Climate Shocks, Cyclones, and Economic Growth: Bridging the Micro-Macro Gap Online Appendix

Transcription

1 Climate Shocks, Cyclones, and Economic Growth: Bridging the Micro-Macro Gap Online Appendix Laura Bakkensen U. of Arizona Lint Barrage Brown U. & NBER January 2019 Contents 1 Theoretical Derivations Stationary Equilibrium Growth Proposition Corollary Proposition Empirical Analysis: Details and Robustness TFP Robustness Varying Lag Lengths HP-Filtering Cyclone Energy Cyclone Intensity Monte Carlo Simulation Details Country-Level Results: Expected Cyclone Impacts Calibration Details DICE Damage Functions

2 1 Theoretical Derivations 1.1 Stationary Equilibrium Growth This section derives the paper s equations defining equilibrium growth (6-8), following the approach in Krebs (2003a,b). Country subscripts j are omitted for legibility. First, note that the household s problem can be written in recursive form as: V (w, k, ε) = max u(c) + βe[v (w, k, ε )] (1) subject to: w = w[1 + r( k, ε)] c (2) where r(.) is as defined in paper equation (5). Substituting (2) into (1) and taking the first-order conditions (FOCs) for c and k yields: u c = βe[v w ] (3) 0 = βe[v k ] Next, substituting in the decision rules c = g(w, k, ε) and k = f(w, k, ε) yields the Benveniste- Scheinkman conditions: V w = βe[v w [(1 + r( k, ε)]] { } V k = βe[v w w [R k (ε) δ k (1 π)η k (ε)] [R h (ε) δ h (1 π)η h (ε)] (1 + k) ] 2 Substituting based on (3) and iterating forward then yields the Euler equation and no-arbitrage condition, respectively: u c = βe[u c [(1 + r( k, ε )]] (4) { } 0 = βe[u [R k (ε ) δ k (1 π)η k (ε )] [R h (ε ) δ h (1 π)η h (ε )] c w (1 + k ] (5) ) 2 Next, invoking the assumed utility function u(c) = c1 γ, the budget constraint (2), and the 1 γ fact that c = c[1 + r( k, ε )]w (where c 1 s denotes the consumption-out-of-wealth ratio), substitution and rearranging in (4) yields the desired result that: s = 1 c = ( ) 1 βe[(1 + r( k, ε )) 1 γ γ ] (6) 2

3 The same substitutions allow us to factor out as pre-determined terms c and w = (1 + r)w c in (5), yielding the desired condition: 0 = βe[ { } [R k (ε ) δ k (1 π)η k (ε )] [R h (ε ) δ h (1 π)η h (ε )] (1 + k ) 2 (1 + r( k, ε )) γ ] (7) Finally, the expression for average growth can be derived by again invoking w = [1+r( k, ε)]w c and c = c[1 + r( k, ε )]w. First, note that the definition of c implies that: c = c [1 + r( k, ε)]w 1 c = [1 + r( k, ε)]w c [1 + r( k, ε)]w (8) Consequently, expected growth can readily be shown to equal paper equation (8), as desired: [ ] c E c [ ] [ ] c[1 + r( k, ε )]w c[1 + r( k, ε )]{[1 + r( k, ε)]w c} = E = E c c = (1 c)(1 + E[r( k, ε )]) = ( s)(1 + E[r( k, ε )]) 1.2 Proposition 1 Proposition 1: Cyclone Risk and Avg. Growth An increase in cyclone risk has a theoretically ambiguous effect on average growth: dg dµ ε 0 Proof: We demonstrate the possibility of both positive and negative effects of cyclone risk on average growth by construction. In order to maintain analytic transparency, we present a simple parameterization where, each period, there is just a binary probability φ that a cyclone occurs with intensity ε t = ε, whereas, with probability 1 φ, no cyclone occurs (ε t = 0). The mean disaster realization is thus µ ε = φε. For clarity, we also separate the average depreciation term δ k back into its underlying components: δ k = δ k + πµ k = δ k + πφη k (ε), and analogously for human 3

