Risk caused by the propagation of earthquake losses through the economy

The economy of a country is exposed to disruptions caused by natural and man-made disasters. Here we present a set of probabilistic risk indicators, the Average Annual Loss (AAL) and the Loss Exceedance Curve (LEC), regarding to production, employment, Gross Domestic Product (GDP), Gross Regional Product (GRP), export volume, inflation, tariff revenue, among others, due to earthquakes. All indicators are computed using a systematic probabilistic approach, which integrates the seismic risk assessment with spatial computable general equilibrium models, both robust and well-known frameworks used worldwide in their respective fields. Our approach considers the induced damage and frequency of occurrence of a vast collection of events that collectively describe the entire seismic hazard of a country, giving us a better and more complete understanding of the full consequence of earthquakes. We illustrate this approach with an example developed for Chile.

1 Response to reviewer comments.

Reviewer #1
Dear authors, thanks for your interesting article that has included elaborate SCGE analysis with many simulations run and uses detailed information about possible future disasters. I am however missing a number of important points in your paper: 1) There is a need for better explanation of the difference between modelling of events with low/long return periods. It is not clear to the reader whether you treat them differently in your SCGE modelling and what are the main differences.
Action taken: There is no difference in the way we model events with short or long return periods. As we will show while answering the following remark, and event with a long return period is not an event that will occur far away in the future, but just an event with a low probability of occurring in the next year. In this sense, large and small earthquakes are modelled using the same techniques, but the small events are more likely to occur -or more frequent-than the large ones.
2) Your paper attempts to make the SCGE modelling for the very long term (100 000 years) without properly explaining if you assume any change in the population or economic structure in this very long-run.
Action taken: we addressed this point with two actions: i) We incorporated a short paragraph in the main paper: 2) we aggregated a supplementary note in Supplementary Material.
Main paper: "Note that in catastrophic risk modeling, it is customary to indicate the likelihood of an event taking place in, say, the next year, by using its return period. (See Supplementary Note 1 in Supplementary Material)." -Page 6.
Supplementary Note: "In catastrophic risk modeling, it is customary to indicate the likelihood of an event taking place in, say, the next year, by using its return period. In this context, the return period of any given loss value, l, is the average time between events that produce losses equal or greater than l. Therefore, if a loss value has a return period of 100,000 years, this means that events that produce losses greater or equal than the given value occur, on average, every 100,000 years. But this does not mean that the event will take place 100,000 years in the future from now. It just means that the likelihood of this event taking place in the next year is very low. How low? Since we are considering a Poisson occurrence process in time, the annual probability of exceedance, Pe, and the return period, T are related through: For large values of T, = 1 Therefore, events with large return periods are not events that will occur far away in the future; they are simply unlikely events. There is, thus, no need to account for changes in population or economic structures. Another heuristic way to see our simulation scheme is thinking that, in reality, we are not simulating the next 100,000 years, but 100,000 times the following year." -Page 8, Supplementary Material.
3) It seems from the current text of the paper that there are no assumptions made about the economic/regional/demographic developments in the very long run and that you only concentrate on the indirect changes via supply chains. In that case it would be good to explain what is the value added of SCGE model as compared to MRIO analysis that is also used in the literature to assess indirect impacts of disasters.
Action taken: We addressed these points in the following way: (i) we highlight the advantages of using the SCGE model as compared to MRIO analysis to assess the indirect impacts of disasters; (ii) we run the simulations in the long-term scenario and included those results as a comparison with the original ones (short-run environment).
The paragraphs that we incorporated in the new version are: "We use a spatial CGE model, unlike a part of previous studies that assess the impact of natural disasters from interregional input-output models. CGE models go much further than the input-output model, in which the principal focus is on links through sales of goods and services between industries and from industries to final users. In contrast, CGE modeling identifies behavior by individual agents and emphasizes links provided by competition for scarce resources (Dixon et al., 2017). Koks et al. (2016) compared natural disaster impacts using an input-output model and a CGE model. They showed that for a detailed assessment of disaster impacts on the economy, including the price effects and effects on employment, the CGE models are better suited. In addition, they highlight that the conventional multiregional input-output models may largely overestimate the losses." -Page 15 "Although our approach mainly uses SCGE models in a short-run environmental, the type of CGE modeling proposed in our work allow us easily changing to a long-run economic scenario, including between other, the labor migration effect. A wide range of aspects can be analyzed and studied using a long-run model, however, we have limited to present the magnification effect that economic losses would have if no mitigation actions and recovery of the capital stocks destroyed by earthquakes took place along the time. We compared some aggregated results regarding the annual average loss and loss exceedance curves of production in Chile obtained using a short-3 run and a long-run environment of economic modeling ( Supplementary Fig. 11). We would like to highlight the potential of our approach to also carry out probabilistic analysis of economic impacts at long-run." -Page 15.  Sciences, 16(8), 1911Sciences, 16(8), -1924) You explain that besides negative effects disasters may also have positive effects for some regions and sectors due to substitution effects along the supply chain. However, the largest positive effects are associated with the recovery process and reconstruction of the lost capital stocks. You do not include recovery process in you modelling. What is the motivation for this?
