WPS5617 Policy Research Working Paper 5617 How Economic Growth and Rational Decisions Can Make Disaster Losses Grow Faster Than Wealth Stéphane Hallegatte The World Bank Sustainable Development Network Office of the Chief Economist March 2011 Policy Research Working Paper 5617 Abstract Assuming that capital productivity is higher in areas at increasingly destructive in the future, average disaster risk from natural hazards (such as coastal zones or flood losses may grow faster than wealth. Myopic expectations, plains), this paper shows that rapid development in these lack of information, moral hazard, and externalities areas--and the resulting increase in disaster losses--may reinforce the likelihood of this scenario. These results be the consequence of a rational and well-informed trade- have consequences on how to design risk management off between lower disaster losses and higher productivity. and climate change policies. With disasters possibly becoming less frequent but This paper is a product of the Office of the Chief Economist, Sustainable Development Network. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://econ.worldbank.org. The author may be contacted at hallegatte@centre-cired.fr. 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 How economic growth and rational decisions can make disaster losses grow faster than wealth St´ phane Hallegatte a,b, e a Sustainable Development Network, The World Bank, Washington D.C., USA b Ecole ee Nationale de la M´ t´ orologie, Toulouse, France Corresponding author: St´ phane Hallegatte. e e Email address: hallegatte@centre-cired.fr (St´ phane Hallegatte). 1 Introduction It is widely recognized that economic losses due to natural disasters have been increasing expo- nentially in the last decades. The main drivers of this trend are the increase in population, and the growth in wealth per capita. With more and richer people, it is not surprising to find an increase in disaster losses. More surprising is the fact that, in spite of growing investments in risk reduction, the growth in losses has been as fast as economic growth (e.g., for floods in Europe, see Barredo, 2009; at the global scale, with much larger uncertainties, see Miller et al., 2008, Neumayer and Barthel, 2010), or even faster than economic growth (e.g., in the U.S., see Nordhaus, 2006; Pielke et al., 2008). Climate change does not seem to play a significant role in these evolutions, except possibly in very specific cases, for some hazards in some regions (Neumayer and Barthel, 2010). In the U.S., the trend in disaster loss relative to wealth can be almost completely explained by the fact that people take more and more risks, by moving and investing more and more in at-risk areas (Pielke et al., 2008). Most of the time, the explanations offered for this increasingly risk-taking trend are the follow- ing: · Information and transaction costs: since the information on natural hazards and risk are not always easily available, households and businesses may decide not to spend the time, money and effort to collect them, and disregard this information in their decision-making process (Magat et al., 1987; Camerer and Kunreuther, 1989; and Hogarth and Kunreuther, 1995). · Externalities, moral hazards, and market failures: since insurance and post-disaster support are often available in developed countries, households and firms in risky areas do not pay the full cost of the risk, and may take more risk than what is socially optimal (e.g., Kaplow, 1991; Burby et al., 1991; Laffont, 1995). Also, Lall and Deichmann (2010) show that risk mitigation has positive externalities and that private and social costs of disaster losses may differ, leading to inappropriate risk reducing investments. · Irrational behaviors and biased risk perceptions: Individuals do not always react rationally when confronted to small probability risks, and they defer choosing between ambiguous choices (Tversky and Shafir 1992; Trope and Lieberman, 2003). Moreover, they have trouble to take into account events that have never occurred before (the "bias of imaginability", see Tversky and Kahneman, 1974). Finally, private and public investment decisions do not always ade- quately take long and very long-term consequences into account (for public decisions, see Michel-Kerjan, 2008; for private decisions, see Kunreuther et al. 1978, and Thaler, 1999). There is no doubt these factors play a key role. But this move toward at-risk areas could also be a rational decision -- motivated by higher productivity in at-risk areas -- rather than a market failure. This paper shows that this possibility cannot be discarded. It is possible, indeed, that investments in at-risk areas bring benefits that justify increased risks. For instance, international harbors and tourism create jobs and activities that attract workers in 2 coastal zones in spite of flood risks. When economic growth is driven by export, the attractiveness of coastal zones is reinforced because these regions allow for easier and cheaper exports. From the activities that benefit from being located in a risk-prone area, additional investments are then carried out to benefit from agglomeration externalities on productivity