metadata: authors: 0: author: Ceriani,Lidia
1: author: Olivieri,Sergio Daniel
2: author: Ranzani,Marco
count: World
docna: 0: docna: Housing, Imputed Rent, and Households' Welfare
docty: Policy Research Working Paper
subtopic: Inequality,Urban Governance and Management,Municipal Management and Reform,Urban Housing,Urban Housing and Land Settlements,Poverty Diagnostics,Poverty Lines,Poverty Assessment,Poverty Impact Evaluation,Small Area Estimation Poverty Mapping,Poverty Monitoring & Analysis,Global Environment,Labor & Employment Law
teratopic: Public Sector Development,Urban Development,Communities and Human Settlements,Poverty Reduction,Law and Development
abstracts: cdata!: Housing is the largest durable good
            consumed by households. As such, any consumption-based
            measure of welfare, to be comprehensive, must include the
            value of the flow of services households derive from their
            dwellings, the so-called imputed rent. However, estimating
            imputed rents is a daunting task, which researchers and
            practitioners tend to overlook. This paper is the first
            attempt to assess the distributional impact of including
            housing in the welfare aggregate; the paper tests two
            estimation methods and analyzes four developing countries.
            The distributional impact cannot be predicted a priori, and
            evidence suggests it is context and method specific.
            Although changes in poverty and inequality are always
            statistically significant, they are only occasionally larger
            than one percentage point. By contrast, shared prosperity
            exhibits sizable changes, which might also determine
            international re-rankings. Albeit the inclusion of imputed
            rents reshuffles the set of poor households, observed
            changes in the socioeconomic profiling of the poor are
            unlikely to affect pro-poor policy design.
repnme: repnme: Housing, Imputed Rent, and Households' Welfare
display_title: Housing, Imputed Rent, and
            Households' Welfare
listing_relative_url: /research/2019/08/31315064/housing-imputed-rent-households-welfare
topicv3: Poverty m1326687 695,Poverty Measurement and Analysis m1326941 707,Environment, Natural Resources and Blue
            Economy m1327391 566,Land and Housing m1327648 817,Household Surveys m1504071 2761
publishtoextweb_dt: 2019-08-06T00:00:00Z
historic_topic: Public Sector Development,Urban Development,Communities and Human Settlements,Poverty Reduction,Law and Development
no_of_pages: 32
author_keys: 0: author_key: 1236578
1: author_key: 926510
2: author_key: 927986
model_extractions: Policy Research Working Paper 8955 Housing, Imputed Rent, and Households’ Welfare _Lidia Ceriani Sergio Olivieri Marco Ranzani_ Poverty and Equity Global Practice August 2019
Policy Research Working Paper 8955

# **Abstract**

Housing is the largest durable good consumed by households. As such, any consumption-based measure of welfare, to be comprehensive, must include the value of the flow of services households derive from their dwellings, the so-called imputed rent. However, estimating imputed rents is a daunting task, which researchers and practitioners tend to overlook. This paper is the first attempt to assess the distributional impact of including housing in the welfare aggregate; the paper tests two estimation methods and analyzes four developing countries. The distributional impact cannot be predicted a priori, and evidence suggests it is context and method specific. Although changes in poverty and inequality are always statistically significant, they are only occasionally larger than one percentage point. By contrast, shared prosperity exhibits sizable changes, which might also determine international re-rankings. Albeit the inclusion of imputed rents reshuffles the set of poor households, observed changes in the socioeconomic profiling of the poor are unlikely to affect pro-poor policy design.

This paper is a product of the Poverty and Equity Global Practice. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://www.worldbank.org/prwp. The authors may be contacted at mranzani@worldbank.org.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
# Housing, Imputed Rent, and Households’ Welfare<sup>1</sup>

Lidia Ceriani<sup>2</sup> Sergio Olivieri<sup>3</sup> Marco Ranzani<sup>4</sup>

**JEL:** C46, D31, I32

**Keywords** : Rent Imputation; Inequality; Poverty Measurement; Shared Prosperity.

> 1 The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent. The authors wish to thank Dean Jolliffe, Peter Lanjouw, Kristen Himelein, and Carlos Rodriguez Castelan for their comments on previous versions of the paper, as well as Carlos Felipe Balcázar and Jikun Wang for their research assistance. 2 Georgetown University.

> 3 World Bank Group, Poverty and Equity Global Practice.

