Social Welfare to of the housing choice policy.

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Social Indicators Research (2020) 147:501–516 https://doi.org/10.1007/s11205-019-02159-z

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O R I G I N A L R E S E A R C H

Refining the Monetary Poverty Indicators Under a Join Income‑Consumption Statistical Approach: An Application to Spain Based on Empirical Data

Antonio M. Salcedo1  · Gregorio Izquierdo Llanes2

Accepted: 13 July 2019 / Published online: 17 July 2019 © Springer Nature B.V. 2019

Abstract In the European Union poverty has been measured indirectly in a one-dimensional way from a perspective based on disposable income. This classical approach has certain limita- tions when representing such a complex phenomenon by means of a single variable, reach- ing sometimes a modest association with regard to other direct poverty measurements such as severe material deprivation rate. In this article we study the measurement of monetary poverty from a two-dimensional point of view favouring a perspective of complementarity rather than one of substitutability. The joint analysis of the monetary income and consump- tion distribution makes it possible to identify different association patterns between these two variables for individuals located on one side or the other of the respective poverty thresholds. Expenditure on housing that is a determining factor in lower-income house- holds and imputed rents that would be paid by the owner household of a dwelling, allow us to calculate an at-risk-of poverty rate which refines the link with material poverty in both temporal and spatial dimensions.

Keywords At-risk-of poverty · Material deprivation · Disposable income · Residual income · Sensitivity · Spain

1 Introduction

In recent decades monetary poverty has been measured, specifically, by means of the poverty risk rate based on disposable income (Atkinson et  al. 2017). This paradigm, generally accepted in the European Union (EU), has been reconsidered since the recent economic crisis, given that the indicators of severe material deprivation have shown more variation than the classical indicator of at-risk-of poverty, which in turn has led to

* Antonio M. Salcedo [email protected]

Gregorio Izquierdo Llanes [email protected]

1 Universidad Complutense de Madrid (UCM), Madrid, Spain 2 Universidad Nacional de Educación a Distancia (UNED), Madrid, Spain

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a lower degree of association between them. One way to solve this possible dysfunction is to understand that the relationship between income and consumption has been modi- fied by the existence of savings and/or by variations in debt service. This would lead to the need to measure the risk of poverty not only from the perspective of monetary income, but also from that of monetary consumption (Meyer and Sullivan 2017). Both visions of poverty have been accepted as valid by the UNECE in its recent Manual for the harmonized measurement of poverty (UNECE 2017).

In this sense, when applying the classical one-dimensional poverty measurement model based on income, some researchers have noted the existence of a relative modest association between the risk of poverty and material poverty (Notten and Guio 2018), when the latter is measured in terms of the proportion of individuals in a situation of severe material deprivation, taking into account both their degree of correlation (Notten 2016) and the intersection between the two subpopulations (Fusco et al. 2010).

Thus, if we focus specifically on the data for a selection of EU countries in 2016 included in Table  1, we see that the sensitivity of the risk of poverty with respect to severe material deprivation stands at only 36.4% in the case of Finland; in other words, approximately one in three of those in a situation of material poverty is at risk of mon- etary poverty but the other two material poor are out of risk of monetary poverty. The corresponding figure is similar in the case of Hungary (38.9%), while it increases for Italy (44.2%) and the United Kingdom (46.7%). In France around one out of two of those in a situation of material poverty is at risk of monetary poverty (a sensitivity of 51.1%), while the results indicate higher values in the cases of Spain (69.0%) and Ger- many (70.3%), the latter being the highest value of all the EU countries.

