In the last few decades we observe an increasing amount of economic activity in areas prone to natural disasters in the world, in combination with a rising frequency of extreme weather and climate events (IPCC, 2012). As a result, the need for high-quality disaster impact models is becoming more urgent. In response, a large number as well as a variety of models have been applied to study the economic impacts of disasters. While the most common economic models for disaster impact analysis are input–output (IO) and computable general equilibrium (CGE) models, an increasing number of scholars employ hybrid models, combining the two or either of them with different (partly noneconomic) models (Baghersad and Zobel, 2015; Carrera et al., 2015; Koks et al., 2015). This wide variety of models, however, leads to an important question: how should (differences in) the outcomes of the models be interpreted?

While both IO and CGE models are widely used, a comparison between their results has only been done on a theoretical level (e.g. Rose, 1995, 2004; Okuyama and Santos, 2014) or on the basis of different case studies (e.g. Okuyama, 2010). Few studies exist in which both model types are empirically compared in a systematic way for the same case study and geographical area using identical input data (Hu et al., 2014; West, 1995). Such a comparison is highly valuable from both a scientific and policy perspective as the magnitude and spatial distribution of losses may vary. It is possible that investments in risk reduction appear justified on account of a certain model while disproportionally high according to another model. Alternatively, regions not directly affected but with trade relations with a region hit by a natural disaster may display either gains or losses depending on the choice of the model. Regional disaster impact loss estimates resulting from a range of model outcomes facilitate better decisions and policy making.

In this study we analyse the disaster impact for two flood scenarios in the Northern Italy (Po River basin district) area using three models: two hybrid IO models and a regional CGE model for Italy. We first discuss the main model characteristics. After that, we apply the models and compare their results. The two hybrid input–output models used in this study are the commonly used the Adaptive Regional Input–Output (ARIO) model developed by Hallegatte (2008) and the MultiRegional Impact Assessment (MRIA) model, developed by Koks and Thissen (2014). The CGE model used in this study is a regionalized version of the CGE model developed by Standardi et al. (2014), which has been applied already in Carrera et al. (2015) for a disaster impact analysis. In the remainder of the paper the CGE model will be indicated as IEES (Italian Economic Equilibrium System).

The paper proceeds as follows. In Sect. 2, we discuss the valuation of economic losses and provide an overview on important modelling aspects involved in disaster impact analysis. This section includes both a theoretical comparison between IO and CGE models and a brief overview of the proven model extensions from the literature. This is followed by an explanation of the used models in this comparison exercise and the used data in Sect. 3. In Sect. 4, we present the study area, in Sect. 5 the results of the comparison are presented, and in Sect. 6 they are discussed. Finally, Sect. 7 concludes with providing some lessons learned and recommendations for practitioners and policy makers in the field of disaster risk modelling.

Before turning to the methodological aspects, it is essential to understand what is conceived as a disaster and what types of economic losses are referred to in this paper. A disaster is not equivalent to a natural hazard. According to the revised UNISDR terminology (UNISDR, 2015), hazards are “potentially damaging physical events, phenomena, or human activities” that may cause harm, while disasters are serious disruptions beyond the capacity to coping with the suffered harm. More generally, hazard strikes turn into a disaster when communities or societies at large are unable to cope, with own resources, with the manifold economic, physical, social, cultural, and environmental impacts of hazard strikes. Consequently, hazard research focuses often on modelling physical disrupting events only, while disaster research should always comprise societal impacts (often in economic terms) as well as the post-disaster reconstruction and recovery (Okuyama and Chang, 2004).

Figure 1 shows the methodological approach undertaken in this study. A flood damage assessment is performed on two flood scenarios along the Po River in Northern Italy. The economic disruption, as a result of each of the floods, will be prepared for each model. Stock losses are then translated into flow losses by means of the three economic models. Outputs are systematically compared to investigate the key characteristics of the models and their significance. Table 2 provides a preliminary analysis of the key characteristics of models, based on the descriptions as provided in the following sections.

