# **Appendix C: Synthetic Panel Method**

This appendix offers a brief overview of the synthetic panel method based on Dang and Lanjouw (2023). Recent validations and applications of the synthetic panel methods by various researchers for different country contexts ranging from Africa to Latin America, the Middle East, and Europe have been encouraging in terms of accurate projections of economic status (Ferreira _et al._ , 2012; Beegle _et al._ , 2016; UNDP, 2016; OECD, 2018; Salvuci and Tarp, 2021; Ghomi, 2022). Let i be a vector of household characteristics observed in survey round _j_ (j= 1 or 2) that are also observed in the other survey round for household _i_ , i= 1,..., N.<sup>17</sup> These household characteristics can include such time-invariant variables as ethnicity, religion, language, place of xx birth, parental education, and other time-varying household characteristics if retrospective questions about the round-1 values of such characteristics are asked in the second round survey. To reduce spurious changes due to changes in household composition over time, we usually restrict the estimation samples to household heads in a certain age range, say 25 to 55, in the first cross section and adjust this age range accordingly in the second cross section. This restriction also helps ensure certain variables such as heads’ education attainment remains relatively stable over time (assuming most heads are finished with their schooling).<sup>18</sup> This age range is usually used in traditional pseudo-panel analysis but can vary depending on the cultural and economic factors in each specific setting. Population weights are then employed to provide estimates that represent the whole population. Then let i represent household consumption or income in survey round _j_ , j= 1 or 2. The linear projection of household consumption (or income) on household characteristics for each survey round is given by yy ′ i i i (C1) Let be the poverty line in period _j_ . We are interested in knowing the unconditional measures ii yy = ββ xx + εε of poverty mobility such as ii zz 1 2) (C2) which represents the percentage of households that are poor in the first survey round (year) but ii1 ii2 nonpoor in the second survey round, or the conditional measures such as PP(yy < zz aai yy > zz 2 1) (C3) which represents the percentage of poor households in the first round that escape poverty in the ii2 ii1 second round. PP(yy > zz | yy < zz

If true panel data are available, we can straightforwardly estimate the quantities in (C2) and (C3); but in the absence of such data, we can use synthetic panels to study mobility. To operationalize the framework, we make two standard assumptions. First, we assume that the underlying population being sampled in survey rounds 1 and 2 are identical such that their timeinvariant characteristics remain the same over time. More specifically, coupled with equation (C1), this implies the conditional distribution of expenditure in a given period is identical whether it is conditional on the given household characteristics in period 1 or period 2 (i.e., implies and have identical distributions) (Assumption 1). Second, we assume that i1 and ii1 ii2 i2 have a bivariate normal distribution with positive correlation coefficient ρ and standard xx = xx ii1 ii1 ii1 ii2 yydeviations |xx yy1 and |xx σ 2 respectively (Assumption 2). Quantity (2) can be estimated by εε εε εε εε σσ

> 17 We suppress the index for countries and FHH types to make notation less cluttered in this appendix.

> 18 While household heads may still increase their educational achievement in theory, this rarely happens in practice.

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