An additional debate exists regarding whether the monetary poverty paradigm, given that it is a one-dimensional measurement system, could be improved by incorporating other dimensions (Alkire et  al. 2015) in order to better represent such a complex phe- nomenon (Serafino and Tonkin 2017). A join statistical approach has been adopted at European level through the so-called Vienna memorandum on Income, Consumption and Wealth statistics, endorsed in 2016, which is consistent with the framework advo- cated by the Organisation for Economic Co-operation and Development (OECD 2013). At micro level, the memorandum promotes additional development and coordination of

Table 1 Intersection and sensitivity of the at-risk-of-poverty and severe material deprivation rate, year 2016. Source: Prepared by the authors based on Eurostat database—intersections of Europe 2020 poverty target indicators

Country At-risk-of-poverty rate (%) (a)

Severe material depriva- tion rate (%) (b)

Intersection of (a) and (b) (%) (c)

Sensitivity (%) (c/b)

Finland 11.7 2.2 0.8 36.4 Hungary 14.4 16.2 6.3 38.9 UK 15.9 5.2 2.3 44.2 Italy 20.6 12.0 5.6 46.7 France 13.7 4.5 2.3 51.1 Spain 22.3 5.8 4.0 69.0 Germany 16.5 3.7 2.6 70.3

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the main statistical data sources, especially EU-SILC, Household Budget Survey (HBS) and Household Finance and Consumption Survey (HFCS).

Concerning the integration of those variables, it is also worth noting that net wealth conditions the need for savings or the direct and indirect financing of consumption; this could explain the discrepancies between the income and consumption of some individuals. In any case, wealth, insofar as it is positive or negative, involves returns or debt service which affect income and/or consumption. In particular some authors have considered hous- ing expenditure as an explanatory factor of some situation of poverty risk (Yang 2018). The so-called income-ratio is a mainstream in the financial economy to measure accessibil- ity, based on linking the information of defaults to indicators constructed from the relative ratio between housing expenditure and household income (Bramley 2012), whose main weakness is that non-housing expenditures must represent a minimum proportion, which is not very applicable to households with incomes far from the average (Haffner and Hey- len 2011). But because of its potential applicability to the measurement of poverty, the alternative accessibility paradigm called residual income is particularly interesting (Stone 2006), which is based on quantifying the absolute level of the difference between income and housing expenses, relating this difference with what is estimated as a fair standard of living. Like the economy of poverty, the residual income approach has the main difficulty of quantifying this fair standard of living since it is different for each temporal and spatial reality (Li 2015).

Based on all previous introductory considerations, we attempt an initial approach to a two-dimensional model using the joint distribution of monetary income and consumption which, applied to the case of Spain, will provide the basis for the construction of an indi- rect estimator of monetary poverty which represents a refinement of the classical poverty rate.

2 Data and Methods

The classical approach to the measurement of monetary poverty has considered as at-risk- of-poverty those individuals whose disposable income in a year t is to be found on the left of what is known as the poverty line (Ravallion and Lokshin 2006). Thus, the monetary poverty risk rate is given by the proportion of individuals whose equivalent disposable income is below the poverty threshold (Lelkes and Gasior 2018). A percentage (p) of the median (Mdn) of the equivalent disposable income is normally used to define this poverty threshold. This percentage is conventionally set at p = 60% in the case of the EU (Atkin- son and Marlier 2010) even though the UNECE or the OECD recommend using values of p = 50% for international comparisons (OECD 2016). Methods of selection of p depending on their sensitivity and specificity with respect to material poverty have been analysed by some authors in order to draw optimal poverty lines (Salcedo and Izquierdo Llanes 2018).

Thus, if we denote the equivalent disposable income of the individuals of a country as Yd, the poverty line or threshold based on a percentage p of its median will be given by yline,p, calculated as follows:

The above calculation can be used for any other monetary variable, either income (Y) or consumption (C), by simply replacing the new income or consumption variable in Eq. (1).

(1)yline,p = p% ∗ Mdn (

Yd )

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Thus, for the purpose of this article, we will denote the poverty threshold of equivalent monetary consumption for p = 60% as cline,60.

