This section concentrates on non-anonymous distributional implications of rent-imputation.<sup>13</sup> First, we check transition matrices to understand whether the rank of individuals changes after rent-imputation. Then, we test whether and how the characteristics of the poor change when both the consumption aggregate and the poverty line are modified to account for imputed rents.

Table 10 shows transition matrices of the two rent-imputation methods with respect to the case of no-rent. To build each matrix, the population in the distributions of consumption with no-rent and the population in the distributions of consumption with imputed rents are first sorted with respect to the per capita consumption levels, and then divided into deciles.<sup>14</sup> We then compare the population in the initial and final distribution by deciles. Each cell of the matrix reports the share of population in each decile of the initial distribution found in the same decile in the final distribution. In case of no re-shuffling, the transition matrix would be a diagonal identity matrix. Table 10 shows that some re-ranking takes place in all countries and across imputation methods, although in most cases individuals move up or down by just one decile. Nevertheless, particularly in countries with low headcount rates, any churning around the first decile may imply a change in the profiling of the poor.

For this reason, we look at the profile of the poor before and after rent imputation. Table 11 summarizes the results and corroborates previous findings: the effect depends on the adopted rent-imputation model, and no regularity can be found across countries. Although most of the socio-economic variables characterizing the poor are affected by the inclusion of rents, the magnitude of these changes is not sufficient, in our view, to justify changes in policies targeting the poor.

# **5. Final Remarks**

Measuring the monetary value of the flow of services that households receive from living in their dwellings poses a challenge to researchers and practitioners. On the one hand, a growing consensus requires that imputed rents should always be included in the welfare aggregate. On the other hand, imputed rents are often neglected, mainly because of inherent technical difficulties in rent imputation as well as due to lack of relevant information in household surveys. Moreover, when imputed rents are indeed included in the welfare aggregate, researchers and practitioners frequently overlook analyzing the distributional impacts of alternative rent-imputation approaches.

This paper is the first attempt to assess the distributional impact of including housing in the welfare aggregate comparing two rent imputation methods in four developing countries at different levels of development. First, the paper introduces a concise theoretical discussion of the expected distributional implications of including rent in the welfare aggregate and concludes that unambiguous predictions of the impact on poverty, inequality, and shared prosperity are possible only under strong assumptions. Second, it provides estimates of the distributional effect of including estimated rental values in the consumption aggregates of four countries.

Results indicate that understanding the distributional impact of including housing in the welfare aggregate is ultimately an empirical question. Including rental values determines statistically significant changes in poverty and inequality indicators, yet such changes are only occasionally larger than one percentage point. Shared prosperity exhibits sizable changes, which might also determine international re-rankings. In countries with low headcount rates, any churning around the first decile may imply a change in the profiling of the poor. Although most socio-economic variables characterizing the poor are affected by the inclusion of rents, changes are rarely substantial. Although any distributional analysis shall include housing in the construction of the welfare

> 13 Precisely, we will be discussing quasi-non-anonymous implications since we are not considering changes affecting any particular individual in the distribution, but rather groups of individuals: e.g. individuals belonging to the same decile in the distribution, or individuals belonging to the set of poor individuals.

> 14 To keep the analysis tractable, we limit the number of groups to 10. We acknowledge that this analysis is still anonymous, because we do not check the movements of each single individual. To do so, we should create transition matrices of size _n_ , where _n_ is the population size.

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