4 capital. In this setting, expressions (6) and (7) become: [ ] 1 γ s = β 1 γ φ (1 + ω k ( k)[r k ( k) δ k πφη k (ε) (1 π)η k (ε)] +(1 ω k ( k))[r h ( k) δ h πφη h (ε) (1 π)η h (ε)] { [ }] 1 +(1 φ) (1 + ω k ( k)[r k ( k) δ k πφη k (ε)] + (1 ω k ( k))[r h ( k) δ h πφη h (ε)] ]) 1 γ γ (9) [ ] [ ] R k ( k) δ k πφη k (ε) (1 π)η k (ε) R h ( k) δ h πφη h (ε) (1 π)η h (ε) ) φ (1 + k) [ ]( 2 (1 + ω k ( k)[r k ( k) δ k η k (ε)(πφ + 1 π)] + (1 ω k ( k))[r h ( k) δ h η h (ε)(πφ + 1 π)] ) [ ] [ ] R k ( k) δ k πφη k (ε) R h ( k) δ h πφη h (ε) +(1 φ) (1 + k) [ ] = 0 2 (1 + ω k ( k)[r k ( k) δ k πφη k (ε)] + (1 ω k ( k))[r h ( k) δ h πφη h (ε)] ) γ While it is possible to apply the implicit function theorem to (9)-(10) to derive analytic expressions for d k, d s dg, and thus ultimately, we have not found these expressions to be instructive. We therefore analytically illustrate the possibility of higher average growth due to higher storm risk in the simplest possible case where human and physical capital are perfectly symmetric. That is, assume that both types of capital are equally vulnerable to cyclone damages η k (ε t ) = η h (ε t ) η(ε t ), enter production symmetrically (with Cobb-Douglas exponents α = 1 α = 0.5), and have equal baseline depreciation rates δ k = δ h δ. In this case, it is straightforward to show that the optimal capital share equation (10) is solved by k = 1, implying equal optimal investment in both types of capital in stationary equilibrium. The optimal savings rate (9) in the symmetric setting then reduces to: ( ) 1 s = βe[(1 + r( k, ε )) 1 γ γ ] [ = β 1 γ φ {(1 + A2 } δ η(ε)(πφ + 1 π))1 γ + (1 φ) {(1 + A2 }] 1 δ γ πφη(ε))1 γ (11) where A denotes total factor productivity. Here, the impact of a change in storm risk on optimal savings depends only on its direct effect in (11), and is given by: 1 d s = β [ s]1 γ 1 γ φ(1 γ)(1 + r(ε)) γ ( 1) η ε (12) where the portfolio return in case of a storm r(ε) = A 2 δ πφη(ε) (1 π)η(ε) and s are both 1 That is, there is no additional indirect effect via a change in k. 4

5 as in (11). Since depreciation damages are assumed to be increasing in storm intensity ( η > 0), expression (12) immediately shows that the equilibrium savings rate is increasing in average ε storm intensity if γ > 1, unaffected by storm risk if γ = 1 (logarithmic preferences), and decreasing in storm risk if γ < 1: 2 d s = > 0 if γ > 1 = 0 if γ = 1 < 0 if γ < 1 The corresponding change in average growth due to storm risk is then given by: (13) dg = d s (1 + E[r(ε )]) + ( s) d(1 + E[r(ε )]) (14) where d s is given by (12), s remains defined by (11), and: E[r(ε )] = A 2 δ πφη(ε) φ(1 π)η(ε) = A 2 d(1 + E[r(ε)]) = φ η ε δ φη(ε) (15) To complete the characterization of dg, we assume the same functional form for η(ε) as in the empirical part of the paper: η(ε) = ξ 1 (ε) ξ 2 (16) Utilizing (16), (15), and (12) in (14) and rearranging then implies that: dg = ( s)[( 1)φξ 1 ξ 2 (ε) ξ 2 1 ] [β[ s] γ 1γ [ φ(1 γ) 1 + A ] ] γ 2 δ πφξ 1(ε) ξ 2 (1 π)ξ1 (ε) ξ 2 (1 + A 2 δ φξ 1(ε) ξ 2 ) + 1 where s remains defined by (11). Consequently, sign( dg ) = ( 1)sign (17) {β[ s] γ 1γ [1 φ(1 γ) + A2 ] } γ δ ξ 1(ε) ξ2 (πφ + 1 π) (1 + A2 δ φξ 1(ε) ξ2 ) This conclusion follows from the fact that all terms in (12) are positive except for and (1 γ), whose sign consequently determines the overall sign of (12). [ ] η(.) ε, which is negative, 5