At this point, and before extending a one-dimensional model to a two-dimensional model, let us consider the following proposition: “Let N be the total number of individuals in a country or region under study. Then the at-risk-of-poverty rate with p = 60%, which we denote in this article as Arop.RYd,60, is the value of the distribution function of the equiva- lent disposable income (FYd) evaluated on the poverty threshold (yline,60)”. Given that Arop. RYd,60 represents the proportion of individuals with an equivalent income below the poverty line with p = 60%, then:

Figure 1 shows the cumulative distribution function and the poverty risk rate of Spain calculated for the year 2017. This rate was 21.6% or, in other words, the risk of poverty rate Arop.RYd,60 is located in percentile 21.6 of the distribution function of Yd. In case of using p = 50% the monetary poverty rate is 15.7%.

Based on the aforementioned proposition, when considering a two-dimensional income- consumption variable we can immediately define a two-dimensional poverty risk rate as the value of the two-dimensional distribution function FY,C evaluated at the centroid deter- mined by the respective one-dimensional poverty thresholds, as follows:

From a methodological point of view, in order to validate the results of this model exter- nally, we will use the degree of association obtained by means of the different correlation coefficients with the rate of population suffering severe material deprivation, a direct meas- ure of poverty (Chzhen et al. 2016). In the EU, a person who cannot afford at least four of the following nine items (Rajmil et  al. 2015) is considered to be in a situation of severe material deprivation (Ayllón and Gábos 2017): to pay rent or utility bills; to keep home adequately warm; to face unexpected expenses; to eat meat, fish or a protein equivalent every second day; a week holiday away from home; a car; a washing machine; a colour TV; a telephone. The results of this indicator have been analysed by various authors with a view to suggesting possible improvements (Guio et  al. 2016). The parameters of sensitivity,

(2)

Arop.RYd,60 = number of individuals with Yd ≤ yline,60

N = P

(

Yd ≤ yline,60 )

= FYd (

yline,60 )

(3)Arop.RYC,60 = FY,C (

yline,60, cline,60 )

Fig. 1 Cumulative distribution function (FYd), poverty line (yline,60) and at-risk-of poverty rates (Arop.RY,60 and Arop.RY,50) in Spain, year 2017. Source: Prepared by the authors based on the Living Conditions Survey microdata

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specificity and accuracy, often used in the estimation of results using ROC curves (Fawcett 2006) are also applied to perform an internal analysis of poverty at the microdata level. The study uses empirical information from two main sources: the Household Budget Sur- vey (HBS) and the Living Conditions Survey (LCS) that is Eurostat’s equivalent of the EU- SILC. All the anonymized microdata files can be downloaded free on the website http:// www.ine.es/en/prody ser/micro datos _en.htm.

3 An Application to Spain

3.1 The Joint Distribution of Monetary Income and Consumption

We begin with the study of the joint distribution of the monetary income and consumption of Spanish households. Figure  2 shows the two-dimensional scatter diagram of these two vari- ables at microdata level obtained from the HBS with 2017 as reference year. This figure shows the representation of the 2D density lines. In the upper part and on the right, the marginal den- sity functions of income and consumption are also shown. The two poverty lines of net income (yline,60) and monetary consumption (cline,60) calculated with p = 60% have also been added. The inclusion of the two poverty lines makes it possible to visualize the two-dimensional

Area I: At risk of income and consumption poverty (10.5%). Area II: At risk of income poverty but out of risk of consumption poverty (10.8%). Area III: At risk of consumption poverty but out of risk of income poverty (8.8%). Area IV: Out of risk of income and consumption poverty (69.9%).

Fig. 2 2D-density scatter plot of equivalent net income and monetary expenditure, year 2017. Source: Pre- pared by the authors based on HBS microdata (2017)

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centroid (yline,60,cline,60) as the intersection of the one-dimensional income and consumption poverty thresholds, respectively. This, in turn, means the quadrant can be divided into four clearly differentiated areas.