For the comparison, we consider two simulated floods in the Po River basin in Northern Italy. As shown in Fig. 3, the two floods affect the administrative regions of Veneto and Emilia-Romagna in the downstream part of the basin. The two flood events considered in this study represent the result of a simulation produced by ARPA Emilia-Romagna (Regional Agency for Environmental Protection). The exercise simulates two levee breach scenarios around the municipality of Occhiobello: one on the southern and one on the northern levee. The southern breach inundates the Emilia-Romagna region, while the northern breach the Veneto region. The case study in Veneto and Emilia-Romagna is selected for their relevance in the Northern Italy economy. Although being simulated, the scenarios are not totally unrealistic. Occhiobello is famous for being the location where in 1951 Italy experienced one of the largest inundations on record. The location is also reported to be one of the most vulnerable sections along the Po River levee system. In 1951 the levee breach (northern) inundated more than 100 000 ha of urban and agriculture land in Veneto, causing large economic losses and more than 100 causalities. The river discharge associated with the levee breach considered in this study corresponds to the discharge recorded during the 2000 Po River flood, which was approximately the discharge recorded in 1951 (10 300 vs. 9750 m3 s-1). The flood caused by a left-bank breach on the Po River levee affected the Veneto region. It resulted in inundation of mainly agricultural land and dispersed small settlements. The flood case on the right-bank breach of the Po River levee affected Emilia-Romagna. It resulted in substantial flooding of industrial areas, in addition to agricultural and residential areas. Table 3 shows the result of the asset loss assessment, performed with the use of depth–damage curves

Please consult Merz et al. (2010) and Jongman et al. (2012) for a complete explanation of the use of depth–damage curves for disaster risk assessments. A complete explanation of this method is out of the scope of this paper.

As can be seen from Table 3, asset losses are very similar for both flood scenarios. There are, however, important differences in the composition of the losses. First, asset losses within industrial areas are more than twice as large in Emilia-Romagna compared to Veneto. They account for amounts to 15 % of the total losses in Veneto and 35 % of the losses in Emilia-Romagna. Second, asset losses in urban areas are 76 % of the total asset losses for the flood in Veneto, whereas only 52 % for the flood in Emilia-Romagna. Finally, the asset losses in agricultural areas are 9 and 10 % of the total asset losses for, respectively, Veneto and Emilia-Romagna.

Table 4 shows the total output losses in Italy for the two floods, the three models, and the three recovery paths. The calculations with the ARIO model result in the highest losses for the whole of Italy, for both floods, and for each recovery path. This is in line with expectations from previous literature that IO models may result in higher estimates of losses (e.g. West, 1995; Rose, 2005). The IEES model has, as expected, the lowest output losses in almost every model set-up. The lowest losses for the IEES model can be explained mostly by the perfect substitution across sectors of labour and capital. This means that labour and capital can move from one sector to another without transition cost and may influence the reduction of losses even more than the potential increase in trade.

Only for the concave recover path for the flood in the Veneto region are the losses in the MRIA model slightly lower. This can be explained on a sectoral level: in the MRIA model, the extra reconstruction demand, which goes directly towards the construction sector, has a clear positive effect on this sector. In the IEES model, this positive effect is marginal. For the convex and linear recovery paths, the higher sectoral losses due to slower recovery largely outweigh this positive effect in the MRIA model. The rigid and flexible versions of the IEES model show comparable results for Italy as a whole. Important to note here is that the difference between the two models only has an effect on the spatial differentiation of the losses (see Fig. 4).

Table 5 shows the losses for the flooded regions region only. It is worth noting that in the affected region the cross-model differences are much smaller and strongly depend on the recovery path. From Table 4 it becomes apparent that the ARIO-estimated losses for Italy as a whole are almost 6 times larger than the IEES – Flex model for the concave recovery path and the Veneto flood scenario (first row). When considering only the losses of the affected region, this difference is a only factor 0.2 (first row in Table 5). This implies that the largest differences in outcome between the models are occurring in the multiregional effects of the disaster. More specifically, this means that the assumptions regarding multiregional spillover effects (with or without substitution, additional imports, or factor mobility) are important determinants of the final outcomes.

A closer look at the differences for the affected region in Table 5 shows additional divergences between the models compared to Table 4. First, in Table 4 the ARIO model always predicts the highest losses for Italy as a whole. In Table 5, where only the losses are shown for the affected region, this is only the case for the concave recover path for the Veneto flood event. In all other scenarios, the induced losses calculated by the MRIA and the IEES – Flex models are higher. This may imply that allowing for more flexibility in the model results in higher losses in the affected region. In the MRIA model, this may be explained by the maximum regional capacity. In contrast to the ARIO and IEES models, the MRIA model sets a maximum capacity on the regional production (see Sect. 3.3). This regional maximum capacity prevents products which are normally considered as a byproduct from becoming the main product to its full extent. When a byproduct will be produced as a main product due to an increase in regional demand, taking into account the Leontief structure of an IO model, the production of the main product will go up as well. This induces the inefficiencies in regional production that are limited by the regional production limit. As such, the model will turn more quickly to alternative suppliers from different regions, which do produce the demanded product as a main product, reducing the inefficient production overall. For the whole of Italy this results in lower losses compared to the ARIO model. In the IEES – Flex model, a similar substitution process occurs with the movement of production factors to other non-affected regions (not possible in the IEES – Rigid).

