Incomplete recovery to enhance economic growth losses from US hurricanes under global warming

Abstract


Introduction
Already in the present climate, tropical storms in the North Atlantic, called hurricanes, cause substantial economic losses in the United States (US).Between 1980 and 2019, these storms caused on average about US$ 31 billion in direct economic losses per year, peaking at US$ 266.5 billion in 2005 according to MunichRe's NatCatSERVICE database 1 .
Moreover, there is increasing empirical evidence that, in addition to these direct losses, tropical storms can substantially reduce economic growth of affected countries for more than a decade 2;3;4 .These long-term growth impacts may have important implications for the adaptation to, and coping with, the impacts of tropical storms under global warming, since there is strong evidence that the proportion of very intense storms may increase 5;6;7 .There are at least two mechanisms through which this increase could overcompensate a possible mild decline of the overall number of tropical storms 5 driving up economic losses.First, the most intense storms cause dis-proportionally larger direct economic losses than smaller storms.For instance, major hurricanes of the two highest categories 4-5 on the Saffir-Simpsons scale 8 have accounted for almost half of normalised economic damage from all hurricanes that made landfall in the US in the period 1900-2005 despite representing only about 6% of landfall events 9 .Second, an increase of the return frequency implies that, on average, there is less time for the economy to recover in between consecutive events; incomplete recovery has been identified as one main factor that may increase the vulnerabilities of the economy to climate extremes and thereby drive up losses 10;11 .
Catastrophe insurance is discussed as a means to reduce economic vulnerabilities of the economy to extreme weather events by shortening the recovery time in the disaster aftermath 12;13;14 , and it may thereby even promote economic growth on the macroeconomic level 15 .These promising findings may explain the rising popularity of multilateral climate risk insurance schemes and the G20 InsuResilience Global Partnership initiative 16 .
However, it remains an open question whether higher insurance coverage and better insurance schemes will be sufficient to counteract climate change impacts in a warming world 17;18 .
Progress in answering this question has been also made difficult by the limitations of state-of-the-art climate integrated assessment models (IAMs).These standard workhorses for climate policy assessments (see 19;20 for detailed reviews of IAMs)) -such as the seminal DICE model 21 which is used by the US government to estimate the cost of carbon emissions to society -have been criticised for not being able to appropriately account for the impacts of climate extremes 22;23 .The main reason is that the coarse temporal resolution of most models (typically 5-10 years) simply does not allow for the representation of individual extreme weather events.In consequence, potentially important nonlinearities arising from a disproportional increase of total economic losses with impact intensity or from incomplete recovery between consecutive events cannot be resolved.In consequence, IAM-based studies usually report relatively small, or even negligible, impacts of climate extremes on the economy 24;25 which are at odds with recent estimates in the climate econometric literature 26;3;2 .

Main
Here, we first study how the heterogeneity of US hurricane impacts has affected economic growth in the period 1980-2014.We then project increases in growth losses that would arise in a 2 °C world from changes in the return frequencies of the storms and associated changes in storm number and impact heterogeneity.Since there is substantial uncertainty on how the return frequencies of hurricanes will change with global warming, and the magnitude of the effect strongly depends on the underlying methodology used to estimate this change 5 , we consider two different approaches at both ends of the uncertainty range.
In addition, we assess the efficacy and limits of disaster insurance in mitigating the climate change-induced increase in growth losses.To this end, we build a simple -and transparent -event-based neoclassical growth model for a national economy.The model accounts for losses to the stock of physical assets that result from individual landfall events.Reconstruction investments can be capped in the disaster aftermath to describe inefficiencies slowing down the economic recovery such as scarcity of trained labour and building materials as well as inefficiencies due to destroyed infrastructure and supply chain interruptions 27 .Further, we integrate a basic non-profit insurance scheme providing contingency funds for reconstruction of insured assets in the disaster aftermath.With a weekly time step, the model is able to resolve the economic response dynamics to individual landfall events, and to therefore capture non-linear loss amplifications that may arise from individual high intensity or consecutive events.Following ref. 10 , we define the latter as subsequent loss events that do not leave enough time in between for the economy to recover.In the standard calibration of the model, the insurance ratio is set to 50% the average ratio of insured losses in the US between 1980 and 2014 according to the NatcatSERVICE database 1 and reconstruction investments are capped to 0.2% of weekly output following ref. 27.This model calibration allows us to obtain average annual output growth losses that are comparable to those reported in the recent climate econometric literature 2;4 when driving the model with the direct asset losses of the 88 hurricanes that made landfall in the US in the period 1980-2014 according to the NatCatSERVICE database 1 .

