lowest RMSE overall for 2005 as testing, is the baseline, linear model. For 2011 testing the best performing model is the parsimonious model.

### **Regional Results**

**Table 5.3: Results of excluding regions**

||Baseline|Model 1|Model 2|Model3|
|---|---|---|---|---|
|RMSEtestHRE|0.0514|0.0546|0.0595|0.0602|
|RMSEtestHDR|0.0302|0.0297|0.0519|0.0544|
|RMSEtestLOE|0.0042|0.0060|0.0055|0.0055|
|RMSEtestLOR|0.0602|0.0080|0.0034|0.0013|

Notes: cv=cross validation. R2=r‐squared; AIC=Aikike information Criterion; BIC= ; boot=bootstrap; RMSE=root mean squared error. HRE=Highlands, Reliable Region; HDR=Highland, drought‐prone Region; LOE=Lowlands Enset growing region; LOR=Lowlands reliable region.

For the regional validation we follow the example of Todd and Wolpin (2007), by non‐randomly holding out one region at a time to use as a testing dataset. Using the Highlands non‐drought as the testing region (row 1), the baseline performs best. Using the highlands drought as the testing region, the parsimonious model (1) is the best performer. Using the Enset lowlands as testing region, the baseline performs best. Using the lowlands‐reliable as testing, the full model performs best.

For the validation using an external dataset we attempted to use the 2012 Ethiopian Rural Sociological Survey (ERSS). This survey was also implemented by the Central Statistical Agency (CSA) of Ethiopia. However the consumption (and some other) indicators were deemed to be incomparable for the purpose of the exercise. The survey was conducted over a full year period, revisiting households three times during the year. See Central Statistical Agency and The World Bank (2013) for further details. The main three differences pertinent to this study are first, the much smaller sample size (3500 observations). Second, that the consumption module has slightly different recall periods for food consumption (7 days as opposed to 3 days in HICES) and non‐food consumption (a less detailed short‐term component, with 3 and 12 month recall). Finally, the data are not nationally representative.

Regarding the validation results overall, the full model with all interactions and a quadratic crop loss function is the preferred specification. We use this model to illustrate below for a simulation of CAT risk modelling outcomes, using the pooled 2005‐2011 model as the training data.

# **6. Application of the derived vulnerability relationships within a probabilistic catastrophe risk modelling framework**

The overall purpose of the exercise presented in this paper is to determine whether valid general form vulnerability functions for poverty outcomes can be applied within a probabilistic catastrophe risk modelling framework. Sections 3 to 5 above describe the outcome of the exercise. The purpose of this section is to demonstrate how the derived functions would be applied in practice, and to propose future work on the basis of the findings of the paper.

## a. **Outcomes for consumption simulation exercise**

In the absence of a probabilistic hazard model for rainfall variability in Ethiopia at the resolution required, and compatible with the LEAP protocol, we have produced illustrative examples based on the results from the regression model.

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