The fade away of an initial bias in longitudinal surveys

We propose a new view of initial nonresponse bias in longitudinal surveys. Under certain conditions, an initial bias may "fade-away" over consecutive waves. This effect is discussed in a Markovian framework. A general contraction theorem for time inhomogeneous Markov chains is presented. The result is that two chains with different starting distributions will eventually converge to equal state distributions. Two conditions are required: transition probabilities must be equal for respondents and nonrespondents, and attrition in later panel waves must not depend on the state of the individuals. The theory is applied to a German survey on social benefit recipience. Minor deviations from assumptions are shown to have only a negligible impact on the strength of the fade-away effect. Results from other European surveys indicate that the fade-away effect is present in them, as well. Extensions are pointed out.