Insurance accelerates economic recovery
To illustrate the interplay of insurance payouts and limits of reconstruction investments, we first study the economic recovery dynamics in the aftermath of an individual storm that destroys 1% of the physical capital stock in month 3 (Fig. 1A).Besides the "realistic" standard calibration of the model (or scenario) (green full lines), we consider two limiting scenarios, one without insurance (red lines) and one with full insurance coverage of all losses (blue lines).Further, to test the sensitivity of the model with regard to the construction investment cap, we consider a 1% reconstruction investment cap (dashed lines) in addition to the 0.2% reconstruction investment cap (solid lines) and contrast both to a limiting case where all available investments (difference between output and savings) can be used for reconstruction ("no investment cap", dotted lines) (Fig. 1B).Since insurance premiums depend on insurance coverage, each growth trajectory is normalised to the balanced growth path of an unperturbed economy with the same insurance premium.
To account for delays in insurance payouts, we fit data on cumulative insurance payouts of the Reinsurance Association of America 28 indicating that 60% (90%) of the insured losses are paid out after one (three) year(s) with a sigmoidal function (see Methods for details).
The resulting weekly payouts are shown in the inset of Fig. 1B.
Generally, the recovery of the economy can be divided into a first phase of rapid reconstruction of destroyed capital, and a second phase, where the economy slowly approaches the balanced growth path of the unperturbed system.The recovery speed in the first phase is reduced when the reconstruction investment cap is lowered.For the scenario with the lowest reconstruction investment cap and no insurance, the cap even limits the recovery dynamics in the slow second phase (red solid lines in Fig. 1A).In line with empirical findings, recovery speed increases with insurance coverage for two reasons 29;30 .First, since insurance provides additional financial means for reconstruction, the reconstruction investment cap can be temporarily exceeded.This accelerates the recovery process especially in the first reconstruction phase.Second, the larger the insurance coverage the lower is the share of the output that has to be reinvested in reconstruction efforts.In consequence, more output can instead be invested in new capital.This fosters output growth especially in the slow recovery phase.Except in the limiting, overly optimistic, case of full insurance coverage and no reconstruction investment cap, cumulative output losses increase super-linearly with the size of the direct asset losses, i.e, indirect losses increase with shock size (Fig. 1C).In consequence, in the aftermath of intense hurricane shocks it can take multiple months or even years for the economy to recovery.For instance, in the standard scenario, it takes more than 5 months for the production capacity to recover after the major hurricanes Andrew and Sandy that struck Florida and Louisiana in 1992 and New York and New Jersey in 2012, respectively, both causing asset losses equivalent to about 0.4% of the US's annual output in the years of landfall, respectively (grey vertical lines in Fig. 1C).Further, our modelling suggests that in the aftermath of the largest historical loss event, the landfall of hurricane Katrina in New Orleans in 2005, that caused asset losses equivalent to 0.8% of the US's annual output in this year, it took more than one year and a half for the production capacity to recover.