Action taken: To better define the interpretation of our results, we added theses sentences in the discussion section of the manuscript: "The capacity to compute probabilistic metrics regarding to positive impacts caused by earthquakes is another contribution of this work. The positive effects are related to the systemic perspective intrinsic to the productive linkages identified through the CGE model -that is, the feedbacks and interactions that occur in the productive system. The spatial CGE model captures the links between different parts of the economy and models it as a set of integrated supply chains. Thereby, the capital stock losses due to an earthquake in one region result in changes in sectoral output in other regions through the spillover effects they cause across the supply chain. The effects on the supply chain are the indirect costs identified by the CGE model, that is, induced by disruption of economic activities in other, linked regions. Some regions may have positive effects (GRP growth) caused by the change in relative prices captured in the CGE model. The change in relative prices causes a change in the interregional trade flows -that is, the interregional exports and imports. This change in trade flow, in turn, will have a negative/positive impact on Regional Gross Product. The negative economic consequences of earthquakes are partly offset by a subsequent period of increased economic activity, due to higher spending on infrastructure and reconstruction (Seville et al., 2014). Nevertheless, recovery process modeling is not part of the scope of our study." -Page 16.
5) The main value added of SCGE models is that they are able to capture the changes in regional and sectoral structure that follow some specific shocks. One would expect that repetition of extreme events would somehow change the allocation of economic activity and population and one would expect that the impacts would be larger in case of frequent event. Could you be more explicit about whether you use comparative static SCGE of recursive dynamic SCGE model and also add a discussion about dynamic effects into the paper.
Action taken: Dynamic general equilibrium models are helpful for modeling the process of capital accumulation in the economy and used to generate forecasts for industries, labor force groups, and regions; these models would not be useful for the hazard assessment caused by the human-physical interactions. To clarify this issue, we add this paragraph to the manuscript: "The human and physical systems are largely connected; human activities influence physical processes and vice versa (European Commission, 2020). Thus, physical factors can influence human adaptive behavior. For instance, risk perception is higher after an earthquake and can cause a higher uptake of adaptation measures. The humanphysical interactions, in general, are missing in the current economic models. This gap can guide the development of future research for extreme events modeling. A way to incorporate these interactions is to alter utility and production functions in various ways and explicitly incorporate uncertainty. However, this involves interdependence of utility functions, which are difficult to model in general, especially in a CGE framework (Dixon et al., 2017). The uncertainty also can incorporate into modeling as done in our methodological approach. Our scenarios understand a range of impacts that disasters can cause in the high-frequency and lower-impact events or the higherimpact and lower-frequency events, considering a loss corresponding to an average loss over a given period, which is obtained from the probabilistic analysis that considers the likelihood of occurs events." -Page 16. Action taken: Thank you. We have revised this literature. We also included the references. Now it reads: "ESPON-TITAN (2020 and 2021) provide evidence on the direct and indirect economic impacts of natural hazards, extreme events and disasters identifying trends, and territorial vulnerability patterns across European regions and cities. This research project uses the multi-regional input-output models to assess the extreme event's costs on the supply chain. European Commission (2020) and World Bank (2021) also use the input-output models to assess direct and indirect economic impacts of disasters in Europe." -Page 2-3.

Reviewer #2
Regarding reviewer #2's point about moving the methods to before the Results section, unfortunately our style is that the methods sit after the discussion.

