metadata: authors: 0: author: Cordella,Tito
1: author: Levy-Yeyati,Eduardo
count: World
docna: 0: docna: CATalytic insurance : the case of natural disasters
docty: Policy Research Working Paper
subtopic: Climate Change Mitigation and Green House Gases,Capital Markets and Capital Flows,Capital Flows,Financial Economics,Finance and Development,Natural Disasters
teratopic: Private Sector Development,Social Protections and Labor,Finance and Financial Sector Development
abstracts: cdata!: Why should countries buy expensive
            catastrophe insurance? Abstracting from risk aversion or
            hedging motives, this paper shows that catastrophe insurance
            may have a catalytic role on external finance. Such effect
            is particularly strong in those middle-income countries that
            face financial constraints when hit by a shock or in its
            anticipation. Insurance makes defaults less appealing,
            relaxes countries' borrowing constraint, increases
            their creditworthiness, and enhances their access to capital
            markets. Catastrophe lending facilities providing
            "cheap" reconstruction funds in the aftermath of a
            natural disaster weaken but do not eliminate the demand for insurance.
repnme: repnme: CATalytic insurance : the case of natural disasters
display_title: CATalytic insurance : the case of
            natural disasters
listing_relative_url: /research/2010/07/12583312/catalytic-insurance-case-natural-disasters
topicv3: Capital Markets m1326967 332,Climate Change Mitigation m1327079 579,Finance and Growth m1327404 1081,Earthquake m1503308 3154,Natural Disaster m1503325 3138
publishtoextweb_dt: 2010-07-01T00:00:00Z
historic_topic: Private Sector Development,Social Protections and Labor,Finance and Financial Sector Development
no_of_pages: 31
author_keys: 0: author_key: 879396
1: author_key: 632154
model_extractions: WPS5377 Policy Research Working Paper 5377 CATalytic Insurance The Case of Natural Disasters _Tito Cordella Eduardo Levy Yeyati_ The World Bank Latin American and the Caribbean Region Brazil Country Management Unit & The Office of the Chief Economist July 2010
Policy Research Working Paper 5377

# **Abstract**

Why should countries buy expensive catastrophe insurance? Abstracting from risk aversion or hedging motives, this paper shows that catastrophe insurance may have a catalytic role on external finance. Such effect is particularly strong in those middle-income countries that face financial constraints when hit by a shock or in its anticipation. Insurance makes defaults less appealing, relaxes countries’ borrowing constraint, increases their creditworthiness, and enhances their access to capital markets. Catastrophe lending facilities providing “cheap” reconstruction funds in the aftermath of a natural disaster weaken but do not eliminate the demand for insurance.

This paper—a product of the Brazil Country Management Unit and the Office of the Chief Economist, Latin American and the Caribbean Region—is part of a larger effort in the department to understand how developing countries can deal with natural disasters more effectively. Policy Research Working Papers are also posted on the Web at http://econ.worldbank. org. The authors may be contacted at tcordella@worldbank.org, and ely@utdt.edu.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
# **CATalytic Insurance: the case of natural disasters.**<sup>**1**</sup>

# **Tito Cordella**<sup>**2**</sup> **and Eduardo Levy Yeyati**<sup>**3**</sup>

Abstract JEL Classification Numbers: G22, Q54, F34 Keywords: Natural Disasters, Insurance, Catastrophe Insurance, Multilateral Institutions, Sovereign Default, Capital Markets 1 The views expressed are those of the author and do not necessarily reflect the views of the institutions they are affiliated with. We would like to thank Roberto Chang, William Maloney, Jean-Charles Rochet for their useful comments. Federico Filippini and Jivago Ximenez provided outstanding research assistance.

> 2 The World Bank

> 3 Universidad Torcuato di Tella, Buenos Aires, Argentina
# 1 Introduction

All countries are exposed and vulnerable to natural disasters.<sup>1</sup> Exposure is mostly determined by geographic characteristics, vulnerability by policies, and depends on levels of economic development. Indeed, richer countries have more resources to finance risk mitigation activities in preparation for, or reconstruction activities in the aftermath of, a shock. This may well explain why the cost of the recent terrible earthquake (both in terms of human lives and economic costs) was much larger in Haiti than in Chile and this despite the fact that the latter earthquake was stronger.

If countries differ in their exposure and vulnerability to natural disasters, should they deal with them differently? What are the pros and cons of purchasing catastrophe insurance versus doing nothing and/or relying on ex-post lending facilities such as the ones offered by international financial institutions? To answer these important questions, this paper presents a simple model that sheds some new light on the main tradeoffs that countries face in making such diffi cult choices.

