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The Benefits of Uniform Flood Insurance

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Abstract

Prevention policies against flood, such as dams or levees, are commonly designed by local jurisdictions and for most, they exert externalities on neighbouring jurisdictions. We study a model in which each jurisdiction chooses its collective prevention effort depending on the flood risk and on the insurance system that covers its inhabitants. As compulsory uniform insurance depends on all insureds’ risk, it enables partial integration of prevention externalities by jurisdictions. We determine under which conditions compulsory uniform insurance Pareto dominates risk-rated insurance.

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Notes

  1. Since 1928 the International Commission on Large Dams has assessed and inventoried large dams. Levees inventory is more recent. In the United States, Congress created the National Committee on Levee Safety in 2007. In France, an important programme of inventory of levees protecting against flood has been set up in 1999 (Mériaux et al., 2003).

  2. Lünenbürger (2006).

  3. Tobin (2007).

  4. A large scale example is the Three Gorges Dam in China. It changed the whole hydraulics of the Yangtse river in its regular regime downstream as well as upstream, and in the case of flood it provides a regulation of flows very different from what was in place beforehand (Zhu and Rong, 2010).

  5. Only a few examples reveal efforts by central governments to coordinate local prevention policies and reduce negative prevention externalities this way. For example, in the Netherlands, the “waterstaat” (central water administration) was created in 1798 to coordinate the construction and maintenance of “polders” by the “waterschappen” (local water communities). For an illustration of limited control of prevention measures in France, see Grislain-Letrémy et al. (2013).

  6. California Hearing (2005).

  7. Ahvenharju et al. (2011), Consorcio de Compensatión de Seguros (2008), Maccaferri et al. (2012).

  8. Less than 10 per cent of German households and about 5 per cent of Italian buildings are insured against floods (Bouwer et al., 2007; Schwarze and Wagner, 2007). In Sweden, public fund compensation coexists with uniform private insurance (Ahvenharju et al., 2011; Maccaferri et al., 2012).

  9. Walker et al. (2009).

  10. The Chinese government allocated 175 m yuan (26.92 m$) relief fund to southern regions hit in 2011 to help victims, in particular to reconstruct destroyed buildings (Hui, 2011).

  11. Dixon et al. (2006).

  12. Kunreuther and Pauly (2005).

  13. In the United States, flood insurance is risk-rated (with subvention of specific risks) and takes collective prevention measures into account: in the framework of the National Flood Insurance Program, insured households receive a rebate on their premium depending on prevention measures taken by their jurisdiction (Burby, 2001).

  14. Maccaferri et al. (2012).

  15. The French natural disasters insurance system was created in 1982 to institutionalise and coordinate numerous aid mechanisms that had lasted for centuries (Favier and Larhra, 2008); in Spain, coverage of extreme risks was first organised after the Civil War (1936–1939) for the needs for compensation arising from the war and was then extended to other extraordinary risks, including natural disasters (Consorcio, 2008).

  16. Lipsey and Lancaster (1956–1957).

  17. Picard (2008).

  18. Hofmann (2007).

  19. Muermann and Kunreuther (2008).

  20. Lohse et al. (2012).

  21. Persson and Tabellini (1996).

  22. Note that taxes providing prevention incentives to individuals would not make sense, as individuals cannot decide the collective prevention effort on their own.

  23. See Lünenbürger (2006) for a study of supply of flood prevention as the outcome of a voting procedure.

  24. This expression is different from the one used by Hofmann (2007) and Muermann and Kunreuther (2008). Both papers assume that a loss directly caused by an agent and a loss indirectly caused via others are independent.

  25. Ehrlich and Becker (1972).

  26. Conditions of validity (6) and (7) imply e1⩽1 and e2+ɛe1⩽1 in each studied case. As prevention efforts decrease expected losses, this upper bound of 1 guarantees positive expected losses (see Appendix section “Conditions of validity” for detailed calculations). Other values correspond to degenerate cases where jurisdictions choose such high prevention efforts that their expected losses are negative.

  27. Coate (1995) explains that the equivalence between ex post taxation and uniform insurance is imperfect. Ex post assistance by government is less efficient because assistance may rely on approximate loss assessments or discretionary decisions. Besides, as natural disasters assistance is provided by various actors (non-profit organisations, States), the uninsured can free-ride. We leave these issues aside.

  28. We do not consider evolution of land-use planning or population in response to prevention measures. See Kousky et al. (2006) for modelling endogenous and long-term location response to protection.

  29. These wealths are detailed in the Appendix section “Wealths in centralisation without transfers between the two jurisdictions”.

  30. The design of the Pigouvian tax depends on the insurance scheme. Under uniform insurance, this tax would correct the loss-sharing effect and reward collective prevention whatever the sign of the externalities, whereas under risk-rated insurance, it would reward collective prevention if and only if externalities are positive.

  31. Indeed, under risk-rated insurance, assuming mandatory insurance would be required in the case of negative externalities with a downstream jurisdiction more populated than the upstream one. In that case, the term ηɛe1 in Eq. (14) strongly increases the premium offered to upstream households; despite their risk aversion, these households could so prefer not to purchase insurance.

