successes with which originally poor households have been able to increase their incomes. This ordering is reversed when we examine growth of average incomes at the top of the income distribution – anonymous top incomes grow faster than non-anonymous top incomes do. Also here the magnitude of the differences we observe is considerable, at over 10 percentage points in the WID and 8 percentage points in PovcalNet. This suggest that anonymous top income growth rates, while a good indicator of changes in inequality in society, are not well-suited for estimating the expected income success of those who occupy the top of the income distribution at any given point in time.

Our paper provides an alternative approach to the large literature on estimating income distribution dynamics using pseudo-panel data techniques that track the evolution of cohorts over time.<sup>5</sup> This literature circumvents the need for true panel data that tracks individuals over time, but it does assume that the researcher has access to microdata from repeated series of cross-sectional household surveys. In contrast, our approach does not require access to any record level data, but instead shows how the parameters governing individual income distribution dynamics can be retrieved from time series data on aggregate moments only.<sup>6</sup> The obvious advantage of this is that by reducing the data requirements to a minimum, it significantly expands the number of countries where this approach can be applied. It also makes it possible to obtain estimates for historic periods for which aggregate moments have been preserved, but record level data will be hard if not impossible to come by. The price we pay for working with time series rather than pseudo-panel data is that we have to work with a much smaller number of observations. We make the most of the data that we have by relying on finite sample estimation methods (Andrews, 1993), and optimizing the trade-off between bias and precision. Finally, while we are by no means the first to notice that anonymous and non-anonymous growth rates can in principle diverge widely in the presence of mobility, we are – to our knowledge – the first to be able to provide estimates of the gap between the two for a large cross-section of countries.<sup>7</sup> The rest of this paper proceeds as follows. In Section 2 we state our main assumptions regarding the lognormal data generating process for individual incomes, and show how mobility is fully

> 5 See for example Deaton (1985), Moffitt (1993), Collado (1997), Verbeek and Vella (2005), Antman and McKenzie (2007), Inoue (2008), and Dang, Lanjouw, Luoto and McKenzie (2014).

> 6 In this respect, our work is similar in spirit to Caselli and Ventura (2000), study a series of growth models with heterogenous agents and show that under fairly general heterogeneity, (1) the aggregate economy behaves as if aggregate variables represent the decisions of a representative agent; and (2) the evolution of the aggregate variables characterizing the decisions of the representative are informative about the individual-level dynamics of income, consumption, and wealth.

> 7 See Jenkins and Van Kerm (2006), Grimm (2007), Van Kerm (2009), and Bourguignon (2011) for discussions of the difference between anonymous growth incidence curves and their non-anonymous counterparts.

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