> 4 World Bank Group, Poverty and Equity Global Practice.
# **1. Introduction**

Housing, measured as the welfare value of the flow of services households derive from their dwelling, is one of the most relevant components of households’ welfare aggregate, which is used as a basis for distributional analysis (Deaton and Zaidi 2002). Nevertheless, due to data limitations and the difficulty of estimating rental values for non-market tenants and owners, the housing component is often neglected in the construction of welfare aggregates. In fact, although we can reasonably assume that the flow of services enjoyed by living in a dwelling is correctly approximated by the monthly rental payment to landlords among tenants, no such measure is readily available for home-owners. Furthermore, not all tenants pay a market price for the dwellings they live in, as many enjoy subsidized rental arrangements (see, for instance, Lara Ibarra et al 2017), or live for free in a dwelling provided by their employer or by a family member. Therefore, in order to include in a measure of the welfare aggregate the value of the flow of services households derive from the dwellings they live in, one would have first to estimate rental values for home-owners and adjust those for non-market tenants.

As argued by Frick et al. (2010), excluding estimated rental prices from the welfare aggregate used in distributional studies may undermine the validity of comparisons of any distributional outcome, both in timeseries within a particular country and in cross-sectional analysis across countries. The need for including the housing component for the purpose of measuring welfare has been stressed by different communities of practitioners. For instance, the US Interagency Technical Working Group on Developing a Supplemental Poverty Measure Census (2010) acknowledges the need to adjust poverty thresholds by housing status. The European Commission financed the project “Accurate Income Measurement for the Assessment of Public Policies” (Sutherland et al., 2009) with the objective, among others, of understanding the distributional impact of the inclusion of rents in income aggregates. Törmälehto and Sauli (2010 and 2013) analyze the implications of including rents in the income aggregate for official poverty and inequality estimates published by Eurostat and conclude that “ _the present data quality does not support adding this component to disposable income concept without major improvements in the comparability of the data between countries and within countries across time”_ (Törmälehto and Sauli 2013, 39).

By contrast, in order to guarantee meaningful international and inter-temporal comparability of countries’ welfare, observed and imputed rental prices are included in National Accounts according to internationally agreed recommendations (SNA 2008). In a sample of OECD countries, for instance, the share of observed and imputed rents in households’ total consumption expenditures range from 6.5 percent in Poland to 25 percent in Finland, according to the latest available National Accounts data (OECD 2018). For the same countries, this share may vary sensitively over time, even within a short period. For instance, in Ireland the share almost doubled from 11 percent in 1996 to 20 percent in 2016, in Spain it increased from 10 percent in 1996 to 16 percent in 2016. In some other countries the share decreased: over the period 1996-2016, in Sweden it declined from 25 to 20 percent and in Mexico from 19 to 14 percent. It is clear then that the exclusion of this large component of household consumption from National Accounts would distort country-rankings in terms of Gross Domestic Product (GDP).

The World Bank has recently started collecting information for understanding the key elements of national methodologies used to produce official poverty estimates. Preliminary results shed light on a sample of 69 country-year observations of recent poverty estimates. Only for 28 observations is it possible to understand whether the welfare aggregate included observed and imputed rents (World Bank, 2015). Nonetheless, when housing is included, researchers and practitioners do not usually test how different imputation methods may affect distributional indicators nor justify why a particular method has been chosen. For example, Ceriani, Olivieri and Ranzani (2019) tell a cautionary tale about the accuracy of rents imputed by using the self2
assessment method. Yet, in 15 of the mentioned 28 surveyed cases, poverty estimates include home-owners’ self-assessed rental values without any (at least documented) assessment on whether there is a bias or not.

In this paper, we analyze the distributional impact of including the value of the flow of services derived from housing in households’ welfare aggregate. Since one of the main results emerging from the previous literature is that the distributional impact may be sensitive to the estimation method (Frick et. al 2010), we implement two approaches in imputing rental values and assess whether and how the method influences our results. Precisely, we investigate the effect of including rent on inequality, poverty (intended both as poverty headcount, depth and severity and in terms of profile of the poor), and shared prosperity, i.e. the annualized growth rate in mean income (or consumption) level of households at the bottom 40 percent of the distribution between two-time periods. To do so, we first provide a theoretical framework to understand the possible distributional outcomes, and then we present results from an empirical application to Albania, Bangladesh, Iraq, and Peru.

While previous studies are conclusive towards a reduction in both inequality and poverty after including rent (for a recent review of the literature, see Balcázar et al. 2017), this paper provides suggestive evidence that the distributional impact is instead context- and method-specific. Results of the empirical analysis indicate that while shared prosperity exhibits sizable changes that might determine international re-rankings, changes in poverty and inequality, albeit statistically significant, are only occasionally larger than 1 percentage point. Nevertheless, including rents in the welfare aggregate is not rank-preserving, and in countries with low headcount rates, any churning around the first decile may imply a change in the profile of the poor. In the examples selected for this study, most of the socio-economic variables characterizing the poor are affected by the inclusion of rents, although changes are rarely substantial. Nevertheless, because housing is an important component of consumption, and it is expected to become even more important as economies grow, then not including imputed rents in the consumption aggregate will result in a noisier welfare indicator, and, in turn, in less precise poverty profiles (Lanjouw and Lanjouw 2001).