Growth losses increase with shock heterogeneity
Next, we study how the economic response dynamics depends upon the heterogeneity of hurricane shocks (Fig. 2).For that, we assume that i) landfall events are Poisson 31 distributed within the US hurricane season (June-November) and ii) direct asset losses (relative to the growth domestic product of the years the hurricanes made landfall) are log-normally distributed 32 (see supplementary Fig. S5 for a log-normal fit of the data).
In the remainder of this paper, we will refer to the distribution of relative asset losses as shock distribution.As detailed in Sec. A. The Gini index G ≡ L e −L i L e as measure for shock heterogeneity is determined by the ratio of the areas under the red (L e , light blue shading) and blue lines (L i , dark blue shading).D Mean cumulative available production capacity (in % of the production capacity of unperturbed system) as a function event number, and value for the cumulative relative asset losses.To isolate the impact of shock heterogeneity, we then vary the heterogeneity of the asset losses -measured by the Gini index (G) of the event distribution -but keep the number of hurricanes with landfall (88) (and thus average hurricane return frequency) as well as relative cumulative direct asset losses (3.24% of cumulative output) at their values reported in the NatCatSERVICE database 1 for the study period 1980-2014 (35 years).For a nearly homogeneous shock distribution (G = 0.018), asset losses (grey circles in (Fig. 2A-C), asset losses are relatively small and production capacity can mostly recover between loss events and stays close to the one of the unperturbed system for the whole study period (Fig. 2A).For higher values of the Gini index, we obtain many small but few high intensity loss events.Since cumulative output losses increase dis-proportionally with event intensity (cf.Fig. 1C), also the risk for incomplete recovery between events increases for higher values of the Gini index (cf.Fig. 2B and C for G = 0.83 and G = 0.87).For instance, when driving the model with the historical sequence of landfall events, we find that the US economy may not have recovered in between the major hurricanes Katrina and Sandy (Fig. 2B).
To gain a systematic understanding on how production capacity depends upon shock heterogeneity, we study the cumulative production capacity over 35 years as a function of shock heterogeneity.For a given shock distribution, cumulative production capacity in general differs between event realisations due to differences in the timing and the size of the shocks.To account for this uncertainty, we generate a large ensembles of 20,000 realisation for each shock distribution.The cumulative production capacity is then plotted as a function of the median Gini index as obtained across all realisations (see Sec. A.2 of Methods) (Fig. 2D).(Note that values of the Gini index for individual realisations may substantially deviate from the median Gini index.For instance, the Gini index for the observed historical storm sequence (G = 0.83) is substantially higher than the median value of the Gini index across all realisations for the historical storm distribution (G = 0.71) (compare red dot to vertical grey line in Fig. 2D).)We find that the available production capacity reduces super-linearly with increasing shock heterogeneity.The reduction is strongest in the high heterogeneity range to the right of the median Gini index for the historical period (grey line in Fig. 2D), where incomplete recovery becomes more likely.
Similarly, economic growth declines super-linearly with increasing shock heterogeneity (Fig. 3).Consider besides the standard scenario with a 0.2% reconstruction investment cap and 50% insurance coverage (red line in Fig. 3B) again scenarios with a 1% and no investment cap (green and blue lines in Fig. 3) as well as the limiting cases of no and complete insurance (Fig. 3A and Fig. 3C), we find that the dependence of economic growth on shock heterogeneity increases when i) the reconstruction investment cap and ii) the insurance coverage is lowered.For low values of the investment cap, the growth reduction with increasing shock heterogeneity can be quite substantial.For instance, for the standard scenario, annual growth losses increase by more than 16% from 0.0238 percentage points (p.p.) for the lowest to 0.0275 p.p. for the highest value of the Gini index (red line in Fig. 3B).While these growth rate reductions may appear small, they imply that for the highest value of the Gini index output losses accumulate over three and a half decade to 16,218 US$ per-capita, an additional 2,196 US$ per-capita compared to the lowest value of the Gini index.The dependence of growth on shock heterogeneity can again be understood by the disproportional increase of indirect losses with shock intensity making incomplete recovery between events more likely with increasing Gini index (cf.Fig. 1A).In line with this reasoning, we find that, in the scenario without construction investment cap, where the recovery time is substantially shorter then in the scenarios with caps (cf.Fig. 1), growth losses are nearly independent of the Gini index.
Further, for each fixed level of shock heterogeneity, growth losses decrease with increasing insurance coverage which can be understood as follows: Insurance provides additional financial means for reconstruction and thereby mitigates the impact of shocks that are large compared to the reconstruction investment cap by reducing the recovery time and therefore suppressing incomplete recovery.For instance, for the standard scenario and the median Gini index of the historical period (grey vertical line in Fig. 3), output losses accumulate over three and a half decades to 14,904 US$ per-capita.They are therefore, on average 832 US$ per-capita and 1,121 US$ per-capita higher than for the corresponding scenarios with a 1% and without reconstruction investment cap, respectively.
The greatest benefit of insurance is, however, that it strongly mitigates the magnitude of growth losses.For the median Gini index of the historical period and the lowest investment cap, hurricanes reduce annual growth on average by 0.048 p.p. in the uninsured scenario.
These losses are already roughly halved to 0.025 p.p. for the standard scenario with 50% insurance coverage and reduced by a magnitude larger than ten to 0.0045 p.p. in the fully insured scenario.Accordingly, output losses accumulate over three and a half decade decrease from 28,807 US$, over 14,904 US$, to 2,746 US$ per-capita.To set all these numbers into context, it is important to keep in mind that our model, by construction, computes growth losses borne by the US in total.Local growth losses in the affected counties may be much larger.

