The estimation of gross flows in the presence of measurement error using auxiliary variables

Classification error can lead to substantial biases in the estimation of gross flows from longitudinal data. We propose a method to adjust flow estimates for bias, based on fitting separate multinomial logistic models to the classification error probabilities and the true state transition probabilities using values of auxiliary variables. Our approach has the advantages that it does not require external information on misclassification rates, it permits the identification of factors that are related to misclassification and true transitions and it does not assume independence between classification errors at successive points in time. Constraining the prediction of the stocks to agree with the observed stocks protects against model misspecification. We apply the approach to data on women from the Panel Study of Income Dynamics with three categories of labour force status. The model fitted is shown to have interpretable coefficient estimates and to provide a good fit. Simulation results indicate good performance of the model in predicting the true flows and robustness against departures from the model postulated.