Natural Disasters: Exposure and Underinsurance - CREST

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Jan 30, 2017 - Bourgeon, J.-M. and Picard, P., “Fraudulent Claims and Nitpicky ..... would force any insurer to comply with the law if any nitpicking had ...
Natural Disasters: Exposure and Underinsurance∗ Céline Grislain-Letrémy† January 30, 2017

Abstract The insurance coverage for natural disasters remains low in many exposed areas, particularly in Latin America and the Caribbean. Reduced availability or unaffordability of insurance are commonly identified as the primary causes for this low insurance coverage. The French overseas departments provide a rare example of a well-developed and regulated supply of natural disaster insurance. They offer an exceptional opportunity to analyze the demandside determinants of insurance coverage in these highly exposed regions. Based on unique household-level micro-data, I estimate a structural model of insurance supply and demand. Because my data set combines detailed information on both insured and uninsured households, I can analyze the extensive margin in the insurance market, that is, the insurance take-up. I show that the low insurance take-up rate in the French overseas departments is mainly due to uninsurable housing and the anticipation of assistance. Keywords: natural disasters, insurance, disaster aid JEL classification: Q54, G22, H84, D12 ∗

The conclusions and analysis expressed in this paper are those of the author and do not necessarily reflect the views or opinions of the institutions to which she belongs. I thank Pierre-André Chiappori, Pierre-Philippe Combes, Keith Crocker, Xavier D’Haultfoeuille, Eric Dubois, Christian Gourieroux, Glenn Harrison, Meglena Jeleva, Guy Laroque, Claire Lelarge, David Martimort, Isabelle Méjean, Philippe Mongin, Corinne Prost, Bernard Salanié, Sandrine Spaeter, Eric Strobl, Yoshihiko Suzawa, Bertrand Villeneuve, and two anonymous referees for their insightful comments. I thank Stephen Coate for his help on public assistance. This paper has also benefited from comments by Lucie Calvet; Nicolas Grislain; Jia Min Ng; Laurence Rioux; Corentin Trevien; Lionel Wilner; and participants at the 2015 ETH/Risk Center and AXA Workshop “Policyholder Behavior in Insurance Decision-Making”, the 2014 CEAR/MRIC Behavioral Insurance Workshop, the 2014 Risk Theory Society Seminar, the 40th Seminar of the European Group of Risk and Insurance Economists, the Applied Micro Theory Colloquium at Columbia University, the lunch seminar of Paris School of Economics “Environmental Economics,” the 20th Annual Conference of the European Association of Environmental and Resource Economists, the Seminar of the Chair “Regulation and Systemic Risk” of the French Prudential Supervisory Authority, the 74th International Atlantic Economic Conference, the CREST internal seminars, the INSEE internal seminar, the Paris-Dauphine University internal seminar, and the 2011 Belpasso international summer school on environmental and resource economics. I also thank “Regulation and Systemic Risk” Chair of the French Prudential Supervisory Authority. † CREST and Université Paris-Dauphine, PSL Research University. Address: INSEE Timbre G230, 15 Bd Gabriel Péri BP 100, 92244 Malakoff Cedex, France. Email: [email protected]

Résumé La couverture assurantielle contre les catastrophes naturelles reste faible dans de nombreuses zones exposées, en particulier en Amérique Latine et dans les Caraïbes. Une raison souvent invoquée pour expliquer cette faible couverture est l’offre d’assurance peu développée ou inabordable. Les départements français d’Outre-mer présentent un exemple rare d’une offre d’assurance contre les catastrophes naturelles développée et réglementée. Ils offrent ainsi une occasion exceptionnelle d’analyser les déterminants de la couverture d’assurance du côté de la demande dans ces régions fortement exposées. Sur la base de microdonnées uniques au niveau des ménages, j’estime un modèle structurel d’offre et de demande d’assurance. Mes données combinant des informations détaillées à la fois sur les ménages assurés et non assurés, je peux analyser la marge extensive du marché de l’assurance, c’est-à-dire la décision de souscrire ou non une assurance. Je montre que le faible taux de souscription de l’assurance dans les départements français d’Outre-mer s’explique principalement par le caractère inassurable de certains logements et par l’anticipation par les ménages d’une aide financière. Mots clef : catastrophes naturelles, assurance, aides post-catastrophe

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Introduction

Natural disasters have a considerable and growing impact on national economies. Over the last few decades, the damages associated with such events have frequently reached several percentage points of GDP.1 The uninsured losses are the main drivers in the subsequent drop in national output after natural disasters (VonPeter et al., 2012). Instead, the insurance coverage of private assets enables countries to partially transfer catastrophic risk to foreign actors.2 However, insured losses represent a small fraction of the economic losses (MunichRe, 2015). The insurance coverage for natural disasters is particularly low in developing countries and developing small island states (Cavallo and Noy, 2009), most of which are highly exposed to natural disasters. In particular, Latin America and the Caribbean form one of the world’s most disaster-prone areas (Borensztein et al., 2009) with damages exceeding 50% of GDP in the last few decades (Heger et al., 2008).3 Yet these two regions have the lowest levels of insurance coverage: insurance covered less than 4% of the losses in Latin America and the Caribbean between 1985 and 1999. Thus, these two regions rank last among the world’s regions along with Asia (4%), and behind Africa (9%) (Charvériat, 2000). Furthermore, the insurance take-up rate in Latin America and the Caribbean is particularly low among households (Charvériat, 2000). Reduced availability or unaffordability of insurance are commonly identified as the primary causes for the low insurance coverage in hazard-prone regions of the world, such as Latin America and the Caribbean.4 This restricted insurance supply is mainly due to unavailable or unaffordable reinsurance and also to limited standardized information on risk exposure 1