Better insurance coverage can help mitigate climate change-induced growth losses
We estimate the growth impacts of hurricanes in a 2 °C world corresponding to an increase of about 1.1 °C relative to the studied historical period.To account for the substantial uncertainty on how climate change will impact on hurricane climatology, we employ two different approaches estimating climate change-induced changes in the return frequencies of hurricanes, one at the lower and one at the upper end of the impacts reported in the recent literature 5 .Both approaches consistently predict an increase of the proportion of very intense storms, though the magnitude of this change -and in consequence the resulting changes to direct asset losses -differs substantially between the two approaches.
Importantly, in contrast to the last section, where only the heterogeneity of events was mutable, these climate change-induced frequency increases may additionally translate into changes of the distribution of direct asset losses with respect to i) the number of hurricanes and ii) the cumulative direct asset losses during the study period (Fig. 4  intense (Cat.4-5) hurricanes by 45% but a reduction of the overall number of hurricanes (of all categories) by 22%, which the authors derive from changes in the maximum lifetime wind speeds of the storms obtained from dynamical down-scaled global circulation model runs 7 ("wind speed-based" estimate).In contrast, Grinsted et al. use observational storm surge data and estimate a considerable increase of relative return frequencies ranging from 1.4 fold for storms with a small surge index to a 6.4 fold for the most intense storms 6 ("surge-based" estimate).The authors' statistical analyses cannot distinguish whether this frequency increase is caused by an overall increase in the number of storms or merely implies a shift of the distribution of storm surges to higher intensity events.However, since there is relatively good agreement in the literature that the average number of hurricane per season will not strongly change with global warming 5 , in our derivation of future direct asset losses according to Grinsted's surge-based estimate, we assume that the number of storms does not change compared to the historical study period (see Methods for details).
For both, the surge-and wind speed-based estimates, we obtain a moderate increase of shock heterogeneity with the median Gini index increasing from its historical value of 0.71 to 0.77 and 0.78, respectively.For the former, the hurricane number (88) remains unchanged compared to the historical period whereas it decreases to 69 for the latter.Further, the estimated cumulative relative asset losses over 35 years increase only moderately from 3.24% for the historical period to 3.75% for the wind speed-based estimate but more than double (7.25%) for the surge-based estimate.In terms of median annual growth losses, we obtain a moderate increase by 7% compared to the historical standard scenario for the wind field-based estimate but a strong increase by 146% for the storm surge-based estimate (Fig. 5A).The reason is that for the former the additional growth losses due to the increases of shock heterogeneity and cumulative direct asset losses are partially compensated by the reduction of growth losses due to the reduced absolute number of hurricanes; whereas for the latter the increases of shock heterogeneity, cumulative direct asset losses, and hurricane number all enhance growth losses.Since we always consider growth losses relative to a baseline scenario with the same reconstruction investment cap (and insurance coverage), these findings are robust with regard to changes in the reconstruction investment cap (cf.Fig. 5B and Fig. 5C).
We finally address the question whether an increase in insurance coverage would be sufficient to compensate for the additional global warming-induced growth losses.We find that, to this end, the historical insurance coverage of 50% would have to be substantially raised from 50% to 84% according to the surge-based estimate, whereas a moderate increase to 58% would suffice according to the wind field-based estimate for the standard scenario (cf.columns 2 and 3 and columns 4 and 5 in Fig. 5, respectively).Again, these findings are fairly robust with regard to different values of the construction investment cap.

Discussion
These numbers suggest that a better insurance coverage could indeed be a viable means to compensate for climate change-induced increases in tropical storm-related losses, even in the absence of other adaptation measures.However, we caution that our simulations may underestimate climate change-induced growth losses by hurricanes for several reasons.
First, we only consider a strong climate change mitigation scenario where the global community manages to limit global warming to +2 °C above pre-industrial levels.Our approach does not easily allow to extrapolate losses to higher levels of warming, since it is not clear from the underlying studies how return frequencies will scale at higher levels of warming.Equally important, our estimates of climate-induced changes in direct asset losses are based on estimates for the changes in the return frequencies of the storms only; other potential channels through which climate change may impact on the economic losses caused by tropical storms, such as increasing storm surge risk due to sea level rise 33;34 , and stronger precipitation associated with hurricanes 35 are neglected.Accounting for these additional drivers would most likely increase future economic losses 36;37 .Further, using a simple macroeconomic growth model with only one homogeneous output good, our analysis cannot provide information on the recovery dynamics of individual sectors and may therefore underestimate delays arising from the scarcity of intermediate goods from strongly affected sectors needed for production in other sectors and the associated scarcityinduced price inflation in the disaster aftermath.In consequence, we may underestimate recovery costs 38;39;40 and, in consequence, growth losses.Finally, we assume a non-profit insurance scheme without any handling charges and the potential insurability of all disaster losses.This might provide an over-optimistic assessment of the efficacy of insurance in mitigating disaster losses.
Our research stresses the importance of non-linear economic responses to consecutive extreme weather events.In particular, our results suggest that only by i) resolving the response to individual events, and by ii) accounting for a realistic timing of the events (e.g., accounting for the hurricane season), it is possible to estimate the full economic impact of extreme events 22 .Further, these findings are key to assess the efficacy of adaptation and coping strategies.For instance, in our study the limited pace of insurance payouts delays reconstruction efforts in the disaster aftermath, but a similar reasoning holds for other adaptation measures such as sea walls or levees, which, once breached, may take months or even years to be reconstructed 41 .Thus, temporally resolving the economic recovery phase is critical for the assessment and comparison of disaster response measures.This aspect becomes especially important since extreme weather events are projected to intensify and become more frequent with global warming, at least on a regional level 42 .In this regard, our findings may also encourage the climate integrated assessment modelling community to consider new approaches allowing to go beyond smooth damage functions translating changes in global mean temperature into aggregate output losses.As shown here, this common approach may underestimate the economic repercussions of extreme weather events since it neglects potentially important non-linearities in the economic response such as the disproportional increases of indirect losses with impact intensity or the case of incomplete recovery 22 .This may also explain the discrepancy between the loss estimates reported in the recent climate econometrics literature and the estimates of climate integrated assessment models.
While our estimates on how climate change may impact on economic losses caused by hurricanes in the US are subject to several sources of uncertainty, they nonetheless show that the mitigating effect of increased insurance coverage is of the same order of magnitude as the climate change-induced loss increase; insurance can therefore be an important building block of future climate change adaptation strategies.However, it most likely has to be complemented with other measures to build resilience to extreme weather events such as investments into better housing standards and resilient infrastructure 43;44 or coping strategies such as managed retreat 45;46 .