6 Avg. Growth Rate It immediately follows from (17) that, within the realm of permissible parameter values (where depreciation does not exceed 100 percent even in case of a storm), average growth is unambiguously decreasing in storm risk whenever γ 1. In contrast, if agents are suffi ciently risk averse with γ > 1, average growth may be increasing in storm risk. Figure A1 showcases this possibility by displaying average growth as a function of average storm risk µ ε = φε (while varying ε) for different values of γ (for example calibration β = 0.985, A = 1, φ = 0.1, δ =.1, ξ 1 = 0.5, ξ 2 = 2): Storm Risk and Average Growth = = 2.0 = Avg. Storm Risk ( ) Figure A1 Figure A1 demonstrates that the dg may be ambiguous in sign not only across but even within calibrations, depending on the level of baseline storm risk at which it is evaluated. This demonstrates the theoretical ambiguity claim of Proposition Corollary 1 Proposition 1 establishes that an increase in cyclone risk can increase average growth. In order to prove Corollary 1, it is thus suffi cient to demonstrate that the increase in cyclone risk in those cases results in a decline in welfare. Following the same approach as Krebs (2003b), one can re-write household lifetime utility (again omitting country j subscripts for legibility and focusing 6

7 on the relevant case with γ > 1) as: U 0 E 0 β t c 1 γ t 1 γ t=0 = c1 γ 0 1 γ + β E 0[{c 0 g( k, ε)} 1 γ ] 1 γ + β 2 E 0 [{c 0 g( k, ε)g( k, ε)} 1 γ ]... 1 γ (18) where initial consumption c 0 = (1 s)(1 + r( k 0, ε 0 ))w 0 is pre-determined (since h 0, k 0, and ε 0 are given) except for the equilibrium savings rate s, and g(.) is the consumption growth factor g t ct c t 1 = ( s)[1 + r( k, ε t )]. Given the assumption of independently distributed shocks and following Krebs (2003b) one can write (18) as: E 0 β t c 1 γ t 1 γ = c 1 γ 0 (1 γ)(1 βe 0 [g( k, ε) 1 γ ]) t=0 (19) For the simple setting studied in Proposition 1, (19) becomes: U 0 = c 1 γ 0 (1 γ)(1 β {φg(ε) 1 γ + (1 φ)g(0) 1 γ }) where g(ε) = ( s) [ 1 + A 2 δ πφξ 1(ε) ξ 2 (1 π)ξ1 (ε) ξ 2]. Differentiating U0 with respect to ε then yields: du 0 = (1 s) γ ( d s )[(1 + r( k 0, ε 0 ))w 0 ] 1 γ + (1 s) 1 γ [(1 + r( k 0, ε 0 ))w 0 ] γ ( πφξ ξ (ε) ξ 1) (20) (1 β {φg(ε) 1 γ + (1 φ)g(0) 1 γ }) ( 1)c 1 γ 0 + [(1 γ)(1 β {φg(ε) 1 γ + (1 φ)g(0) 1 γ }] 2 [ ] where: [ ] = (1 γ) 2 γ dg(ε) γ dg(0) β φg(ε) + (1 φ)g(0) dg(ε) = d s [ 1 + A ] 2 δ πφξ 1(ε) ξ 2 (1 π)ξ1 (ε) ξ 2 + s [ πφξ 1 ξ 2 (ε) ξ 2 1 (1 π)ξ 1 ξ 2 (ε) ξ 1] 2 dg(0) = d s [ 1 + A ] 2 δ πφξ 1(ε) ξ 2 + s [ πφξ 1 ξ 2 (ε) ξ 1] 2 For the relevant case where γ > 1, we have already shown that d s > 0, so that the first part in (20) is unambiguously negative. If the parameters are such that dg(ε) > 0 and dg(0) > 0, this is suffi cient to ensure that the second line in (20) is also negative as it then follows that > 0, and, 7