and reduced transportation costs (Ciccone et al., 1996; Ciccone, 2002; Lall and Deichmann, 2010). New Orleans started as a port, and then became an important city that attracted a growing population. This population faced a scarcity of land that induced it to settle in low-lying areas, protected by fragile sea walls and pumping systems. More generally, the drivers of economic growth are concentrated in cities. Combined with re- duced income from agriculture -- especially in the poorest countries -- these opportunities have created strong incentives for rapid rural-urban migration. Confronted with land scarcity and high land costs in large cities, this migration has led to construction in at-risk areas (e.g., Burby et al., 2001; Burby et al., 2006; Lall and Deichmann, 2010). In the most marginal and risky locations, informal settlements and slums are often present, putting a poor and vulnerable population in a situation of extreme risk (e.g., Ranger et al., 2011). One can make the case, therefore, that population and asset migration to at-risk areas is not solely due to lack of information, irrational behaviors and moral hazard, as often suggested, but also to a rational trade-off between lower disaster losses and higher productivity in risky areas. This paper proposes an economic framework to analyze this possibility. Compared with previ- ous investigations of the economics of risk mitigation (e.g., Lewis and Nickerson, 1989; Strobl, 2008), this analysis stresses the existence of benefits from investing in at-risk areas, investigates both investments in at-risk locations and risk mitigation choices in a common framework, and highlights the trade-off between lower disaster losses and higher productivity. Assuming this framework is valid, and under some conditions, it is found that -- even with no change in climate conditions and hazard characteristics -- natural disasters may become more destructive in the future and that average losses may increase faster than wealth and income. This possibility has important consequences on how to design risk management and risk reduction policies and how to deal with climate change. These aspects are discussed in the conclusion. 2 Larger disasters in a wealthier world? It is generally accepted that richer populations invest more to protect themselves from natural hazards. A richer population, however, may also invest more in at-risk areas, increasing exposure to natural hazards. These two trends have opposite impacts on risk, and the resulting trend in risk is thus ambiguous. This trend is investigated in this section with a simple model. 3 2.1 A balanced growth pathway Let us assume a balanced economy, in which economic production is done using productive capital only, with decreasing returns: Yb = f (Kb ) = Kb (1) The variable Yb is annual production (i.e. value added) in the balanced growth pathway; K b is the corresponding amount of productive capital; and is total productivity. All variables are time dependent, and are assumed to growth over time. Productivity is growing at a rate . (t) = (0)et (2) Assuming the economy is on a balanced growth pathway, production and capital are also growing at the same rate: Yb (t) = Yb (0)et (3) Kb (t) = Kb (0)et (4) To be consistent, Eq.(1 to 4) require: Yb (0)et = (0)et Kb (0)et (5) which means: = (6) 1- and Yb (0) = (0)Kb (0) (7) 2.2 The trade-off between higher productivity and lower disaster losses Let us now assume that the amount of capital K b can be either located in safe locations (Ks ) or in risky locations (Kr ), with Kb = Ks + Kr . Examples of risky locations are coastal areas, where storm surge and coastal floods are possible, as well as areas at risk of river floods, high- concentration urban areas at risk of floods in case of heavy precipitations, and even earthquake- 4 and hurricane-prone regions. We assume that risky locations are more productive, thanks to their location (e.g., proximity from port infrastructure for export-oriented industries; coastline ameni- ties for tourism; easier access to jobs in at-risk locations in crowded cities). This increase in production has decreasing returns, however. As a consequence, total production becomes: Y = Yb + Y = Yb + Kr (8) where Y is the additional output produced thanks to the localization of capital in risk-prone areas; is a relative productivity advantage, and is assumed to growth at the same rate as the general productivity (i.e., at the rate ). The capital located in the risky area can be affected by hazards, like floods and windstorms. If a hazard is too strong, it causes damages to the capital installed in at-risk areas, and can be labeled as a disaster. To simplify the analysis, we assume that in that case, the capital at-risk is totally destroyed. It is assumed that this is the only consequence of disasters; no other impacts like fatalities and casualties are considered in this simple model, and additional indirect economic consequences (Hallegatte and Przyluski, 2011) are not taken into account. These disasters (i.e. hazards that lead to capital destruction) have a probability p 0 to occur every year, except if protection investments are carried out and reduce this probability. These protec- tion