A.1 Modeling approach
As the standard neoclassical Solow-Swan growth model for a closed economy 47 Here, ( •) denotes the derivative with respect to time t.We assume that total factor produc- tivity (TFP) A growth exponentially with trend growth rate Λ, and s, y, and δ denote savings rate, production function, and depreciation rate of capital, respectively.The insurance premium r I ≡ r I (r c ) depends on the economy's insurance coverage r c , and F I (t) denotes the insurance payouts in the disaster aftermaths.Both terms are detailed below.Further, we assume that the production process can be described by a Cobb-Douglas production function y (t) ≡ A(t )k (t) α , where α ∈ (0, 1] denotes the capital share of income.We model the impact of extreme weather events as shocks to the capital stock.Following 27 , we describe the economic recovery in the disaster aftermath as the superposition of two different mechanisms: i) a fast reconstruction process of the damaged capital and ii) the comparably slow growth of the capital stock due to technological development.To this end, we write the capital stock as the product of the fraction of remaining production capacity The Copp-Douglas production function is derived from the assumption that the process of capital accumulation is optimal and the last unit of capital added is the least productive 48 .
However, it appears unlikely that a disaster strikes in such a way that it "de-constructs" the capital in the same optimal way, starting with the least productive unit, and this method is likely to underestimate direct production losses (see discussion in 49 for details).Following previous works 27;50;49 , we therefore assume that a shock does not merely destroy the least efficient capital, but equally affects all "productivity layers" of capital.For that, we may write y as a function of ξ and k p , Noteworthy, this implies that at the time of the shock t s , y reads where ξ(t s ) < 1, and k p (t s ) represents the pre-disaster value of the capital stock.Thus, production is reduced by the same factor 1 − ξ(t ) as the capital stock, i.e, direct asset losses equal direct production losses, and the marginal productivity of capital remains unchanged.
To derive the dynamical equations for k p and ξ, we first decompose total investment I(t ) into the sum of two different investment channels: short-term reconstruction investments I ξ (t), and regular investments increasing production capacity I k (t), By employing Eqs. ( 2), ( 3) and (4), we may then rewrite the dynamical equation for the capital stock (1b) as By comparing the right-hand sides of Eqs.(5a) and (5b), we obtain the dynamical equations for k p and ξ as Next, we derive an expression for I ξ (t) which then permits us to calculate I k from Eq. (4).
To this end, we have to make four assumptions: First, we assume that reconstruction investments yield higher returns compared to investments in the potential capital stock and are therefore prioritised.Second, we assume that reconstruction efforts are limited by shortterm constraints such as a lack of skilled labour or reconstruction materials, which may significantly slow down the economic recovery.In consequence, only a fraction f max ∈ [0, 1] of the output available for investment sy (t) can be used to finance reconstruction; the actual value of the investment cap f max depends upon the economy under consideration 50 .
Third, we assume that reconstruction efforts cease when the capital stock equals the potential capital stock, no overshoot is possible.Fourth, we assume that the insurance primarily finances reconstruction efforts.In the presence of insurance, the investment cap may be temporally exceeded since the insurance provides additional financial means.This assumption is motivated by empirical findings that higher insurance coverage can lead to a faster economic recovery 29;30 .However, if reconstruction is completed before all of the insured capital is reimbursed, the remaining insurance payout will be invested into the potential capital stock.With these assumption, we may express I ξ (t) as where I r (t) ≡ (1 − ξ(t ))k p (t) is the investment needed to reconstruct the capital stock in the present time step.

