Relative income dynamics of individuals in New Zealand

This paper reports estimates of simple models of income dynamics, using longitudinal income data for 1994 to 2012 from New Zealand Inland Revenue. Income changes are described using a simple autoregressive stochastic process in which Galtonian regression is combined with serial correlation in the stochastic term. The parameters of the model have convenient interpretations. Substantial regression towards the mean combined with negative serial correlation is observed, with remarkable parameter stability over the whole period. The estimates imply that, on average, relatively high income individuals have lower proportional increases in income from year to year compared with lower income individuals, and those with large increases in one year are more likely to experience decreases the following year. These dynamics are shown to be sufficient to ensure that cross-sectional indices of inequality fall as the accounting period increases.