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# find - Thomas Piketty - Ens

find - Thomas Piketty - Ens

## 11 years of average

11 years of average income y t (µ t x β t = 12.5). One can then introduce distributional issues: about half of decedents have virtually no wealth, while the other half owns about twice the average (i.e. about 25 years of average income); and so on. What kind of data do we need in order to compute equation (3.1)? First, we need data on the wealth-income ratio β t =W t /Y t . To a large extent, this is given by existing national accounts data, as described below. Next, we need data on the mortality rate m t . This is the easiest part: demographic data is plentiful and easily accessible. In practice, children usually own very little wealth and receive very little income. In order to abstract from the large historical variations in infant mortality, and in order to make the quantitative values of the m t and µ t parameters easier to interpret, we define them over the adult population. That is, we define the mortality rate m t as the adult mortality rate, i.e. the ratio between the number of decedents aged 20- year-old and over and the number of living individuals aged 20-year-old and over. Similarly, we define µ t as the ratio between the average wealth of decedents aged 20-year-old and over and the average wealth of living individuals aged 20-year-old and over. 23 Finally, we need data to compute the µ t ratio. This is the most challenging part, and also the most interesting part from an economic viewpoint. In order to compute µ t we need two different kinds of data. First, we need data on the cross-sectional age-wealth profile. The more steeply rising the age-wealth profile, the higher the µ t ratio. Conversely, if the agewealth profile is strongly hump-shaped, then µ t will be smaller. Next, we need data on differential mortality. For a given age-wealth profile, the fact that the poor tend to have higher mortality rates than the rich implies a lower µ t ratio. In the extreme case where only the poor die, and the rich never die, then the µ t ratio will be permanently equal to 0%, and there will be no inheritance. There exists a large literature on differential mortality. We simply borrow the best available estimates from this literature. We checked that these differential mortality factors are consistent with the age-at-death differential between wealthy decedents and poor decedents, as measured by estate tax data and demographic data; they are consistent. 24 Regarding the age-wealth profile, one would ideally like to use exhaustive, administrative data on the wealth of the living, such as wealth tax data. However such data generally does not exist for long time periods, and/or only covers relatively small segments of the population. Wealth surveys do cover the entire population, but they are not fully reliable (especially for top wealth holders, which might bias estimated age-wealth profiles), and in any case they are not available for long time periods. The only data source offering long-run, reliable raw data on age-wealth profiles appears to be the estate tax itself. 25 This is wealth-at-death data, so one needs to use the differential mortality factors to convert them back into wealth-of-the-living age-wealth profiles. 26 This data source combines many advantages: it covers the entire 23 Throughout the paper, “adult” means “20-year-old and over”. In practice, children wealth is small but positive (parents sometime die early), so we need to add a (small) correcting factor to the µ t ratio. See Appendix B2. 24 See Appendix B2 for sensitivity tests. We use the mortality differentials due to Attanasio and Hoynes (2000). 25 This does not affect the independence between the economic and fiscal series, because for the economic flow computation we only use the relative age-wealth profile observed in estate tax returns (not the absolute levels). 26 Whether one starts from wealth-of-the-living or wealth-at-death raw age-wealth profiles, one needs to use differential mortality factors in one way or another in order to compute the µ t ratio.

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