8 consequently, that the welfare effects of cyclone risk increases are negative. Intuitively, dg(ε) > 0 if the precautionary savings effect is suffi ciently strong to dominate the direct depreciation effect even during cyclone events. However, the present focus on areas of the parameter space where average growth impacts are positive (i.e., dg = φ dg(ε) + (1 φ) dg(0) > 0) is not suffi cient to guarantee that dg(ε) > 0. While it is less analytically transparent in this case to show that du 0 < 0, intuitively cyclone risk increases should always be welfare-decreasing as households could have chosen to save more and throw away more of their income (representing higher insurance premia) even in the absence of such risk increases, if this would make them better off. In order to formally demonstrate that such welfare declines can exist in the same settings giving rise to positive growth effects, we resort to a numerical evaluation of (19) at the same parameters as in Figure A1 (β = 0.985, A = 1, φ = 0.1, δ =.1, ξ 1 = 0.5, and ξ 2 = 2, evaluated variably for initial conditions ε 0 = 0 or ε 0 = ε). Figure A2 shows that welfare declines with cyclone risk, even in the area of the parameter space where output growth increases. 10 Storm Risk and Welfare Welfare U = 1.8, = 1.8, = 2.0, = 2.2, 0 = Avg. Storm Risk ( ) Figure A2 0 = 0 = 0 0 = 0 To summarize, we have shown that, in the same setup used in Proposition 1 to illustrate the possibility of a positive effect of cyclone risk on output growth, the effect of an increase in cyclone risk on welfare is negative. Consequently, we have shown that cyclone risk may affect output growth and welfare in opposite ways. 8

9 1.4 Proposition 2 The claims of Proposition 2 follow from (i) the equation for realized growth in stationary equilibrium (paper eqn. 9) with the definition of portfolio returns (paper eqn. 5) substituted in: g j,t = c j,t c j,t 1 = ( s j )[1 + ω k ( k j ){R k j ( k) δ k j (1 π j )η k j (ε j,t )} (21) +(1 ω k ( k j )){R h j ( k) δ h j (1 π j )η h (ε j,t )}] Claims (1)-(2) focus on the case where financial markets are incomplete (π j < 1): 1) Cyclone realizations have a negative effect on contemporaneous growth ( dg j,t j,t < 0). This claim follows directly from differentiating (21): dg j,t j,t = ( s j )(1 π j )( 1) [ ω k ( k j ) ηk j ε j,t + (1 ω k ( k j )) ηh j ε j,t ] < 0 (22) 2) Cyclone realizations have a persistently negative effect on output levels in the sense that there is no compensating positive growth rebound after the storm ( L dg t+j j,t < 0). This statement follows from the AK-nature of the model. In particular, the contemporaneous growth rate (21) returns to baseline levels following the disaster realization, so that dg j,t+l j,t = 0 for l > 0. Adding up these terms with (22) thus yields the desired result that L dg t+l j,t < 0. Finally, claim (3) pertains to the case where financial markets are complete (π j = 1). In this case, all cyclone damages would insured (i.e., contained in δ m j, m = k, h) and ε j,t would vanish from equation (21). Consequently, cyclone realizations ε j,t would not affect growth realizations if π j = 1, showing the desired result that dg j,t j,t πj =1 = 0. j=0 l=0 2 Empirical Analysis: Details and Robustness 2.1 TFP Robustness Varying Lag Lengths Tables A1 and A2 present TFP impacts across varying cyclone lag lengths, along with Akaike/Bayesian Information Criteria (AIC/BIC). Table A1 focuses on the DICE TFP measure, whereas Table A2 focuses on our benchmark model measure. We restrict the sample to be the same across these specifications, so that Tables A1 and A2 extend main Tale 1 Columns (1) and (2), respectively. 9

