Poverty, richness, and inequality: evidence for Portugal using a housing comfort index

With data for Portugal we propose an index of housing comfort based on the Household Budget Survey. This index covers housing and durable goods grouped in two dimensions: basic comfort and complementary comfort. Taking this index as starting point we make two contributions. First we quantify the phenomena of poverty, richness, and inequality in housing comfort. Second, using an ordered probit model, we evaluate the determinants of housing comfort in Portugal. The results show significant rates of poverty (12.41%) and richness (22.03%). The evidence sustains that the differences between households derive mainly from complementary comfort and to a lesser extent from basic comfort items. Inequality in housing comfort, measured by the Gini coefficient, stands at 0.1263. The econometric study reveals that the region of residence of the household and the educational level and labor market state of the household reference person are among the most critical determinant factors of housing comfort.


Introduction
Theoretical and empirical attention to inequality, poverty, and more recently, richness has been a dynamic research field in the economic literature [1,2]. Critical to this emphasis is, obviously, the social importance of these phenomena and the consequent impact on policy agenda. The quality of the policy decisions critically depends on the correct evaluation and quantification of the phenomena [3]. This is usually grounded on well-established indicators of inequality and poverty (with the last ones also adapted for the case of richness).
Measuring these phenomena implies a vast range of methodological options. One of the most critical in this regard is the selection of the indicator of resources. In developed countries, where the majority of the empirical studies have been carried out, income and expenditure are the variables traditionally considered. However, this is due mainly to data restrictions as it is widely recognized that they are second-best proxies for measuring these critical social dimensions. As suggested by Cowell [1], wealth, lifetime income, and income are, in that order, the most adequate ones. Interestingly, this question arises with different contours in low-and middle-income countries, where income and expenditure data are in many cases unavailable, hard and expensive to collect, unreliable, or incomplete, thereby limiting the ability to adequately capture welfare trends.
Taking the considerations above into account, Montgomery et al. [4], Sahn et al. [5] and Filmer et al. [6] proposed the consideration of an asset based-approach. To that end, they create asset indices capturing dwelling infrastructures, building materials, and durable assets. These indices, extensively used since these pioneering contributions, can be seen as proxies for a household's welfare, long-run wealth, long-run economic status, permanent income, capabilities, and living conditions [7][8][9][10][11][12]. 1 One important reason for the recent popularity of this approach derives from the fact that, contrary to income or expenditure data, there are large databases for several years and countries regarding asset ownership (e.g., USAID-sponsored Demographic and Health Surveys). In addition, in several developed countries, the national household budget surveys include questions about this topic.
Of course, the consideration of asset indices as proxies for wealth is not immune to criticism. Two aspects are especially noteworthy. First, the data usually give us information only on the presence of goods and not on the ownership, except for the incurred expenditure in the reference period of the survey. Using the presence of goods as a proxy for asset ownership has the underlying assumption that the amortization of debts arising from consumption credit is achieved in the short-term. Second, the family's preferences regarding, for instance, the quality of the goods or the use of credit are not available in the surveys and therefore are not taken into account.
Even if we accept the gravity of these limitations, a measurement of poverty, richness, and inequality in terms of critical assets is still a valuable contribution to our knowledge of well-being. In this context, special attention is usually given to housing conditions since, as expressed by Navarro et al. [13], 'housing is undoubtedly one of the main components of material well-being' [p.597]. The idea that inequality, poverty, and richness depend on many dimensions of human life, including income, but also other aspects goes back to the seminal works by Townsend [14], Streeten [15], and Sen [16] and has recently received a great deal of attention. The list of areas already studied is long, covering dimensions such as health, education, time use, water, and food, among 1 For additional discussion on the roots of the asset-based approaches, see for instance Filmer et al. [9] and Ward [12]. others. Housing conditions can be considered through an analysis of this aspect and its multiple facets alone or through its inclusion in composite measures of well-being.
The present paper belongs to the asset based approach and, more specifically, assumes that access to house-related assets is a critical dimension of well-being. 2 More specifically, we consider a new concept, which we designate as "housing comfort". In this case the focus is put on house related variables, meaning that we try to capture, with the highest possible level of detail, the characteristics and quality of the house in which a household lives (both housing conditions and durables are taken into consideration).
As occurs in the dominant literature, we derive an index to measure this concept. In comparison to other asset indices, our indicator has two main differences. First, it is built from a much larger set of housing features (see McKenzie [8] for a proposal with the highest degree of similarity to the one we present here). On the other hand, it excludes assets that are related to the house.
This study uses microdata from the Household Budget Survey for Portugal (2005/2006) and proposes an index of housing comfort that covers housing and durable goods grouped in two dimensions: basic comfort and complementary comfort. Based on this index we establish two additional goals. First we characterize housing comfort in Portugal through measures of poverty, richness, and inequality based on a wealth measure. Second, we identify the main determinant factors of housing comfort. 2 The literature analysing the level of deprivation suffered by households also gives this level of attention to housing attributes [21][22][23]. Nevertheless, in this case, the analysis is concerned with the lack of access to basic conditions. Portugal is a very interesting case study because it is among the European countries with the highest levels of income inequality and poverty. According to the European Union Statistics on Income and Living Conditions (EU-SILC), in 2013 Portugal was the second country in the EU-15 with the highest level of inequality 3 (5th in the EU-28) and the fourth country in the EU-15 with the highest level of poverty 4 (9th in the EU-28).
Despite its importance and specificities, the Portuguese case has received little attention to date. Some studies have characterized poverty using income or expenditure, such as Rodrigues [24], Ferreira [25], Alves [26], Peichl et al. [27], Rodrigues et al. [28], and Crespo et al. [29]. Nevertheless, knowledge about the Portuguese case would benefit from studies capturing other features of wealth.
The remainder of the paper is structured as follows. Section 2 presents the index that supports the empirical analysis developed in the study. Section 3 discusses the measures of poverty, richness, and inequality in housing comfort. Section 4 presents the econometric model, and Section 5 performs a sensitivity analysis. Section 6 has some final remarks. 3 Gini coefficient of equivalised disposable income. 4 People at risk of poverty after social transfers(cut-off point: 60% of median equivalised income after social transfers).