Reviewer #3
1) The manuscript proposes an approach to combine a probabilistic seismic risk model with an economic model to forecast direct and indirect economic costs of earthquakes for Chile. It is written that the main novelty is the combination of these two models and that the model results are illustrated with the case of Chile. However, in the main text, main emphasis is on the Chilean results and the combination and approach is not that much detailed. It could thus be explained more carefully that the approach in the manuscript is exclusively on Chile, and Chile could also be included in the title.
Action taken: We thank very much for her/his comment because it touches on an important point. We agree that perhaps too much importance is being given in the paper to explaining the results at the expense of space and detail devoted to explaining the calculation approach. We have tried to achieve a better balance in the new version of the paper by emphasizing to the approach.
We have emphasized our approach by expanding the discussion section, writing the results section more succinctly, and integrating some modifications in the abstract and introduction section, as you can see in the paragraphs highlighted through the manuscript.
In the new version of the manuscript, we address the issues about the methodology and treatment of data regarding the choice of assumptions, validation and seismic risk techniques. In addition, we improve the discussion about the modeling, concept, and results, place our work in the context of the broader literature, and explore its implications. In particular, we show how our findings can be applied in the context of other economies.
Having said that, we hope that it is now clearer that the approach is general and that we use the case of Chile just as an example. Given this, we have deemed unnecessary it to include reference to Chile in the title.
2) It is also written in the main text, that the approach is merely a proof-of-concept instead of being a final product, as all data could not be collected. However, being a proof-of-concept, the approach could be detailed, justified and discussed more, as currently the focus is on the results.
Action taken: The reviewer is correct. As indicated in the previous response, we have tried to change the balance of the paper, giving more emphasis to describing the approach and less on describing the results. All modifications done are highlighted throughout the manuscript.
3) It is discussed that the results are feasible and robust but it is not properly justified why it is so. Therefore, some kind of validation, e.g. in relation to 7 historical data could have made a good extension for the manuscript and increase its robustness Action taken: The reviewer raises a good point, to which we dedicated just a few lines in the original version of the manuscript. To address this point, we have included the following paragraphs in the main paper: "Empirical validation of catastrophe models is, by definition, a difficult task. Fortunately, catastrophes are relatively rare events so observed values of losses are never a sample big enough to allow for empirical validation. Moreover, even if we had observed losses for a long time, cities change, construction materials change as well, so the information loss about events that took place more than a few decades ago is not very useful. In a way, the reason to start developing catastrophe models, back in the 1990s, was precisely the need to compensate for this data shortage. So direct validation of the models, in the sense of empirically establishing the exceedance frequency of losses of various sizes, is never possible.
Nevertheless, efforts are made to carry out partial validations of different kinds. First, the rate of occurrence of earthquakes of various magnitudes and their spatial distribution are estimated from appropriate earthquake catalogs and knowledge of the regional tectonic setting. This guarantees that the model for future occurrences will not introduce too many or too few events and that the spatial distribution of future, hypothetical events, will be coherent with the observed distribution and coherent with geological science.
Additional validations are made regarding the relation between earthquake source characteristics (magnitude, hypocentral location, rupture plane orientation, etc.) and the ground acceleration field produced by the event. These guarantees that, on average, the observed ground accelerations and the accelerations predicted for future events will be unbiased.
In some cases, it is possible to compare the real losses produced by an event with those computed with the model for a synthetic event of similar characteristics. We presented an example of this comparison with the Maule earthquake of 2010, finding that the modeled losses are coherent with those observed. In some cases, several loss-producing events can be used in this validation phase but, in our case, the last big event before the Maule earthquake took place in 1985, which was considered to be too far away in the past." Page 17.
In addition, in the results section, we have aggregate simulations of the losses caused by three large earthquakes occulted in Chile in 1960, 1985, and 2010 and compared the real losses estimated by the Chilean government and those computed with our model for the Maule 2010 Earthquake.
"For instance, we present the direct losses, production losses, and GRP reductions estimated for simulations of three large earthquakes occulted in Chile in 1960, 1985, and 2010 Fig. 8 and Supplementary Fig 9)." Page 13.