investments take many forms, depending on which hazard is considered. Flood protections include dikes and seawalls, but also drainage systems to cope with heavy precipitations in ur- ban areas. Windstorm and earthquake protections consist mainly in building retrofits and stricter building norms, to ensure old and new buildings can resist stronger winds or larger earthquakes. It is assumed that better defenses reduce the probability of disasters, but do not reduce their consequences. This is consistent with many types of defenses, like seawalls that can protect an area up to a design standard of protection but fail totally if this standard is exceeded. Better defenses are also more expensive, and the annual cost of defenses C and the remaining disaster probability p are assumed linked by the relationship: 1 1 C(p) = - (9) p p0 so that the cost of reducing the disaster probability to zero is infinite. Depending on the value of , protection costs increase more or less rapidly when the disaster probability approaches zero. The parameter therefore corresponds to more or less optimistic assumptions on protection costs. Any given year, the economic output is given by: Y = Yb + Kr - C(p) - L (10) 5 where L is the damages from disasters, and is given by a random draw with probability p. If a disaster occurs, losses are equal to Kr , i.e. all the capital located in the risky area is destroyed. Any given year, the expected loss E(L) is equal to pK r and the expected output is equal to: E(Y ) = Yb + Kr - C(p) - pKr (11) 2.3 Optimal choice of p and Kr Assuming a social planner -- or an equivalent decentralized decision-making process -- decides the amount of capital Kr to be located in the risky area and the level of protection that is to be built, its program is: 1 maxp,Kr E(Y ) (12) s.c.Kr Kb and 0 p p0 We neglect risk aversion and we assume that the expected production is maximized, not the expected utility. Doing so is acceptable if disaster losses remain small compared with income, consistently with the Arrow-Lind theorem for public investment decisions (Arrow and Lind, 1970). However, this condition holds only if disaster losses can be pooled among a large enough population (e.g., a large country), and with many other uncorrelated risks, i.e. in the presence of comprehensive insurance coverage or post-disaster government support. For small countries (where a disaster can strike a large share of the population), or where insurance and post-disaster support are not available, the objective function should need to include risk aversion. First order conditions lead to the optimal values of p and K r : -1 1 p = () +(-1) () +(-1) (13) 1 +1 - +(-1) Kr = () +(-1) () (14) Assuming for now that Kr Kb and that p p0 , the expected annual loss at the optimum is equal to: E(L) = () +(-1) ()- +(-1) (15) 1 This model is different from the Strobl's (2008) model. In the latter, the only decision concerns protec- tion investments that mitigate disaster consequences, and there is no benefit from taking risks and thus no trade-off between safety and higher income. 6 At the optimum, the loss in case of disaster is equal to: 1 +1 L = () +(-1) ()- +(-1) (16) When productivity is growing over time at the rate , there are two possibilities, depending on the value of , the exponent representing decreasing returns in the additional productivity from capital located in at-risk areas (see Eq. (8)). Proposition 1 If > /( + 1), then Kr and E(L) are decreasing over time in absolute terms. In that case, less and less capital is installed in the risky area when productivity and wealth increase. So, the absolute level of risk is decreasing with wealth. It is also noteworthy that, in such a situation, annual mean losses and capital at risk counter-intuitively decrease if protection costs () increase. If < /( + 1), then the amount of capital at-risk increases, and the risk (both in terms of average loss and maximum loss) is increasing with wealth, and mean annual losses and capital at risk are augmented if protection costs () increase. But the absolute level of risk is not a good measure of risk: a wealthier society is able to cope with larger losses. The question is therefore the relative change in risk. One way of investigating this question is to assess whether K r and E(L) are growing more or less rapidly than Yb and Kb , i.e. at a rate larger or lower than . - If is growing at a rate , expected losses E(L) are growing at a rate +(-1) and maximum -(+1) losses (i.e., the losses in case a disaster occurs), Kr , are growing at a rate +(-1) . Since K and Y are growing at a rate = /(1 - ), we have the following result: Proposition 2 If +1 < < +1 , then mean annual losses E(L) are growing faster than 1 baseline economic output Yb . If - +1 < < +1 , then the capital at risk and the losses in case of disasters (i.e. Kr ) are growing faster than Y b . With usual values for , i.e. about 1/3, and the simplest assumption for protection cost, i.e. = 1, losses in case of disasters are growing faster than Y for any , positive and lower than 1/2. Mean annual losses increase faster than Yb if is between 1/6 and 1/2. Therefore, it is possible that disaster maximum losses and mean annual losses increase