Natural Disasters. Counting the Cost. March 21st, 2011. The Economist. In almost all developing countries, insurers rely heavily on international reinsurance (Outreville, 2000). Local insurance companies can cede a significant part of their risks to reinsurers, which are mainly foreign companies. For example, the local insurers in the Caribbean that cover households and firms for natural disasters retain less than 20% of the amount they insure and cede the remaining share to reinsurers (Pollner, 2000). 3 For example, the 2010 earthquake in Haiti caused damages exceeding 120% of GDP (author’s calculations based on 2016 World Development Indicators and EMDAT). 4 In Latin America and the Caribbean, developments in the supply of insurance for households are rare. In Brazil, the government-owned reinsurance institute is largely in charge of developing the supply of flood reinsurance; in Puerto Rico, the government created a reserve for catastrophe losses in 1994 to improve the availability and the affordability of catastrophe insurance Charvériat (2000). Moreover, this insurance supply can be fragile. Montserrat is a particularly telling example. In 1997, after several volcanic eruptions, the insurance companies responsible for most policies withdrew from the island entirely (Oxford Analytica, 1997). 2

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(Cavallo and Noy, 2009). The French overseas departments provide a rare example of a well-developed and regulated supply of natural disaster insurance in Latin America, the Caribbean, and other exposed small island countries. They include French Guiana (South America), Guadeloupe (Caribbean Sea), Martinique (Caribbean Sea), and Réunion (Indian Ocean).5 They have benefited from the French system of natural disaster insurance since 1990. This broad and regulated supply of coverage offers a unique opportunity to analyze the determinants of insurance coverage while focusing on the demand side. This paper investigates the demand-side reasons for the low insurance take-up in disaster prone areas. Besides perception biases, several major reasons might explain the low demand for natural disaster insurance. First, insurance might be too expensive for households. When insurance is available, the insurance premiums in Latin America and the Caribbean are high because of the restricted or expensive reinsurance supply (Auffret, 2003). For example, in Mexico, natural disaster premiums in earthquake-prone areas amount to 0.5% of the value of housing on an annual basis; in the Caribbean, natural disaster premiums exceed 1% of the insured value (Charvériat, 2000). Second, in developing countries, many houses are of low quality, do not meet building standards, and have poor resilience to natural events.6 The insurance companies could consider these houses as uninsurable. The proportion of uninsurable housing in Latin America, the Caribbean, and many other developing countries is high (Gilbert, 2001). In Mexico, uninsurable houses built with no solid materials or access to drinking water represent about 50% of the total housing stock (Charvériat, 2000). 60% of the total housing stock in the Caribbean is built without any technical input (IDB, 2000). In the French overseas departments, houses made of light materials (such as wood or sheet metal) represented 13% of the housing in 2006 (Casteran and Ricroch, 2008). All of these low quality homes are legal. In the Caribbean region, building standards and location restrictions are either nonexistent, outdated, or inadequate (Auffret, 2003). The French overseas departments do not require a permit to build a house because the property law allows households to own the walls of their home without owning the ground on which it is built. 5

Because this study uses data on the French overseas departments for 2006, Mayotte (Indian Ocean), which became a French overseas department in 2011, is excluded from the empirical analysis. 6 Apartments are rarely concerned, because most of them are built with technical input and meet building standards.

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Third, assistance is a substitute for formal insurance and decreases the demand for insurance. This phenomenon, called the charity hazard and first introduced by Browne and Hoyt (2000), is a typical example of the Samaritan’s dilemma. The charity hazard has a considerable impact in many developing countries, including Latin America and the Caribbean (Gilbert, 2001). Households can garner financial assistance from local authorities, non-governmental organizations, or relatives. Further, the World Bank and the Inter-American Development Bank provide a considerable and growing amount of assistance to victims of natural disasters in the Caribbean region (Auffret, 2003). The French overseas departments also benefit from significant financial assistance from the French government (French Senate, 2005).7 The charity hazard is all the more of an issue because the expected award of assistance is endogenous. The neighbors’ decision to be uninsured can increase the neighborhood’s eligibility for assistance and so decrease the individual benefit of purchasing insurance, as predicted by Arvan and Nickerson (2006), or on the contrary increase this benefit if assistance has to be shared among uninsured households. Fourth, the neighbors’ insurance choices also impact individual decisions through peer effects and sustain also this way a low level of insurance take-up. Social norms impact the decision to purchase insurance, because individuals might think that their relatives have similar preferences to them or have already contributed the search costs of obtaining information on risk and insurance (see Lo (2013) for a detailed analysis of the impact of social norms on insurance demand). Fifth, although insurance obligations logically increase insurance demand, in reality they do not guarantee that targeted households purchase insurance. Even if purchasing home insurance is often a condition for obtaining a mortgage, some homeowners with outstanding loans might not renew their insurance contracts once they have settled in.8 Indeed, because banks rarely perform checks once people have moved in, some households choose to cancel their insurance as soon as possible. This situation prevails in most Caribbean countries (Auffret, 2003). In the French overseas departments, purchasing home insurance is also compulsory for tenants. Similarly, business practices indicate that landowners do little monitoring of 7

For example, the disaster relief fund for overseas areas is funded by budgetary credits and covers damages caused by natural disasters in the primary residence, including rebuilding (see order of December 8, 2010 relative to the implementation of assistance by the disaster relief fund for overseas areas). 8 In France, if a home is destroyed, the homeowner still has to repay the loan. Thus, the homeowner bears the majority of the risk. However, the bank loses the home as collateral.