It is well known<sup>2</sup> that market insurance, if reasonably priced, is the most effective way for risk adverse agents to cope with large and rare events. This is true for individuals as well as for sovereigns. Indeed, there are a few recent examples of countries that insured themselves against natural catastrophes:<sup>3</sup> In May 2006, the Mexican government issued a US 160 million dollar parametric catastrophe bond to finance rescue and rebuilding in the case a major earthquake hits some densely populated areas of the country;<sup>4</sup> in 2007, a pool of Caribbean countries developed a Caribbean Catastrophe Risk Insurance Facility (CCRICF) that facilitates their access to the insurance market. However, catastrophe insurance is expensive and even in the most successful cases, such as the two we just discussed, the cost of coverage turned out to be a multiple of the fair price (around three times in either case).<sup>5</sup> Why is insurance so costly? Several reasons are invoked, including supply-side constraints induced by either agency costs or adverse selection, problems of information opacity of tail events, coordination failures,<sup>6</sup> and oligopolistic practices. While the securitization<sup>7</sup> of catastrophic risk through the issuance of catastrophe bonds may in the future induce greater market discipline, until now it has fallen short of reducing the costs of insurance to actuarially fair levels.<sup>8</sup> If insurance is so expensive, why do countries still buy it? One reason could be risk aversion; another could be the presence of concavities in the production function and/or convexities in the borrowing cost function that create hedging opportunities as in Froot et al. (1993). While both these assumptions may play an important role for the demand of insurance, nonetheless we think that they only partially justify why a

> 1 By exposure we denote the probability of being hit by a natural disaster and by vulnerabilty the expected loss associated with any of such disasters.

> 2 See Elrich and Becker (1972).

> 3 See Hofman and Brukoff (2006) for a survey of the insurance opportunities available to developing countries against natural disasters.

> 4 This was the the first tranch of a 450 milion US dollars insurage coverge plan. Payment are triggered if a earthquake of magnitude 7.5 or 8 hits some predefined zones of the country. See Nell and Richter (2004) for a discussion of the of parametric insurance, that is of insurance policies with payments linked to measurable events such as the magnitude of an earthquake, or the wind-speed of an hurricane.

> 5 Note that a loading equal to two to three times the fair price is considerably lower than industry averages that range from 5 to 6 times expected outlays.

> 6 See Ibragimov et al. (2008)

> 7 For a comprehensive discussion of the market for catastrophe risk, see Froot (2001).

> 8 For a discussion of the securitization of catastrophe risk and the development of a catastrophe bond market, see Doherty (1997).

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country may decide to rely on expensive insurance. Indeed, risk aversion does not necessarily transfer from individuals to countries and the production smoothing argument may not be always a critical one in dealing with fat tails events such as natural disasters.

For the above reasons, in our model we assume that (i) agents are risk neutral, to abstract from consumption smoothing motives, and (ii) that the premium requested to insure the stock of infrastructure against a natural disaster is higher than the expected return of rebuilding the same infrastructure, to rule out hedging motives. In such a setting, demand for insurance arises because of its “catalytic”role on external finance. By this we mean that by guaranteeing resources that limit economic contraction in the aftermath of a shock, insurance makes default relatively less appealing. This relaxes a country’s borrowing constraint, increases its creditworthiness, and enhances its access to capital markets. For large rare events such as the ones we consider here, such a benign effect may well outweigh cost considerations.

Of course, not all countries benefit the same from catastrophe insurance. The ones that benefit the most are those medium-income countries that have limited access to the international capital market and face financial constraints either when they are hit by a shock or in its anticipation. Conversely, catastrophe insurance should not appeal to either poor countries without access to capital markets, that cannot profit from such catalytic effect, or to rich countries that preserve market access even in the aftermath of a large disaster and thus have no reason to rely on expensive insurance.

Even in those cases in which it is beneficial for a country, one may nonetheless wonder whether insurance is an effective choice for low-income catastrophe-prone economies that are likely to receive (belated but cheap) offi cial loans in the aftermath of a catastrophe. To explore whether such donors’Samaritan dilemma may hinder the demand for insurance, we introduce a multilateral catastrophe lending facility guaranteeing access to reconstruction funds at the risk-free interest rate in the event of a natural disaster. Unlike private lenders, multilateral lenders are assumed to enjoy a preferred creditor status that allows to “ignoring”credit risk.<sup>9</sup> The introduction of the facility weakens but does not eliminate the demand for insurance because of the catalytic effect we just mentioned. While insurance entails a positive transfer after the shock (hence, its catalytic effect), the repayment of the multilateral loan tightens the borrowing constraint, crowds out private lending, and reduce the country’s investment opportunities in good times. This in turns implies that the more credit constrained a country is, the greater the drawback of the lending facility relative to catastrophe insurance, and the larger the demand for the latter.<sup>10</sup> The paper is organized as follows: Section 2 presents the model and characterizes the benchmark case. Section 3 introduces and discusses catastrophe insurance. Section 4 does the same for the multilateral catastrophe lending facility. Finally, Section 5 discusses the findings from a welfare perspective and Section 6 concludes.