A.1.1 Insurance payout dynamics
Observational data of insurance payouts of the Reinsurance Association of America 28 reveal that the reimbursement of insured losses f I (t) can spread over several years; 60% (90%) of the insured values are reimbursed with in one (three) year(s).This may significantly delay the reconstruction process.We describe the cumulative insurance payouts with a sigmoidal function, Here, t s denotes the time of the shock, the insured losses are given by the product of the insurance coverage r c , the asset loss ∆ s at time t s relative to the pre-shock potential capital stock k p (t s )1 .The three parameters a, τ I and β 28 are specified in Tbl. 1 (see supplementary Fig. S2 for a fit of the observational data).The cumulative insurance payout in response to multiple successive asset losses {∆ s i } i at times {t s i } i are then given by the sum of the individual payouts where index i labels the shock number, and N s denotes the total number of shocks.

A.1.2 Model calibration
We assume that, in the absence of shocks, the economy evolves along its balanced growth path (BGP), where output growth is constant and only driven by TFP growth (growth rate Λ), where we have used in the second identity that if y growth constantly with rate g, k also growth constantly with the same rate2 .Since in the absence of shocks F I (t) = 0 ∀t ∈ [0, T ], where T denotes the length of the simulation, the dynamic equations for k and k I decouple (cf.Eqs. ( 1)), it suffices to solve the equations of motions for the dynamic variables A and k along the BGP.The corresponding equation for k I can then be derived from Eq. (1c).To this end, we insert the coordinate transformation into the dynamic equations for A and k yielding, where we have introduced the output in BGP coordinates ỹ (t) ≡ A 0 k α (t).Equating the right-hand-sides of Eqs.(8) to zero, yields the steady states for A and k in BGP coordinates where (•) ⋆ and k 0 denote the steady state values of variables and k 0 initial capital stock, respectively.This allows to write the BGP solution of Eqs.(1) as To calibrate the model to the US, we set initial per-capita annual output y 0 and output growth rate g to the per-capita growth domestic product (GDP) and the GDP growth rate of the US in 2015 according to the World Banks' and OECD's National Accounts database 3 , whereas capital depreciation rate δ, savings rate s, and capital share of income α are set to their standard values for developed economies 47 .Using the Cobb-Douglas relation for the production function y = Ak α and the steady state relation for k 0 (cf.Eq. ( 9)) then allows to express initial TFP and initial per-capita stock as A 0 = y 0 δ+r I +g s α and k 0 = sy 0 (δ + r I + g) −1 , respectively.
Table 1 lists all exogenous parameters used in the simulations.It is worthy to note that our model results are very robust with regard to changes of the GDP growth rate g since we only consider changes of the perturbed economy relative to an unperturbed economy evolving along the BGP.Even large variations of g ∈ [0.2%, 4%] result in changes of growth losses that are small compared to the climate uncertainties (cp.lines and shaded areas in supplementary Fig. S6) Modelling a non-profit insurance scheme, we have to ensure that, averaged over many realisations, the insurance does neither make profit nor losses.However, deriving an exact analytical formula for the corresponding insurance premium r I is challenging since -as output losses and growth losses -it would depend upon shock heterogeneity.Instead, we here motivate a simple heuristic formula neglecting this dependence and show that the resulting average insurance profits or losses are negligible compared to the cumulative payouts of the insurance.In the worst case, the total relative asset losses occur at the last k I (T ) = r c ∆ T k (T ), where T denotes the length of the simulation.Inserting this relation in the BGP solution for k I (cf.Eq. ( 10)) provides us with the following expression for the insurance premium where we have added an empirically determined factor ε ensuring that average insurance profits (or losses) are negligible.(cf.supplementary Fig. S4 revealing that average profits or losses of the insurance are about five magnitudes smaller than the insured capital.