The rest of the paper is organized as follows. Section 2 lays out a simple theoretical framework that describes the expected distributional impact of including rental values in the consumption aggregate. Section 3 introduces the data sources used in the analysis and the empirical strategy adopted to impute rental values. Section 4 assesses the distributional impact of imputing rental values on inequality, poverty, and shared prosperity indicators. Finally, Section 5 presents a set of concluding remarks.

# **2. Theoretical Framework**

This section introduces the expected distributional impact of including rental values in the consumption aggregate using a stylized theoretical framework. Given the original distribution of welfare net of rent (which is used as baseline), different assumptions can be made on the corresponding distribution of rental values, where rents include both the level of per-capita market rent for market tenants and imputed rents for homeowners or non-market tenants. We assume three hypothetical scenarios: (i) all individuals pay the same amount of rent; (ii) rent is a fixed proportion of each individual’s welfare; (iii) rent is a share, different for each individual, of each individual’s net-of-rent welfare. Regardless of the scenario, since rent is a non-negative value for all individuals, the new welfare distribution including rents is shifted to the right with respect to the baseline welfare distribution.

In this paper, the impact of imputing rents on inequality is assessed by looking at changes in the Gini index. Since the Gini index satisfies the property of scale invariance, there would be no change in inequality if rents were a fixed share of each individual’s net-of-rent welfare (scenario (ii)). However, the Gini index does not satisfy translation invariance. Therefore, adding a constant value to the baseline distribution (scenario (i)) would imply a change in inequality. In particular, this would imply a reduction in inequality since welfare would 3
increase proportionally more at the top than at the bottom of the distribution (and the mean of the well-being indicator would increase). Nothing can be stated a priori regarding inequality under scenario (iii). If rent were a growing (decreasing) share of individuals’ welfare, inequality would increase (decrease). Yet, if there is no linear relation between the original welfare distribution and rents, the distributional impact of imputed rents cannot be predicted ex-ante.<sup>5</sup> For example, if rents are higher for some specific subset of the population, such as individuals living in urban dwellings, individuals belonging to that subgroup may also present higher rent shares relative other subpopulations _._ The effect of adding rents on inequality would not be straightforward in this case.

The distributional impact of imputed rents on poverty is assessed analyzing changes in poverty incidence, depth and severity. Recall that poverty measurement involves three steps: defining a welfare indicator (usually consumption or income), setting a poverty line, and finally aggregating all information into a single poverty indicator. Recall, moreover, that the poverty line is usually defined as a function of the welfare indicator itself. This holds true not just in case of a relative poverty line, e.g. 60 percent of median income, but also in case of an absolute poverty line. An absolute poverty line, e.g. based on the cost of basic needs approach, is generally computed in two steps, first by identifying a food poverty line and then by adding to it a non-food poverty line. Seeking simplicity, we can think of the non-food component as determined residually by inflating the food poverty line with the ratio of non-food consumption to food consumption for the reference population.<sup>6</sup> Therefore, if the welfare distribution changes, it should be good practice, whenever possible, to re-estimate the poverty line accordingly. Trivially, if rents are included in the welfare aggregate, but the poverty line is left unchanged, poverty will decrease. When both the poverty line and the original welfare distribution increase as a consequence of including rents in the welfare aggregate, the effect on poverty becomes unpredictable, unless the poverty line is relative, and rents are modeled following scenario (ii). In this case, given that the poverty indices used in this analysis satisfy scale invariance, poverty will not change.

The third indicator of well-being taken into account in this paper is shared prosperity. In 2013, the World Bank adopted two new targets: ending extreme poverty by 2030 and promoting shared prosperity. The emphasis on reducing extreme poverty is in line with the commitment to eliminate extreme poverty enshrined in the first target of the Sustainable Development Goals, which were adopted by the United Nations in 2015 (United Nations 2015). Shared prosperity focuses on the less well-off more broadly. It is defined as the annualized growth rate of the average welfare of the bottom 40 percent of the population between two years and , where stands for the number of years between two data surveys. yy yy+ ττ Let us define the average welfare aggregate at timeττ , for the bottom 40 percent of the population as<sup>,</sup> Monitoring shared prosperity is challenging, as it requires building comparable welfare aggregates over time. For our purposes, the three scenarios we introduced before are here increased to nine, as summarized in Table 1, depending on the prevalent rent-imputation scenario in each one of the observed years.