> 9 As documented by Jeanne and Zettelmeyer (2003) for the IMF, multilateral lending to middle income countries is virtually default risk-free. However, for our purposes it is suffi cient to assume that the associated default costs are higher than for private claims.

> 10 To our knowledge, these issues have not been yet examined in the economic literature. By contrast, there is growing economic literature assessing the economic costs of natural disasters. See, inter alia, Mauro (2006), Ramcharan (2005), Toya and Skidmore (2006).

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# 2 The model

Consider an economy endowed with a two-factor Leontief technology: to produce a single consumption good. The first factor, denoted by L, can be thought of as infrastructure, which we assume to be at its maximal level L = 1 at the beginning of the production cycle (t = 0). The second factor, K, represents installed productive units (or capital, for short), which we assume to be zero at t = 0, and needs to be externally financed (see below). ρ (ρ > 1) denotes a total factor productivity parameter.

The timing of the model is as follows: At time t = 0, the country issues bonds for an amount D0 to finance capital investment K = D0. The gross borrowing cost i is assumed to be equal to the risk free rate rf (which we normalize to 1 without loss of generality) plus a risk premium δ, itself a function of the probability that the country defaults on the bond We thus have that i = 1 + δ.

In the interim period,<sup>11</sup> t = 1, with a probability π—which we assume to be “small enough”throughout the paper—the country is hit by a natural disaster that destroys a fraction β > 0 of its infrastructure. Faced with such a negative shock, the country has the option to issue new bonds for an amount D1 to finance infrastructure reconstruction, so that L = 1 − β + D1.

At the end of the production cycle, t = 2 output is realized and consumption takes place.

Denoting by the subscript b and g “bad” and “good” states of nature, according to whether the shock occurs or not, output X in period 2 can be written as: where <u>x, x</u> ∈R<sup>+</sup> , denotes period 2 endowment which we take as a proxy for the country’s income level. The country’s ability to raise new funds D1, after suffering the adverse shock, depends on its access to capital market, which depends on its creditworthiness and thus on its perceived willingness to repay its debt obligations. Specifically, following the “old”sovereign debt literature à la Cohen and Sachs (1986), we assume that a default causes the country to lose a share γ < 1 of its current output X, a loss that is not fully appropriated by the lenders. For simplicity, and without great loss of generality, we then assume that no part of this lost income accrues to the latter.

The country thus faces two distinct borrowing constraints depending on whether default is avoided altogether, or it is expected only in the event of an adverse shock. In the first case, the constraint requires that default costs, in bad states, exceed the cost of servicing the debt, or:

> 11 For the sake of simplicity, and without great loss of generality, we assume that the interim period is close enough to the initial period so that the borrowing costs are the same in both periods.

3
Of course, if the country does not default in bad states it would a fortiori not default in good ones. In the second case, instead, (4) does not hold, lenders anticipate default in bad states and charge a risk-adjusted <u>1</u> interest rate i = 1−π<sup>.Theborrowingconstraintthatensuresthatdefaultisavoidedingoodstatescanthen</sup> be written as: Finally, we assume that where the first inequality implies that investment increases default costs by less than it increases debt so that a country without endowment has no access to finance. The second inequality, instead, ensures that investing in period 0 is always optimal.

In our model, consumers are risk neutral, and policy makers maximize expected income Y , where superscript j ∈{d, nd} denotes whether the country defaults if hit by an adverse shock or it does not, and Note that in this set-up, income and welfare are mostly determined by the borrowing constraints, and the latter are, in turn, a function of endowment <u>x.</u> This implies that they are more likely to bind in poor countries than in richer ones. In fact, given that default costs are proportional to total income, which, in turn, depends on endowments, the latter plays the role of “implicit”collateral to the bond issuance: richer countries have more to lose if default is the avenue of choice.

We exploit this dimension in the characterization of the general solution of the “benchmark case” by distinguishing five intervals according to the value of the country’s endowment <u>x.</u> In the main text, we will provide an intuitive characterization of our main results and we refer the reader to the Appendix for the complete analytical treatment.

# 2.1 Benchmark Scenario

In high-income countries,<sup>12�</sup> <u>x ≥</u> x<sup>B</sup> 1 � default costs are large enough to ensure that the borrowing constraint (4) is never binding. As a result, the country can borrow at the risk-free rate the optimal amount D0 = 1 in period 0, and the optimal amount D1 = β in period 1, if it is hit by a shock. Production is always maximized, and so is expected income.

> In less rich countries (x<sup>B</sup> 2<sup><</sup> <u>x</u> < x<sup>B</sup> 1<sup>),endowmentnolongerprovidesenough“collateral”toensurethat</sup>

> 12 The exact values of the thresholds are provided in the Appendix.