10 10

11 Table A1: DICE TFP Impacts at Varying Lag Lengths MaxWindt ** ** ** ** * * * ** (0.355) (0.398) (0.423) (0.437) (0.538) (0.560) (0.589) (0.646) (0.936) (0.911) MaxWindt *** *** *** *** ** ** ** ** ** * (0.281) (0.331) (0.354) (0.370) (0.403) (0.498) (0.532) (0.600) (0.593) (0.777) MaxWindt ** ** ** ** ** ** ** * * (0.384) (0.415) (0.431) (0.465) (0.495) (0.595) (0.662) (0.655) (0.655) MaxWindt (0.474) (0.486) (0.499) (0.514) (0.537) (0.739) (0.720) (0.710) MaxWindt ** * * * * (0.348) (0.381) (0.402) (0.441) (0.516) (0.659) (0.657) MaxWindt ** ** * * (0.361) (0.397) (0.442) (0.523) (0.525) (0.650) MaxWindt ** ** ** * (0.315) (0.378) (0.479) (0.496) (0.515) MaxWindt ** * (0.403) (0.516) (0.543) (0.571) MaxWindt ** * (0.491) (0.519) (0.550) MaxWindt (0.855) (0.872) MaxWindt (0.676) Obs. 5,787 5,686 5,585 5,484 5,383 5,281 5,179 5,076 4,973 4,870 Adj. R AIC BIC(n=#Clusters) Regression of log DICE TFP ln(a DICE jt ) on a constant, country fixed-effects, year fixed-effects, country-specific linear time trends, and cyclones (max. wind speed/km) for various lags. Standard errors are heteroskedasticity-robust and clustered at the country level. *** p<0.01, ** p<0.05, * p<0.1 11

12 Table A2: Benchmark TFP Impacts at Varying Lag Lengths MaxWindt ** ** ** ** * * * (0.347) (0.387) (0.411) (0.424) (0.531) (0.554) (0.588) (0.651) (0.924) (0.899) MaxWindt *** *** ** ** ** * * * (0.274) (0.322) (0.344) (0.358) (0.392) (0.494) (0.530) (0.606) (0.600) (0.769) MaxWindt ** ** ** ** * * (0.375) (0.405) (0.420) (0.454) (0.488) (0.596) (0.669) (0.663) (0.663) MaxWindt (0.468) (0.478) (0.492) (0.508) (0.535) (0.748) (0.729) (0.718) MaxWindt * * * (0.341) (0.374) (0.397) (0.437) (0.516) (0.664) (0.660) MaxWindt * * (0.354) (0.392) (0.438) (0.520) (0.522) (0.653) MaxWindt ** * (0.316) (0.379) (0.479) (0.494) (0.510) MaxWindt * (0.392) (0.503) (0.527) (0.554) MaxWindt (0.478) (0.503) (0.530) MaxWindt (0.802) (0.817) MaxWindt (0.624) Obs. 5,787 5,686 5,585 5,484 5,383 5,281 5,179 5,076 4,973 4,870 Adj. R AIC BIC(n=#Clusters) Regression of log benchmark TFP ln(ajt) on a constant, country fixed-effects, year fixed-effects, country-specific linear time trends, and cyclones (max. wind speed/km) for various lags. Standard errors are heteroskedasticity-robust and clustered at the country level. *** p<0.01, ** p<0.05, * p<0.1 12

13 The results are generally similar across lag lengths, but cease to be precisely estimated as more observations are excluded at higher lag lengths. The information criteria also imply that lower lag lengths are preferred HP-Filtering Table A2 shows TFP results based on HP-filtering of each country s TFP series (using annual smoothing parameter λ = 6.25), and regressing the natural logarithm of the cyclical components, ln(t F P j,t ) on year fixed-effects and cyclone measures ε j,t (with robust errors ɛ j,t clustered at the country-level). L ln(t F P j,t ) = δ t + β A 1+lε j,t l + ɛ j,t l=0 13