with wealth in the future, even in relative terms. In this case, all capital will eventually be installed in at-risk areas (K r = Kb ), and a dis- aster would lead to the complete destruction of all production capacities, with a probability 1 1+ p= Kb . Figure 1 summarizes these findings, for = 1/3. It shows four zones, as a function of the values of the parameters and . In a significant portion of the parameter space, labeled "zone 2", the 7 1 Zone 1 0.5 Zone 2 Parameter /2 Zone 3 0 -1/2 -1 Zone 4 -1 0 0.5 1 1.5 2 2.5 3 Parameter Fig. 1. Behaviors of the optimal mean annual losses (E(L)) and of the optimal capital in at-risk areas (or, equivalently, of the losses in case of disaster) (Kr ), as a function of the values of the parameters and . There are four zones delimited by continuous lines. In the first zone, on the top of the figure, mean annual losses and capital at risk decrease in absolute terms when the productivity increases. In the second one, the capital at risk and the mean annual losses increase with productivity, both in absolute and relative terms (with respect to to total output and productive capital). In the third zone, the capital at risk still increases in absolute and relative terms, but the mean annual losses increase only in absolute terms (they decrease in relative terms). In the fourth zone, at the bottom of the figure, mean annual losses and capital at-risk increase in absolute terms but both decrease in relative terms. capital at-risk and the mean annual losses increase, even in relative terms when compared with total economic output. In this zone, therefore, disasters become less and less frequent, but they are more and more destructive, in such a way that the risk -- i.e., the average losses -- increases more rapidly than wealth and income. Surprisingly, the increase in risk happens when is small enough, i.e. when additional productiv- ity from locating capital in at-risk areas exhibits sufficiently diminishing returns. Consistent with intuition, however, is the fact that increase in risk is more likely when is large, i.e. when pro- tection costs are increasing rapidly with the protection level. It is interesting to note that absolute protection costs () and the absolute additional productivity () do not influence the behavior of mean annual losses and capital at risk, but only their levels. If = /( + 1), there is no inside maximum in Eq. (12). Instead, there are two possibilities depending on the protection cost relative to the additional productivity in at-risk areas. If the additional productivity is high enough (relative to protection costs), then all capital is located in at-risk area (Kr = Kb ). If the additional production is not sufficient, then no protection is 8 provided (p = p0 ). The limit between these two possibilities depends on the protection costs, relative to the addi- tional productivity in at-risk areas. The limit protection cost ( l ) can be written as a function of the additional productivity as: (1+) l () = (17) 1+ and -- equivalently -- the limit additional productivity can be written as a function of protection costs: 1 l () = (1 + )c- 1+ 1+ (18) Proposition 3 If = /( + 1) and > l () (or, equivalently, < l ()), then no protection (1+) is provided (p = p0 ) and the capital in at-risk areas is equal to K r = p0 (1+) . If = /( + 1) and < l () (or, equivalently, > l ()), then all capital is located in at-risk areas 1 (Kr = Kb ), and the protection is such that the disaster probability is equal to p = Kb 1+ . 2.4 Preliminary conclusion In a reasonable framework and in a large parameter domain, a simple optimization suggests that, as observed by ISDR (2009), poor countries suffer from frequent and low-cost events, while rich countries suffer from rare but catastrophic events. Our analysis also suggests, however, that overall risk -- i.e. mean annual losses -- can increase with time, and that it can increase faster than wealth, even if all decisions are based on rational trade-offs between income and safety. This behavior appears consistent with time series of globally aggregated disaster losses. On the other hand, econometric analyses of the relationship between wealth and disaster losses have reached contradicting results. Skidmore and Toya (2007) find that the ratio of economic losses to GDP is decreasing linearly with GDP. Schumacher and Strobl (2008) reach more complicated results, with a nonlinear relationship that depends on the risk level. Their econometric analysis concludes that disaster losses can increase with wealth for low GDP levels where the risk is low or moderate, and for all GDP where the risk level is particularly high. 2 These results should be used with care, however, because of low data quality for global disaster data and methodological issues. In our model, the risk -- i.e. mean annual losses -- can increase with time as a result of a rational trade-off. Model assumptions can always be discussed, and this model does not demonstrate that 2 Note that in our analysis, loss behavior does not depend on the absolute risk level, but on the shape of the protection cost function and on the exponent of decreasing returns from investing in at-risk areas. 