On the fade-away of an initial bias in longitudinal surveys

We propose a novel view of selection bias in longitudinal surveys. Such bias may arise from initial nonresponse in a probability sample, or it may be caused by self-selection in an internet survey. A contraction theorem from mathematical demography is used to show that an initial bias can "fade-away" in later panel waves, if the transition laws in the observed sample and the population are identical. Panel attrition is incorporated into the Markovian framework. Extensions to Markov chains of higher order are given, and the limitations of our approach under population heterogeneity are discussed. We use empirical data from a German Labour Market Panel to demonstrate the extend and speed of the fade-away effect. The implications of the new approach on the treatment of nonresponse, and attrition weighting, are discussed.