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insurance renewals once their tenants have moved in. I estimate a model of insurance supply and demand within the French overseas departments. To do so, I build a unique household-level micro-database combining detailed information on both insured and uninsured households. Because my data set also covers uninsured people, contrary to most company data, I can analyze the extensive margin in this insurance market (insurance take-up), instead of focusing on the intensive margin (level of coverage for each policy). I model the households’ decision on whether to purchase insurance or not based on its expected utility. The supply equation explains the insurance premium offered by insurers under the assumption of zero expected profit. The tariff regulation of the natural disaster insurance system entails a particular form of pricing distortion that I precisely model. I estimate the insurance premiums while taking into account selection bias. Because in turn the premiums impact the households’ insurance decision, I estimate the demand and supply equations simultaneously. The households’ anticipation of financial assistance is difficult to quantify because of numerous assistance channels. This is why I build a test for the presence of the charity hazard based on the impact of past sinistrality. Because past disasters inform households of their probability of receiving assistance, the past sinistrality can decrease their probability of purchasing insurance. However, past sinistrality also increases the households’ estimation of the probability of being hit again, thus increasing their probability of purchasing insurance. The charity hazard’s effect can be detected if the first effect overcomes the second one. This paper provides demand-side explanations for the low insurance take-up rate in disasterprone areas and compares their magnitudes.9 While the research widely studies the impacts of the insurance’s price and the household’s income on insurance demand, it rarely quantifies the other determinants, especially in developing countries and developing small island states. I show that the low demand is mainly due to low quality housing and also likely to the charity hazard. These results are the first quantification, to my knowledge, of the impact of low quality housing on insurance demand in developing countries, and contribute to the growing literature on the charity hazard in the case of natural disasters (see Raschky et al. (2013) for a review and Kousky et al. (2014)). In particular, I show that the neighbors’ insurance choices impact the individual’s insurance decisions through the neighborhood’s eligibility for 9

A companion paper in French draws initial basic and robust qualitative conclusions (Calvet and GrislainLetrémy, 2011).

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assistance. The theory predicts this mechanism (Arvan and Nickerson, 2006) but there is no empirical evidence to support the prediction. This study fills that gap. Further, I show that the neighbors’ insurance choices impact the individual’s insurance decisions through peer effects and that having grown up in metropolitan France where the vast majority of people are insured increases the probability of being insured. These results confirm the causal effect of social networks on insurance purchase established by literature and are consistent with the fact that the main channel is the diffusion of knowledge about insurance functioning and performance (Cai et al., 2015; Karlan et al., 2014). The regulated insurance price in the French overseas departments does not significantly contribute to the low insurance demand, as confirmed by the low price elasticity of the insurance demand. I also estimate the income elasticity of the insurance demand, and its order of magnitude is comparable with other studies. Finally, the existing insurance obligations (de facto for homeowners with outstanding loans, as in most Caribbean countries, and de jure for French tenants) are operant but do not guarantee that targeted households purchase insurance, because some households might not renew their insurance contracts once they have settled in. The paper is organized as follows. Section 2 presents an overview of the model. Section 3 details the data. Section 4 details the specification of the model. I comment on the estimation results in Section 5. Section 6 concludes.

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Model overview

I estimate a model of insurance supply and demand. Because my data set also covers uninsured people, contrary to most company data, I can incorporate in the model the households’ decision on whether to purchase insurance or not based on its expected utility. The supply equation explains the insurance premium offered by insurers under the assumption of zero expected profit. The tariff regulation of the natural disaster insurance system, which is guaranteed by the government, entails a particular form of pricing distortion that I model precisely.10 In this section, I model the supply and demand for home insurance because France requires 10

There are other countries where natural disasters insurance pricing is regulated and distorted. In the United States, flood insurance is actuarial with subvention of specific risks and 22% of flood insurance policies are subsidized (Hayes and Neal, 2009).

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by law that natural disaster coverage be part of comprehensive home insurance.11 Although the tariff regulation for natural disaster insurance is specific to France, the inclusion of this coverage in home insurance is common in many developed countries, such as many EU countries (see Maccaferri et al. (2012) for a review) and Canada, Japan, and Mexico (Dumas et al., 2005).

Risk structure. A home suffers a loss Ld caused by natural disasters with probability pd . I assume that uninsured households only receive assistance A after a disaster, because insured households have a much lower probability of receiving a substantial aid.12 Ordinary risks (such as theft, fire, explosion or water damage) cause a loss Lo with probability po . For the sake of simplicity, I assume that the losses caused by natural disasters and damages caused by ordinary risks are independent events. Because the product of the two probabilities pd po is negligible with respect to any of the two probabilities, three states of nature exist for a household: a loss Ld − A with a low probability pd , a loss Lo with a probability po , and no loss with probability 1 − pd − po . The households’ risk perception is potentially biased and might differ from the accurate risk assessment performed by the insurers, not only for probabilities but also for damages after natural disasters, which can be underestimated (Botzen et al., 2015). I denote p0o as the probability of ordinary damages, p0d as the probability of natural disasters, and L0d as the potential losses caused by natural disasters, as perceived by the households. For the sake of simplicity, I assume that the households have the same estimation for their potential ordinary losses Lo as the insurers.