9 disaster economic losses need to increase. It shows, however, that the observed increase in dis- aster losses may not be due to irrational behaviors and could be the result of rational decisions. If these assumptions are correct, an increasingly wealthy world could see less disasters, but with increasingly large consequences, resulting in average annual losses that keep increasing more rapidly than income. These disasters, therefore, would have increasing macroeconomic conse- quences, and a growing welfare cost (see, on "rare economic disasters", Barro, 2006, 2009). Accounting for indirect disaster impact (see, e.g., Hallegatte and Przyluski, 2011) or for changes in risk aversion with wealth may alter this conclusion by augmenting disaster impacts in Eq. (11) or changing the objective function in Eq. (12). 3 Taking into account myopic behaviors This result assumes that both protection (i.e., p) and capital investment (i.e., K r ) decisions are made rationally and with perfect knowledge of natural risks. This last assumption appears unre- alistic, since many decisions are made using risk analysis based only on recent past experience, when risk is not simply disregarded (Magat et al., 1987; Camerer and Kunreuther, 1989; and Hogarth and Kunreuther, 1995). This section proposes a modified model to take into account this under-optimality in decision-making. In this modified model, we assume that capital investment decisions are made with imperfect knowledge, using risk assessments based on events of the recent past. This assumption is consis- tent with the observation that most capital investment decisions are not made using all available disaster risk information, and that risk-based regulations (e.g., zoning policies) have had a lim- ited impact on new developments in at-risk areas (on the U.S. National Flood Insurance Program regulations, see for instance Burby, 2001). On the other hand, we model protection decisions as made with perfect knowledge of natural risks and assuming (wrongly) that capital investment decisions will then also be made optimally and with perfect knowledge. There is thus an inconsistency in the model between protection decisions and capital investment decisions. This hypothesis is justified by the fact that (public and private) protection decisions are most of time designed through sophisticated risk analyses, taking into account all available information and assuming optimal behaviors. To assess the consequence of this myopic behavior, it is necessary to go beyond analytical calcu- lations, and use a numerical model. This model is extremely simple, and based on the calculations from the previous section. The model has a yearly time step. Each year, the baseline output Y b increases at the rate , and the additional productivity from at-risk capital increases at the rate . To decide on the optimal protection level, perfect knowledge is assumed, leading to the same protection levels as in the previous section: 10 -1 1 p = 2-1 () 2-1 (19) Then, a decision is made on the amount of capital to install in at-risk areas. We assume that this decision is made independently each year, with no inertia. It means that the optimization can be done in a static manner, with no intertemporal optimization. We assume decisions on the amount of capital to install in the risky area are based on a disaster probability that is estimated empirically, not on the exact probability. To do so, the model includes a random process, which decides -- each year -- whether a disaster occurs. In practice, F (t) = 1 if there is a disaster during the year t, and F (t) = 0 otherwise. The real disaster probability is p. ^ The empirically estimated disaster probability is p(t) and is given by: j=t t-j p(t) = ^ e- F (j) (20) j=- This modeling corresponds to backward-looking myopic expectation, in which past events have an exponentially decreasing weight (with time scale ). In other terms, agents assess future dis- aster risks from past events, with a memory characteristic time . The consequence is that the estimated disaster probability is higher than the real one just after a disaster, and lower than the real one when no disaster has occurred for a while. This behavior appears consistent with many observations (e.g., Kunreuther and Slovic, 1978; Tol, 1998). Investment decisions are based on this empirical probability, and the amount of capital in at-risk area is: 1 ^ ^ p -1 Kr = (21) ^ Just after a disaster, p(t) is larger than p(t), disaster risks are overestimated, the capital in the risky area is lower than its optimal value, and output is lower than its optimal value. After a ^ period without disaster, p(t) is lower than p(t), disaster risks are underestimated, the capital in the risky area is higher than its optimal value. As a consequence, output is higher than its optimal value in absence of disaster, but losses are larger if a disaster occurs. On average, output is also lower than its optimal value, since additional production thanks to higher productivity in risky areas does not compensate for larger disaster losses. The efficiency of this empirical process depends on the disaster probability. If there are many disasters over a period (i.e. if 1/p << ), the estimated probability