4
borrowing constraints are always slack. As a result, the country cannot borrow D0 = 1 in period 0 and D1 = β in the event of a shock. In this case, policy makers have a choice between maximizing period 0 investment or “underinvesting” initially, that is choosing a D0 < 1 in order to “save” additional access to finance should an adverse shock occur in period 1. We can show that, if the shock is rare enough—so that the underinvesting “self insurance”option is extremely expensive in terms of lost consumption—the country always chooses to maximize period 0 investment at the expense of period 1 additional access to finance in the event of an (unlikely) adverse shock. We thus have that D0 = 1, D1 < 1 − β.

If income further decreases <u>(x < x</u><sup>B</sup> 2<sup>),theborrowingconstraintnowpreventsthecountryfromfinancing</sup> the optimal amount of capital in period 0 and avoiding default in bad states. As before, for rare shocks, the country chooses to maximize borrowing in period 0 at the expenses of borrowing after a shock in period 1, so that we have D0 ≤ 1, D1 = 0. The relevant borrowing constraint (4) now becomes where the superscript nd denotes non default in the bad state. Note, however, that the financially constrained country now has the option to increase its indebtedness up to the level that ensures repayment in good (but not in bad) states. Specifically, it can borrow up to (5), which now becomes: from which where the superscript d denotes default in the good state. It can be shown that for suffi ciently high endowment values (x<sup>B</sup> 3<sup>≤</sup> <u>x < x</u><sup>B</sup> 2<sup>)totalincomeismaximizedbythelower(default-free)levelofindebtedness,</sup> whereas for lower values of endowment (x<sup>B</sup> 3<sup>></sup> <u>x ≥</u> x<sup>B</sup> 4<sup>)thecountrychoosesthehigherlevelofindebtedness,</sup> borrowing and investing D0<sup>dinperiod0,anddefaultingwheneveritishitbyashock.</sup> Finally, poor countries <u>(x</u> < x<sup>B</sup> 4<sup>)choose,again,torestraintheirborrowinginperiod0soastoavoid</sup> default if hit by a shock in period 1.

The above analysis is summarized in Figure 1.a, where we plot D0 and D1 as a function of initial income <u>x,</u> setting the rest of the intervening parameters at reasonable (albeit arbitrary) values.<sup>13</sup> Intuitively, for rich countries (x ≥ x<sup>B</sup> 1<sup>)creditworthinessisneveraproblem:endowmentsprovideenoughimplicitcollateral</sup> to ensure access to finance to exploit investment opportunities in good states, and to fully rebuild the infrastructure in bad states.

By contrast, all other countries face a trade-off between the amount they can invest in period 0 and what they can invest in period 1 if they are hit by a shock. For rare events, countries are better off investing more in period 0, even if this means losing access to finance in the (unlikely) event of a shock in period 1. In this context, relatively rich upper middle-income countries (x ≥ x<sup>B</sup> 2<sup>)canstill(partially)financetherebuilding</sup> of infrastructure in period 1. This option is lost to when <u>x < x</u><sup>B</sup> 2<sup>.</sup> Moreover, because for <u>x</u> < x<sup>B</sup> 2<sup>countriesareforcedtounderinvestinperiod0inordertoavoiddefault</sup>

> 13 In particular, we assume that π = 0.02, γ = 0.3, ρ = 1.25, and β = 0.4.

5
in period 1, they face the choice between borrowing more today and defaulting tomorrow in the event of a shock, and borrowing less today and avoiding default costs tomorrow; a decision that ultimately depends on the extent to which investment can be expanded by accepting the higher risk-adjusted interest rate.

In the case of middle-income countries with good access to capital (x<sup>B</sup> 3 ≤ <u>x</u> < x<sup>B</sup> 2<sup>),theadditional</sup> resources do not justify the higher rate, and default is avoided. These resources becomes relatively more valuable as endowments decline and the financing gap widens so that, for lower middle-income countries (x<sup>B</sup> 3<sup>></sup> <u>x</u> ≥ x<sup>B</sup> 4<sup>),overborrowingisthepreferredstrategy.</sup> However, because of the higher interest rate charged to the overborrowing country, the financial constraint tightens faster in this case (<sup>∂D</sup> ∂x0<sup>d</sup> ><sup>∂D</sup> ∂x0<sup>nd),</sup> which, in turn, explains why low-income countries (x < x<sup>B</sup> 4<sup>)prefertolimitinvestmenttoavoiddefault.</sup>