14 Dep. Variable: Table A3: HP-Filtered TFP Impacts (1) (2) (3) CY CLE+ ln (A DICE CY CLE jt ) ln (Ajt ) ln (Ajt ) ln (A DICE jt ) Labor Measure: Pop. hc Pop hc Empl. Pop. MaxWind t *** *** ** (3.322) (3.126) (5.223) (0.494) MaxWind t *** *** *** 1.172*** (3.661) (3.224) (3.216) (0.382) MaxWind t ** ** * 1.520*** (3.421) (3.615) (60.31) (0.440) MaxWind t ** ** (3.135) (4.183) (5.626) (0.492) MaxWind t (2.842) (3.452) (2.642) (0.720) MaxWind t (2.154) (2.457) (1.759) (0.695) MaxWind t * (80.68) (89.82) (37.64) (0.591) Obs. 2,643 2,640 2,678 3,327 Clusters Adj. R Table presents regression of natural log of cyclican component of TFP (based on HP-filtering, with λ = 6.25) on a constant, year fixed-effects, and cyclone intensity (max. wind speed/km 2 ). Cols. 1 and 4 use DICE Model TFP (labor measured by population). Col. 2 uses benchmark model (labor measured by population times human capital); Col. 3 extended model (labor measured by workers times human capital). Cols. 1-3 use consistent sample of country-years with available Penn World Table data on human capital and workers. Col. 4 uses extended sample incl. countries without education, labor data. Standard errors are heteroskedasticityrobust and clustered at the country level. *** p<0.01, ** p<0.05, * p< Cyclone Energy Table A4 presents results analogous to main paper Table 1 but using cyclone energy (sum of maximum wind speeds cubed) per square kilometer - rather than maximum wind speeds per square kilometer - as cyclone intensity measure. While the point estimates continue to suggest negative TFP impacts that last for several periods, these estimates are generally imprecise (perhaps due to the additional weight given to outliers by the energy measure). 14

15 Dep. Variable: Table A4: TFP Impacts (1) (2) (3) CY CLE+ ln (A DICE CY CLE jt ) ln (Ajt ) ln (Ajt ) ln (A DICE jt ) Labor Measure: Pop. hc Pop hc Empl. Pop. Energy t *** -1.16e-06 ( ) ( ) ( ) (1.77e-05) Energy t e e e-05* ( ) ( ) ( ) (1.46e-05) Energy t e-05 ( ) ( ) ( ) (1.47e-05) Energy t e e-05 ( ) ( ) ( ) (1.18e-05) Energy t e e e-06 ( ) ( ) ( ) (5.83e-06) Energy t e e e e-06 ( ) ( ) ( ) (3.73e-06) Energy t e e e e-06 ( ) ( ) ( ) (5.73e-06) Obs. 5,281 5,281 5,281 6,685 Clusters Adj. R Table presents regression of natural log of countries TFP on a constant, country fixed-effects, year fixed-effects, country-specific linear time trends, and cyclone energy/km 2 (sum of max. wind speeds cubed) Cols. 1 and 4 use DICE TFP (labor measured by population). Col. 2 uses benchmark (labor measured by population times human capital); Col. 3 extended (labor measured by workers times human capital). Cols. 1-3 use consistent sample of country-years with available Penn World Table data on human capital and workers. Col. 4 uses extended sample incl. countries without education, labor data. Standard errors are heteroskedasticityrobust and clustered at the country level. *** p<0.01, ** p<0.05, * p< Cyclone Intensity Monte Carlo Simulation Details First, we use the Emanuel et al. s (2008) cyclone frequency data to estimate the projected mean number of storms making landfall in each country j under the future climate T Next 3 Specifically, we compute the relative increase in the number of landfalls in the synthetic track data between present and future conditions, and apply this increase (e.g., +5%) to each country s observed mean landfall count ( ) in the actual historical data. 15