remains close to the real one. If the memory is too short, i.e. if is too low, then the estimated probability will often be different from the real one. 11 Name Description Value Y (0) Initial production 10. phi Capital decreasing return parameter 1/3 Growth in general productivity 2% 0 Initial value of the additional productivity from capital in at-risk areas 0.4 Parameter describing the decreasing returns of investments in at-risk areas 0.2 p0 Disaster probability in absence of protections 0.8 Parameter for absolute protection costs 0.035 Exponent in protection costs 1 Probability estimation memory timescale 5 years Table 1 Parameters of the model. This numerical model is created and simulated with ad hoc parameter values, as an illustration of its results. Parameters are provided in Tab. 1; results are robust for different choices for these parameters, except for , as shown in Section 2.3. In this numerical exercise, we choose = 1 and select a value for such that mean annual losses increase with wealth in relative terms, i.e. +1 < < +1 (the second zone in Fig. 1). Results from one simulation are provided in Fig. 2 and Fig. 3. Figure 2 shows the real disaster probability p, which is decided through a perfect-information cost-benefit analysis (see Eq.(19)), ^ and the estimated disaster probability p, which is assessed through a myopic estimation (see Eq.(20)). After each disaster, the estimated disaster probability is higher than the real one; when no disaster occurs for a long enough period of time, the estimated disaster probability is below the real value. Figure 3 shows in the left-hand panel the additional output thanks to the presence of capital in the risky area (i.e. Kr - C(p) - L, see Eq.(10)), with perfect information or myopic behavior. 3 It shows a production that depends on the amount of capital at risk: the larger the amount of capital, the larger the additional production. But when a disaster occurs, this capital located in the risky area is wiped out, and this loss is recorded as an output loss, i.e. through a drop in output. With myopic behavior, the amount of capital at risk is too low when disaster probability is overestimated, and too high when this risk is underestimated. When the risk is underestimated, additional output is larger than its optimal value when no disaster occurs, but the drop in case of disaster is augmented, such that the average output is lower. The right panel of Fig. 3 shows the total output, i.e. Y , with perfect information and myopic behavior. As a baseline, the output 3 In this figure, the recovery and reconstruction are instantaneous, like in a world with infinite recon- struction capacity. In reality, there are strong constraints on reconstruction, and it can take several years to return to the pre-disaster situation; see, e.g., Hallegatte (2008). 12 1 Real annual disaster probability 0.8 Estimated annual disaster probability Annual disaster probability 0.6 0.4 0.2 0 0 10 20 30 40 50 60 70 Time (years) Fig. 2. Real disaster probability p, decided through a perfect-information cost-benefit analysis (see ^ Eq.(19)), and estimated disaster probability p, assessed through a myopic adaptive reactive anticipation process, for one random realization. 5 90 4 With perfect information 80 Net annual economic output in risky locations With myopic behavior 3 Net annual economic output Baseline with no capital at risk 70 2 1 60 0 50 -1 40 -2 With perfect information With myopic behavior 30 -3 -4 20 -5 10 0 10 20 30 40 50 60 70 0 10 20 30 40 50 60 70 Time (years) Time (years) Fig. 3. In the left panel, additional output thanks to the presence of capital in the risky area (i.e. Y = Kr - C(p) - L, see Eq.(10)), with perfect information or myopic behavior. In the right panel, to- tal output, i.e. Y , with perfect information and myopic behavior, and the baseline output when no capital is in at-risk locations. when no capital is located in the risky area is also represented. The total output is higher than the baseline output thanks to the location of capital at risk. When a disaster strikes, however, total output is lower than the baseline. 13 In the myopic behavior case, at the end of the period, the productivity is high, and the standard of protection is thus high. In other terms, the disaster probability is very low thanks to good protection. In such a situation, disasters are rare and the estimated disaster probability gets rapidly lower than the real one, prompting an over-investment in the at-risk area. The consequence is a larger disaster with myopic behavior than with perfect information. So, adding myopic behaviors amplifies our previous results. With perfect information, the pop- ulation is more protected when it gets richer, the disaster probability decreases over time. But disasters become larger and larger when they occur. With myopic behavior, the interval between two disasters rapidly becomes larger than the memory of the probability estimation process, and there is over-investment in at-risk areas, making disasters more catastrophic. This trend toward larger disasters is even likely to be enhanced by other processes influencing vulnerability, and especially indirect disaster impacts. In their industrial