finite number of contracts, the joint distribution of risk and risk aversion is identified under a full support assumption and a conditional independence assumption involving the car characteristics. When the damage distribution is truncated, the joint distribution is identified up to the probability that the damage is above the deductible. In a third part, we derive the restrictions imposed by the model on observables for the fourth scenario. We also propose several identification strategies for the damage probability at the deductible. These identification results are further exploited in a companion paper developing an estimation method with an application to insurance data

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Paper provided by Australian National University, College of Business and Economics, School of Economics in its series ANU Working Papers in Economics and Econometrics with number 2011-538.

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Length: 48 Pages
Date of creation: Feb 2011
Date of revision:
Handle: RePEc:acb:cbeeco:2011-538
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  1. Philip Haile, 2000. "Inference with an Incomplete Model of English Auctions," Econometric Society World Congress 2000 Contributed Papers 1546, Econometric Society.
  2. Pierre-André Chiappori & Bernard Salanié, 1997. "Testing for Asymmetric Information in Insurance Markets," Working Papers 97-11, Centre de Recherche en Economie et Statistique.
  3. Matzkin, Rosa L., 1993. "Nonparametric identification and estimation of polychotomous choice models," Journal of Econometrics, Elsevier, vol. 58(1-2), pages 137-168, July.
  4. Arthur Lewbel, 1999. "Semiparametric Qualitative Response Model Estimation with Unknown Heteroskedasticity or Instrumental Variables," Boston College Working Papers in Economics 454, Boston College Department of Economics.
  5. Matzkin, Rosa L, 1992. "Nonparametric and Distribution-Free Estimation of the Binary Threshold Crossing and the Binary Choice Models," Econometrica, Econometric Society, vol. 60(2), pages 239-70, March.
  6. Pedro Carneiro & Karsten T. Hansen & James J. Heckman, 2003. "Estimating Distributions of Treatment Effects with an Application to the Returns to Schooling and Measurement of the Effects of Uncertainty on College," NBER Working Papers 9546, National Bureau of Economic Research, Inc.
  7. Heckman, James J., 2001. "Econometrics and empirical economics," Journal of Econometrics, Elsevier, vol. 100(1), pages 3-5, January.
  8. Donald J. Brown & Marten H. Wegkamp, 2001. "Weighted Minimum Mean-Square Distance from Independence Estimation," Cowles Foundation Discussion Papers 1288, Cowles Foundation for Research in Economics, Yale University.
  9. Gaurab Aryal & Isabelle Perrigne & Quang Vuong, 2011. "Nonidentification of Insurance Models with Probability of Accidents," ANU Working Papers in Economics and Econometrics 2011-552, Australian National University, College of Business and Economics, School of Economics.
  10. Emmanuel Guerre & Isabelle Perrigne & Quang Vuong, 2009. "Nonparametric Identification of Risk Aversion in First-Price Auctions Under Exclusion Restrictions," Econometrica, Econometric Society, vol. 77(4), pages 1193-1227, 07.
  11. Guerre, E. & Perrigne, I. & Vuong, Q., 1995. "Nonparametric Estimation of First-Price Auctions," Papers 9504, Southern California - Department of Economics.
  12. Su, Liangjun & White, Halbert, 2008. "A Nonparametric Hellinger Metric Test For Conditional Independence," Econometric Theory, Cambridge University Press, vol. 24(04), pages 829-864, August.
  13. Phillip Leslie, 2004. "Price Discrimination in Broadway Theater," RAND Journal of Economics, The RAND Corporation, vol. 35(3), pages 520-541, Autumn.
  14. Sandra Campo & Emmanuel Guerre & Isabelle Perrigne & Quang Vuong, 2003. "Semiparametric Estimation of First-price Auctions with Risk Averse Bidders," Working Papers 2003-09, Centre de Recherche en Economie et Statistique.
  15. Victor Chernozhukov & Han Hong & Elie Tamer, 2007. "Estimation and Confidence Regions for Parameter Sets in Econometric Models," Econometrica, Econometric Society, vol. 75(5), pages 1243-1284, 09.
  16. Jean-Charles Rochet & Philippe Chone, 1998. "Ironing, Sweeping, and Multidimensional Screening," Econometrica, Econometric Society, vol. 66(4), pages 783-826, July.
  17. Athey, Susan & Haile, Philip A., 2007. "Nonparametric Approaches to Auctions," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 60 Elsevier.
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