Rescaled additivity non-ignorable (RAN) model of generalized attrition

Abstract

We augment the Additively Non-ignorable (AN) model of Hirano et. al. (2001) so that it is suitable for data collection efforts that have a short panel component. Our modification yields a convenient semi-parametric bias correction framework for handling selective non-response that can emerge when multiple visits to the same unit are planned. Selective non-response can be due to attrition, when initial response is followed by nonresponse (the commonly studied case), as well as a phenomenon we term reverse attrition, when initial nonresponse is followed by response. Accounting for reverse attrition creates an additional identification problem, which we circumvent by rescaling. We apply our methodology to data from the Household Labor Force Survey (HLFS) in Turkey, which shares a key design feature (namely a rotating sample frame) with popular surveys such as the Current Population Survey and the European Union Labor Force Survey. The correction amounts to adjusting the observed joint distribution over the state space (inactive, employed, unemployed in our example) using reflation factors expressed as parametric functions of the states occupied in the initial and subsequent rounds. Our method produces a unique set of corrected joint probabilities that are consistent with externally obtained marginal distributions (in our case published official statistics). The linear additive version has a closed form solution, a feature which renders our method computationally attractive. Our empirical results show that selective attrition/reverse attrition in HLFS-Turkey is a statistically and substantially important concern.