organization, businesses make trade-offs between their efficiency in normal conditions and their resilience in case of un- expected shock (e.g., Henriet et al., 2011). For instance, there is a tendency to reduce inventories and the number of suppliers to increase efficiency and reduce costs. This strategy increases ef- ficiency and reduces costs when all suppliers are able to produce on demand. But in case of an exogenous shock, a disaster or the bankruptcy of a supplier, reduced inventories and reliance on few suppliers can easily turn into operational problems. In the same way, networks-shaped infrastructure (e.g., transportation or electricity infrastructure) can be designed with redundancy to increase robustness in case of disasters, but this option make them more expensive in ab- sence of disaster. In a situation in which disasters are more and more exceptional, it is likely that businesses and other decision-makers will focus even more on efficiency and less on disaster resilience. Such a trend would increase the overall economic vulnerability, and would enlarge the welfare and economic consequences of any disaster. 4 Conclusion This paper proposes an economic framework to analyze the trade-off between disaster losses and higher capital productivity in areas at risk from natural hazards. Even though hypotheses can always be discussed, it shows that natural disasters may become less frequent but more intense when productivity and wealth increase. It is even possible to observe a long-term increase in average disaster losses, even in relative terms with wealth and income. Current trends in disaster losses appear consistent with this prediction (e.g., Etkin, 1999; Nordhaus, 2006; Pielke et al., 2008). These results are also in line with ISDR (2009), which observes that poor countries suffer from frequent and low-cost events, while rich countries suffer from rare but high-cost events. This trend is illustrated by the case of Japan. Thanks to strict building norms, the country can cope with no damages with frequent earthquakes that would cause disasters in any other place of the world. But this resilience allows for higher investments in at-risk areas, and exceptional quakes like the recent Tohoku Pacific earthquake can then lead to immense losses. 14 These results also suggest that the overall risk -- i.e. mean annual losses -- can increase with time, and even faster than wealth, in spite of continuously improving protection. A consequence of these findings is that future increase in disaster losses might be difficult to avoid. Increasing losses may even be desirable from an economic point-of-view, provided that (i) human losses can be avoided (thanks to warning and evacuation); (ii) affected populations are supported in disaster aftermaths or have access to insurance, to make sure individual losses remain small and the conditions of the Arrow-Lind theorem are respected (i.e., risk aversion can be neglected). This paper suggests a strong and increasing need for post-disaster support, through insurance, ad hoc support, emergency and crisis-management arrangements, in addition to investments in disaster protections, hazard forecasts, and early warning. All risks are not linked to rational choices, however. We showed that imperfect information and myopic expectations can amplify risk-taking behaviors. This effect can be reinforced by other sub-optimalities. In particular, some economic agents have little flexibility in their localization choices, like the poorest households who locate in informal settlements in developing-country cities. Also, risk involves externalities: when many buildings are destroyed by an earthquake, the economic system is paralyzed and collective losses exceed the sum of initial private losses (Lall and Deichmann, 2010; Hallegatte and Przyluski, 2011; Henriet et al., 2011). These risk amplification mechanisms and externalities may lead economic agents to accept more risk than what is socially optimal. These important sub-optimalities provide ample justification for public action to manage risks and limit risk-taking behaviors. But our results suggests that this action should not systematically aim at reducing the level of risk. Instead, it should aim at managing the level of risk, to limit disaster losses while making sure that we can still take the worthwhile risks that yield large benefits. In other terms, disaster risk management policies should be favored over disaster risk reduction policies. These results also have consequences on climate change policies. It is likely that socio-economic drivers will remain the dominant drivers of future changes in disaster losses. Some have de- rived from this result the idea that policy-makers should focus on reducing trends in disaster exposure and vulnerability, not on mitigating climate change (e.g., Pielke et al., 2005). But if socio-economic drivers of losses are the consequence of a desirable trade-off and yield signif- icant benefits, as suggested here, it might not be rational to oppose them in a systematic way. Climate change, on the other hand, may increase disaster losses without providing any benefits in return. 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