# **1.5** **<u>Addressing jointly top income underreporting and the national accounts discrepancy</u>**

The underreporting of top incomes in household surveys and their discrepancy with national accounts are closely connected issues. It is reasonable to expect, and there is some empirical evidence to corroborate it, that the discrepancy between surveys and national accounts is not distribution neutral and is largely due to non-participation of the rich in household surveys (Mistaenen and Ravallion 2003; Korinek et al 2006).<sup>21</sup> Deaton (2005) points out that because national accounts consumption tracks money rather than people, national accounts data are more likely to capture large transactions. Using Indian tax record data, Banerjee and Piketty (2010) find that a significant part of the discrepancy between consumption growth in national accounts and household surveys can be accounted for by underreporting of the rich. Finally, it could be argued that household surveys offer a good approximation to the bottom 90% of the distribution (thus, however, ignoring any underreporting of incomes among the very poor).<sup>22</sup> In the second part of the analysis we allocate the gap between household final consumption in national accounts and household surveys to the top 10% of the distribution and obtain more disaggregated top quantiles by fitting a Pareto distribution to the upper tail. Our approach builds on Atkinson (2007) who uses a Pareto imputation in combination with the Bourguignon and Morrisson (2002) data. Atkinson uses GDP per capita, thus spreading the discrepancy between national accounts and household surveys _evenly_ across the distribution, but for the very top “elongates” the distribution by using a Pareto interpolation.<sup>23</sup> We call Atkinson’s approach the “proportional adjustment with Pareto tail”. By contrast, our methodology proposes to allocate the “excess” consumption recorded in the national accounts only to the top decile and to use a Pareto are represented by the tax data and which are covered by the household survey. CBO (2012) matches US tax records with household survey records using income. It adds the non-taxable income (e.g. transfers or in-kind income) from the survey. Armour et al. (2013) also match records by income but they add capital incomes to the household survey because these incomes tend to be poorly measured in this type of data.

21 This can also explain why the discrepancy is increasing in countries such as China or India as they become richer (Anand et al 2010).

> 22 The inclusion of the poor may be insufficient because of the very definition used by surveys, such that they exclude the homeless and institutionalized populations (see Carr-Hill, 2013) or because of sampling issues (excluding remote and probably poorer regions). Thus the very bottom of the distribution may be truncated. But, in addition, incomes of the poor included in the survey may be mismeasured due to extensive home production or benefits received in kind which may not be always included.

> 23 The Pareto imputation does not add “new” observations, but rather “stretches out” the top decile. This implies that the imputation by itself does not change the mean.

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