increases further). Similarly, the overall income level in the country (here represented by ̃ ) affects resilience: increasing income reduces the marginal utility of consumption (both ( ̃) and ̃ ), and thus decreases the welfare vulnerability (and thus the welfare impact of any disaster).

# **3.2 Instantaneous impacts, basic needs, and smoothing**

But assuming that utility only depends on the net present value of future consumption is appropriate only if we assume that households have the capacity to smooth the shock over time, through selfinsurance (i.e. savings), market insurance (i.e. paying a premium every year instead of the losses when they occur), or full access to credit (and that disasters remain relatively limited in magnitude). In many countries, this is not an acceptable assumption<sup>23</sup> , so it is important to investigate impacts in the situation without smoothing.

To do so, we have to account for the impact of immediate consumption and income. To approximate this impact, we assume that the households with “negative income” the year of the shock (i.e., those for which immediate income losses are larger than annual income<sup>24</sup> ) are unable to fulfil their basic needs and suffer from losses that go beyond the impact of a change in aggregate consumption.

We will use the impact on these households as an indicator of the impact that cannot be smoothed over time. We assume that for these households, the shock is mostly related to the immediate impact, not to the net present value of the flux of consumption losses, and that they suffer from economic and noneconomic losses (reduction in food intake, health effects, stunting on children, etc.) that are monetized independently of the size of their loss. This is a strong simplification of the reality – which consists of a continuum of intertwined impacts on wealth and instantaneous consumption – but it allows including in the calculation in a simple way an essential component of disaster impacts.

Since we are looking at a nonlinear process, it would be highly misleading to assess the impact on welfare using the average impact of the disaster. As already stated, direct losses of disasters are heterogeneous. Investigating the 2004 hurricane season in Florida, (McCarty and Smith, 2005) find that – in their study area – 74% of housing units were damaged, but only 2.2% were totally destroyed while 40% had only minor damages. Looking at the Northridge earthquake in 1994 in Los Angeles, (Tierney, 1997) finds that the median dollar loss from physical damage is US$5,000 while the average loss is US$156,000.

In Appendix C, we calculate the fraction X of households who are experiencing negative income the year of the disaster.<sup>25</sup> To do so, we assume that direct losses are distributed as a Gumbel distribution (a

> 23 (Carter et al., 2007) find evidence of asset smoothing among the poorest households in Ethiopia following the drought in 1998-2000, suggesting that households prefer to support a large decrease in consumption when the shock hits than reducing their asset stock too much.

> 24 In this section, the income loss during the first year is given by the reduced _output_ of capital, but the entire asset losses are not accounted for as a one-year income loss. In other terms, the asset losses are “amortized” over the reconstruction period.

> 25 Note that we do not remove the value of asset losses from their income; instead we calculate the lost income from lost assets, and remove this lost income from their pre-disaster income.

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