A.2 Gini index as measure for shock heterogeneity
We fit the relative asset losses of the N s = 88 historical hurricanes with landfall included in the NatCatSERVICE database 1 (cf.Tbl.S1) with a log-normal distribution (supplementary Fig. S3) with standard deviation σ 0 .To change the heterogeneity of the loss events, we vary the standard deviation σ of the log-normal distribution from σ 0 100 to 4σ 0 .We use the Gini index G ≡ L e −L i L e ∈ [0, 1] as measure for the shock heterogeneity, which is derived from the difference of the areas below the Lorenz-curves for a uniform distribution L e and the given shock distribution L i (cf.Fig. 2).Shock heterogeneity increases from small to large values of the Gini index.Noteworthy, the Gini index of the historical timeseries of hurricanes with landfall equals 0.829, whereas the median Gini index of the historical shock distribution -obtained by averaging over many synthetic realisations of asset loss time series (see Sec. A.3 for details) -equals 0.71.

A.3 Generation of synthetic time series of asset losses
In this section, we discuss the generation of synthetic time series of asset losses from their historical distribution as reported by the NatCatSERVICE 1 and TCE-DAT databases 51 .For the study period 1980-2014 of T = 35 years, these databases list N s = 88 hurricanes with landfall that have caused asset losses corresponding to at least 10 −4 % of the GDP in the year of their landfall (see supplementary Tbl.S1).Over this period, relative asset losses accumulated to ∆ T = 3.24%.We generate synthetic time series of asset losses of length T keeping N s and ∆ T at their historical values in three steps illustrated in supplementary Fig. S5.First, following ref. 31 , we assume that the number of hurricanes with landfall n a in each season a is Poisson distributed, f P (n a ) ≡ λ n a e −λ n a ! .Further, we assume that the mean number of landfalls per season λ is constant over the study period T .To ensure that each synthetic track contains exactly N s shocks, the shock number for the last season of the track is set to the remainder of available shocks N s − ∑ T −1 a=1 n a .To avoid that the last season always receives the remainder of available shocks, seasons are shuffled afterwards.
Second, we assume that for each day of the season the likelihood of a hurricane making landfall is the same, but exclude the possibility that two hurricanes make landfall at the same day.Third, following ref. 32(cf.Fig. S3 in SI), we assume that relative asset losses , where we have , m ≡ ln( ∆ T N s ) − s 2 2 , and the standard deviation σ of the log-normal distribution.Similarly, to step one the size of the last shock of each realisation is set to the difference between ∆ T and cumulative relative asset losses before the last shock in order to ensure that total cumulative relative asset losses equal ∆ T ; then shock sizes are reshuffled.

A.4 Storm surge-and wind field-based climate change projections of asset losses
Storm surge-based projections of asset losses.Grinsted et al. 6 estimated the relative increase in the return frequency of hurricanes with landfall in dependence of the severity of their storm surge (measured by the surge index 52 ) per degree of global mean temperature (GMT) warming relative to the reference period 1980-2000.We employ these findings to project asset losses for a +2 • C increase of GMT above its pre-industrial level4 .To this end, we first map the surge indices {∫ s i } of the N s = 88 historical hurricanes that made landfall in the US between 1980-2014 to the corresponding relative asset losses {∆ h s i } reported in the NatCatSERVICE database 1 (supplementary Tbl.S1).Next, we determine the statistical correlation between historical asset losses and surge indices, yielding the damage function f (s) (supplementary Fig. S7).As discussed in the main text, we assume that the average number of hurricanes with landfall will not change compared to the historical study period.
In consequence, we interpret the increases in return frequency reported by Grinsted et al. as increases solely in storm surge intensity, and not as an increase of the average number of hurricanes making landfall (in each season).This allows us to map the set of historical sure indices {∫ s i } to a set of estimated surge indices in a +2 °C world {∫ cc s i }.
We then assume that each future relative asset loss ∆ cc s i can be written in terms of the corresponding historical asset loss.This allows to express future relative asset losses in terms of the historical relative asset losses as well as future and historical storm surge indices, Note that with this relationship historical asset losses are reproduced for ∫ cc

Fig. 1 .B
Fig. 1.The impact of insurance and reconstruction investment on the economic recovery dynamics in the aftermath of an individual hurricane with landfall.Response dynamics in the aftermath of a 1% shock to the capital stock with with no (red), 50% (green), and full (blue) insurance coverage, for scenarios where maximum weekly reconstruction investment is not limited (dotted lines) as well as limited to 0.2% (solid lines) and 1% (dashed lines) of weekly output, respectively.A Time series of weekly output relative to the output of an unperturbed economy on the balanced growth path.B Time series of weekly reconstruction investment (in % of weekly output) and weekly insurance payout (in % of direct asset losses to the capital stock, inset).C Cumulative output losses until full recovery of production capacity as a function of the direct asset losses (both in terms of annual output in the year before the landfall).Vertical grey lines indicate the asset losses caused by the historical major hurricanes Sandy, Andrew, and Katrina according to the NatCatSERVICE database 1 .
of the Gini index.Red dots and grey shaded areas indicate the values of the Gini index obtained for the runs in A-C and the 16.7-83.3percentile confidence interval, respectively.The grey vertical line indicates the median Gini index of the historical shock distribution (see Methods).Other parameters: Insurance coverage 50%; reconstruction investment cap 0.2% of weekly output.