> 5 Blades (2009), for example, shows that the share of housing on total consumption is positively correlated to GDP per-capita. However, there is still no evidence that the share of housing on total consumption is correlated to the distribution of the welfare aggregate in developing countries. More evidence on this is needed, preferably using large samples of countries.

> 6 Specifically, the lower level of the total poverty line is defined based on those households whose total consumption is close to the food poverty line. On the other hand, the upper level of the poverty line happens when households whose total _food_ consumption is close to the food poverty line (Ravallion 1994). In the following we assume that the reference population for the estimation of the food poverty line does not vary under different definitions of the consumption aggregate, namely, including or not the housing component.

4
In scenario (i,i), rents added to the original welfare aggregate are a fixed amount in each year ( yr<sup>and</sup> y+τr<sup>).</sup> For growth of the bottom 40 percent not to be lower compared with the scenario where rents are not included in the consumption aggregate, the following condition must hold: <u>y</u> ≥ <u>y</u> (2) rr y+ττrr yyBB40xx̅ yy+ττBB40xx̅ In scenario (ii,ii), rents added to the original welfare aggregate are a fixed proportion of the original welfare aggregate for each individual in each year ( yλ<sup>and</sup> y+τλ<sup>). Therefore, if</sup> y+τλ<sup>≥</sup> yλ<sup>, shared prosperity cannot be</sup> lower after rent imputation. The opposite holds if y+τλ<sup><</sup> yλ<sup>.</sup> In scenarios (i,ii) and (ii,i) rents added to the original welfare aggregate are, for the first year , a fixed proportion of the original welfare aggregate and a fixed amount for each individual, respectively. The reverse applies for yy the second year . For shared prosperity post-rent imputation not to be lower relative to shared prosperity before-rent imputation, the following conditions must be satisfied: yy+ ττ λ <u>y</u> for scenario (i,ii) rr (3) yy+ττλ<sup>≥</sup> <u>yyyBB40xx̅</u> for scenario (ii,i) y+ττrr yy<sup>≥</sup> yy+ττBB40xx̅ In all scenarios where rents in one (or both) period follow hypothesis (iii), we cannot guess a priori the sign of the change when adding rents to the consumption aggregate because ranking is not preserved in at least one of the two years.

Even if inequality and poverty indices are not affected by rent-imputation, there is still the possibility that changes could happen to the underlying distribution. Unless rent-imputation is rank-preserving, in fact, the same individual might be found in two very different positions before and after the imputation, e.g. above the poverty line, when before imputing rents she was below the poverty line, or at the bottom of the welfare distribution, when before she was at the top of the welfare distribution. Analyzing such changes is important, because they might imply adjustments to redistribution policies. For instance, in anti-poverty strategies, the target population (the set of poor individuals) might change after the inclusion of rental values. One way to check if adding rent to the welfare aggregate determines churning to the distribution is to build transition matrixes with respect to the baseline scenario with no-rents in the welfare distribution. Each i − cell of a transition matrix represents the probability (or the incidence) to find some individuals belonging the quantile of the original no-rents distribution in the quantile of the distribution tth mm× mm including rents. In case no churning occurs, the transition matrix will appear as an identity matrix. Notice that a true non-anonymous analysis would require a transition matrix as large as the population size, although a ii−tth ii−tth matrix would not be tractable or particularly useful. Therefore, a transition matrix typically cluster population into quintiles or deciles. This implies that even in the case the transition matrix is an identity matrix, nn× nn some reshuffling in the underlying distribution takes place within the subset of population belonging to the same cluster. For instance, some individuals might change position in the distribution, yet they remain within the poorest 10 percent of the population. For the purpose of re-assessing anti-poverty policies, we believe that this level of precision is typically sufficient.

Another important component consists of checking whether rent-imputation changes the characteristics of the poor. Any time transition matrixes show some churning, there is a possibility that the set of poor individuals is composed of individuals with different socio-economic characteristics. This is true even if poverty indices do not change with imputed rental values. For instance, imputed rents among individuals living in urban 5
settlements might be much higher relative to imputed rents for individuals in rural settlements, pushing all urban dwellers above the poverty line. This, in turn, could suggest a need for a re-allocation of anti-poverty funds from urban to rural areas. Again, assessing the distributional impact of imputed rents on socio-economic characteristics of poor individuals is hard to define a priori, and it remains an empirical question.