When comparing the spatial distribution of the losses across the three models for the concave recovery curve of the Emilia-Romagna flood (Fig. 4), we find some interesting results. First, the two “IO-based” models (i.e. the ARIO and MRIA models) show large differences in the spatial distribution of losses. Whereas the ARIO model shows negative results in all regions, the MRIA model only shows negative results in the affected region. What is notable is that the losses in the affected region are higher in the MRIA model (as also shown in Table 5). As such, by allowing for substitution between producers in the model, the affected region is affected more heavily, while the non-affected regions benefit. This can be explained by the inefficiency losses, which are modelled in the MRIA model, but not in the ARIO model. Second, we find some interesting similarities between the IEES – Rigid and IEES – Flexible with, respectively, the ARIO and MRIA models. The rigid version of the IEES model, with immobile production factors, shows relative little substitution effects, resulting in negative (albeit small) effects in almost all non-affected regions. The flexible version, however, shows, similar to the MRIA model, benefits in all other regions due to large substitution effects. For the IEES models, it is important to note that the productivity shocks decrease the demand for labour and capital because of lower productive capacity and income. This means that remunerations of capital and labour go down and in the IEES – Flexible model capital, and labour can move towards non-affected regions. This determines the exacerbation of the profit and losses dynamics and is the main cause for the difference in regional economic losses between the IEES – Flexible and – Rigid model.

Figure 5 shows a comparison of the results presented in Table 4 (the left box plots for Veneto and Emilia-Romagna in Fig 5) with the same modelling set-up but without additional reconstruction demand due to the disaster (the right box plots for the two scenarios). The figure shows that not considering reconstruction demand in the model results not only in higher losses but also in a larger difference in losses between the several recovery curves within one flood scenario. The difference can be addressed in the increase in production (and thus increase in value added) due to the increased reconstruction demand from the affected sectors towards the construction sector. Important to note is that mainly the outliers change; for both the Veneto and Emilia-Romagna scenario, the median losses remain almost the same between the reconstruction and no reconstruction methods. From Fig. 5 we can interpret that especially with higher losses and slower recovery (the highest losses occur, as can be seen in Table 4, in the convex and linear recovery curves), including reconstruction demand will substantially reduce the total output losses.

In our comparison exercise the ARIO model, but also traditional multiregional IO models in general, is lacking the capacity to estimate the potential substitution effects in other regions. This can be seized in CGE or (non-)linear programming methods, as shown by the MRIA and IEES models. Both the MRIA and IEES model can show how substitution effects can dampen the negative effects of a disaster in a larger economic entity. Due to the linearity of IO models, other regions always yield losses, which is consistent with results in MacKenzie et al. (2012) and in den Bäumen et al. (2015). However, this is contrary to the expected gains in non-affected regions around the affected area (see e.g. Albala-Bertrand 2013). Hence it is highly unlikely that all regions will suffer losses. In contrast, it is in a real situation also unlikely that substitution in production between regions is possible without any barriers to trade and movements of production factors.

Although the empirical literature finds that the sign and size of population responses vary substantially between different flood events, there is some evidence of post-disaster labour mobility. Husby et al. (2014) find that the large-scale flood in the Netherlands as well as the reconstruction activities following the 1953 flood had a positive long-term effect on population growth in affected municipalities. This study thus finds some evidence that the reconstruction of affected areas was not restricted by fixed labour force. Nonetheless, since much is still unknown on the potential post-disaster movement on capital and labour, more empirical studies should analyse the post-recovery process in high-income countries.

Besides the differences in multiregional spill-over effects, two additional results within this paper contribute to the current literature. First, the losses in the affected region (Table 5) itself are relatively similar throughout all model set-ups compared to the losses for the whole of Italy (Table 4). This indicates that the different multiregional models considered in this study all capture the economic effects for the region directly affected by the flood in a similar order of magnitude. In West (1995) and Hu et al. (2014), the differences in outcomes between the IO and CGE models are much larger (in relative terms) in a single-economy framework. This implies that the difference in use between the multiregional models is less of an issue when one wants to know what the impacts are for the flood-affected region(s). Second, the mobility of capital and labour across sectors and regions in the IEES model and the inefficiency costs of the MRIA model can indicate how resilient an economy is, both on a regional and national level. Large interregional mobility effects (IEES) or high inefficiency costs (MRIA) within the affected region may indicate that the region struggles with the impact of a disruption. However, as also shown by the positive results in the other (non-affected) regions, the national economy may be rather resilient, with low inefficiency and high factors mobility. The ARIO model, using a more traditional IO framework, may be less straightforward in interpreting the economic resilience, lacking the characteristics of either inefficiency costs or mobility effects.

