Table 7 , including rent determines an increase in the poverty lines ranging between 7.5 percent (in Bangladesh for both the self-assessment and log-linear model) to above 20 percent (in Iraq, with the log-linear model). There is no regularity as of which imputation methods determines the largest variations.

When the poverty line is modified consistently with the rent imputation method used in the construction of the consumption aggregate, predicting the sign of changes in poverty becomes challenging from a theoretical perspective. Table 8 illustrates that only in the case of Bangladesh both imputation methods generate an increase in the poverty headcount. In the case of Iraq, the share of poor decreases when the self-assessment approach is applied. In the case of Peru, it decreases with both imputation method. Variations in the depth and severity of poverty do not necessarily follow the same signs of the corresponding poverty headcount variations. For instance, self-assessment in Iraq determines a decrease of poverty headcount, but an increase in the depth of poverty. Regardless of the direction of the variations, the magnitude of the changes has modest economic significance: only in one case (Iraq, self-assessment) poverty headcount changes by more than one percentage point; in all other instances, changes are much smaller. However, such changes, although modest in magnitude, are always statistically significant and can lead to sizeable differences in the profile of the poor if ranking is not preserved, particularly in countries with low poverty headcount rates, as illustrated in section 4.4.

# **4.3. Shared Prosperity**

Table 9 summarizes the impact of the different rent-imputation approaches on shared prosperity, measured by the annualized average growth rate of the consumption level of the bottom 40 percent. To get a coherent measure, the index was built by applying the same rent-imputation method in both years.

Except for Bangladesh, where including rents does not affect shared prosperity, in all other countries the housing component has a sizable and statistically significant effect. In the case of Iraq and Albania, including rents, obtained via the log linear model, reduces shared prosperity. The log-linear model has instead a positive effect on shared prosperity in the case of Peru. However, it is worth noticing that in the case of Albania selfassessment was recorded only for 3 percent of the total non-market-tenants in the 2008 survey. Therefore, the large increase in shared prosperity observed in the analysis (4.7 percent) is due to the missing information in 2008: for 97 percent of the non-market-tenants, a vector of zeros was added in 2008 as self-assessment value.

Our results suggest that, although size and magnitude of the effect of including housing in the consumption aggregate are not predictable and might vary within country according to the imputation method selected, shared prosperity does change as a result and the change can be substantial and might imply churning in country-rankings (see the case of Peru and Iraq), or altering our estimates of a country’s performance over time.

# **4.4. Non-anonymous Distributional Implications**

Gini index, poverty indices and shared prosperity all satisfy anonymity: a permutation of the underlying welfare vector does not affect the distribution as long as welfare levels do not change. Nevertheless, rent imputation may determine a proportional shift in the welfare vector with no distributional consequences (e.g. on the Gini index, which is invariant to scale), but at the same time it may imply a churning of individuals along the distribution. In an extreme scenario, it may be possible that after rent is included in the welfare aggregate all individuals below the poverty line become non-poor and the same number of initially nonpoor individuals become poor. In this case, poverty indices may remain the same, leading us to conclude that rent imputation has no effect on poverty, but the characteristics of the poor might change, with important policy implications.

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