Regression Models of Mobility

Chapter 7 turns to income dynamics, and shows that the pattern of relative income changes, despite being subject to considerable complexity, can be described succinctly using a simple autoregressive stochastic process in which ‘regression towards the mean’ is combined with serial correlation in the stochastic term. The parameters of the model are shown to have convenient interpretations and can be estimated using limited longitudinal data. Using New Zealand data for individual taxpayers over three consecutive years reveals substantial regression towards the mean combined with negative serial correlation. Remarkable stability in the estimated parameters is observed across the samples over the 1997 to 2012 period. These imply that relatively high income individuals have, on average, lower proportional increases in income from one year to the next compared with those with lower incomes, and those with a large increase in one year are more likely to experience a decrease the following year. Despite the simplicity of the dynamic process specified, it is nevertheless capable of explaining about 75 per cent of the variation in annual incomes.