# **II. Methodological approach**

The study proposes a two-step methodology for updating the LAC region middle-class thresholds. The first step consists of constructing synthetic panels given the lack or scarcity of long panels in most countries. The second step defines the lower and upper middle-class thresholds.

## II.1 Constructing synthetic panels:

Ideally, a proper study of welfare dynamics entails following the same observation (household or individual) for at least two—or preferably, multiple—periods. However, in many developing countries panel data sets are not readily available, span few periods, or suffer from “non-random” attrition issues, hindering the capacity to study elements such as the factors that help households escape or remain in poverty (Dang and Lanjouw, 2013; Bourguignon and Moreno, 2015). To overcome the absence of panel data or longitudinal surveys, authors such as Deaton (1985), Deaton and Paxson (1994), and Pencavel (2006) have proposed methodologies to construct pseudo-panels by following similar age cohorts across multiple cross-section surveys. Nevertheless, as argued by Dang et al. (2014), these methodologies typically rely on having several rounds of cross-section surveys but do not allow for analyzing mobility at a more disaggregated level than the cohort. In addition, Fields and Viollaz (2013) argue that pseudo-panel methodologies might not perform well in predicting income mobility in some cases.

Dang et al. (2014) propose both a parametric and a non-parametric approach to construct synthetic panels and estimate an upper-bound (assuming zero correlation between error terms) and a lower-bound (assuming a perfect positive correlation between error terms) for the transitions using two rounds of cross sections. In addition, Dang and Lanjouw (2013, 2016) extend this method and calculate point estimates of poverty mobility based on the synthetic panels. However, this approach relies on the key assumption that the residual terms of the income equations in two periods are distributed according to a bivariate normal distribution.

To avoid the strong distribution assumption for residual or error correlation estimates, Lucchetti et al. (2020) introduce a Least Absolute Shrinkage and Selection Operator method with multiple imputations by Predictive Mean Matching (LASSO-PMM) for constructing synthetic panels. Among the several advantages this method has over those above, a very important one is that it does not require estimating any error correlation terms or assuming a certain distribution of residuals in the underlying regressions. As mentioned by Ñopo (2004), matching avoids any parametric assumptions that may impose restrictions on the behavior of the random variables involved in the analysis. The LASSO-PMM method allows for obtaining point estimates as well as upper and lower bounds of welfare dynamics. This penalized regression method uses regularization and takes advantage of machine learning techniques to minimize the mean square error (MSE) of predictions. As a result, it allows for the estimation of more accurate welfare predictions outside the estimation sample compared to traditional regression models, since variables and model selection are performed automatically by penalizing the coefficients and crossvalidation (Tibshirani, 1996). Lucchetti et al (2020) found that the LASSO-PMM predictions are statistically indistinguishable from actual poverty rates, transitions, and income changes calculated using 4