Fig. 3 .
Fig. 3. Impact of hurricane shock heterogeneity on annual output growth rate.Median annual growth rate change of the economy under hurricane shocks relative to the growth rate of the corresponding unperturbed economy, as a function of shock heterogeneity -measured by the Gini index -for no (A), half (B), and full (C) insurance coverage.Blue, green, and red lines depict median growth rate changes for scenarios where reconstruction investment is not limited, limited to 0.2%, and 1% of weekly output, respectively; shaded areas mark the corresponding 16.7-83.3percentile confidence intervals.The grey vertical line indicates the median Gini index of the historical distribution of relative direct asset losses.

Fig. 5 .canes on economic growth in a 2 °C
Fig. 5. Projected impacts of hurricanes on economic growth in a 2 °C world and the effectiveness of insurance as coping strategy.Annual growth losses (relative to the corresponding unperturbed economies evolving on the balanced growth paths) as obtained for the historical shock distribution (50% insurance coverage, period 1980-2014; 1 st column) and for +2 °C warming above preindustrial levels (2 nd through 5 th column) for reconstruction investment caps of 0.2% (A, standard scenario), 1% (B) and without reconstruction investment cap (C).Climate change projections of growth losses are derived from two different methods to estimate climate change-induced changes in the return frequencies of hurricanes by Grinsted et al. 6 and Knutsen et al. 7 (50% insurance coverage, 2 nd and 4 th columns, respectively).Additionally, for both estimates the insurance coverage that would be necessary to reduce growth losses to the historical level are shown (3 rd and 5 th column).Orange lines, boxes, and whiskers indicate median loss estimates as well as the 25 th -75 th and 5 th -95 th percentile ranges, respectively.

i= 3 .Fig. S1 .
Fig. S1.Recovery dynamics of production capacity in dependence of shock heterogeneity for 1% reconstruction investment limit.Same as Fig. 2 but for a 1% reconstruction investment cap.

Fig. S2 .
Fig. S2.Insurance payout dynamics.Cumulative (brown) and monthly (violet) insurance payouts in the aftermath of an individual shock to the physical capital stock.The sigmoidal function for the cumulative payouts is calibrated such that 60% (90%) of the insured values are reimbursed within one (three) year(s) according to insurance data of the Reinsurance Association of America 28 .The monthly payouts are then obtained by deriving this function with respect to time.
Fig. S3.Distribution of the historical asset losses of hurricanes that made landfall in the US in the period 1980-2014.Black dots depict the asset losses as reported by the NatCatSERVICE database 1 in the period 1980-2014 relative to the US growth domestic product of the years in which the hurricanes made landfall.The red line depicts a fit with a log-normal cumulative density function.

Fig. S4 .
Fig. S4.Insurance is non-profit.Median insurance capital stock in terms of the insured potential capital stock after T = 35 years.Same scenarios and colour code as in Fig. 1.

Fig. S5 .
Fig. S5.Sketch of construction of synthetic asset loss time series caused by hurricanes with landfall.Synthetic time series of asset losses are generated in three steps: First, the number of hurricane shocks in each US hurricane season (June-November) is drawn from a Poisson distribution f P .Second, the times of landfalls are determines assuming the same probability of landfall within each season, excluding the possibility of two landfalls on the same day.Third, the relative asset loss of each landfall is drawn from the log-normal distribution of Fig. S3.

2. Recovery dynamics of production capacity in dependence of hurricane shock het- erogeneity. Economic
3 of the Methods, drawing from this shock distribution allows us to generate synthetic time series of asset losses with defined length, DFig.

. Right panel: Lorenz
curves to illustrate the heterogeneity of the shock distribution.Red lines indicate the cumulative share of production capacity losses as a function of the cumulative share of the shocks.Grey diagonal lines indicate the Lorenz curves for equally distributed shocks.
) (see Methods for details).Knutsen et al. report a moderate increase of the return frequency of the most , our model InGroClIM (Insured Growth under Climate Impacts) describes the growth of a percapita stock of physical capital k for a unique indistinguishable good under investments and capital depreciation.Here, we neglect changes in labour market and population growth as drivers of capital growth.In extension to the standard model, we account for a non-profit insurance scheme and obtain two coupled differential equations for k and the per-capita capital stock of the insurance k I reading