# 1. INTRODUCTION

Longitudinal surveys, based on repeated observations of the same statistical units over time, are an invaluable source for analyzing the current state and changes in human populations over time. The Living Standards Measurement Study – Integrated Surveys on Agriculture (LSMSISA) initiative demonstrates the value of longitudinal surveys by disseminating household panel data on issues such as health, agriculture, access to basic services, nutrition, poverty status, and much more, for countries across Sub-Saharan Africa. The European Union’s Statistics on Income and Living Conditions (EU SILC) and the US Bureau of Statistics’ Survey of Income and Program Participation (SIPP) are other key examples of the value of longitudinal studies.

In panel surveys, accuracy depends on many of the same factors as in cross-sectional surveys. However, maintaining the accuracy of estimates from a panel sample becomes more difficult as the length of the panel survey increases. One key concern is the panel attrition of respondents who drop out of the survey, which can become increasingly troublesome for long-running panels. Additionally, movers – that is, people who have moved away from where they were interviewed in the first observation of the longitudinal study – represent a dynamic subpopulation and are complex and costly to interview. Finally, new entrants to the population, such as immigrants and newborns, are particularly difficult to capture in traditional panel surveys.

The correct design, implementation, and use of a panel survey considers several methods to address these problems at different stages of the statistical process, namely the sample design, data collection, and estimation stages. To the extent possible, sample design should minimize the loss of representativeness of panel data due to attrition, leavers, and new entrants. Practical approaches to this include the use of refreshed samples (i.e., rotating panels or split panels) and protocols for incorporating individuals not previously involved in the study to capture population dynamics. Based on tracking rules to follow the movers, the data collection stage should be designed to retrieve essential information on individuals or households that have dropped out of the sample. The use of flexible modes of data collection (e.g., telephone interviews) makes it possible to reach those who may not respond to traditional techniques. Additionally, collecting a minimal set of variables on dropouts (e.g., by proxy or doorstep interview) can improve the quality of the survey estimates. The estimation stage considers dropouts, movers, new entrants, and the dynamics of the target population over time. This is achieved by defining a weighting procedure that updates the direct sampling weights to account for new individuals in panel households and by using calibration estimators with upto-date known population totals.

This work proposes to improve the quality of panel surveys by considering the three aspects of survey design outlined above. We consider the estimation at the current time of cross-sectional and longitudinal parameters of a target population. Estimates are computed from sample data collected at the current time on individuals who entered the sample previously and were subsequently followed according to the rules of longitudinal observation considered in the survey. This approach clarifies many aspects of the representativeness of data collected in panel studies. It applies to the many cases that characterize current large-scale household panel surveys (e.g., EU SILC, LSMS, etc.) and can be easily extended to more complex issues in actual survey situations.

The paper is structured as follows: Section 2 gives a formal definition of longitudinal and crosssectional populations and the target parameters to be estimated in longitudinal studies. Section 3 presents the sampling framework and the estimator based on multisource (Singh and Mecatti 2011) and indirect sampling (Lavallée 2007; Falorsi, Righi and Lavallée 2019), which addresses 2