Demand equation. The households’ coverage choices are very limited: they can purchase home insurance (α = 1) or not (α = 0); if they do, they cannot choose the coverage for their building value, which is estimated by the insurer, but only for the contents of their home (furniture and value items). 11

See French Insurance Code, section L. 125-1. To my knowledge, no other insurance policy provides coverage for natural disasters. 12 The main channel of governmental assistance to overseas France is the disaster relief fund for overseas areas. This fund compensates uninsured households for the damages caused by natural disasters in their main home, including rebuilding and furniture (see order of December 8, 2010 relative to the implementation of assistance by the disaster relief fund for overseas areas).

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A household purchases insurance if and only if its expected utility is higher when it is insured than when it is not.13 Because of the wide and regulated coverage offered by the French system of natural disasters insurance, I assume that insurers offer full coverage.14 I denote its price as π. α = 1 ⇔ U (W − π) ≥ U (W ) − p0o [U (W ) − U (W − Lo )] − p0d [U (W ) − U (W − L0d + A)].

(1)

Supply equation. The supply equation explains the premium offered by the insurers for the coverage of the home against ordinary damages and natural disasters. The insurance market’s competition and the risk neutrality of insurers imply that the insurers’ expected profit is zero for each policy. The zero expected profit means that the premium π equals the sum of the expected losses from ordinary risks po Lo and the expected cost of natural disasters for the insurers. This cost differs from the expected losses of natural disasters borne by the uninsured households. Indeed, the Caisse Centrale de Réassurance (CCR) offers all insurers an attractive and non-actuarially based reinsurance policy,15 because the government provides an unlimited guarantee. The insurers transfer half of their risks to CCR, and for the remaining half, they are exposed up to a deductible, which equals the natural disaster premium. In return, they have to pay a fixed share k = 0.635 of the natural disaster premium (51.5% to CCR as the price of the reinsurance policy,16 and 12% to the government as a tax to fund prevention 13

The standard expected utility framework may not be most appropriate for analyzing the economic consequences of fat-tailed events (Weitzman, 2009). However Weitzman’s alternatives may be less appropriate for studying the purchase of catastrophe insurance by highly exposed households. Indeed, in the sample, households live in municipalities damaged in average eight times (and sometimes 18) by natural disasters during the last 16 years (Table 2). These frequent and important natural disasters, which do not correspond to the rare and extreme events studied by Weitzman, are the historical background on which are based households’ perception of natural disasters and decision to purchase insurance. 14 For example, the natural disasters insurance deductible paid by individuals is fixed by the government to =C380 (around $420), except for movements due to clayey soils (inter-ministerial order of September 5, 2000). 15 As CCR captures more than 90% of market share on the natural disasters reinsurance market (private communication to the author), I assume that all insurers are reinsured against natural disasters by CCR. 16 A good approximation for the price of a reinsurance policy is the amount paid by insurers to CCR; in 2006, it corresponded to =C670 million over =C1.3 billion of insurance premiums (Letrémy, 2009), that is, 51.5% of the insurance premiums.

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measures).17    Ld π = c po Lo + pd min πd , + kπd , 2 Ld = c(po Lo + pd πd ) + kπd as πd < , 2

(2)

where the loading factor c represents the transaction costs (information search, negotiation, policy drafting, controls, and claim disputes). The home insurance premium π is the sum of the premium for natural disasters πd and the premium for other risks πo . The French law requires that πd amounts to 12% of πo , that is, πd =

r π with r = 0.12, 1+r

(3)

independently of the share of total losses attributable to natural disasters.18 Thus, I get   kr r − cpd log(π) = log(cpo Lo ) − log 1 − with r = 0.12, k = 0.635. 1+r 1+r

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(4)

Data

Scope. This article focuses on the French overseas departments. The five French overseas departments are French Guiana (South America), Guadeloupe (Caribbean Sea), Martinique (Caribbean Sea), Réunion (Indian Ocean), and Mayotte (Indian Ocean). Because this study uses data on the French overseas departments for 2006, Mayotte, which became a French overseas department in March 2011, is excluded from the empirical analysis. Table 1 presents the statistics for the population, exposure to major natural risks, and insurance take-up in the four French overseas departments at the time of data collection; similar data are presented for metropolitan France to illustrate great exposure and underinsurance in the overseas departments. Like many countries located in Latin America and the Caribbean, the French overseas departments are highly exposed to tsunamis, floods, and ground movements. Guadeloupe and Martinique are exposed to intense seismic activity.19 Each of the three 17

See French Environment Code, section L. 561-3. See French Insurance Code, sections L. 125-2 and A. 125-2. 19 See the French earthquake map: http://www.planseisme.fr/IMG/jpg/Poster_alea_sismique_ avril_2008-2.jpg. Major earthquakes occurred in Guadeloupe in 1843 and in Martinique in 1839. Earth18