"According to estimations of the Central Bank of Chile, The Maule 2010 Earthquake caused a 3% of losses in the total net capital stock of Chilean economy, 3.2% in the residential buildings and 2.6% in non-residential infrastructure (Banco de Chile 2010). Our model estimates direct losses in nonresidential buildings of 2.5% of their total value. Furthermore, the Chilean Government (Gobierno de Chile 2010) estimated a GDP decrease of 7,600 million dollars for the next four years after the 2010 Maule Earthquake. Our simulation for this event estimates a yearly GDP contraction of 1.65%, which is coherent with the official estimation, assuming that the first year after the earthquake, at least half of the total 7,600 million loss took place, that it is, a 1.74% GPD contraction (Total Chilean GPD 2010: 218,500 million dollars)." Page 14. 5) Discussion section of the manuscript is currently very short and the relevancy and importance of findings could be discussed much more carefully. In particular, how do you know that your results are realistic? This is also visible in the abstract which does not currently include a proper conclusion, and in the final sentence of introduction (lines 112-113) in which the idea could be extended and clarified.

9
Action taken: We have included more extended and substantial discussions regarding the relevance of our findings. We have also included/modified the conclusion in the abstract and the introduction section.
We expanded the discussion section by adding the paragraphs presented in the previous responses and also adding the following sentences: "Our main results show that damage prevention activities must consider sectoral and regional linkages in disaster management measures. These findings can be used with information about patterns of regional vulnerability to provide inputs for the formulation of strategies that better considering the systemic effects of natural hazards in an integrated framework of inter-regional supply chains and trade flows." -Page 5.
"The possibility to aggregate and transfer the macro-economic assessment of disaster impacts to regional levels of adaptation and analysis is limited (European Commission, 2020). However, regional modeling is essential as an exercise to measure the systemic effects of disruptions in supply chains, whether caused by natural hazards, extreme events, or disasters. The regional evaluation of the wider indirect economic impacts of climate change still requires the development of new analysis tools. Therefore, as done in our analysis, mapping the economic impact of the natural disaster is essential for risk management and prevention since it provides tools for spatial planning decisions. In this context, our study has the potential to contribute to the literature by considering the economic impacts of natural hazards at the regional level using integrated modeling based on the probabilistic risk model and the spatial CGE model." -Page 15.
European Commission (2020 6) The results of the manuscript suffer from multiple problems. In particular, the reference to tables and figures could be given in parentheses in the end of sentences instead of writing " Figure 1 shows" etc. There are also some unnecessary parts that could be removed and/or moved to figure/table captions (e.g. lines 142-145, 166-168,170-173). The results are currently mostly descriptive and could be of interest for some, but for a wider audience, they could be written more succinctly, and could also be more in-depth. One option is to conduct a proper validation, as I already wrote above. Another option is to provide some kind of uncertainty estimates or confidence intervals. It is written that the economic model is deterministic but this choice is not justified. Tables and figures could also be reworked a bit; for instance, table 1 would need a better caption (are main results in the AAL column?) and there could be an additional volume showing the AAL in percentages of total value. Then, sector and region names should be explained somewhere in main text, as currently e.g. Figure 2 is difficult to interpret. Finally, "per mile" is written several times in results. This should be translated into English as mile is a unit of length in English.
Action taken: Thank you. We have revised this part and addressed it as follows. We have moved all references to tables and figures to the end of the corresponding sentences. We have removed/moved some parts (lines 142-145, 166-168, 170-173) from the main text to the Figures/ Tables captions/description (revised manuscript lines 160-161, 193-195, 206-208, 222-223). We have reworked Table 1 with a better caption, and we included an additional column showing the AAL in the percentage of total value as suggested. We have included Table 2 in the main text with the description of the regions and sectors of our Chilean's case of study. Finally, we have replaced the word "mile" by "thousand" throughout the entire document.
We have addressed the concern of the reviewer about our model being deterministic on the CGE side. For that purpose, we have added the following lines: "Our modeling approach is fully probabilistic on the earthquake occurrence side, but for now, it is deterministic on the CGE side; the reason for this is that, while earthquake risk modelling is a 50-year old discipline, within which uncertainties have been thoroughly studied and characterized, we feel that characterization of uncertainties in CGE modelling is still a work in progress". -Page 4.
We also have rewritten our results more briefly and trying to be more in-depth and for a wider audience. We have addressed the comments regarding the proper validation of our results above (in point 3). 7) Although the language seems to be mostly fine, there are some problems with it. For instance, in abstract line 6, "catastrophe-induced" seems to be unnecessary, and in line 12 word "respectively" is missing. There are also problems in main text (e.g. end of sentence in line 44, awkward phrasing of the approach in lines 63-65, missing references in line 74, unnecessary use of "etc." in line 82, somewhat normative statement of Chilean economy in lines 96-98, "C" and "being" being in wrong order in line 152 and so on). Response to reviewer comments.

