Cost efficiency of repeated cluster surveys - ARCHIVED

We analyze the statistical and economic efficiency of different designs of cluster surveys collected in two consecutive time periods, or waves. In an independent design, two cluster samples in two waves are taken independently from one another. In a cluster-panel design, the same clusters are used in both waves, but samples within clusters are taken independently in two time periods. In an observation-panel design, both clusters and observations are retained from one wave of data collection to another. By assuming a simple population structure, we derive design variances and costs of the surveys conducted according to these designs. We first consider a situation in which the interest lies in estimation of the change in the population mean between two time periods, and derive the optimal sample allocations for the three designs of interest. We then propose the utility maximization framework borrowed from microeconomics to illustrate a possible approach to the choice of the design that strives to optimize several variances simultaneously. Incorporating the contemporaneous means and their variances tends to shift the preferences from observation-panel towards simpler panel-cluster and independent designs if the panel mode of data collection is too expensive. We present numeric illustrations demonstrating how a survey designer may want to choose the efficient design given the population parameters and data collection cost.