  32. For example, in the absence of prevention externalities, transfers between the two jurisdictions are necessary to increase the wealth of each of them when their two cost parameters strongly differ (transfers are necessary if and only if c1/c2<1/2 or c1/c2>2, see the Appendix section “Comparison of centralisation without transfers between the two jurisdictions and no coordination”).

  33. Specifically, under risk-rated insurance, a marginal increase in each jurisdiction’s prevention effort decreases the premium of its inhabitants by 1. Under uniform insurance, for jurisdiction 1, it decreases the premium by (1+ηɛ)/(1+η), which is strictly less than 1 if and only if ɛ<1; for jurisdiction 2, it decreases the premium by η/(1+η)<1.

  34. In a general setting, we get:

  35. Specifically, for small η, jurisdiction 1’s wealth is larger under uniform insurance than under risk-rated insurance if and only if ɛ⩾1. Consistently, in that case, jurisdiction 1’s prevention effort is larger under uniform insurance (Proposition 4, Eq. (24)).

  36. Specifically, for small η, jurisdiction 2’s wealth is larger under uniform insurance than under risk-rated insurance if and only if ɛ<1 (Eq. (A.21) in the Appendix section “Proof of Lemma 1”).

  37. Indeed, the decrease of wealth in one jurisdiction can be compensated by a transfer from the other jurisdiction if and only if the wealth loss in one jurisdiction is lower than the wealth gain in the other, that is if and only if social welfare increases.

  38. The Netherlands is particularly vulnerable to a rise in sea level since about 70 per cent of properties lie below either the current sea level or the river water level (Kok, 2003).

  39. White (1942).

  40. Burby (2006).

  41. Kydland and Prescott (1977).

  42. Kousky et al. (2006).

  43. Kydland and Prescott (1977) quote the specific case of floods: “the rational agent knows that, if he and others build houses there [on a flood plain], the government will take the necessary flood-control measures”.

  44. can be higher or lower than −1, depending on the values of η and c2/c1.

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Acknowledgements

The authors thank David Martimort, Pierre Picard, Sandrine Spaeter, Bertrand Villeneuve, two anonymous referees and Michael Hoy for their insightful comments. This paper has also benefited from comments by Marcel Boyer, Françoise Forges, Christian Gollier, Nicolas Grislain, Dominique Henriet, Philippe Mongin, Jean-Marc Tallon, and participants at the Research Center for Economics and Statistics and University Paris-Dauphine internal seminars, the 2010 Association Française de Science Economique conference, the 2010 Association of Southern European Economic Theorists conference, and the 2010 Association of Public Economic Theory conference. The authors thank Cédric Peinturier for interesting technical discussions on flood externalities and the Fondation du Risque.

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Authors and Affiliations

  1. CREST and University Paris-Dauphine,

    Céline Grislain-Letrémy

  2. Ecole Polytechnique and AgroParis Tech ENGREF,

    Sabine Lemoyne de Forges

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  1. Céline Grislain-Letrémy
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Additional information

The conclusions and analysis set in this paper are those of the authors and do not indicate the views or opinions of their institutions.

Prevention can decrease the loss probability (self-protection in the sense of Ehrlich and Becker, 1972) or the potential loss (self-insurance in the sense of Ehrlich and Becker, 1972, also called protection in common language).

Appendix

Appendix

Conditions of validity

Under centralisation, under either uniform or risk-rated insurance, conditions of validity (6) and (7) imply e1⩽1 and e2+ɛe1⩽1, respectively. This upper bound for prevention efforts guarantees positive expected losses for inhabitants in the two jurisdictions.

In the absence of coordination, under uniform insurance, conditions (6) and (7) imply positive expected losses for inhabitants in the two jurisdictions:

In the absence of coordination, under risk-rated insurance, conditions (6) and (7) imply positive expected losses for inhabitants in the two jurisdictions:

Wealths in centralisation without transfers between the two jurisdictions

In centralisation and in the absence of transfers between the two jurisdictions, the wealth of each jurisdiction is, respectively, under uniform and risk-rated insurance

Wealths in the absence of coordination

In the absence of coordination, the final wealths are, respectively, under uniform and risk-rated insurance

Comparison of centralisation without transfers between the two jurisdictions and no coordination

Under uniform insurance, the wealth difference in each jurisdiction is:

In the absence of externalities, the necessary and sufficient condition for and is 1/2⩽(c1/c2)⩽2.

Under risk-rated insurance, the wealth difference in each jurisdiction is:

Proof of Lemma 1

Using and given in the Appendix section “Wealths in the absence of coordination”, we directly get . Uniform insurance leads jurisdiction 1 to a larger wealth than risk-rated insurance if and only if

Therefore,

Similarly, using and given in the Appendix section “Wealths in the absence of coordination”, we directly get . Uniform insurance leads jurisdiction 2 to a larger wealth than risk-rated insurance if and only if

Therefore,

Proof of Proposition 6

By adding up (A.19) and (A.21), we get the difference of social welfare between uniform insurance and risk-rated insurance:

Therefore

We get

andFootnote 44

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Grislain-Letrémy, C., de Forges, S. The Benefits of Uniform Flood Insurance. Geneva Risk Insur Rev 40, 41–64 (2015). https://doi.org/10.1057/grir.2014.14

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