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islands is composed of an active volcano (Grande Soufrière in Guadeloupe, Mount Pelée in Martinique, Piton de la Fournaise in Réunion) and is exposed to strong hurricanes or cyclones.20 Table 1: Population, exposure to major natural risks, and home insurance take-up rate for primary residences in France in 2006 French overseas departments

Population

(? )

Metropolitan

French Guiana

Guadeloupe

Martinique

Réunion

France

205,954

400,736

397,732

781,962

61,399,733

Households exposed to natural hazards (∗ , in %) Tsunamis and floods

85(† )

84

100

100

21(† )

Ground movements

70

100

100

100

19 59(‡ )

Earthquakes

0

100

100

55(‡ )

Volcanic eruptions

0

30

100

65

0

Wind effects

0

100

100

100

8(‡ )

Insured households (∗∗ , in %)

52

43

50

59

99

Sources: (? ) Population census in 2006; (∗ ) GASPAR database by the French Ministry of Ecology; (∗∗ ) 2006 French Household Budget survey. Notes: (†) French Guiana and metropolitan France are exposed to low intensity tsunamis but to high intensity floods. (‡) Réunion and metropolitan France are exposed to low intensity earthquakes; metropolitan France is also exposed to low intensity wind effects.

Data building. I construct a unique household-level micro-database to explain the low insurance take-up rate in the French overseas departments. My data set combines information about the insurance expenditures of the insured, the risk exposure, and the economic variables for the insured and for the uninsured. To construct the data set, I match the GASPAR database, which provides information about the exposure to natural disasters at the municipal level and is compiled by the French Ministry of Ecology, with the 2006 French Household Budget survey. The 2006 French Household Budget survey includes 3,134 households living in the French overseas departments. Because I study the individual decision on whether to purchase insurance or not, I exclude from quakes of smaller intensity happen more frequently, such as Les Saintes (Guadeloupe) earthquake on November 21, 2004 and Martinique earthquake on November 29, 2007. According to scientists, a major earthquake can be expected on both of these islands in the very next decades. 20 For example, Hurricane Dean hit Guadeloupe and Martinique on August 16, 2007; Cyclone Dina occurred in Réunion on January 22 and 23, 2002.

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the study the households insured by their relatives or their employer. I also exclude 40 observations for which the annual income or the number of rooms is missing. These exclusions leave a total of 2,809 observations in the estimated sample. The GASPAR database specifies which of hazards each municipality is exposed to among tsunamis or floods, ground movements, earthquakes, volcanic eruptions, and hurricanes or cyclones (a dummy for each hazard).21 I use this objective risk assessment to estimate the probability of natural disasters as considered by the insurers. The database also provides the number of disasters by hazard type in each municipality from 1990 (date of the enforcement of the system of natural disaster insurance in the French overseas departments). After an event, the French government decides whether the event is a natural disaster and for what period and municipality. The decision relies on the conclusions of an interministerial commission, which analyzes the phenomenon on the basis of scientific reports. The insured households can benefit from the insurance compensation only if an order is published for the event concerned. This past sinistrality is used to assess the households’ perception of their risk exposure. The French Household Budget survey, managed by the French National Institute of Statistics and Economics Studies, is a comprehensive national survey of household expenditure. Regarding home insurance, the households declare whether they have purchased home insurance; and if so, then the amount of the premium they pay. The survey provides detailed information about the household, such as its occupancy status, size, income, and standard of living. This analysis uses that information to estimate wealth and the insured value of the home’s contents. Further, the data give detailed information about housing. I use the number of rooms to estimate the insured building value, as suggested by the different insurance quotes of the main insurance companies I have compared. Following the characterization of uninsurable housing by the Inter-American Development Bank (Charvériat, 2000), I use the dummies for houses still under construction and for houses without modern conveniences (hot water, drainage, indoor toilets) to identify low quality homes that can be declared as uninsurable by insurers. Moreover, the survey also provides information about the reference person, such as gender, age, and place of birth. 21

The exposure to these physical hazards is determined using engineering calculation. For example, the dummy for flood exposure relies on the atlas of flood-prone areas, which is built on hydrogeomorphological studies at the watershed scale.

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Table 2: Descriptive statistics Mean

Minimum

Maximum

Number of natural hazards in a municipality (∗) 4 0 5 Number of past natural disasters in a municipality since 1990 (∗) 8 0 18 Insured households living in the same municipality (%) 48 0 92 Premium paid by the insured (2006=C) 254 20 2,000 Annual income (2006=C) 22,694 600 169,637 = Standard of living (2006 C) 13,359 407 87,266 Number of rooms 4 1 12 Tenants in a municipality (%) 32 0 77 Homeowners with outstanding loans in a municipality (%) 13 0 38 Houses still under construction in a municipality (%) 3 0 18 Houses without hot water in a municipality (%) 28 0 86 Houses without drainage in a municipality (%) 58 0 100 Houses without indoor toilets in a municipality (%) 4 0 76 Reference person born in metropolitan France in a municipality (%) 10 0 67 Reference person born abroad in a municipality (%) 7 0 54 Gender of the reference person (female) in a municipality (%) 48 14 71 Age of the reference person 49 17 95 Sources: 2006 French Household Budget survey and GASPAR database. 2,809 observations. Notes: (∗) These variables represent the municipality level and are public information.