# 3 Insurance

The presence of borrowing constraints—that limit initial investment, the post-shock rebuilding effort, or both— create effi ciency losses in all but the richest countries. The natural arrangement to mitigate the problem is an insurance contract that, in exchange of a premium, pays off the country in bad states. To discuss the effect of the availability of such an insurance policy, we assume that in period 0 the country has the option to purchase an insurance contract that pays off an amount Z in the interim period in case the country is hit by a negative shock. To buy one unit of insurance, the country pays a premium φ = πν. π is the net present value of a unit expected insurance outlay, and ν is a margin that reflects, inter alia, intermediation costs and a risk premium (alternatively, the insurer’s cost of capital, including potential increases if the event materializes). We assume that the insurance premium is paid up front and financed through debt issuance. In addition, we also assume that a non-empty interval for small enough π (π < γ), to explicitly model the fact that insurance is expensive<sup>14</sup> but not so expensive that the country would ever buy it. Furthermore, to simplify the analysis, we also assume that which guarantees that no default occurs in the insurance case.<sup>15</sup> The expected income of a country that in period 0 borrows D0+ φZ to invest K0 and to purchase Z units of insurance is With this new instrument available, we revisit the country’s choices as a function of income levels. In the case of rich countries <u>(x</u> ≥ x<sup>B</sup> 1<sup>)noinsuranceisneededtoattaintheoptimum(theborrowingconstraintis</sup>

> 14 This stylyied contract applies more directly to the case of a parameterized CAT bond with principal Z and coupon φ, which, in the case of a verifiable natural disaster, virtually eliminates the need for costly state verification. Standard CAT insurance, by contrast, are typically based on actual losses and cover pre-specified layers, defined by a deductible or “retention” (below which no loss is covered) and a “limit” above which no loss is covered.

> 15 Such assumption does not alter the qualitative results of our analysis (insurance always reduces the likelihood of default) but limit the number of cases that we have to analyze.

6
not binding). Moreover, because ν > 1, the effective cost of insurance exceeds that of international capital, and no insurance is purchased. The solution is then identical to benchmark case.

For lower values of <u>x</u> (x<sup>B</sup> 1<sup>></sup> <u>x</u> ≥ x<sup>I</sup> 2<sup>)theborrowingconstraintlimitsperiod1borrowing.Asinthe</sup> benchmark case, for rare events the country always chooses to maximize period 0 investment (which in this case attains the optimal D0 = 1), so that period 1 is the residual variable. In this regard, insurance plays a complementary role: by ensuring the availability of resources in the aftermath of a shock, it increases output in bad states and, through this channel, relaxes the borrowing constraint (4) that becomes: so that and This implies that insurance has a “catalytic”effect on private lending: by purchasing insurance the country enhances access to the international capital market in bad states. This effect explains why the country might be willing to purchase insurance even if it is expensive relative to capital markets. More precisely, the derivative of expected income on insurance is given by: where the expensive premium (the first RHS term) is counterbalanced by the positive catalytic effect (the second RHS term). On the other hand, given its costly nature, the country would purchase insurance only as a complement to market funds, so that since increasing coverage beyond Z would simply substitute expensive insurance for less costly debt. In this way, insurance fills in for private markets, both crowding in additional private funds and providing the resources that the market does not offer to allow the country to insure against the shock.

For lower income countries <u>(x</u> < x<sup>I</sup> 2<sup>),insurancewillnolongerhaveacatalyticeffect,asthecountry</sup> cannot borrow in period 1. However, the country may still be interested in buying insurance. Why? To relax its borrowing constraint in period 0, which now becomes from which we have that: It is easy to check that for small values of π,<sup>∂D</sup> ∂Z0<sup>nd</sup> > 0 and<sup>∂E</sup> ∂Z<sup><u>(Y)</u></sup> > 0. In other words, since insurance increases access to capital market in period 0, the country fully insures, that is, purchases insurance for an 7
amount Z = D0<sup>nd</sup> − (1 − β) so as to bring infrastructure to L = K in the event of a shock. It is important to note that it is never in the best interest of the country to overborrow at the risk of defaulting in bad states and purchasing insurance. The intuition is the following. Consider a country that overborrows and defaults in bad states; the anticipation of default eliminates the catalytic effect of insurance (through its role in the now irrelevant (4)). In turn, without this effect, insurance is simply too expensive and no insurance would be purchased if default in bad states is inevitable. Note that insurance does not work as a substitute for lending. Rather, it pays off to insure only if the country reaps the crowding-in benefits, for which insurance funds need to work as collateral to prevent default in bad states. If default in bad states is anticipated, the collateral value of insurance vanishes.

Finally for poor countries (x<sup>I</sup> 3<sup>></sup> <u>x),</u> access to insurance no longer plays a role as the catalytic effect disappears because the lack of creditworthiness limits investment opportunity in period 0. The previous analysis is summarized in Figure 1.b, where we plot debt and insurance outlays under the insurance case for the same parameter as in Figure 1.a. In addition, we assume that the overhead parameter ν = 1.3.

