actual panels.<sup>5</sup> On average, the predicted poverty rates using LASSO-PMM were one percentage point away from the observed rates, when using data from the four validation countries.

To build the synthetic panels required to define the new vulnerability and middle-class lines, this paper follows Lucchetti et al. (2020) as a starting point. and introduces several improvements in its methodology. First, matching is performed only between subsets (donation classes) of individuals with the same time-invariant features. These constrained donation classes are built based on gender, birth year, and educational attainment. Second, sampling weights are used to harmonize the joint distributions of identified common variables across the two surveys (Renssen, 1998). This method (known as Renssen’s procedure) consists of a series of calibration steps of the survey weights (in both the donor and receiver surveys<sup>6</sup> ) implemented to achieve consistency between some aggregate estimates, e.g.: income, gender or age distributions. Third, when several donors are equidistant in terms of the predicted income, one of them is randomly chosen according to their sampling weights. The fourth improvement is a direct consequence of the two previous ones: this method allows to preserve the marginal distribution of income from the donor survey, which is essential not to alter welfare dynamics. In addition, although synthetic panels have their own set of limitations, they represent a significant improvement over using cross-sectional data to estimate the probability of falling into poverty. Without actual panels available, this would have been the case. Starting from two available rounds (i.e., = rounds 1 and 2) of cross-sectional microdata. Let i be the per capita household income for household i, (i.e., ), in survey round with sample size , jj yy and i be a vector of household head characteristics observed for household i in survey round j. These ii= 1, ... , NN jj NN household head characteristics, observed in both survey years, can include time-invariant variables (e.g., XX household head’s gender, ethnicity, place of birth, etc.), deterministic variables (e.g., such as age, education, literacy, etc.), and retrospective questions collected in round 2 about round 1 such as assets (Cruces et al, 2015; Dang and Lanjouw, 2018). Changes in household composition can help identify matching errors, which could lead to spurious measures of change. To avoid this, the estimation samples are constrained to household heads’ age: 25 to 65 in the first cross-section and adjust this age range accordingly in the second cross-section. The linear model where -th household’s log per capita income<sup>7</sup> i is explained solely by household head characteristics i for each survey round is given by: ii yy XX i i i (1) TT where i is an error term and yy = ααii + ββi is a vector of ii XX + εε _K_ regressors, and jj = 1, 2 is the intercept. In this context, + i would represent the portion of log income explained exclusively by deterministic and time-ii ii εε XX αα αα invariant household head characteristics. TT ii ββ XX

> 5 Lucchetti et al (2020) use 36 panels from Argentina, Chile, Peru, and Nicaragua to validate their estimates of mobility using harmonized variables frequently used in many regional and global studies. After the validation exercises, the authors implemented the LASSO-PMM method in 43 countries worldwide.

> 6 The donor survey is the one that contains the actual income data from the first-round survey. The receiver is the second-round survey where the income is imputed.

> the second-round survey where the income is imputed.

> 7 To simplify notation, in this document i will be used to refer to the logarithm of household per capita income. yy

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