(Mechler, 2009). And since capital and output losses partly interact, it is incorrect to simply sum them to estimate welfare losses. In this section, we assess the aggregate consumption losses due to a disaster.

# **2.4.1 Aggregated consumption losses**

Consider first a scenario in which all losses are repaired instantaneously by reducing consumption and directing all the goods and services that are not consumed toward reconstruction investments (this is a scenario where reconstruction capacity is infinite). In this theoretical scenario, there is no output loss since all asset damages are instantaneously repaired, and the reconstruction duration, N, is equal to zero in Eq. (11). There are however consumption losses, since consumption has to be reduced to reconstruct, and this reduction is equal to the reconstruction value (i.e. the replacement cost of damaged capital). In that case, the net present value of consumption losses ( ̃ ) are simply equal to the value of lost assets that need to be replaced (i.e., direct asset losses ).

Consider now another scenario with no reconstruction, in which output losses are permanent (like in Figure 2) and all losses in output are absorbed by a reduction in consumption (but no share of income is used for reconstruction). In that case, consumption losses are equal to output losses (with no reconstruction), and N is equal to infinity in Eq. (11). The loss in consumption at is thus equal to + ⁄ , see Eq. (7), and the net present value (discounted at the rate _r_ ) of consumption losses is + ⁄ . Consumption losses and welfare losses are thus larger than the value of lost assets in a no-reconstruction scenario (at least if > 0 ).

In the instantaneous reconstruction scenario, consumption losses are equal to the share of consumption needed to repair and rebuild, i.e. to asset losses . In the no-reconstruction scenario, consumption losses are equal to output losses + ⁄ , i.e. larger than direct losses . 13F<sup>14</sup> As a result, consumption (and welfare) losses are magnified when reconstruction is delayed or slowed down. 14F<sup>15</sup> And in all realistic scenarios where reconstruction takes some time (from months for small events to years for large-scale disasters), welfare losses are larger than direct losses.

For intermediate scenarios (with reconstruction over a given period), the actual welfare loss is the sum of the net present value of reconstruction cost (i.e. the direct capital cost) and the net present value of indirect (output) losses.

> 13 Another major issue is the potential loss of jobs, which affect households. Loss of assets and reduction in output may lead to job losses. Here, we assume that the consequence of job losses can be represented through consumption losses, even though unemployment can have social and human consequences that go beyond the loss of income and consumption (e.g., exclusion, loss of skills).

> 14 The reality is more complex that what has been described here because not all output losses are translated into consumption losses. In practice, the loss in output changes the terms of the inter-temporal investmentconsumption trade-off and translates into ambiguous instantaneous changes in consumption and investment. But the main conclusions of the analysis are not affected by this complexity.

15 The fact that rapid reconstruction is better for welfare than slow reconstruction – or equivalently, that reconstruction has a return that is much higher than that of “normal investments” and the interest rate – explains why reconstruction is usually a priority and crowds out consumption and other investments in the affected region.

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