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Identification of Insurance Models with Multidimensional Screening

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  • Gaurab Aryal

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  • Isabelle Perrigne

    ()

  • Quang Vuong

Abstract

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

Suggested Citation

  • Gaurab Aryal & Isabelle Perrigne & Quang Vuong, 2011. "Identification of Insurance Models with Multidimensional Screening," ANU Working Papers in Economics and Econometrics 2011-538, Australian National University, College of Business and Economics, School of Economics.
  • Handle: RePEc:acb:cbeeco:2011-538
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    File URL: https://www.cbe.anu.edu.au/researchpapers/econ/wp538.pdf
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    References listed on IDEAS

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    Cited by:

    1. Yao Luo, 2011. "Nonlinear Pricing with Product Customization in Mobile Service Industry," Working Papers 11-28, NET Institute.
    2. An, Yonghong & Tang, Xun, 2015. "Identification and Estimation of Auctions with Incomplete Contracts: A Structural Analysis of California Highway Construction Projects," MPRA Paper 62602, University Library of Munich, Germany.
    3. 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.
    4. Gaurab Aryal, 2014. "Identifying Multidiemsnional Adverse Selection Models," Papers 1411.6250, arXiv.org, revised Nov 2015.
    5. Xavier d'Haultfoeuille & Philippe Février, 2010. "Identification of a Class of Adverse Selection Models with Contracts Variation," Working Papers 2011-27, Center for Research in Economics and Statistics.

    More about this item

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • L62 - Industrial Organization - - Industry Studies: Manufacturing - - - Automobiles; Other Transportation Equipment; Related Parts and Equipment
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D86 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Economics of Contract Law

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