We follow the approach proposed by Skoufias et al. (2023) to estimate a measure of “vulnerability to poverty” over different countries of LAC using cross-sectional household data and aggregate data on the propensity of climate hazards in the region. The method is based on Gunther & Hartgen (2009) following Hox (2010) and Chaudhuri’s (2002, 2003) model. The approach includes covariate (aggregate) and idiosyncratic (specific) shocks, modeling them as a function of observable households and community (district or state) characteristics. Moreover, the model distinguishes between povertyinduced (PI) and risk-induced (RI) household vulnerability.

Specifically, the following two-level hierarchical model of income is estimated: ln I I i i 2 i i (1) where denotes the households ( ) at level one, and j denotes the communities where households resided at level two (such as districts or states, depending on the country’s data). We exploit five rounds of surveys per country, so we control for a vector of dummies ii ii= 1, ... , NN i where each dummy takes value 1 if data correspond to each period survey.<sup>2</sup> We further assumed that the tt coefficients and vary across communities. In hierarchical models, this is a varying-intercept and varying-slope model. The varying coefficients are modeled using community characteristics 0ii 1ii ββ ββ related to socioeconomic conditions and climate change as ii ii ZZ II 00 01 02 , (2) 0ii ii ii ooii ββ = γγ10 + γγ11 ZZ + γγ12 II + uu . (3) 1ii ii ii 1ii The error terms and ββ are residuals of level two, representing the unexplained differences in = γγ + γγ ZZ + γγ II + uu income across communities. Replacing equations (2) and (3) into equation (1), we obtain the full ooii 1ii uu uu model re-written as ln I I i 00 01 02 10 11 12 i 2 i i i , (4) ii ii ii ii ooii 1ii = γγ00 + γγ01ZZ + γγ02II + �γγ10 + γγi 11ZZ + γγi II �XX12 + ββi tt 2+ uui + uu XX + eei i . ii ii ii ii ooii 1ii The (natural logarithm) per capita household income (= γγ + γγ ZZ + γγ II + γγ XX + γγ ZZ ln IXX + γγI i ) is assumed to be affected by observed II XX + ββ tt + uu + uu XX + ee characteristics, including a set of specific household characteristics i , community characteristics and , and an unexplained part i i named error term. The error term includes a ii XX ZZ community component capturing the covariate shocks on the household’s income. This term ii ooii 1ii II uu + uu XX + ee includes an error term representing the unexplained variance across communities of the intercept ooii uu and the error term i reflecting the unexplained variance across communities of the slope . 0ii ββ This last term includes an idiosyncratic part through i , which can capture an indirect effect of 1ii 1ii uu XX ββ covariate shocks through household characteristics.<sup>3</sup> At the same time, i captures the remaining XX idiosyncratic household shocks. ee

> 2 Here and in the rest of the paper, we drop subscript t for simplicity. For some countries, data for five rounds is unavailable; in these cases, we use at least two rounds of surveys.

> 3 It is important to note that in analyzing the impact of covariate shocks on households’ income at the community level, the error terms and i play a crucial role. However, following Skoufias et al. (2023) and Gunter and Harttgen (2010), we chose not to analyze and together. Instead, these studies focused solely on the 0ii 1ii uu uu XX 0ii 1ii uu uu

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