where Φ is the Gaussian standard cumulative distribution, and hb hb b = 0) and �v hb hb b ) are the conditional expected value and conditional +1bb bb bb standard deviation of the random variable l hb , respectively (e.g. see Gallardo, 2018). PP(l CC | XX , WW +1bb bb +1bb PP(l CC |XX , WW The above steps are not sufficient to identify a vulnerable household, since all households +1bb CC have a nonzero probability of falling below the poverty line. The identification of the vulnerable households requires setting a threshold for the probability of being vulnerable to poverty. For this purpose, two thresholds for vulnerability to poverty are chosen. The first, is 24.9% which is the poverty threshold in 2003.<sup>8</sup> In a steady state, the prevailing poverty rate may be considered as the likelihood that any household may face at being poor (e.g., see Chaudhuri, 2003). Based on this reasoning, a household is identified as vulnerable if it has a likelihood of being poor greater than or equal to the baseline poverty rate of 24.9% in 2003. The second threshold is higher, since it classifies a household as vulnerable if the household has a likelihood of being poor greater than or equal t0 50%.<sup>9</sup>

The advantage offered by the proposed methodology is that it allows the identification of “chronically” poor households as well as of the households vulnerable to poverty due to exposure to community-level aggregate shocks (i.e., typhoons). Household welfare is defined by observable characteristics of the household and exposure to shocks. The chronically poor are identified by the relation between their observable characteristics in the absence of a shock, which is analogous to the predicting the poverty status of a household using a traditional PMT. In contrast, the vulnerable can be identified from the potential direct welfare effect of the wind speed associated with a new typhoon on future PCE and thus the possibility of falling below the poverty line.<sup>10</sup> One should bear in mind that an analogous similar modeling approach can be followed for the identification of the households vulnerable to other kinds of natural disasters, such as earthquakes, floods and droughts. Alternatively, if the interest is on identifying the vulnerable to all kinds of covariate and idiosyncratic shocks, and not just to a particular shock as in this paper, it would be worthwhile exploring the method proposed by Gunther and Harttgen (2009).<sup>11</sup>

> 8 Annex 3 provides an estimate of the evolution of the poverty rate in the Philippines, based on the household PCE measure adjusted by the year/month province specific CPI used in this study.

> 9 The 0.5 probability threshold is justified in the following arguments provided by Pritchett _et al._ (2000, p. 5) and by Suryahadi and Sumarto (2003, p. 48): “First, this is the point where the expected consumption coincides with the poverty line. Second, it is intuitive to say a household is “vulnerable” if it faces at least 50% probability of falling into poverty. Third, if a household is just at the poverty line and faces a mean zero shock, then this household has a one period ahead vulnerability of 0.5. This implies that, in the limit, as the time horizon goes to zero, then being _in current poverty_ and being _currently vulnerable to poverty_ coincide.”

> 10The potential effect of the shock may also be inclusive of the interaction of the shock with other household characteristics, if the term 3 b hb ) is included in equation (1). 11 A comparison of the vulnerable identified by the two different approaches is left for a companion paper. bb bb ββ (WW ∗XX

> 10The potential effect of the shock may also be inclusive of the interaction of the shock with other household

> 11 A comparison of the vulnerable identified by the two different approaches is left for a companion paper.

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