In area I, all individuals are below the two poverty thresholds (yline,60,cline,60). Given that everyone in this zone experiences low levels of both income and consumption, a high degree of correlation between the risk of poverty and the rate of the population in severe material deprivation would be expected. In area II, individuals have a low level of income but their lev- els of monetary expenditure are medium–high, since they are located above the poverty line for consumption (cline,60). This situation could be related to the sale of household goods, the reduction of previously accumulated savings, indebtedness, family assistance or might even suggest the existence of informal or illegal shadow economy activities (Eurostat 2018). The individuals in area III have a low level of monetary expenditure but their income levels are medium–high since they are located above the income poverty line (yline,60). They could be saving and/or facing debt service. It should be noted that low levels of monetary consump- tion could be significantly affected by the different price levels (PPP) to be found in Spain’s autonomous communities (Salcedo and Izquierdo Llanes 2017), which could condition the measurement of the risk of poverty. Finally, the individuals in area IV have medium–high lev- els of income and monetary spending; they are all located above the two poverty lines. This situation indicates that these individuals are not at risk of poverty.

Given the existence of a high degree of association between household income and expenditure, it would be expected, a priori, that the percentage of people at risk of income and consumption poverty would be very high in relation to the total population in one or another risk. However, we observe that only 1 in 3 of those at risk of income or consumption monetary poverty (30.1%, total of areas I + II + III) is simultaneously at risk of income and consumption poverty (10.5%, area I); this seems to suggest an anomalous situation in the one-dimensional models of income or consumption poverty when these are considered separately.

Table 2 shows the correlation coefficients obtained between the proportion of people in a situation of severe material deprivation and the monetary poverty risk rates in Spain based on EU-SILC and HBS data. The period analysed spans the years 2008 to 2017, which is espe- cially significant since it covers the whole period affected by the recent financial crisis. It can be observed that the two-dimensional model offers a very high degree of association, sur- passing even the good results obtained from the one-dimensional models, in particular the standard used in the EU-SILC. Therefore, a two-dimension rate based on low income and low consumption could be a better monetary poverty indicator than low income or low consump- tion alone, which are the most prevalent approaches of relative poverty at present.

The results of this table and the joint distribution income-consumption suggest the possible existence of an indicator, based on a linear combination of the variables of income and con- sumption, which could offer a better approximation to the measurement of poverty than the one-dimensional classical indicator based exclusively on disposable income, as it is applied in the European Union among others. Following an analysis of the joint distribution of the equivalent income and monetary consumption in Fig. 2 and the poverty measurement results presented in Table 2, we proceed to a principal components analysis of the income and con- sumption data for 2017, which provides us with the following standardized linear equations:

It can be seen that the first principal component (PC1) provides an eigenvector on the diagonal of the first quadrant. In Table  3 we show the cumulative proportion of total

(4) {

PC1 ∶ 0.707 ∗ Y + 0.707 ∗ C

PC2 ∶ 0.707 ∗ Y − 0.707 ∗ C

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variability explained by this component (76.93%), which can be considered as significant and indicates that most of the two-dimensional variability is concentrated in this first com- ponent, that is, along the straight line on which standardized income and consumption are equal.

The second principal component (PC2), meanwhile, explains 23.06% of the remain- ing variability with a subtraction, indicating a contrast between net income and monetary expenditure; this could be interpreted as the different levels of monetary savings of house- holds. According to this second principal component, in the case of simultaneously low values of Y and C, the range of variation of savings (positive or negative) is also low; this in turn implies the existence of a low capacity of indebtedness of households and could result in situations of poverty and/or financial exclusion (Krumer-Nevo et al. 2017) affect- ing the financial well-being of households (Lee and Sabri 2017).