# **3. Data and Approaches to Rent-Imputation**

This section describes first the data sources used in the analysis and second introduces the empirical strategy adopted for assessing the distributional impact of imputing rent on inequality, poverty, and shared prosperity. Two different rent-imputation models, namely, a log-linear econometric model and self-assessment method will be used in the empirical analysis.

## **3.1. Data and the Preliminary Evidence**

The analysis makes use of data from nationally representative household budget surveys that are used for the computation of official poverty figures in Albania, Bangladesh, Iraq and Peru. The countries were selected following three criteria: (i) completeness of information, (ii) broadness of regional coverage, (iii) heterogeneity in terms of development stage. The analysis requires detailed information on dwelling characteristics, tenancy status, self-assessed rental price for owners and non-market tenants, and the official methodology followed to compile the consumption aggregate used in the official distributional analysis. Further, the four countries belong to different regions and represent different stages of development, maximizing as much as possible the generalizability of the results.<sup>7</sup> The analysis for Albania is based on the 2008 and 2012 waves of the Living Standard Measurement Survey (LSMS). The two surveys are representative at urban and rural level as well as at region and prefecture level. Official poverty figures are consumption-based, and the official consumption aggregate does not include rent or imputed rent. It is important to note that we were not able to access to the methodology for determining the official poverty line. Therefore, in the following, Albania does not appear in some parts of the analysis. Data for Bangladesh come from the 2005 and 2009/10 Household Income and Expenditure Survey (HIES). The surveys are representative by divisions at urban/rural/statistical metropolitan area. Official poverty statistics are based on a consumption aggregate that includes imputed rents, although is not clear which imputation method is adopted in the official methodology. The data sets used for Iraq are the 2007 and 2012 rounds of the Iraq Household Socio Economic Survey (IHSES). IHSES is representative by governorate at urban/rural/statistical metropolitan area. The consumption aggregate for official poverty statistics includes rents following the self-assessment approach. Finally, figures for Peru are based on the 2010 and 2013 rounds of the Peruvian Household Survey on Living Conditions and Poverty ( _Encuesta Nacional de Hogares sobre Condiciones de Vida y Pobreza_ - ENAHO). Official distributional statistics are based on consumption and the official consumption aggregate includes rents following the self-assessment approach with adjustments for nonresponse.<sup>8</sup> Typically, the housing section of household budget surveys contains a question about occupancy status of households, allowing selection of different categories, broadly referable to (i) owners (sometimes specifying whether outright or still paying mortgage), (ii) tenants, (iii) tenants living in subsidized dwellings, (iv) individuals living for free in dwellings provided by relatives or employer. These categories sometimes are more finely

> 7 The World Bank classifies countries by region (East Asia and Pacific; Europe and Central Asia; Latin America & the Caribbean; Middle East and North Africa; South Asia; Sub-Saharan Africa) and by development stages (low-, lower middle-, upper middle-, high-income). The four countries analyzed in this paper belong to four different regions: Europe and Central Asia (Albania), South Asia (Bangladesh), Middle East and North Africa (Iraq), Latin America and the Caribbean (Peru). And two income levels: Upper-Middle Income (Albania, Iraq; Peru); Lower-Middle Income (Bangladesh).

> 8 We do not use officially imputed rents when making our own estimations.

6
defined. For instance, in the case of Iraq, the questionnaire allows to separate out private/public/governmental sector ownership from occupancy status. Moreover, household surveys may allow for country-specific ownership statuses as in the case of Peru for the category “ownership by invasion.” Starting from the occupancy status, as a preliminary step in the analysis, households have been regrouped in two mutually exclusive ownership sets: owners and non-market tenants in one group and market tenants in the second group. The first group includes outright owners, owners paying mortgage, and individuals living for free or paying a subsidized rent; market tenants are defined residually as households paying a rent. The rent paid by market tenants is reported either in monthly or annual values. Table 2 summarizes categories and regrouping specifications for each country and year.

Table 3 summarizes the main differences between tenants and owners with respect to dwellings’ and households’ characteristics, focusing on the most recent year of analysis. The share of market tenants is typically rather small in all four countries, ranging from 3.6 percent in Albania (2008) to 11.1 in Bangladesh (2010). The large majority of tenants live in urban areas: 82 percent in Albania, about 90 percent in Bangladesh, and virtually all tenants in Iraq and in Peru. In all 4 countries, individuals living in rented dwellings are concentrated in the region of the capital. For instance, one out of three in the region of Tirana (Albania) and two out of three in the region of Dhaka (Bangladesh).