A better understanding of production losses is important for public budgeting, as well as for private resilience choices. On the public income side, a drop in production implies lower tax proceeds and other revenues in the current, and possibly in future, accounting periods. Even if the production is restored quickly, the losses of affected firms can influence state revenues through tax deductions conceded in the subsequent periods. On the spending side, post-disaster recovery programs and restoration of public infrastructure inure financial obligations which may increase government debt. Unfolded through cumulative or cascading paths, a series of medium-sized disasters or single large disasters may produce or aggravate existing economic imbalances and expand disparities across states or regions. It would be wise to consider economic risk embodied in natural hazards as a liability. The European Cohesion Policy measures states' economic performance using gross domestic product (GDP), GRP, and gross national income (GNI). Both are susceptible to disaster risk in a way that is not fully understood. Considering disaster risk as liability would help to prevent countries and regions from satisfying economic performance thresholds in one period but not in the next one. The GNI and GRP are also referred to in the thresholds that trigger solidary financial assistance through the European Solidarity Fund (EUSF). In this context the threshold is specified as a ratio of structural damage to GNI or GRP. In principle, the solidarity payments would be better targeted if triggered by the post-disaster drops in GNI/GRP or public revenues collected. The recent advancements in economic risk assessment, as presented in this paper, make it possible to base similar decisions on sound and robust knowledge.

In this study we have analysed several risk scenarios in a pilot study area using three regional economic models: two hybrid multiregional IO models (ARIO and MRIA) and a regionally disaggregated instance of a global CGE model (IEES). The pilot study area is located in the downstream part of the Po River. The two flood scenarios comprise levee breaks on a Po River levee at the same place where it occurred in 1951. The economic losses for the flood scenarios have been calculated for all three models, using three different recovery paths (concave, convex, and linear).

Relatively large differences in model outcomes have been found on the national scale for all flood scenarios and considered recover paths. The most substantial differences were found between the ARIO model on the one hand and the MRIA and the IEES models on the other hand (results vary by up to a factor of 7). Differences between the MRIA and the IEES models were relatively minor, whereas the results of the ARIO model were approximately 3 to 6 times higher compared to the results of the IEES model for Italy as a whole. The main reason for this difference is the linear structure assumed in the ARIO model and its lack of substitution in production, trade, or products. Due to the linear characteristics of the model, all other (non-affected) regions will be negatively affected due to the disaster. We argue that this negative effect for all other regions may not be realistic and, therefore, we suggest that multiregional disaster impact studies should apply more flexible economic models such as the MRIA or IEES models.

The different recovery paths showed that the speed of recovery is crucial for the total losses. A quick recovery (a concave recovery path) results in substantial lower losses compared to a slow recovery (convex recovery path). This outcome is observed in all three models. The empirical research on this, however, is rather limited. As such, future research is required to explore which recovery paths are empirically observed and what resilience measures are required to make sure an affected area will be recovered quickly to reduce losses. We argue that solutions could be explored in the field of public–private partnerships.

This study showed that some model outcomes are susceptible to underlying assumptions, while others are not. Therefore, for a detailed assessment of disaster impacts on economy, including the price effects and effects on employment, the CGE models are better suited. For assessing cost–benefit ratio of specific resilience measures, both the MRIA and the IEES model seem to be equally useful and produce similar outcomes in terms of output losses. The conventional multiregional IO models may largely overestimate the losses. For future research, more empirical data are needed to better explore the trade-off between the analysed models.

The PBL data on multiregional supply and use tables as used in this paper are available on request from the corresponding author. The original source data are available for the purpose of transparency and checking the outcomes obtained with this paper on request from the PBL Netherlands Environmental Assessment Agency. The interregional trade data that are part of this dataset are largely made publicly available on the European Regional Competitiveness Scoreboard (http://themasites.pbl.nl/eu-trade/). GTAP 8 data are covered by a license. Documentation on the dataset can be found at https://www.gtap.agecon.purdue.edu/databases/v8/v8_doco.asp. Italian data which have been used to split the GTAP 8 data for Italy can be found at http://www.istat.it/it/archivio/12718. GIS-based local data are not publicly accessible due to its protection level (owned by local authorities).