# **Appendix B: SHIW empirical evidence on the value of use rights**

In sections 3 and 4, we have examined the theoretical reasons why use rights associated with usufruct should be quantified and included in the net wealth of the households benefiting from them (and subtracted from that of the bare owners). We have also recalled that in Italy, as in many other countries, the use rights of houses are valued on the market, although this market is sometimes of a limited extent, and we have shown some possible estimation strategies using survey data.

In this Appendix, we will attempt to provide some empirical evidence of the appropriateness of this line of reasoning based on the data collected in the SHIW. We have considered a model in which the subjective judgment on the household's economic well-being is explained by the economic resources in terms of household income and wealth, controlling for a set of socio-demographic conditions (year, number of components, geographical area, municipality size, gender, age, education, and civil status of the adult with the higher income).

In the first experiment, wealth is measured without considering the value of use rights. To assess whether usufruct affects the perceived economic well-being, two dummy variables were introduced in the model, indicating whether the household is a usufructuary or a bare owner. According to the thesis advocated in this study, the coefficient of these dummies should be significantly different from zero, with a positive sign in the first case, and a negative in the second.

The analysis is conducted using an ordinal probit model, as the dependent variable has an ordinal nature. To avoid the potentially adverse effects of outliers often present in income and wealth distributions, both variables were subjected to the inverse hyperbolic sine (IHS) transformation, which is similar to the logarithmic transformation but allows for the treatment of negative values as well (Friedline et al., 2015).<sup>11</sup> The results show that, conditionally to all the socio-demographic conditions considered in the model and to household income and wealth (that have both – obviously – a positive effect on subjective economic well-being), the dummy variable indicating the usufructuary condition has a positive and significant coefficient, suggesting a residual content in terms of the well-being of this condition, not captured by the two variables reporting the economic resources (Table B1; Model 1).<sup>12</sup> The coefficient of the dummy indicating the bare ownership, instead, is slightly negative but insignificant. This result could depend on the low frequency of bare owners caught by the SHIW, also due to the limited attention paid to this phenomenon in the questionnaire.<sup>13</sup> In the second experiment, we used the same model with the only difference that household wealth is adjusted for the value of the use rights, i.e., obtained adding and subtracting respectively the estimated value of the usufruct. In such a model the coefficients of both the dummy variables become not significantly different from zero (Table B1; Model 2), suggesting that the adjustments done have caught the essence of well-being incorporated in those ownership conditions.

> 11 In a limited number of households, net wealth is negative, with debts being greater than assets. In some cases, income can also be negative, mainly due to the presence of business costs greater than the corresponding revenues.

> 12 It is worth noting that, analogously to the properties held, the houses occupied in usufruct contribute to the household income with imputed rents provided by the respondents themselves. Thus, the dummy in the model captures a benefit that goes beyond the value of the current occupation of the house free of charge.

> 13 The filter question defining the list of properties included in the roaster refers to those “held”, without any specific reference to bare ownership. This ambiguity could have emphasized the general tendency of households to under-report the properties owned.