The high prevalence of tenants in largely urbanized areas, and within these areas mainly in the capital region, poses a problem to the rent-imputation exercise as the characteristics of dwellings as well as rental markets in such areas might be very different compared to those in the rest of the country. Hedonic models assume that urban and rural rental markets price houses similarly, although this is well-known to be very unlikely, whereas self-assessment might be less accurate in areas of the country where the rental market is thin (or absent). Further, tenants are more likely to live in households were the household head is younger and also more educated. For example, in the case of Peru, the incidence of individuals living in households where the head has no schooling or incomplete primary education is 18 percentage points lower among tenants than among owners. By contrast, again in Peru, tenants are 19 percentage points more likely to have tertiary education than owners. Similar patterns, even if less accentuated, emerge in the other three countries. Individuals residing in rented dwellings belong to smaller households, although the difference between tenants’ and owners’ household size is significant only in the two countries with the larger household size on average. In the case of Bangladesh, there is a difference of about 1 member (-0.8 members, from an overall average of 5.3 members) and in the case of Iraq where the gap is of over 2 members (-2.3 members from an overall average household size of 8.9 members). Finally, rented dwellings, although smaller, are on average of better quality than owners’: for instance, in Bangladesh, 93 percent of tenants have electricity as opposed to 52 percent of homeowners; in Peru, 94 percent of tenants have a bathroom inside the dwelling as opposed to only 76 percent of homeowners.

# **3.2. Estimation Approaches to Rent-Imputation**

The first step of the exercise requires identifying a vector of rental values for the observed population—object of the distributional analysis. For each household, the rental value to be used in the construction of a welfare aggregate is the actual rent paid by market tenants ( h ), and the imputed rental value for home-owners and tenants not paying the market price ( h ). Information on rent paid by market tenants is generally available in TT rr household budget surveys as the regular payment to landlords for living in the dwelling, although data from OO rr other sources might be also used (e.g. administrative registers, listings, mortgage transactions, experts’ survey). Imputed rent for home-owners and non-market tenants must instead be estimated.

Several different imputation approaches have been developed, and no one has emerged as superior to others so far (Balcázar et al. 2017). Notwithstanding the lack of consensus about the best method to adopt, two approaches, in addition to excluding the housing component _tout court_ from the welfare aggregate, are commonly 7
used by practitioners in preparing welfare aggregates for distributional analysis: the log-linear hedonic model and the self-assessment method. According to a World Bank survey on the main characteristics of the welfare aggregates used for measuring poverty in 70 developing countries, only 28 cases include housing. Among these 28, 12 use a hedonic model, 11 use self-assessment, and other four adopted a combination of hedonic model and self-assessment (World Bank 2015).<sup>9</sup> While we refer the reader to Balcázar et al. (2017) for an extensive review of the literature on rent imputation for welfare analysis, we briefly discuss in the following the log-linear hedonic model and the self-assessment method.

As underlined by Malpezzi (2002), the semi-logarithmic model has several advantages. First, the coefficients have a straightforward interpretation: they show approximately the percentage change in the imputed rent for a given unit-change in the covariates.<sup>10</sup> It also mitigates the heteroskedasticity problem (Diewert 2003). Second, it allows for flexible specifications of the covariates that can be either continuous or binary. Third, and most importantly, it allows the marginal rental value to be a nonlinear function of size and quality of the dwelling, which is a theoretical requirement of the hedonic model (Rosen 1974; Freeman 1993).

The second imputation approach used in this analysis is self-assessment. The self-assessment method relies on the assumption that owners can provide a good estimate of the market value of their dwellings, perhaps with the help of interviewers, as suggested in Garner and Kogan (2007). This information is frequently found in household budget surveys, where home-owners and tenants enjoying subsidized arrangements are asked to estimate the rental price they would pay to live in the current dwelling (Frick et al. 2010). The question may be asked in two ways that differ in whether the homeowner is asked to play the role of the landlord or the tenant. In the first case, the question would be some variant of “ _How much would you receive as a rent if you were to lend your apartment?_ ” In the second case, the question would read like “ _How much would you pay if you were to rent the dwelling you are currently living in?_ ” The extensive theoretical and experimental literature on the difference between willingness to accept (WTA) and willingness to pay (WTP) for the same good (among others, Hanemann 1991; Fehr et al. 2015; Tunçel and Hammit 2014) argues that measures of WTA usually exceed measures of WTP. This is due to the fact that a person’s perceived value of an item is often higher when the person owns the item