As we already pointed out, for high income countries the borrowing constraint does not bind, no insurance is purchased, and the results are the same as in the benchmark case. Less rich countries (x<sup>B</sup> 1<sup>></sup> <u>x</u> ≥ x<sup>I</sup> 2<sup>),</sup> instead, start purchasing insurance to increase their ability to rebuild infrastructure in the aftermath of the shock. Notice that in this case insurance plays two roles. On the one hand, by ensuring the availability of “prefinanced” reconstruction funds, it increases output in bad states and, in turn, default costs, crowding in private lenders. As a result, in this region, insurance enlarges the amount of resources available in the aftermath of the shock relative to the benchmark, and complements private funds. Also, the more credit constrained a country is, the more insurance it buys. Relatively poorer countries (x < x<sup>I</sup> 2<sup>),instead,areless</sup> affected by the shock (because of their limited capital investment in period 0)), and this negatively affects their demand for insurance.

# 4 A catastrophe lending facility

The previous analysis focused on the “supply side”of the problem showing that the availability of insurances allows a country to relax the borrowing constraint—albeit at or despite a considerable cost. However, because large events of a systemic nature such as natural disasters involve massive economic losses and affect a large number of people, they typically trigger ex-post government intervention which agents correctly anticipate. This often creates Samaritan dilemma type of problems that lead individuals to underinvest in catastrophe insurance. Similarly, at the international level, catastrophes in low-income countries elicit an almost immediate reaction by the international community in the form of (often concessional) loans for social expenditure and reconstruction. Why would a country bear the exorbitant insurance premiums if it is likely to have access to offi cial resources at a small cost? Is this version of the Samaritan’s dilemma what is behind the scarcity of catastrophe insurance in middle- and low—income countries? Would it be there any demand for insurance should the latter be made available to all?

We can easily adapt our model to look into this issue and examine whether insurance is still purchased by the country in presence of a catastrophe lending facility offering unlimited funds at the risk-free rate in the event a shock. For expositional purposes, it is easier to tackle this question in two steps, solving first for 8
the lending facility in the absence of insurance, and then introducing the insurance.

Consider now the case in which a multilateral lender offers a catastrophe lending facility, as in the case of the recent approved World Bank CAT DDO facility,<sup>16</sup> from which a country can draw (only) in the event of a shock. It is easy to show that this facility cannot be offered by private markets because loan amounts will be restricted by the borrowing constraint in exactly the same way D1 was in the previous case. However, a multilateral lender could in principle exploit its preferred creditor status to provide access in period 1 beyond what the borrowing constraint allows. Indeed, preferred offi cial creditors (the government at the national level, multilaterals and donors at the international level) are the ones that usually come to the rescue after large natural disasters.

In order to represent the preferred creditor status of the multilateral lender, we assume that defaulting on the multilateral is prohibitively costly so that multilateral loans are always repaid. Therefore, in this case, selective default on private creditors could be an equilibrium outcome.<sup>17</sup> Given the debt D0 (with private lenders) and M (with offi cial lenders), in period 2 the country faces two choices: repay or default on bonds.

More formally, in period 2, the sovereign does not default on bonds if, and only if whereas the unconstrained M is set to maximize period 2 output, i.e., M = D0 − (1 − β). Replacing M into (22), we obtain Note that the fact that M is chosen ex post (i.e., the country cannot commit not to borrow from the facility in period 1) simplifies the problem, which now boils down to the choice of period 0 borrowing, D0. Also note that, under the assumption that multilateral and private lending command the same interest rate, the actual composition of period 1 lending is immaterial for the current analysis. Then, without loss of generality, we can set D1 = 0.

In the non default case, expected income can be expressed as However, the country can also borrow beyond the limit imposed by (23) and, after a shock, withdraw from the facility and default on the bond. In this case, expected income is given by As before, the equilibrium can be characterized by income levels. In the case of rich countries (x > x<sup>B</sup> 1<sup>)</sup>

> 16 The CAT DDO is a new financial product offered to middle-income country governments by the International Bank for Reconstruction and Development (IBRD), part of the World Bank Group.

> 17 We implicitly assume that the multilateral has no way of conditioning its lending on the continued service of the debt with private lenders, which in our setup simply reflects a sequencing issue: the fact that the contingent loan is disbursed in period 1, before the bond matures. However, we come back to this point in the final section.

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the borrowing constraint is not binding: the country borrows and invests D0<sup>nd</sup> = 1 in period 0, and D1 = β, in period 1 in the event of a shock. However now, less rich countries <u>x</u> ∈ [x<sup>M</sup> 1<sup>, xB</sup> 1<sup>],canborrowfromthe</sup> facility as much as they need because defaulting on it is not an option.