It should be pointed out, following on from the previous reflection, that there is a wide range of financial ratios for households calculated for different purposes (Harness et  al. 2008). The European Central Bank, for example, has considered various consumption- to-income ratios in the scope of the Household Finance and Consumption Survey (ECB 2016). Besides, in the framework of the EU-SILC, a transformation of disposable income is also frequently used by adding the imputed rents from the dwelling to the equivalent

Table 2 Direct and indirect poverty rates, period 2008–2017

Prepared by the authors based on the EU-SILC database (*) and HBS microdata (**)

Year Direct poverty measurement (%)

Indirect poverty measurement (%)

One dimension Two dimensions

Severe material deprivation rate*

Arop.RYd,60* Arop.RC,60** Arop.RYC,60**

2017 5.1 21.6 19.3 10.5 2016 5.8 22.3 19.0 10.3 2015 6.4 22.1 19.6 10.6 2014 7.1 22.2 19.1 10.7 2013 6.2 20.4 18.1 9.8 2012 5.8 20.8 18.2 9.1 2011 4.5 20.6 18.2 9.1 2010 4.9 20.7 18.6 8.8 2009 4.5 20.4 17.9 8.7 2008 3.6 19.8 17.8 8.3  Pearson corr. coef. 0.73 0.59 0.83  Spearman corr. coef. 0.68 0.61 0.88  Kendall corr. coef. 0.60 0.48 0.75

Table 3 Summary of principal components analysis, year 2017. Source: Prepared by the authors based on HBS microdata

PC1 PC2

Standard deviation 1.2404 0.6792 Proportion of variance 0.7693 0.2306 Cumulative proportion 0.7693 1.0000

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income (Törmälehto and Sauli 2013), in order to offer a complementary measure of mon- etary poverty; although imputed rents are not, by definition, part of equivalent income, it can be considered as an aggregate income in national accounting terms (Eurostat 2013). In this context and for the purpose of this article we denote as Yid the variable disposable income adding imputed rents and equivalised following the usual procedures.

Given that housing is usually purchased using a loan and, if income is not adjusted with financial expenses this could have the perverse effect that someone who bought a home with a loan of 100%, and whose imputed income was dedicated to servicing the loan, would be considered to have a greater income than just before buying the home, that coin- cides with the temporary moment when that person did not pay any mortgage although he or she could be facing the payment of a rent (Attanasio et al. 2012). This possible dysfunc- tion leads to the incorporation of the expenses related with housing, mainly debt service and rent, into the indicators used to calculate the at-risk-of-poverty. In addition, in the case at hand, the expression of the first principal component of the joint distribution of income and monetary consumption induces us to search for linear combinations, in the form of subtractions between income and consumption, in order to obtain the greatest variability possible.

Taking into account all of the above, we analyse the HBS to identify the item of highest monetary expenditure in the lowest income households, based on the international classi- fication COICOP (Berardi et al. 2017) which breaks down household expenditure into the following twelve groups: (1) Food and non-alcoholic beverages; (2) Alcoholic beverages, tobacco and narcotics; (3) Clothing and footwear; (4) Housing, water, electricity, gas and other fuels; (5) Furniture, household equipment and ordinary expenses for the maintenance of the dwelling; (6) Health; (7) Transport; (8) Communication; (9) Leisure, performances and culture; (10) Education; (11) Restaurants, cafés and hotels; (12) Miscellaneous goods and services.

Of these twelve groups, spending on group 4 (housing) is clearly the largest of all expenditure items in households with the lowest income. Table 4 shows the proportion of expenditure on housing (including rent, interest payments on mortgages, water, electricity, gas and other fuels) by income quintile in five European countries in 2015. We can see that the percentage of monetary expenditure associated with this group is around 40% of total expenditure for households in the first income quintile, while in the case of households in the top quintile this percentage decreases by between − 9.5 and − 15.3 percentage points.

It is clear that, unlike other COICOP items such as alcoholic beverages and tobacco, leisure and culture or eating out, this item of expenditure is obligatory for households and its high proportion in the lower income quintile clearly conditions the capacity to pay for other fundamental goods or services; this could be related to situations of severe material deprivation in low-income households.

Table 4 Percentage of monetary expenditure in housing, water, electricity, gas by income quintile (year 2015). Source: Prepared by the authors based on Eurostat database - Structure of consumption expenditure by income quintile and COICOP consumption purpose

Country Income quintile Diff. (p.p.)

