Relative Income Dynamics of Individuals in New Zealand: New Regression Estimates

This paper reports new estimates of simple regression models of income dynamics, using a special New Zealand anonymous dataset compiled from Inland Revenue data. The pattern of relative income changes, despite being subject to considerable complexity, can be described succinctly using a simply autoregressive stochastic process in which Galtonian regression towards the mean is combined with serial correlation in the stochastic term. The parameters of the model have convenient interpretations and can be easily estimated using limited longitudinal data. There is substantial regression towards the mean combined with negative serial correlation: 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. Both these effects, though combined with a stochastic component that on its own would tend to increase inequality over time, are sufficient to ensure that inequality falls as the accounting period over which incomes are measured increases, and there is no systematic tendency for annual inequality to rise.