Microdata from the Household Budget Survey (Inquérito às Despesas das Famílias
-HBS) carried out in 2005/2006 by Statistics Portugal has been used in this study. The HBS is a large survey focusing on gathering information from the Portuguese households on income and expenditure as well as detailed data about the characteristics of the housing, the households, and the individuals.
The Household Budget Surveys are among the most comprehensive household surveys applied in all Member States of the EU. The particular version adopted in each country contains some specific elements regarding the structure and the group of topics covered but is based on common methodological guidelines provided by Eurostat. For a more detailed discussion of this survey see, for instance, the Methodological Manual [30] or the Quality Report [31].
Concerning the Portuguese case, the HBS sample is composed of 10,403 households and 28,359 individuals. The survey is associated to a questionnaire including a log-book to be fulfilled by the selected private household. The information includes the whole set of collective and individual expenditures during two weeks.
Additionally, it is also collected (through interview) demographic data, income data and data on non-frequent consumed goods and services. In the sampling process, representativeness of monetary expenditure by region and product class was assured, through a strengthening of the sample in areas where non-response rates are more frequent.
Initial data management and file creation was completed using Microsoft Excel 2010 from Microsoft Office Professional Plus 2010. All software used in this paper were run on a Toshiba Qosmio F750 laptop equipped with an Intel ® Core TM i7-2630QM CPU, running at 2.00GHz with 8GB of memory, with Windows 7 32-bit Enterprise operating system.
In this study, the demographic unit is the household. The corresponding extrapolation coefficients are used as the weighting structure in determining the average housing comfort for all the households based on the sampling results. The use of simple averages based on sample observations would not be correct to make inferences about the population given the characteristics of the sample [32] and the calibration process associated with extrapolators [33].

