Relative income dynamics of individuals in New Zealand

Abstract

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.

Acknowledgments

We are grateful to the NZ Inland Revenue Department for making the anonymous longitudinal data available, and to three referees for helpful comments and suggestions.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 In principle, tax return data are available from 1981, but PAYE information for non-filers (a large fraction of total taxpayers) is only available from 1994. The data are discussed in more detail in Laws (2014).

2 See https://www.classic.ird.govt.nz/aboutir/external-stats/revenue-refunds/.

3 The mobility measure ranges from zero, for complete rigidity, to unity, where the income distribution is completely equalised over the period considered. This contrasts with the idea of ‘perfect mobility’, introduced by Prais (1955), where the probability of being in an income class in period, t, is independent of the class occupied in period, t−1. Shorrocks (1978a) considered in more detail the measurement of mobility in a transition matrix framework. In Shorrocks (1993) he compared his approach with that of Hart (1976a), who defined mobility in terms of the correlation coefficient between incomes in two periods. On an early analysis of the reduction in inequality as the time period is extended, see Creedy (1979).

4 The tolerance for leaks clearly depends on the assumed ratio of incomes of transferor and transferee. For example, if $y_2/y_1=3$, then when $\epsilon =0.2$, the maximum leak tolerated is 20 cents. Some surveys have found an average inequality aversion in the context of the Atkinson inequality measure of about 0.2; see Amiel, Creedy, and Hurn (1999).

5 To check the impact of income limit restrictions on the regression results, comparable results were also obtained for alternative restrictions on both the maximum and minimum income allowable. The former was set $500,000 in 2012, with previous years' values adjusted for inflation using the New Zealand Consumer Price Index time series. This gave a maximum criteria in 1994 of $325,300. The alternative minimum requirement was set at one quarter of the gross annual rate of superannuation in each year. In this case, taxable income had to exceed $5,059 in 2012 and the threshold diminished to $3,001 in 1994. See Laws (2014, pp. 44–45) for further details. Regression results from this exercise were very similar to those shown here and are therefore not reported.

6 In this case, individuals were included if their income exceeded $5,000 in each year. This was approximately the same value as the mimimum taxable income used to be eligible for inclusion in the sample in section 5.2; namely $5,059 in 2012.

7 For example, Creedy et al. (2018) suggest that the rise in measured inequality of taxable incomes during the 1980s and 1990s may partly reflect responses to tax reforms in this period such that previously ‘hidden’ (non-taxable) income earned by higher income taxpayers was more likely to be reported as taxable income when marginal tax rates fell post-reform.