16 we assume a Poisson distribution of cyclone counts (Emanuel, 2013) to randomly sample the number of storms making landfall in each country j per year under the future climate (taking n = 5, 000 draws from the Poisson(#landfalls j T 2090 ) distribution for each country j). Third, for each draw of a number of storms making landfall in country j, we then randomly sample storm characteristics (e.g., maximum wind speed) from one of the 3,000 synthetic tracks per basin 4 in the Emanuel data (with replacement). This process thus generates random draws over annual cyclone realizations ε j,2090, including years without storms. This process captures changes in expected future intensity driven both by changes in the number and characteristics of storms. Finally, we then fit appropriate distributions for each cyclone variable in each country. The resulting parameter estimates for each country are listed below. 2.3 Country-Level Results: Expected Cyclone Impacts Tables 1-4 below display country-level results for expected annual damages to TFP, physical capital, and human capital (%/year), along with the estimated Weibull distribution parameters for each country s annual maximum wind speed distribution (based on Emanuel et al. s (2008) synthetic cyclone tracks for IPCC A1B scenario). 3 Calibration Details 3.1 DICE Damage Functions This section describes the derivation of the climate change damage function coeffi cients in Table 9 based on the results of Table 8, which represent total expected cyclone depreciation. Holding socioeconomic factors constant, total future cyclone depreciation reflects a combination of baseline impacts and warming damages: δ T otal (T τ ) = δ Base + δ Additional (T τ ). First, given the scientific literature s common finding of linearity in the global cyclone intensity-temperature relationship (see, e.g., Holland and Bruyere, 2014), we linearly interpolate from T 2090 and specify δ Additional (T τ ) = αt τ.table 3 provides pairs of observations of total damages at current and future climates that we thus use to solve for slope parameters α via: α = δt otal (T 2090 ) δ T otal (T 2015 ) (T 2090 T 2015 ) (23) The synthetic cyclone tracks from Emanuel et al. (2008) underlying our T 2090 simulations reflect the IPCC s A1B emissions scenario, which different climate models estimate to result (on average) 4 5,000 tracks were used in the North Atlantic Ocean. 16

17 Table 1: Country-Level Expected Future Damages, Part I TFP Physical Capital Weibull Coeffi cients ξ j,2015 ξ k j,2095 Scale Shape Anguilla E Netherlands Antilles American Samoa Antigua and Barbuda E Australia E E Bangladesh E The Bahamas E E Belize Bermuda E E Barbados E Brunei E E Cambodia E Canada E E China E E Colombia E E Comoros Cape Verde E Costa Rica E Cuba Dominica Dominican Republic E Fiji E F.S. Micronesia United Kingdom E E Guadeloupe Grenada E Greenland Guatemala E Guam Honduras E Haiti Indonesia E E Isle of Man India Ireland E E Jamaica E Japan E E Malaysia E Martinique Mauritius E Mayotte

18 Table 2: Country-Level Expected Future Damages, Part II TFP Physical Capital Weibull Coeffi cients ξ j,2015 ξ k j,2095 Scale Shape Madagascar Mexico E E Montserrat E Morocco E Mozambique Myanmar E N. Mariana Islands New Caledonia New Zealand E Nicaragua E Niue North Korea Oman E E Pakistan E Philippines E Palau Papua New Guinea Puerto Rico Portugal E E Reunion Russia E E Samoa Saudi Arabia E E Solomon Islands Somalia South Korea E E Sri Lanka E St. Kitts & Nevis E St. Lucia E St. Pierre & Miquelon St. Vincent & Grenadines E Turks and Caicos E Thailand E E East Timor Tonga Trinidad and Tobago E E Tanzania E USA Venezuela E E British Virgin Islands E U.S. Virgin Islands Vietnam E Vanuatu Wallis & Futuna Yemen

19 Table 3: Country-Level Results, Part III Expected Fatalities (Fraction of Pop.) ξ j,2015 ξ h j,2095 Anguilla 6.96E-07 Antigua and Barbuda 1.51E E-07 Australia 7.76E E-08 Bangladesh 2.99E E-07 The Bahamas 2.24E E-07 Belize 5.65E E-07 Bermuda 6.39E E-07 Barbados 4.36E E-06 Brunei 1.33E E-13 Cambodia 2.39E E-07 Canada 6.12E E-08 China 1.04E E-08 Colombia 1.44E E-08 Comoros E-05 Cape Verde 2.32E E-07 Costa Rica 9.89E E-07 Dominica 4.73E E-06 Dominican Republic 2.04E E-07 Fiji 5.78E E-07 United Kingdom 2.45E E-07 Grenada E-06 Guatemala 1.90E E-07 Honduras 2.26E E-07 Haiti 2.63E E-06 Indonesia 1.87E E-08 India 2.44E-07 Ireland 2.97E E-08 Jamaica 8.63E E-07 Japan 2.81E E-07 Morocco 5.66E E-07 Madagascar 2.57E E-07 Mexico 2.66E E-07 Myanmar 6.24E E-07 Mozambique 2.02E E-07 Montserrat 7.55E-07 Mauritius 7.55E E-07 Malaysia 4.34E E-08 19

