present given the distribution of hazards is changing over time with climate change and historical data forms the basis of all simulations presented in this paper.

The models built in this paper are an important first step toward constructing vulnerability or damage functions as used in the catastrophe risk modeling literature, and can inform disaster response planning and financing. However, these limitations mean that care is needed in interpreting the results of the analysis. We envisage that the set of tools developed herein will provide the basis for refining the analysis as more data become available, and expanding coverage to other regions. Accompanying this paper is code designed to extract a large set of potential shock measures and determine which of these are consistent with changes in the welfare measures (outof-sample). The modular code used is intended to be transparent, to aid in replicability, and to be available for others to improve upon. The goal is to encourage both learning and common standards, which in turn contribute to the implementation of drought-responsive policies that are objective and transparent.

The paper is structured as follows. Section 2 presents the empirical framework for assessing the relationship between welfare and hazards in rural areas where rainfall-dependent agricultural production is dominant, and where rainfall deficits (droughts) thus may have very serious welfare consequences. It sets out the approach used to estimate the vulnerability function and an exceedance probability curve that describes the welfare losses likely to occur because of rainfall deficits of increasing severity. Section 3 discusses in detail the historical hazard database and the household survey data used, the merging of the hazard data to the household survey data, and the specifications used for the hazard measures. Section 4 presents estimates of vulnerability functions. Section 5 shows how these vulnerability functions can be used to project welfare losses and presents some exceedance probability curves. Section 6 offers some conclusions.

# 2. An Empirical Framework for an Ex Ante Assessment of the Welfare Costs of Drought

A catastrophe risk modeling framework uses three components to generate an ex ante assessment of the costs of a catastrophe: hazard, exposure, and vulnerability function. Hazards capture data on the possible weather outcomes that may occur in a given place, such as possible tropical cyclones. Exposure captures what could be affected by the hazard in that location, such as the number and type of buildings. A vulnerability function provides an estimate of the cost of damage that will occur as a result of a given hazard and a given exposure. In the example of tropical cyclones and buildings, it would indicate the cost of damage for a given windspeed affecting a given type of building. Combining the three components allows development of a probabilistic impact curve, which indicates how the cost of hazard varies with the probability of the hazard for a specific place, given the expected hazards and the exposed assets.

This section of the paper shows how this framework can be applied to generate a probabilistic impact curve for drought in SSA. For drought in SSA, the hazard is rainfall deficits during the growing season. As noted in the introduction, there are different ways of measuring this hazard, and the next section discusses the relevant data in more detail, including the time period for which historical data are available and use of the data to generate an estimate of the probability distribution of hazards in the near future.

Exposure in the current case is not about physical infrastructure and its location and characteristics, but about households that may be impacted differently by rainfall deficits depending on their location and characteristics. The data on households are also described in more detail in the next section.

The vulnerability function in this case is the income or welfare losses among households engaged in different livelihoods, which result from lower yields, lower demand for labor, and increased prices that may result from that. The rest of this section focuses on the estimation of the vulnerability function and how it is used to derive a probabilistic impact curve. The estimation of the vulnerability function is widely present in the microeconometric literature, even though it is not referred to as such or used for generating estimates of probabilistic impact.

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