across communities. In this paper, community is all households within the province level, which is a large area, so it is implicitly assumed that covariate shocks are not correlated across provinces. Finally, it is important to consider the benefits and costs of merging climate and natural hazards data with household survey data. The main costs involved are time, effort, limitations, and the need to make adhoc decisions to match the climate and natural hazards variables with households, as detailed in Skoufias and Baez (2023). Moreover, if the vulnerability related to idiosyncratic shocks is significantly higher than the vulnerability related to covariate climate shocks, the benefit of including climate and natural shocks in the multilevel approach might be attenuated. This paper aims to capture the part of the expected variance related to N so that the proposed model could provide insights from a conceptual perspective. However, from a cost perspective, there might be better options. If the costs of including climate and natural hazards data are very high, running a simple model with only Z as covariate variables in the equations may offer a more suitable alternative. Nonetheless, the interpretation of the volatility in each case would be different.

The analysis is conducted individually for each country, using country-specific variables to estimate the household’s expected mean income, and the expected variances. In practice, **t** he following steps are carried out to measure vulnerability to poverty due to climate risk (CR) in each country:<sup>8</sup>

- 1- Estimate the natural logarithm per capita income equation (1) assuming constant coefficients at the household level, including only household-specific variables ( i ): XX

- ln I I i 0 1 i 2 i i = ββ + ββ XX + ββ tt + ee

To perform this estimation, we first estimate the equation considering 19 pre-determined household variables with LASSO and choose the final sub-set of variables following LASSO results. 2- Once the household-specific variables ( i ) are chosen from LASSO, we estimate a multilevel model with random intercept, and the variables , , i and interactions ( i and i ): XX ln I I i 1 i 2 3 i 3ZZii IIii XX4 i 5 i i ZZiiXX IIiiXX where = ββ0ii00+ ββ XX. + ββ ZZii + ββ ZZiiXX + ββ IIii + ββ IIiiXX + ββ tt + ee Then, we identify the interactions that are significant for the estimation of the final full model (step ββ0ii = γγ + uuooii 4). 3- Estimate a multilevel model with i , random intercept and slopes. ln I I i i 2 i XXi where = ββ0ii00+ ββ1iiXX, + ββ tt + ee and ββ0ii = γγ10 + uu.ooii In order to reduce computation time, we only consider 4 variables from ββ1ii = γγ + uu1ii i having random slope each time. Then, we identify the significant random slope effect parameters to keep them in the estimation XX of the final full model (step 4). 4- Run the full multilevel model (equation 4) with random intercept and random slope including , , i , the significant interactions ( i and i ) identified in step 2 and the variables with ii ZZ statistically significance random slope identified in step 3. ii ii ii II XX ZZ XX II XX

> 8 We use the Skoufias et al. (2023) toolkit and manual accessed by the Equity Policy Lab to implement these steps.

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