> 9 According to World Bank (2015), countries using hedonic models to impute rents are the following: Afghanistan (2008); Timor-Leste (2007); Malawi (2004); Sierra Leone (2003); Kenya (2005); Mozambique (2002); Nigeria (2004); Guatemala (2006); Bangladesh (2005); Peru (2010); Tanzania (2007); Zambia (2006). Among countries using self-assessment to impute rents, there are Nepal (2010); Nicaragua (2009); Zimbabwe (2011); Cambodia (2011); Jordan (2010); Belize (2002); Uganda (2005); Indonesia (2010); Panama (2008); Ecuador (2006); West Bank and Gaza (2007). Countries using a combination of hedonic models and self-assessment: Mongolia (2008); Nicaragua (2001); Peru (2013); Zambia (2010). 10 This is not accurate for dummy variables. In this case, Halvorsen and Palmquist (1980) demonstrate that the percentage change is better approximated by �−1�. ii �100 ∗exp�ββ̂

8
(i.e., the role of the landlord), then when she does not own it (i.e. the role of the tenant). This would suggest that the second version of the question (WTP), may mitigate the possibility of misreporting due to sentimental attachment to the property. In the selected surveys, we observe both types of self-assessed rent questions previously discussed. In particular, in the case of Albania and Peru, the questionnaire uses the first version: (a) “ _Assume that you want to rent [out] this dwelling what would be a monthly rent you will be able [to] ask for? If you rented out this dwelling, how much do you think you would make?_ ”, respectively. In the case of Iraq, the instrument uses the second version: (b) “ _How much would you pay if you were to rent a dwelling similar to the one you are currently living in?_ ”<sup>11</sup> For the reason explained above, we expect that the question as it is asked in Iraq is likely to mitigate the possibility of misreporting due to sentimental attachment to the property, while in Albania and Peru selfassessment might be inflated. Table 2 reports questions asked in each country and year.

As noted by Deaton and Zaidi (2002, 37), rental value from self-assessment _must be treated with caution and carefully inspected prior to use_ , as home-owners might not have a precise idea of the market value of their dwelling. The scope of this analysis is to illustrate whether and to what extent different methods can lead to different poverty and inequality estimates. Therefore, we do not ascertain the accuracy of self-reported rental values by homeowners and non-market tenants. Ceriani, Olivieri and Ranzani (2019) test the accuracy of home-owners’ selfassessed rental value in an application to Peruvian data.

# **4. Results**

In this section, we analyze the distributional impact of including the flow of services from dwellings in the consumption aggregate using data from four developing countries: Albania, Bangladesh, Iraq and Peru. We measure the effect on different outcomes including inequality and poverty indices, profiling of the poor and shared prosperity by comparing consumption aggregates without the housing component with aggregates that include rental values imputed by means of one of the two approaches described above.

This section summarizes the distributional impact of including rents in the consumption aggregates of the selected countries, differentiating between (i) the baseline scenario, with no rent, and two rent-imputation methods: (ii-a) self-assessment and (ii-b) log-linear hedonic model.<sup>12</sup> We start off by illustrating the relevance of the housing component as a share of the total consumption aggregate on average and along the distribution (by quintile of the original welfare indicator) (Table 4). On average, rents’ shares range from a minimum of 4.8 percent of total per capita household welfare (Bangladesh, 2010, self-assessment imputation method) to a maximum of 22.7 percent (Albania 2008, log-linear imputation method). In Albania and Iraq, two upper-middle income countries, housing contributes about 20 percent of total household consumption. Yet, we cannot generalize this result to upper-middle income countries since Peru exhibits a rent share of 14 percent maximum. Rent shares vary according to the rent imputation method. In line with the expectation associated with the type of question used to collect self-assessed rental values, Albania is the only country where on average rental shares based on self-assessment are higher than those obtained with a log-linear model. However, this does not hold all along the distribution: the log-linear approach produces higher rent shares in the bottom three deciles. A similar pattern is recognizable in Bangladesh (2005), although the differences between the two imputation methods are smaller than in the case of Albania. In the case of Peru, under both methods, and in the case of Albania and Bangladesh, under the self-assessment approach, rent shares increase along the distribution. This is in line with findings from Blades (2009), whereby the share of housing in total consumption is positively correlated with GDP per capita. However, in the case

> 11 Bangladesh’s questionnaire does not specify the type of question asked by the enumerators.

> 12 Results of the log-linear hedonic models are reported in the Appendix.

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of Albania and Bangladesh, under the log-linear approach, and in Iraq with both methods, rent shares are a decreasing function of households’ consumption.

As a reminder to the reader, in the following analysis we report all results using also the official consumption aggregate (denoted in the tables that follow as _original_ ). The main tables are shown only for the most recent year, with the exception of shared prosperity, where both years are used, and poverty results for Bangladesh, where we show 2005 instead of 2010. This is because the 2005 HIES was used to update the official poverty line, and we were able to get hold and to modify the original code for this year.