Q1 Q5

Bulgaria 39.7 28.6 − 11.1 Finland 39.1 27.0 − 12.1 Germany 43.3 28.0 − 15.3 Hungary 46.1 31.0 − 15.1 Spain 38.6 29.1 − 9.5

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For all these reasons and based on the above results, we define the equivalised income characterized by expenditure on housing, which henceforth we will call Ydc, as the disposa- ble income of the household once the total expenditure on housing has been deducted; this latter figure is reflected in the EU-SILC at the microdata level and it has been recently used by Eurostat to calculate other poverty rates that differ from the standard use of Eq.  (1). This variable has also commonalities with the concept of residual income (Stone 2006). Finally, the equivalised imputed income characterized by expenditure on housing (Yidc) is also defined analogously to Ydc but adding imputed rents to the characterized income. In the next section we investigate whether the characterized income offers an improvement over the classical poverty risk estimator based solely on disposable income.

3.2 Refining the Classical Measurement of the Monetary Poverty

To check the quality of the estimation of the monetary poverty risk based on characterized income, we will take the last available year (2017) as our reference year and, using the classical estimator based on Yd and with p = 60% of the median, we will carry a compara- tive study of the poverty rates based on the three income variables previously presented in this paper, that is, Yid, Ydc and Yidc, and also with p = 60% of their respective medians according to Eq. (1).

Firstly, we verify that the areas under the ROC curve (López-Ratón et al. 2014) obtained with the variables Yd, Yid, Ydc and Yidc in 2017 are 0.82, 0.84, 0.83 and 0.84, respectively. It can be shown that the area under the ROC curve (AUC), which takes values between 0.5 and 1.0, is equivalent to that of the Mann–Whitney test (Hand and Till 2001). We can see that in this case Yid and Yidc offer the highest values of the AUC.

Our second test consists of an analysis -external and internal- of the temporal dimen- sion. Table 5 shows the proportion of individuals in a situation of severe material depriva- tion as well as the poverty risk rates obtained using the variables Yd, Yid, Ydc and Yidc for the decade 2008–2017.

Table 5 Severe material deprivation and at-risk-of poverty rates (%) based on variables Yd, Yid, Ydc and Yidc. Source: Prepared by the authors based on LCS microdata (2008–2017)

Year SMD rate Arop.RYd,60 Arop.RYid,60 Arop.RYdc,60 Arop.RYidc,60

2017 5.1 21.6 19.7 25.6 22.6 2016 5.8 22.3 19.8 25.8 22.6 2015 6.4 22.1 19.5 25.4 22.8 2014 7.1 22.2 19.9 26.1 23.5 2013 6.2 20.4 18.7 24.5 22.5 2012 5.8 20.8 19.0 24.9 22.3 2011 4.5 20.6 17.8 24.6 21.6 2010 4.9 20.7 17.6 24.3 21.6 2009 4.5 20.4 17.3 24.0 21.2 2008 3.6 19.8 17.1 23.6 20.7  Pearson corr. coef. 0.73 0.82 0.78 0.94  Spearman corr. coef. 0.68 0.80 0.74 0.91  Kendall corr. coef. 0.60 0.66 0.61 0.81

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It is observed that the monetary poverty rate derived from disposable income by add- ing imputed rents (Yid) is lower than the classical one, between − 1.7 and − 3.1 per- centage points. On the contrary, the disposable income characterized by expenditure in housing (Ydc) increased the rates from + 3.3 to + 4.1 percentage points. The inclusion of imputed rents in the characterized income (Yidc) offers more similar rates than the classi- cal indicator, with differences ranging from + 0.3 to + 2.1 percentage points. The corre- lation coefficients obtained are very high in all cases, although the variable Yidc offered very high values (0.94, 0.91 and 0.81).

