Economic losses from disasters, particularly indirect losses resulting from disruptions beyond direct physical damage, can significantly exceed direct losses. Recent catastrophic events like the 2004 Indian Ocean tsunami, Hurricane Katrina, the 2010 Haiti earthquake, and the 2011 Japan earthquake underscore this reality, highlighting the need for improved risk assessment methodologies that incorporate indirect economic impacts. While catastrophe modeling for physical damage is well-established, modeling indirect losses lags behind due to difficulties in translating property damage into economic consequences and the lack of suitable models linking them. Existing approaches often estimate indirect losses as a percentage of direct losses, a method lacking reliability. Although there is substantial literature on the economic impact of disasters, focusing mostly on individual events, it often neglects the crucial aspect of frequency of occurrence. This research proposes a novel framework to systematically integrate probabilistic seismic risk assessment with CGE modeling to address these limitations. The approach utilizes spatial CGE models which can incorporate the geographic locations of economic agents and endowments. By considering the stochastic nature of earthquake occurrences, the frequency of events, and the linkage between physical damage and economic components, the study aims to provide more comprehensive and robust estimates of the full economic consequences of earthquakes.

The literature on the economic impact of natural disasters has seen advancements in both quantitative models and integrated frameworks. Researchers have improved models for various disaster types (cyber-attacks, extreme weather, earthquakes, etc.) and incorporated factors like transportation and critical supply chains. Tools have been developed to directly estimate economic damages using physical data or satellite imagery (nighttime light intensity). The ESPON-TITAN project, for example, provides insights into the direct and indirect economic impacts of hazards across European regions using multi-regional input-output models. However, the existing literature often focuses on individual events rather than considering their probability of occurrence, hindering proper risk assessment and policy making. This study uniquely addresses this gap by incorporating event frequency into the analysis.

This study proposes a systematic integration of probabilistic seismic risk assessment and Computable General Equilibrium (CGE) modeling frameworks to estimate higher-order economic losses from earthquakes. The methodology comprises several key steps: 1. **Seismic Risk Model:** A stochastic earthquake catalog, consistent with a seismic hazard model for the region (Chile in this case), is generated. Each earthquake event is characterized by its frequency of occurrence and intensity distribution. The exposure database includes all assets at risk, categorized by location, vulnerability characteristics, and economic sector. Using vulnerability functions, the model calculates the probability distribution of losses for each asset for each earthquake event. 2. **Spatial CGE Model (BMCH):** A spatial CGE model (BMCH, Chilean version of B-MARIA) is employed. The BMCH model incorporates the interregional economic structure of Chile (15 regions, 12 sectors) and considers interregional linkages through trade and factor mobility (capital and labor). 3. **Integrating the Models:** Direct losses (physical damages) from the seismic risk model are introduced into the CGE model as shocks to the capital stock. This perturbs the economic equilibrium. The CGE model is then re-run to determine a new equilibrium reflecting the economy's adjustment to these shocks. This process is repeated for each earthquake event in the catalog. 4. **Risk Metrics:** Based on the CGE model output, probabilistic risk metrics are computed. These include Average Annual Loss (AAL) and Loss Exceedance Curves (LEC) for various economic variables (production, employment, GDP, GRP, exports, inflation etc.). AAL represents the expected loss in a given year, while LEC shows the probability of exceeding different loss levels. The study specifically focuses on non-residential buildings whose damages directly affect the production process. The model incorporates probabilistic aspects of earthquake occurrences but uses a deterministic approach for the CGE model parameters, recognizing that uncertainty in CGE modeling requires further research.

The study's key findings, using Chile as a case study, are as follows: * **National-Level AAL:** The AAL for direct losses (non-residential buildings) was estimated at $302 million, while the AAL for production losses reached 0.132% of the country's total yearly production. Other AALs were calculated for GDP ($305 million, 0.122% contraction), employment (7786 workers, 0.115% of total employment), and export volume ($62 million, 0.075% reduction). * **LECs:** LECs for production losses show that for less severe events (short return periods), production losses are proportional to direct losses. However, for more severe events (longer return periods), the relationship becomes less proportional, indicating non-linear impacts. * **Sectoral Differences:** The riskiest sector varied depending on the loss measure. For direct losses, it was "Commerce, hotels, and restaurants", while for production losses, it was "Transport, communications, and information services". The sector contributing most to the total AAL also differed between direct and production losses. * **Regional Differences:** The Metropolitan Region of Santiago concentrated the largest share of both direct and production losses. However, the riskiest regions differed between direct and production losses, highlighting the importance of considering indirect economic effects. * **Positive Economic Effects:** The model also captured positive economic impacts (average annual gain of $18.32 million, 0.0041% of yearly production), mainly due to substitution effects. These positive impacts were relatively small compared to negative losses. * **Scenario Analysis:** The model simulated the effects of three major past Chilean earthquakes (1960, 1985, and 2010), providing estimates of losses for specific events and allowing comparison with observed losses. The Maule 2010 earthquake simulation, for example, showed results consistent with official estimates of GDP loss.

This integrated approach successfully demonstrates the interconnectedness of seismic risk and macroeconomic consequences, providing a more complete picture of earthquake impacts than traditional methods. The study highlights the necessity of considering both direct and indirect losses in disaster risk management. The use of CGE modeling offers valuable insights beyond production losses, encompassing employment, GDP, regional product, exports, and even inflation. The findings underscore the importance of considering intersectoral and interregional linkages in economic planning for disaster mitigation and preparedness. The model's ability to capture both negative and positive economic effects enhances its value. The approach is readily adaptable to other natural disasters and offers significant potential for improving disaster risk management strategies, informing financial hedging instruments for governments and insurance companies, and aiding in the design of effective emergency response and recovery plans.

This paper presents a novel approach that integrates probabilistic seismic risk assessment with spatial CGE modeling, allowing for a comprehensive estimation of earthquake-related economic losses. The application to Chile demonstrates the capacity of the model to capture both direct and indirect economic effects, including positive substitution effects. The results highlight the importance of considering the interconnectedness of different economic sectors and regions in assessing disaster risk and planning for mitigation and recovery. Future research could focus on further refinement of the CGE model to incorporate uncertainty and human-physical system interactions, leading to even more robust and reliable estimates of disaster impacts.

While this model represents a significant advancement, some limitations exist. The CGE model currently uses a deterministic approach for its parameters, while the earthquake occurrences are probabilistic. Future work could explore incorporating uncertainty in the CGE model parameters. Furthermore, the model does not explicitly include aspects such as human-physical system interactions, risk perception influencing adaptation measures, or the long-term effects of reconstruction. Finally, the empirical validation of catastrophe models, by its nature, is challenging given the rarity of catastrophic events.