Descriptive statistics. Table 2 describes my sample. The average municipal exposure to natural risks is high but strongly heterogeneous: according to the GASPAR database, while municipalities are on average exposed to four distinct natural hazards, some are exposed to five hazards, and others to none. On average, eight natural disasters have occurred since 1990 in each municipality; this number reached 18 in some municipalities, whereas others were spared. Of the households in the French overseas departments, 48% purchased home insurance (and so natural disaster coverage) for their primary residence in 2006. This insurance rate also varies considerably between municipalities: in some municipalities, a household can be surrounded by 92% of insured households among his neighbors, whereas in one municipality a considered household can be the only one to be insured. The insured households pay an average premium of =C254, with premiums ranging from =C20 to =C2,000. The annual income ranges from =C600 to =C169,637 for an average of =C22,694. 32% of the households are tenants, 13% are homeowners with outstanding loans, the remainder own their home freehold. Many houses lack modern conveniences: 28% are without hot water, 58% without drainage, and 4% without indoor toilets. 3% of houses are still under construction. The 11

number of these low quality houses is strongly heterogeneous between jurisdictions. Further, good quality houses are on average built in more exposed areas, probably because the risk exposure also provides positive amenities (river and sea view, fertile ground).

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Model specification

This section details the specification of the demand and supply equations (Equations 1 and 4) given the available data. Each household decides to purchase insurance or not, whatever provides it the higher expected utility. Its insurance decision is determined by its attitude towards risk, individual factors (income, housing characteristics), and subjective beliefs built on its past experience about natural disasters (events, received assistance). Its decision can also be impacted by its neighbors’ decision or by having grown up in a place where a majority of people purchase insurance. Insurance premiums are estimated while taking into account selection bias. Because in turn the premiums impact the households’ insurance decision, the demand and supply equations are simultaneously estimated. The dependent variables are the households’ choice or not to purchase insurance and the premium for the insured households. The explanatory variables are the individual households’ data and risk data. Some parameters are imposed by the regulation of the natural disaster insurance system. The calibrated parameters are the utility function and two risk parameters.

4.1

Construction of explanatory variables

Loss probabilities. The insurers estimate the probability pd of natural disasters using information about physical hazards. Business practices indicate that French insurers use very basic information about natural risk exposure, probably because their financial exposure to natural risk is limited due to the reinsurance contract offered by CCR. I assume that the probability of natural disasters estimated by insurers for each household i increases linearly with respect to the sum of hazards Ri to which its municipality is exposed. pd := pR, p ≥ 0.

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(5)

I have no specific information on the probability po of ordinary damages, because I observe neither past ordinary losses nor other proxies for the probability of suffering these losses. I calibrate po by using statistics provided for metropolitan France: po = p0o ≈ 0.075 (FFSA, 2006). The significance and sign for all estimated coefficients are robust when the estimation is performed for po ∈ {0.05, 0.5} and p0o ∈ {0.05, 0.5}, while allowing p0o to be different from po .

Losses. The potential losses depend on the insured value for the building and for its contents. I have compared the insurance quotes, online or by phone, of the main insurance companies (including mutual ones). The building value is not chosen by the insured but estimated by the French insurers mainly from the number of rooms and sometimes from the living space. The insured value for contents (furniture and valuable items) is chosen by the insured. Based on this, I proxy the potential ordinary losses Lo with a log-linear function of the number of rooms N and the standard of living Y .22 The losses also depend on the occupancy status, because in rental properties the landlord is responsible for potential damages to the structure (walls, foundations) and to the contents in furnished homes. I assume that tenants, denoted by Ot = 1, bear only a fraction (1 − τ ) of the losses with the remaining being borne by their landlord. Lo := lN n Y y (1 − τ Ot ), τ ≥ 0.

(6)

The potential losses L0d caused by natural disasters fundamentally depend on the same housing characteristics as the potential ordinary losses Lo . For the sake of simplicity, I assume that they are proportional to the ordinary losses. L0d := βLo , β ≥ 1.

(7)

I calibrate the proportional coefficient using statistics provided by the insurers: β = 15 (FFSA, 2006).23 As a sensitivity test, I perform estimations for β ∈ {10, 20}. The significance 22

The standard of living is measured by the income per consumption unit. The first adult is worth one consumption unit; the second adult and each child older than 14 are worth 0.5; younger children are worth 0.3. 23 Because of this intrinsic link between ordinary losses and losses caused by natural disasters (that remains even in a nonproportional specification), the decrease in expected utility caused by ordinary damages p0o [U (W ) − U (W − Lo )] and the decrease in expected utility caused by natural disasters p0d [U (W ) − U (W −

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and sign for all estimated coefficients are robust to the choice of this parameter.24

Charity hazard. The households’ anticipation of financial assistance is difficult to quantify because of numerous assistance channels. This is why I build a test for the presence of the charity hazard based on the impact of past sinistrality. Because the households’ expectation is based on compensation provided to them after past events, the past sinistrality can increase their expectation of receiving assistance A, which decreases their expected utility loss due to natural disasters. However, it also increases their estimation of the probability p0d of suffering another disaster, which on the contrary increases this loss in expected utility. The weight qd (S) of the utility loss due to natural disasters “summarizes” the two channels through which the number S of past disasters affects the households’ expected utility.25 EU |α=0 = U (W ) − p0o [U (W ) − U (W − Lo )] − qd (S)[U (W ) − U (W − βLo )].