In the case of poorer countries, (x ∈ [x<sup>M</sup> 2<sup>, xM</sup> 1<sup>]),period0borrowingconstraintbinds:D</sup> 0<sup>nd</sup> < 1 and, as a result, M = D0<sup>nd−(1 −β) < β.Forlowerlevelofendowments</sup><sup><u>(</u></sup> <u>x ∈</u> [x<sup>I</sup> 3<sup>, xM</sup> 3<sup>])thecreditconstrainedcountry</sup> chooses to borrow D0<sup>d=min</sup> � 1−(1(1−−π)πγ)xγρ<sup>, 1</sup> � in period 0 at a risk-adjusted rate i = 1−1π<sup>,and,ifhitbythe</sup> shock, borrows M<sup>d</sup> = D0<sup>d−(1 −β)fromthecontingentcreditlineinperiod1,anddefaultsinperiod2</sup> on its obligation to private creditors. The intuition is similar to that in the benchmark case, except that now the overborrowing country still has access to financial resources in period 1. Indeed, overborrowing also increases output in bad states, since reconstruction funds are not restricted by the borrowing constraint and increase linearly with period 0 investment. For this reason, default has a smaller impact on income than in the benchmark. Finally, for the same reason as before, low income countries <u>(x ∈</u> [x<sup>I</sup> 3<sup>, xM</sup> 3<sup>])choosetoavoid</sup> default and borrow from the facility as long as they face capital needs in period 1 A visual comparison of how the multilateral facility (see Figure 1.c) compares with the benchmark case reveals that the presence of the contingent credit line narrows the interval in which the country chooses to default. This is so because the contingent credit line increases the value at stake in case of a default. Given that default costs in this setup are proportional to output, the benign output effect of the contingent line increases the cost of defaults and reduces their incidence—even though the defaulting country still has access to the multilateral loan.

In turn, comparing with the insurance case, borrowing in period 0 is never higher under the lending facility. Again, the intuition is relatively straightforward: whereas the insurance premium entails a transfer from good to bad states (and, in particular, is arbitrarily small for rare events), the catastrophe loan transfers the cost of the shock intertemporally within bad states (that is, states marked by the occurrence of the shock), creating a sharp asymmetry between good and bad states, and tightening the borrowing constraint associated with the latter. Hence, the lower borrowing amounts (due to the crowding out of period 0 bond borrowing by period 1 multilateral lending) and the positive probability of default.

Regarding this point, note that for simplicity we assumed that the lending facility extended one-period loans. While this realistically reflect the short-run nature of most emergency and concessional lending, it bears the question of whether a longer loan can substitute insurance in those cases in which, because of market imperfections or political economy reasons, supply or demand for insurance is likely to be insuffi cient. More specifically, can a 1 in 30 years event be covered indistinctly by insurance and by a 30-year contingent loan?

According to the previous analysis, it cannot. A country that optimally borrows from the facility after it is hit by a shock inherits the full stock of debt, irrespective of the duration of the loan. In other words, since default in this case is not the result of a liquidity crisis but rather the consequence of a cost-benefit analysis, it is the stock of debt rather than its flow cost that determines the decision.

Consider now the case in which the country has access to both insurance and the lending facility. Would the country still purchase insurance in this case, or would it rely entirely on catastrophe lending? In other words, does the facility make the supply of insurance redundant for the country?

To answer the question, first note that for relatively rich countries <u>(x</u> ∈ [x<sup>M</sup> 1<sup>, xB</sup> 1<sup>]),borrowingfromthe</sup> facility is clearly superior to insurance, because it allows the country to circumvent the borrowing constraint 10
at a lower cost. On the other hand, it is easy to verify that, for x < <u>x</u><sup>~~M~~</sup> 1<sup>,insuranceisalwaysdemanded.</sup> In particular, for x ∈ <u>[x</u><sup>~~I~~</sup> 2<sup>,</sup> <u>x</u><sup>~~M~~</sup> 1<sup>],seeFigure3a,thecountry’sproblemconsistsininvestingL0=1,and</sup> L1 = β, at the lowest cost, which in turn implies minimizing the amount of (costly) insurance compatible with that objective. The borrowing constraint (4) now becomes: and substituting (26) can be rewritten as: It is easy to verify that within this interval, both insurance and multilateral lending coexist. In addition, for <u>x</u> ≤ <u>x</u><sup>~~I~~</sup> 2<sup>,lowperiod0investmentlevelsmakethelendingfacilityredundant,andinsurancebecomesthe</sup> only source of funding in bad states. Thus, we are back to the insurance case discussed previously.

In summary, the demand for insurance is crowded out by the presence of the facility only for those relatively high income countries for which the facility is enough to lift the borrowing constraint. However, because multilateral lending crowds out access to capital markets in period 0, insurance still plays a helpful role reducing the burden of period 1 debt, thereby relaxing the borrowing constraint. In other words, while the Samaritan’s dilemma considerations eliminate the need for insurance as a source of funds in bad states, it does not eliminate its catalytic role in good states.

