- 1) **A regression model to derive quantitative relationships between a selected drought hazard measure and household poverty outcome** for rural households in Ethiopia. This is a survey‐weighted regression model combining historical household data with historical data on drought hazard, which effectively constitutes our ‘vulnerability module’;

- 2) **Testing of the derived ‘vulnerability module’ to evaluate its robustness** , and therefore the validity of its future application onto a forward‐looking probabilistic view of drought occurrence generated from a catastrophe risk modelling framework. This evaluation is conducted through interpretation of the regression results and the application of Statistical Learning Methods (drawing from James et al (2013)) as described in Section 4.

Our evaluation of validity of the resulting damage functions will be centred around concepts of internal and external validity as described by Anttila‐Hughes and Sharma (2014). Anttila‐Hughes and Sharma emphasize that ensuring that estimates of damage functions are both internally and externally valid is the major econometric challenge in the development of general form damage functions from historical data on disaster impacts. In the context examined, internal validity is considered as the extent to which impacts statistically associated with disaster occurrence can actually be causally linked to the disaster occurrence, i.e., that the estimates are econometrically “well‐identified.” External validity is considered as the extent to which relationships estimated in the context of one disaster event can be generalized to other contexts and locations. More detail on these concepts is outlined in section 4.

The framework for damage function development described above, allows for the application of the derived functions out of the context in which they were derived. This is a fundamental feature of catastrophe risk models, as their purpose is to provide a forward‐looking view of risk beyond the historical events used in their development.

**2. A methodology for deriving vulnerability relationships for the impact of drought on poverty in Ethiopia**

For our chosen area of focus – the impact of drought hazard on the welfare of rural households in Ethiopia – we aim to determine the validity of applying a derived set of damage functions onto a forward‐looking view of drought risk. The methodology follows a purely empirical approach using a survey‐weighted regression model combining historical household survey data with historical data on drought hazard. Within catastrophe risk modelling, there are two principal methods used to derive damage functions; empirical and analytical derivation. For example, content for the Global Earthquake Model<sup>6</sup> demonstrates statistical methods for empirical derivation of damage functions from historical damage and loss data, and also analytical methods based on numerical models of response of different structures/structural components (for further information, see D’Ayala et al, 2014 and Rossetto et al, 2014). The analogy for drought damage to crops, for example, would be the use of mechanistic agro‐meteorological models based on a process approach versus statistical methods using historical crop loss and drought hazard data.

This model will also attempt to separate out observed relationships for different vulnerability‐ determining characteristics, analogous to how catastrophe risk models incorporate distinct damage functions for different classes of exposed asset; for example, by structural ‘class’ for buildings or by crop type. For example, a set of primary building characteristics that determine seismic response (such as those shown in table 2.1 from the Global Earthquake Model project) will form the basis of a

> 6 http://www.nexus.globalquakemodel.org/gem‐vulnerability/posts/guidelines‐for‐empirical‐vulnerability‐ assessment

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