(8)

Thus, a test for the presence of the charity hazard can be based on the sign for ∂qd /∂S. If ∂qd /∂S < 0, then there is an important effect from the charity hazard. In contrast, ∂qd /∂S ≥ 0 is consistent with a small or null value of the charity hazard’s effect. Perception bias, uncontrolled differences in risk aversion, or learning about contract nonperformance in insurance do not imply a negative sign for the ∂qd /∂S; full insurance assumption might lead to an overestimation of charity hazard (see Appendix A.1 for a discussion of the test). The rate of insured households around an individual household can reduce the charity hazard’s effect, because it decreases the likelihood of obtaining assistance after a disaster, as predicted by Arvan and Nickerson (2006). For example, financial assistance from the French government is provided only if uninsured losses in the neighborhood are important enough.26 βLo +A)] are fundamentally linked, and (p0o , p0d , β) cannot be simultaneously identified. I favor the estimation of the natural disasters parameters that make it possible to capture the charity hazard, and I calibrate β and p0o . 24 Because the potential losses cannot exceed the wealth of the household, wealth determines the upper limit of the range of values for β. For β = 20, the potential losses already exceed the wealth of 17 households. Estimations provide consistent orders of magnitude: losses Lo are between =C295 and =C2,728 (for β = 15). 25 Simultaneous estimation of the functional forms of p0d and A (Equation 1) with respect to S delivers non-robust results, because it can lead to assistance higher than losses (A > Ld ) that makes households gain from natural disasters and requires a negative probability p0d to balance this effect. 26 To be accepted, the request for compensation by the disaster relief fund for overseas areas has to establish the importance not only of the physical hazard but also of the material uninsured losses (see order of December 8, 2010 relative to the implementation of assistance by the disaster relief fund for overseas areas).

14

An opposite effect would occur if the assistance had to be shared among uninsured households, which could be the case for compensation provided by NGOs or local authorities; the rate of insured households around an individual household would then increase the charity hazard’s effect. To test for this endogenous nature of anticipated assistance and to determine which of these two effects dominates, I supplement the term that captures the charity hazard with the take-up rate α ¯ M among the households living in the same municipality, that is, for each considered household i, the ratio α ¯ M,i of the insured among all the others households living in the same municipality M than i.27 qd (S) = (q + θα ¯ M,i )S,

(9) P

where, for household i living in municipality M , α ¯ M,i =

α(j) . card(M ) − 1 j∈M,j6=i

This model corresponds to a degenerated Nash equilibrium, where the decision of the group impacts the household’s decision but where the reverse impact is negligible because of the size of each group.

Other controls in the demand equation. An individual household’s decision to purchase insurance can also be impacted by its neighbors’ decision via social norms. To test for the presence of peer effects, I add the take-up rate α ¯ M among households living in the same municipality to the demand equation. I test different definitions for the two groups of peers and of joint eligibility for assistance (allowing them to differ) by combining the municipal level (which is the smallest geographical level that I observe) with any other observed household characteristic (such as age, gender, occupational groups, place of birth). The two effects are both significant at the municipal level. The place of birth can also explain the probability of purchasing insurance via an “initial peer effect”, since having grown up in a place where the vast majority of people are insured can increase the probability of purchasing insurance. Because the home insurance take-up rate of metropolitan France is exceptionally high (Table 1), I test for the impact of the place 27

This ratio is computed in all municipalities, which can be small or large in the estimated sample. However, its distribution is comparable among the small municipalities and the large ones. For example, the subsample with the less populated half of municipalities shows very comparable statistics for the average take-up rate to the other subsample. Besides, the smallest municipalities are not extreme points in the distribution (either with a very low or a very high take-up rate).

15

of birth by adding the dummies Bm and Ba for households born in metropolitan France and abroad, respectively, to the demand equation. The insurer can declare low quality houses as uninsurable after an inspection once a loss occurs (Section 4.2). Concerned households can anticipate the inspection and therefore be less likely to buy insurance. Following the characterization of uninsurable housing by the Inter-American Development Bank (Charvériat, 2000), I test for the impact of uninsurability by adding the following dummies for low quality housing: a dummy Hc for houses still under construction and three dummies for houses without modern conveniences (without hot water Hw , without drainage Hd , and without indoor toilets Ht ). I add dummies for tenants Ot and for homeowners with outstanding loans Ol to control for these insurance obligations and to measure their impact. The results are robust when tenants and homeowners with outstanding loans are excluded from the sample and also when the model is estimated for tenants only.28

Choices of utility function and of wealth. The utility function is a constant relative risk aversion U (W ) = W 1−λ /(1 − λ), which is a reasonably good approximation of an individual’s attitude toward risk in an expected utility setting (Chiappori and Salanié, 2008). The benchmark results assume U is a log function, which is the limit case when λ tends to one. The results are robust when using λ = 2 or λ = 3.29 The wealth measure used to perform the estimations corresponds to the households’ holdings, because the households can lose almost all their possessions in the case of a natural disaster. For the sake of simplicity, I assume that the household’s observed annual income is constant over time until the death of the household’s reference person. I calculate his/her life expectancy by linear interpolation using the French Registry Office’s statistics (Niel and Beaumel, 2010). The significance and sign for all coefficients are robust when using different definitions for holdings or alternative discount rates.30 28