# 5 Welfare analysis

So far, we have concentrated on the implications of the models in terms of access to finance in both states. Naturally, there is more to this exercise than simply comparing access. Indeed, an evaluation of the different alternatives would have to ponder their consequences in terms of expected income which, without great loss of generality, we perform graphically for the set of parameters used in the figures. Our welfare analysis is summarized in Figure 2. The top panel (2a) of the figure plots net income from production in good and bad states (that is, output net of borrowing costs and endowments, or Yg,b − <u>x),</u> for each of the three main scenarios under study: the benchmark, up-front insurance and ex-post catastrophe lending. The second panel (2b) does the same for expected income. Not surprisingly, both insurance and catastrophe lending are (weakly) superior to the benchmark: income under each alternative (and in both states) is always greater or equal than in their absence. But their relative benefits differ according to the country’s endowment.

If access to finance is not critical (richer countries), the insurance option yields a lower expected income than the less expensive multilateral lending facility. However, in the case of low-middle income countries the multilateral facility may, at the same time, crowd out private lending and be ineffective in avoiding costly default. Since for these countries access to finance is critical it is not surprising that higher levels of expected income are associated with the insurance option. What is somehow more surprising is that for a large set of endowment values a country may enjoys higher income in both states of nature if it relies on insurance rather than on the multilateral facility.

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Such welfare trade-offs are clearly illustrated in Figure 3, where we cast a closer look at the situation in which insurance and the catastrophe lending coexist. As can be seen, the demand for insurance kicks in at the endowment level for which the borrowing constraint starts limiting investment in period 0. Thus, by crowding in private lending in period 0, insurance enables a financially constrained country to reach the optimal level of investment, albeit at a premium that detracts from the optimal expected income.

A potentially undesirable characteristic of the lending facility examined above is that it involves a multilateral institution lending to a country at a time when the country is expected to default on its private creditors. Unlike implicit arrangements, an explicit facility could still condition access to the facility ex ante, so as to make sure that the borrower has the incentives to avoid default.<sup>18</sup> This is not far from standard multilateral practice: multilateral loans are often granted provided that the recipient country meets certain debt sustainability criteria.<sup>19</sup> In this way, the offi cial lender ensures that the country does not take the new money the minute before it defaults on third parties. Intuitively, to the extent that overborrowing excludes the country from the facility, this new condition should detract from the incentives to default, and reduce its incidence.

The solution for a contingent catastrophe lending facility (contingent on not defaulting on the private sector) does not differ much from the one presented in the previous section (see Appendix). Interestingly, a comparison between the contingent and the uncontingent facility reveals the latter to be better, at least in terms of expected income, see Figure 4. The reasons is that, for those endowment levels for which the two differ, the contingent facility saves the default costs at the expense of leaving the country underfinanced after an adverse shock. However, because the shock is exogenous, the situation involves no moral hazard and no value is created by reducing the incidence of default. On the contrary, the punishment (exclusion from the facility) translates in a lower overall welfare.

# 6 Conclusion

In this paper, we have analyzed how countries with different degree of access to credit markets can cope with natural disasters. More precisely, we have shown that insurance, even when very expensive, can be an effective instrument to improve a country’s creditworthiness. We have also shown that the presence of a credit line that provides automatic access to reconstruction funds ex-post, at a cheaper cost, does not completely crowd out the demand for insurance.

The previous discussion, however, needs to be qualified in three ways. First, the insurance and the credit line differ in one crucial aspect: the loan has to be paid after a bad shock while the cost of insurance is transferred to good states. In other words, income (and consumption) volatility is bound to be lower with insurance than in any other scenario. Trivially, if income smoothing—from which we deliberately abstracted so far—were a policy objective, insurance would become relatively more appealing, a result that would only add to the case for insurance that our findings support.

Second, we assumed that the ex-post credit line is not concessional and that the lender recoups the cost. In reality, often disaster help is highly concessional. Our main results would hold true for a limited level of

> 18 To enhance incentives without distorting its automatic nature, the facility could involve temporary subscriptions on a rolling basis, to ensure that the country is not cut off overnight but still faces frequent exams.

> 19 However, in the aftermath of a natural catastrophe it is not unlikely that other creditors (especially bilateral) agree to write-off part of their credit to allow multilateral lending.

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concessionality. Of course, if the country expects pure grants, these will completely crowd out the demand for insurance.

Finally, while insurance (particularly when reasonably priced) would seem the logical option for disasterprone middle-income countries, the fact that it entails a payment up front in exchange for an infrequent positive transfer makes this type of arrangement a political hard sell. Thus, from a policy perspective, a multilateral catastrophe lending facility may be the only feasible alternative even for those cases in which insurance is a possible choice. Such political economy considerations should be carefully analyzed and this could be the focus of future research.

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