The index
We start the empirical analysis by constructing an index of housing comfort for each household (hereinafter designated as  Table 1 presents the scores given to each element. In our baseline scenario we attribute a maximum score of 65 points to basic comfort and 35 to complementary comfort, for a total of 100 points (the best possible situation).
[Insert Table 1] sensitivity analysis in order to check the robustness of the conclusions. A preliminary exercise in this direction will be conducted in Section 5. Table 2 presents the effective (average) scores for the several items of housing comfort (disaggregation levels 1 -4). Additionally, with the aim of facilitating the interpretation of the results, column (3) shows the ratios between these effective scores and their potential maximum values (column (2), which corresponds of course, for each level of disaggregation, to the values already presented in Table 1). 5 [Insert Table 2] The evidence shown in Table 2  In order to get a more comprehensive perspective on this topic it is also interesting to explore the distribution of the housing comfort index (Figure 1). 5 The individual indices of housing comfort were calculated through Microsoft Office Excel 2007.
The distribution of the housing comfort index presented in Figure 1 was also obtained using this software.
[Insert Figure 1] The housing comfort index leads to a distribution whose minimum value lies at 2.25 and the maximum at 94.83, with a mean of 58.04 (as we saw in Table 2) and a standard deviation of 13.00. Approximately 20.0% of households show a comfort index less than 50.0 while about 20.0% show comfort indices above 70.0.

Measures
To measure poverty and richness, we first need to define poverty and richness lines.
A poverty line separates the poor from the non-poor, while a richness line sets the limit above which individuals are classified as rich. The key methodological option here is between absolute or relative lines. In the first case the thresholds are defined without reference to the pattern prevailing in the society. In the second case that reference is taken into account and thus the poverty and richness lines correspond to a given percentage of the average or median level of housing comfort in society. Following the most common option, we adopt a relative poverty line ( ) defining as poor a household with a housing comfort index below a given proportion ( ) of the median of . The richness line (δ) is obtained in a symmetric way, a rich household being one with a value for above that threshold.
We evaluate the incidence, intensity, and severity of poverty through the wellknown proposed by Foster et al. [34]. For α = 0, the poverty incidence is measured by the headcount index, applied to households, which gives us the percentage of poor households compared to the total number of households. With α = 1, the intensity of poverty is obtained, measuring the amount of housing comfort necessary to bring poor households up to the poverty line, divided by the total number of households. For α = 2, a greater weight is assigned to larger deviations in order to evaluate the inequality among the poor, capturing the concept of poverty severity. Therefore, we have: in which is the number of poor households and is the overall number of households.
Households at risk of poverty ( ) are obtained through the difference between the poverty incidences calculated for two different poverty lines: (i) z = ρ × median; and Regarding the evaluation of richness, we can conceive, with the appropriate adaptations, indicators similar to those used in the analysis of poverty to measure the corresponding richness dimensions (which we will designate as " , , and & ). The richness line (') is defined as: In conclusion, households are classified as having one of three possible housing comfort states (/ ): Finally, inequality is measured through alternative indicators: the Theil measures and the Gini index.

Evidence
The measures presented in Section 3.1 were applied to Portuguese data and the results are shown in the first column of Table 3. 6 [Insert Table 3] In this analysis, the following values were considered for the parameters: In order to provide a more detailed perspective, Table 3 also shows, in columns (2) and (3), the inequality, poverty, and richness measures applied to and . The most remarkable result that emerges from this evidence is the greater levels of inequality and poverty associated with . For example, it is possible to see that the incidence of poverty corresponds to 36.57% when we consider and only 4.78% when is taken into account. Considering this evidence together with the results for inequality measures makes clear the existence of a much more homogeneous distribution in the case of basic comfort.