An estimation for homeowners with outstanding loans only is not possible, because they are only 336 of them. 29 The estimation of risk aversion raises numerical problems. Indeed, risk aversion determines the orders of magnitude of the terms expressing the expected utility losses. If these orders strongly differ with the ones for the other controls in the demand equation, then the equation might be estimated incorrectly (coefficients corresponding to the negligible terms might appear as non significant). In the case of the log function, I use U (W ) = cU log(W ), with cU = 10. The adequate value of cU is different when using another value for the risk aversion λ. 30 The results are similar when using the annual income as wealth. The results are also robust when

16

Errors and selection bias. The demand equation is augmented with the term ν, where  is the error attached to the insurance premium. This term allows for selection bias, that is, for correlation between the unobserved heterogeneity factors that affect the insurance premium and the decision to purchase insurance.

Estimated model. For each household i,  αi = 1 ⇔ [U (Wi − πi ) − U (Wi )] + p0o [U (Wi ) − U (Wi − Loi )]       +[qq Si + θ α ¯ M,i Si ][U (Wi ) − U (Wi − βLoi )] + δ α ¯ M,i + bm Bcli + ba Bai    hc Hci + hw Hwi + hd Hdi + ht Hti + ot Oti + ol Oli + ν i + ηi ≥ 0, +h (10)      where log(πi ) = cπ + n log(Ni ) + y log(Yi ) + log(1 − τ Oti ) − log(1 − κ − ρ Ri ) + σ i if αi = 1, (11)     and πi = 0 if αi = 0, where errors  and η follow independent centered normal distributions with a unit variance       η 0 1 0   ∼ N   ,   .  0 0 1

(12)

The covariance structure between the hazards in the two equations is indeed already modeled by the selection bias ν added in the demand equation. The utility function is U (·) = cU log(·) with cU = 10. The estimated parameters are in bold and the calibrated parameters, p0o and β, are underlined. κ = kr/(1 + r) = 0.068 is given, because r = 0.12 and k = 0.635 are imposed by the government and CCR (Section 2). The estimation of cπ = log(cpo l) in the supply equation provides a value for the multiplicative constant l in ordinary losses, which also appears in the demand equation. I calibrate po as specified above and use a value of c ≈ 1.3 (Gollier, 2003) as the loading factor. The results are robust when using c ∈ {1, 1.5}. calculating the holdings with a discount rate of 4% until 30 years and 2% beyond as recommended by Gollier (2007), 10% as recommended by Andersen et al. (2008), 20%, or when uniformly multiplying annual income up to 100.

17

4.2

Estimation and identification

Simultaneous estimation. The insurance premiums are estimated while taking into account a selection bias. In turn the premiums impact the households’ insurance decision. This is why the demand and supply equations (Equations 10 and 11) are simultaneously estimated by using the maximum likelihood.31 The calculation of the log-likelihood is detailed in Appendix A.2.

Identification and its economic interpretation. Typically, the identification of these models estimated by maximum likelihood requires the presence of one variable that explains the selection (the decision by households to purchase insurance or not) but does not enter the censored equation (the premium equation, which is censored because the premium is observed only for the insured). The dummies for houses still under construction (Hc ) and without drainage (Hd ) explain the probability of purchasing insurance but do not significantly explain the insurance premium.32 The model is overidentified, because there are two identification variables. These variables are compatible. Indeed, when only one of them is excluded from the premium equation, the remaining one is not significant in the premium equation and both variables are significant in the demand equation. The economic meaning of these variables is that houses still under construction or without drainage have a lower probability of being insured but, once a house is covered, the price of its coverage does not depend on these characteristics. Business practices indicate that most of the time insurers check the building quality once a loss has occurred, before paying compensation. After a claim, the insurance adjuster checks the loss and the building quality. If the adjuster records that the quality is low, he/she either offers to raise the premium, or cancels the insurance contract and pays off the premiums received until then. For example, if the house was still under construction before the loss, the insurance policy is canceled. This check and its consequences can easily be anticipated by the concerned households, who will be less likely to buy insurance.33 31

Heckman’s two-step estimation method does not enable the estimation of the premium for the uninsured, realized in the second step, to enter the insurance decision, estimated in the first step. 32 Houses still under construction and houses without drainage do not significantly explain the losses, even when considering that losses can be estimated differently by households and by insurers. These dummies correspond to 3% and 58% of the homes, respectively (Table 2). 33 Information about business practices detailed in this paragraph has been provided to the author in private

18

5 5.1

Results Supply

Insurance pricing. Table 3 presents the results of the estimation of the insurance premium (Equation 11). As expected, the insurance premium increases with respect to the number of rooms in the home (n > 0) and the standard of living (y > 0). Further, because tenants insure only a fraction of the total value of the home, the insurance premium is lower for tenants (τ > 0). The premium increases with respect to exposure to natural disasters (ρ > 0), which confirms that insurers’ potential loss depends on the exposure of their policyholders, even if only to a limited extent (Section 2). Table 3: Estimation results: supply equation Coefficient Constant Number of rooms Standard of living Tenant Natural hazard Error Constant in the impact of natural disasters probability

cπ n y τ ρ σ

Estimate 2.348 0.319 0.225 0.289 0.058 0.616

Standard error 0.157 0.047 0.016 0.027 0.007 0.015

κ

0.068

0 (given)

Pr > |t value|