20 Table 4: Country-Level Results, Part IV Expected Fatalities (Fraction of Pop.) ξ h j,2015 ξ h j,2095 Nicaragua 2.37E E-07 New Zealand 2.68E E-07 Oman 2.56E E-08 Pakistan 4.93E E-07 Philippines 1.65E E-07 Portugal 5.53E E-07 Russia 4.80E E-08 Saudi Arabia 9.55E E-08 Saint Kitts and Nevis 1.98E E-07 South Korea 4.33E E-07 Saint Lucia 5.23E E-06 Sri Lanka 1.35E E-07 Turks and Caicos Islands E-06 Thailand 4.67E E-07 Trinidad and Tobago 1.38E E-07 Tanzania 9.37E E-07 United States of America 8.74E E-08 Saint Vincent and the Grenadines 7.57E E-06 Venezuela 1.61E E-08 British Virgin Islands 2.08E E-07 Vietnam 1.58E E-07 Yemen 9.56E E-07 20

21 in 2.8 C warming over temperatures by 2100 (IPCC, 2007). Based on Hawkins et al. s (2017) estimates that warming between and 2015 was 0.45 to 0.2 C, we thus have T 2090 T C. Given that global temperatures in 2015 were already around 1 C above pre-industrial levels, one additional question is whether to treat current cyclone patterns as already having been affected by this warming. A recent review by GFDL "conclude[s] that despite statistical correlations between SST [sea-surface temperatures] and Atlantic hurricane activity in recent decades, it is premature to conclude that human activity and particularly greenhouse warming has already caused a detectable change in Atlantic hurricane activity" (GFDL, 2018). In particular, they argue that, while a trend can be observed in recent years, over a longer time horizon back to the 1880s, one fails to detect a significant trend in cyclones (concurrent with the observed trend in warming) once observational biases are adjusted. In this case, the damage function would apply only to warming over the DICE model base year (2015), so that δ Additional (T t ) = α(t t T 2015 ) (for T t > T 2015 ). On the other hand, if anthropogenic warming has already been affecting cyclone patterns, the damage function is defined over warming since pre-industrial level as for other damages in DICE. Since both our overall global impact estimates and the difference between these scenarios are already small, we focus on the latter case where δ Additional (T t ) = α(t t ). We thus back out annual impact coeffi cients via (23). For example, the benchmark TFP impact coeffi cient is calculated via: α A = ( ) ( ) 2.35 = The remaining parameters in Table 9 are computed analogously. References [1] Emanuel, Kerry, Ragoth Sundararajan, and John Williams. "Hurricanes and global warming: Results from downscaling IPCC AR4 simulations." Bulletin of the American Meteorological Society 89.3 (2008): [2] GFDL (Geophysical Fluid Dynamics Laboratory). "Global Warming and Hurricanes." Available online at: Accessed July 2, [3] IPCC Solomon, S., D. Qin, M. Manning, Z. Chen, M. Marquis, K.B. Averyt, M. Tignor and H.L. Miller (eds.) Contribution of Working Group I to the Fourth Assessment Report of 21

22 the Intergovernmental Panel on Climate Change, Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA. (2007). [4] Krebs, Tom. "Human capital risk and economic growth." The Quarterly Journal of Economics 118, no. 2 (2003a): [5] Krebs, Tom. "Growth and welfare effects of business cycles in economies with idiosyncratic human capital risk." Review of Economic Dynamics 6, no. 4 (2003b):