Model and results
In order to complement the descriptive analysis conducted in Section 3, we now investigate the most important determinant factors of housing comfort states (/ ). Since this variable is classified into discrete categories that have an ordinal nature (1,2,3), the ordered probit model is a fairly used framework [36]. This model is based on a latent measure of housing comfort (/ * ) -a continuous and unobserved variable -which can be defined as a linear function of the observed explanatory variables (I) and a random error term (J) normally distributed with zero mean and unit variance: The value observed in / is determined by the value of / * : in which O and O & are thresholds to be estimated.
The probabilities associated with the possible values assumed by / are: where Φ is the standard normal cumulative distribution function. The parameters of the ordered probit model are estimated by the method of maximum likelihood.
The vector of explanatory variables (I) includes two groups of factors that are likely to affect housing comfort: household related variables (region of residence and household type) and household's reference person related variables (gender, age, education, and labor market state). The household's reference person is the individual with the largest proportion of the annual net total income of the household. Table 4 presents the definition of the explanatory variables and shows the estimation results.
These estimations were obtained using Stata/SE version 12. No special packages or code modules were used.
The final size of the sample used in this econometric exercise dropped to 10,396 due to the need to exclude households that did not respond to the questions supporting the explanatory variables.
[Insert Table 4] The changes in the probability levels of the dependent variable are also estimated, providing an interpretation of the impact of the independent variables (Table 5). These are measured relative to a reference case in which all the dummy variables are set equal to 0, allowing us to interpret changes in the probability of the housing comfort states for a change in a given parameter relative to the reference case. Since all the independent variables are dummy variables, the marginal effects correspond to a discrete change from 0 to 1 in the dummy variable. In the reference case the estimated probabilities of being poor, middle class, and rich in terms of housing comfort are 5.29%, 75.38%, and 19.33%, respectively.

Some further analysis
In the above sections we quantified the phenomena of poverty, richness, and inequality in terms of housing comfort in Portugal and analyzed their determinant factors. This was done through the consideration of a baseline scenario, which implies the assumption of specific values in order to obtain the poverty and richness lines as well as the weight given to basic and complementary comfort in the overall index.
However, obviously this is a subjective exercise that should be submitted to sensitivity analysis to test the robustness of the conclusions. This is the goal of the present section. Columns (4) to (7) from Table 3  Regarding the influence on the determinants of housing comfort, we now estimate the model presented in Section 4 to each of the four new scenarios. Tables 6 and 7 show the evidence.
[Insert Table 6] [Insert Table 7] Focusing on the major conclusions that can be drawn from a comparative analysis of these tables, there are four findings to highlight. Furthermore, the evidence sustains that the differences between households derive mainly from complementary comfort and to a lesser extent from basic comfort items.
To further understand which factors are most important in determining the probability of a household being poor, middle class, or rich in living conditions, an ordered probit model was estimated using two groups of explanatory variables: household related variables and household's reference person related variables.
Concerning the first group of variables, we conclude that: (1) there are important regional differences; and (2) households with children have higher probability of richness and lower of poverty. As for the impact of the characteristics of the reference person, the worst housing conditions occur when this person belongs to extreme age groups, has a low level of education, and is unemployed.
In order to assess the sensitivity of our conclusions to the methodological options concerning the definition of the poverty/richness lines and to the weights given to complementary comfort, we constructed four alternative scenarios and repeated the empirical analysis. The evidence obtained in this exercise points to two key points.
First, in qualitative terms the main conclusions remain valid in the four scenarios.
Second, there seems to be more sensitivity to changes in the lines than in the weights given to basic and complementary comfort.
The empirical results suggest the existence of a wide space for intervention in terms of regional, labor market, and education policies seeking to improve the welfare for the Portuguese population. Let us consider some of the most important potential actions.
First, the Portuguese population has for many years been below the European average levels in educational attainment, with a clear deficit in terms of secondary and tertiary education. Several governments have prioritized this issue and significant convergence has been achieved. However, the crisis that started to affect the country in 2008/2009, which culminated in the sovereign debt crisis and bailout program, helped to mitigate these efforts, prioritizing fiscal consolidation instead. Putting education back at the center of the economic policy is crucial to promote social cohesion. Second, the regional differences are in large part explained by specialization patterns. Living conditions seem to be better in regions more diversified in terms of economic activities.
A long-term strategy should be defined in order to explore the comparative advantages of these less developed areas, so that these populations can also seek and achieve higher levels of welfare. Third, another important action could be the promotion of