The situation is similar when an internal study—at micro level—of the sensitivity, specificity and accuracy of the four variables over time is carried out. Table  6 shows that, in all cases, the characterized income is more sensitive than that of Yd, reaching a maximum of 76.2% in 2016; this is an indication that the intersection between the risk of poverty rate and severe material deprivation is greater with this variable. As far as specificity is concerned, the highest values are obtained when considering imputed rents only (84.6% in 2008 and 2009), that is, this variable offers the largest intersection between individuals that are not materially poor and out of risk of poverty, simultane- ously. Finally, the accuracy of the variable Yid is again the highest of the four cases considered, with a maximum of 83.8% in 2008. This table also shows that all sensitivity results for Yidc are greater than those for the classical Yd with p = 60%, reaching + 10.8 percentage points in 2011, while the specificity and accuracy are rather similar, around 80% every year.

Finally, as a third test, we studied the spatial dimension, focusing on the results cal- culated for the seventeen Spanish autonomous communities at the NUTS2 level with ref- erence year 2017. In the internal analysis, Table 7 shows the severe material deprivation and poverty risk rates obtained from the equivalent disposable income and the equiva- lent characterized income for all regions. To simplify this analysis, only the sensitivity (Se.) of the poverty risk rate with respect to severe material deprivation is used.

Table 6 Sensitivity, specificity and accuracy (%) with regard to the severe material deprivation. Source: Prepared by the authors based on LCS microdata (2008–2017)

2008 2009 2010 2011 2012 2013 2014 2015 2016 2017

Sensitivity (Se.)  Yd,60 57.8 58.8 58.9 53.9 57.9 56.0 63,1 62.0 69.6 63.8  Yid,60 62.3 58.6 59.0 54.2 59.7 61.1 64.1 64.7 69.9 62.6  Ydc,60 70.1 67.1 66.3 63.6 67.7 65.5 72.0 72.3 76.2 70.4  Yidc,60 68.3 66.5 64.2 64.7 65.3 65.9 70.4 70.6 74.1 68.7

Specificity (Sp.)  Yd,60 81.6 81.4 81.3 80.9 81.5 82.0 80.9 80.6 80.6 80.7  Yid,60 84.6 84.6 84.5 83.9 83.5 84.1 83.5 83.6 83.3 82.6  Ydc,60 78.1 78.0 77.8 77.3 77.8 78.2 77.4 77.8 77.3 76.8  Yidc,60 81.1 80.9 80.6 80.5 80.4 80.4 80.0 80.4 80.5 79.9

Accuracy (Acc.)  Yd,60 80.7 80.4 80.2 79.7 80.1 80.4 79.6 79.4 79.9 79.8  Yid,60 83.8 83.4 83.3 82.6 82.2 82.7 82.1 82.4 82.5 81.6  Ydc,60 77.8 77.5 77.3 76.7 77.2 77.4 77.0 77.5 77.2 76.5  Yidc,60 80.7 80.2 79.8 79.8 79.5 79.5 79.4 79.8 80.2 79.3

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The classical variable Yd offers low sensitivity in regions ES23 (Rioja) and ES21 (País Vasco) of only 23.2% and 35.7%. The inclusion of imputed rents Yid increases the sen- sitivity in eight of the seventeen autonomous communities, is unchanged in three and reduces in six. All sensitivity values improve significantly when the characterized equiva- lent income is considered. It is also noteworthy that in the autonomous communities ES13 (Cantabria) and ES24 (Aragón) the new variable reaches a sensitivity of 100%; that is, in these cases the maximum possible intersection is achieved. Besides, ES30 (Madrid) and ES43 (Extremadura) are the regions with highest and lowest GDP per capita in Spain respectively; they have a severe material deprivation rate rather similar (5.4% and 5.6% respectively, + 0.2 percentage points only) but the situation is quite different when check- ing the classical risk of monetary poverty (16.9% and 38.8%, that is, + 21.9 percentage points). After adding imputed rents the poverty rate doesn’t change too much in Madrid but in Extremadura the risk of poverty is reduced to 33.5%. If deducing housing costs, Madrid increases the monetary poverty to 22.7% and Extremadura to 41.0%. The com- bined effect of imputed rents and housing costs (Yidc) set the risk of poverty in 20.8% in Madrid and 33.7% in Extremadura, reducing the difference to + 12.9 percentage points. In this last case it is remarkable that the sensitivity is also increased to 71.4% in Madrid and 79.9% in Extremadura.

