the different representativeness of the various sampling subpopulations and the changes in household composition over time. Section 4 presents improvements in field operations and data collection to facilitate the implementation of the proposed methodology. Section 5 briefly introduces the Living Standards Measurement Study (LSMS), defining its objectives and key aspects of the quality of the estimates. Section 6 illustrates the empirical application of the proposed methodology to the LSMS-ISA data, using the 2009, 2013 and 2015 waves of the Uganda National Panel Survey as a case study. Section 7 summarizes the main findings and concludes.

# 2. FORMAL DEFINITION OF CROSS-SECTIONAL AND LONGITUDINAL POPULATIONS

2.1. Populations observed at different points in time is . We represent tt tt tt Let UU be the population of NN individuals of a given country at the current time t. UUt = tt tt,1 tt,ii tt,MM partitioned into MM∑ . subpopulations of households denoted as UU , ... , UU , ... , UU tt tt,ii tt,ii tt the set of households as HHMMtt = {1, ... , ii, ... , MM }. The household UU has NN individuals and NN ii=1 tt,ii as cross-sectional populations of individuals and households since NN they refer to a specific point in time. tt tt We can refer to UU and HH To analyze the dynamics of cross-sectional populations in a longitudinal setting from an initial longitudinal-populations . For the sake of simplification, we first introduce a population not partitioned in households. Thus, point in time tt<sup>∗</sup> , to the current time tt, we introduce the concept of individuals. The longitudinal-population identification is complicated by both the scope of study and the longitudinal observation's tt←tt<sup>∗</sup> tt←tt<sup>∗</sup> operability over time (Helliot et al. 2009). The most common definitions are the intersection-let UU denote the longitudinal population of NN . tt←tt<sup>∗</sup> tt<sup>∗</sup> tt tt←tt<sup>∗</sup> , and includes the individuals tt<sup>∗</sup> tt population, UU = UU ∩UU , and the union-population UU = UU ∪UU who are still living and resident in the country at the time t. The longitudinal survey tt<sup>∗</sup> tt observes the same individuals over time, excluding both births and deaths during the period of The intersection-population is a proper subset of both UU and UU tt<sup>∗</sup> of UUstudy. However, the longitudinal population definition based on the intersection-population has some drawbacks related to the representativeness at time t and to the limitations in the study of the dynamics in the households’ composition. While the union-population best describes the population dynamics, it requires a dynamic sample design which introduces births and entrants to avoid bias. For this study, we propose a definition that takes the advantages from both approaches. , include: - tt←tt<sup>∗</sup> tt←tt<sup>∗</sup> ; Based on this, the NN individuals of UU<sup>∗</sup>

- , include:

- - tt←tt<sup>∗</sup> tt←tt<sup>∗</sup> ; - tt<sup>∗</sup> tt

- all the people of the intersection-population of households UU ∩UU

- all new members of the household of the individuals in the intersection-population, even<sup>∗</sup> .

- With this definition, the newborns and those immigrants who become be part of the tt<sup>∗</sup> if they were not part of UU

households of the individuals in the intersection-population are new entries into the . If immigration to the country and newborns are numerically approximates the crosspopulation from time tt<sup>∗</sup> is conceptually tt←tt<sup>∗</sup> insignificant phenomena, then the longitudinal population UU, and then in the following survey we observe tt←tt<sup>∗</sup> sectional population at time tt. Moreover, the longitudinal observation of UUall household members for the initial sample of individuals. simple. We select a sample at the initial time, tt<sup>∗</sup> 3