# **4.1. Inequality**

The impact of including rent on inequality is assessed by looking at changes in the Gini index. Table 5 shows the Gini index calculated on the consumption aggregate without the rental component (first row) and the difference, in absolute value, between the initial Gini index and the value of the same indicator calculated on consumption aggregates that include imputed rents according to one of the two imputation methods, namely the self-assessment approach and the log-linear model.

Albeit always statistically significant, only in few instances the impact on inequality of including rents in the consumption aggregates is over one percentage point, although the exact magnitude of the changes varies across countries and for the same country across rent-imputation approaches. A notable exception is Iraq 2007 (Table 5, panel a), where we observe an increase of almost 3 percentage points in the case of the log-linear model relative to the case of no rent. In Albania and Peru, the increase in inequality is as large as 2 percentage points when the self-assessment approach is used. This is likely explained by the large variation introduced by selfassessed values of home-owners, who in most cases tend to overestimate the rental market price due to their attachment to the dwelling they own and in some cases they built (see Heston and Nakamura 2009 for the home-owner pride effect, and Ceriani, Olivieri, and Ranzani 2019 for a general discussion on the accuracy of self-assessment and ways to test it).

As for the sign of the impact, in most instances we observe an increase in inequality, in contrast with the rest of the literature where findings seem to build consensus around an equalizing effect of rent imputation (see Balcázar et al. 2017 for a recent review of the literature). Nevertheless, no general conclusion can be drawn: the sign of the impact varies across countries and for the same country across rent-imputation approaches. For instance, the Gini index increases in all countries in the first round of data (Table 5, panel a). In the second waves, instead, the Gini index increases in the case of Albania and Bangladesh using the log-linear approach, while it decreases in the case of Iraq using the log-linear method (Table 5, panel b). These findings seem to corroborate our hypothesis that the sign and magnitude of the rent imputation impact are an empirical question and no a priori theoretical conclusion can be drawn.

# **4.2. Poverty**

The analysis of the impact of rent imputation on poverty is ascertained following two different approaches. First, we show how poverty (as measured by the headcount, poverty gap and squared poverty gap indices) varies when the initial consumption aggregate, which excludes rent, is modified to include imputed rent and the poverty line is left unchanged. Then, we show the impact on poverty indices of including rent both in the construction of the poverty line and in the consumption aggregate.

As expected, poverty decreases if we keep constant the poverty line to the case of no-rent, independently of the rent imputation method. Table 6 shows in fact that the three poverty indices, i.e. incidence, depth and severity of poverty, decrease as a consequence of the shift to the right of the consumption distribution.

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Nevertheless, the practice of modifying the consumption aggregate while leaving the poverty line unchanged is inadvisable. For a sound poverty analysis, the poverty line and consumption aggregate should be drawn from the same welfare measure (see, for an extensive discussion on this issue, Lanjouw and Lanjouw 2001). In particular, the poverty line is typically composed of a food and a non-food component. A change in the welfare aggregate measured by adding rent should be accompanied by a similar adjustment of the non-food component of the poverty line.

Therefore, the effects of the different rent imputations on the consumption aggregates were re-assessed by modifying the official poverty line accordingly. As summarized in 11
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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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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aggregate, the choice of the most appropriate imputation method is not trivial, as different approaches generate households’ re-ranking along the welfare distribution within country and may potentially imply reshuffling in intertemporal and international comparisons. Therefore, all practitioners in charge of the preparation of welfare aggregates for distributional analysis should add to the list of sensitivity checks a careful examination of the distributional impact of different imputed rent methods, as proposed in this study.

This paper offers three main messages. First, the poverty estimation process must be internally consistent in terms of methodology. Most prominently, poverty lines should always be adapted to the definition of the welfare aggregate. Second, methodological consistency should be maintained over time, by using the same definition of welfare aggregate, including using the same rent-imputation approach. Trends in poverty, inequality and shared-prosperity risk otherwise to be fictitiously driven by differences in the adopted rentimputation approach. Third, methodological consistency should be sought internationally, after conducting an accurate sensitivity analysis of the distributional impact of different methods on a larger scale. Implementing these three key points calls for a coordination effort of researchers and practitioners involved in all stages of data collection and analysis: from the design of homogeneous questionnaires over time and across countries, to the construction of welfare aggregates allowing for consistent comparisons. In an effort to push forward the research agenda, new data sources may be explored to obtain more reliable and standardized estimates of housing quality and of rental prices. A promising avenue, recently applied in a study for Sub-Saharan Africa, could be the combination of high-resolution satellite photography with household survey data (Tusting et al 2019).

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