Reviewer #2
Apart from a few minor omissions pointed out by the reviewer and corrected by the authors, unfortunately, most of the suggested corrections were not only not commented on (explained) by the authors but also were not taken into consideration at all and implemented in the latest version of the manuscript. It is, it must be admitted, really unexpected and unacceptable for this category of journals.
Therefore, the authors of the manuscript are once again asked to take into consideration the comments (and provide a detailed point by point response to each one of them), which have been suggested only for the reasons of improving the quality of the manuscript as well as its better and simpler understanding.
Response: As kindly explained by the editor, unfortunately, in the previous decision, the comments of referee #2 were not forwarded to us, so we were not aware of these comments. Our apologies for this misunderstanding.
We appreciate the comments and suggestions from referee # 2, and below, we proceed to provide a point-by-point response.

I. GENERAL OBSERVATIONS:
Comment 1: In terms of the title "Risk caused by the propagation of earthquake losses through the economy of a country", instead of the part "the economy of a country", "the economy of Chile" (or possibly, "the economy of a country on the example of Chile") would be more adequate, which more precisely states the place (location, area) of the conducted research.
Response: Unfortunately, in the format and style required by the Nature Communication Journal, the is no space in the main manuscript for the keywords.
 It is noticeable that the order of the sections presented in the paper is not usual. Thus, for example, the Section METHODS (page 18) is after the Sections RESULTS (page 5) and DISCUSSION (page 14), and in fact, should instead precede them -according to the IMRAD scheme (Introduction, Methods, Results, and Discussions), which is generally accepted (by all scientific journals).
Except for the remark that the authors remained the original order of the sections (Results, Discussion, Methods), no other explanations were given regarding any of the suggestions given within Comment 2. If the style used by the authors is in accordance with the recommendations and policy of the Journal itself, then no corrections need to be made, but the authors should have already given such an explanation in their response.
Otherwise, the suggested corrections should definitely be implemented in the manuscript.
Response: Unfortunately, the nature communication journal style is that the methods appear after the results and discussion. The order of the section is a journal´s requirement.
the full width of the page. The authors are once again asked to correct this.  (NEW) COMMENT (Figure 3 caption (added explanation) -lines 206-207): "AAL is presented as a percentage of its corresponding total value to see the influence of each region in the total AAL". Is this correct, considering the given figure and the preceding explanation within the figure caption ("The average annual loss in production by region is shown in panel d in millions of USD")? Or maybe to rephrase the caption and give a more precise (and thus correct) explanation?
Action taken: We have attended the reviewer"s suggestions as follows: 1) we have increased the width and the height of Figure 3, and we increased its resolution; 2) we have removed from the caption of Figure 3 the sentence "as a percentage of its corresponding total value to see the influence of each region in the total AAL". (New manuscript, Page 9, lines 204-206).
Comment 3: (page 10, Figure 4) For the sake of better visibility and understanding of the given problem, it is suggested to:  increase the height of the diagrams;  instead of in the legend, to write the appropriate marks (R1, R2, R3, ...) next to each curve (since there are numerous curves in the figure, as well as similar color tones that are difficult to distinguish). The authors are once again asked to correct this.
Action taken: We have increased the height of the graphs, and we wrote the appropriate marks next to each curve as suggested by the reviewer. (New manuscript, page 10).
Comment 4: (page 11, Figure 5) For better visibility, it is suggested to:  increase the width of the figure to the full width of the page;  instead of in the legend, it is recommended to write the appropriate marks (R1, R2, R3, ...) next to each curve ( Fig. 5, b, d, f);  (NEW COMMENT) the figure caption should be provided on the same page as the figure itself. The authors are once again asked to correct this.
(NEW) COMMENT 5: (lines 240-241) In the added sentence "For instance, we have computed the AAL of employment, GDP, and export volume for Chile in 7,786 workers, 305 million (0.122% GDP contraction), and 62 dollars, respectively". According to Table 1 (which should also be mentioned here in the text, as the given results are presented precisely in this table), the data are not completely specified.
Action taken: We have increased the graphs' width and height, and we wrote the appropriate marks next to each curve as suggested by the reviewer. We have provided the caption on the same page where Figure 5 is located. (New manuscript, page 12).