not available<sup>10</sup> ; it is thus unknown which share of the full value of the property to apply. In order to obtain a tentative estimate of the value of the use rights to be subtracted from the full value of these properties, and then from the wealth of these households, we will resort to some imputations based on different hypotheses, to test the robustness of our results.

# **4. Taking account of use rights in Italy**

As recalled earlier, standard household wealth estimates do not include use rights. According to our approach, this implies an underestimate of the wealth for those households who live in usufruct and an overestimate for the households who grant usufruct rights to others. Some evidence on the need to assign a wealth value to the use rights based on SHIW data is provided in Appendix B.

Using data from SHIW we can estimate both cases in several waves (1991, and from 2004 to 2016). However, as explained before, information on the age of the usufructuary is available only when the interviewed household is the usufructuary and not when he is the bare owner. For such cases we have assumed (H1) that the usufructuary is 25 years older than the corresponding bare owner, being this the approximate age gap between fathers and sons. This situation approximately corresponds to that of a parent who transfers bare ownership to their child, retaining usufruct. A similar age gap could also be the case of an elderly person who, perhaps in the absence of heirs, sells bare ownership of the house of residence to ensure a more comfortable old age while retaining the right to live there for free.

As we have seen in the previous section, partial support for this hypothesis is offered by the interviewed usufructuaries that, when asked about the bare owners of the homes they occupy, most of the times indicate their children, with a share little below 50 percent (Table A3, top panel). However, in one-third of the cases the relationship is reversed, being the parents the bare owners and the children the usufructuaries and in a further 20 percent the age gap between bare owners and usufructuaries is totally unknown. This uncertainty suggests testing the robustness of the results by evaluating also two alternative assumptions: H2) the usufructuary is as old as the bare owner; H3) the usufructuary is 6 years older than the bare owners, being approximately 6 years the average gap between the sample age average estimates of usufructuaries and bare owners.

The results of the 3 hypotheses are shown in Table A4. The estimates of the net wealth adjusted for the use rights are almost always higher than the unadjusted ones; the increase of the net wealth values is, on average across the considered SHIW waves, between 0.9 (H1), 0.7 (H2) and 0.6 per cent (H3). The increase tends to characterize more frequently the households whose reference persons are less than 40 years old (from 1,9 to 1,6 percent on average across years, depending on the hypothesis done) and those residing in the South and in the Islands (from 1.3 to 1.2 percent). The higher impact on average wealth observed for the households with a younger reference person compared to the others is due to their higher life expectancy, which implies a higher value attributable to the observed use rights. This effect more than counterbalances the higher share of usufructuaries among the elderly.

In terms of concentration, the changes induced by the adjustments show a reduction of the Gini index of almost 1 percentage point (on average across the years approximately 0,008), regardless of the assumption made (Figure 1). This change seems attributable to a double effect. On the one side, the share of adjusted net wealth held by the richest 20 percent stably decreases compared to the unadjusted estimates (-0.43 and -0.13 percent on average for the top and the following tenth of household); on the other, the share of the third and fourth tenths of households (i.e. those from the 20<sup>th</sup> to the 40<sup>th</sup> percentile of the wealth distribution) increases in both cases of a quarter of a percentage point (Table A5). In sum, the phenomenon seems to favor more markedly usufructuary households

> 10 In future waves this information should be collected to allow a more precise estimate of this amount.