Regarding the analysis evaluated via different degrees of association, in Fig. 3 it can be observed that the correlation between poverty risk rates and severe material deprivation by regions is increased by using Yidc, with the coefficient of determination rising from 0.39

Table 7 At risk of poverty rates and sensitivity (%) with regard to the population on severe material dep- rivation, year 2017 (highest sensitivity values in italics). Source: Prepared by the authors based on LCS microdata

NUTS 2 SMD rate Yd,60 Yid,60 Ydc,60 Yidc,60

Arop.R Se. Arop.R Se. Arop.R Se. Arop.R Se.

Total 5.1 21.6 63.8 19.7 62.6 25.6 70.4 22.6 68.7 ES11 Galicia 2.4 18.7 80.9 16.6 77.5 20.3 80.9 17.8 78.7 ES12 Asturias 3.5 12.6 78.4 12.3 78.0 15.7 88.4 14.9 83.3 ES13 Cantabria 2.2 17.6 84.5 13.0 84.5 21.9 100.0 18.8 100.0 ES21 País Vasco 3.7 9.7 35.7 8.6 40.7 14.0 50.7 11.4 58.6 ES22 Navarra 0.3 8.3 68.3 8.4 68.3 11.6 88.3 11.4 88.3 ES23 Rioja 2.9 9.7 23.2 11.2 30.4 16.2 64.0 14.2 64.0 ES24 Aragon 0.5 13.3 88.6 10.2 88.6 16.0 100.0 12.4 88.6 ES30 Madrid 5.4 16.9 67.8 16.6 61.4 22.7 74.9 20.8 71.4 ES41 C. León 1.0 15.4 52.4 14.1 57.4 20.2 76.3 16.6 76.3 ES42 C. Mancha 4.4 28.1 50.6 26.9 38.8 31.6 57.5 31.1 48.8 ES43 Extremad. 5.6 38.8 64.5 33.5 70.8 41.0 75.0 33.7 79.9 ES51 Cataluña 5.0 15.0 60.0 13.3 54.3 20.2 66.9 18.5 66.0 ES52 C. Valenc. 7.4 25.6 64.3 24.2 65.0 29.1 67.2 25.4 66.9 ES53 I. Balears 6.9 21.3 61.2 23.8 64.0 28.6 64.6 26.8 64.0 ES61 Andalucia 5.2 31.0 71.1 27.5 77.1 33.8 80.1 28.4 74.5 ES62 Murcia 6.2 30.1 67.9 25.9 69.8 35.3 77.3 27.9 73.8 ES70 Canarias 13.6 30.5 58.0 25.9 52.7 32.2 59.0 32.1 62.0

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to 0.53, which means a greater proportion of variability which can be explained using the new variable. The Spearman and Kendall correlation coefficients, meanwhile, also improve from 0.69 and 0.51 with the classical poverty rate to 0.76 and 0.54 respectively with the estimator based on Yidc.

To conclude the analysis of the spatial dimension, Table  8 shows the poverty rates by degree of urbanisation. Severe material deprivation rate is higher in very populated areas (cities, 6.0%) than in medium populated or rural areas (4.9% and 3.7%, respectively). On the contrary, the classical at-risk-of poverty rate is lower in cities (19.2%) than in towns (22.1%) and rural areas (25.9%). The risk of poverty based on Yidc increases the poverty rate in cities (+ 1.9) and towns and suburbs (+ 1.3) but decreases the poverty rate in rural areas (− 1.0). The sensitivity is increased in all cases and, in this regard, it is worth noting that in rural areas the monetary poverty rate based on Yidc (24.9%) is lower than the classi- cal one (25.9%) but the sensitivity is increased + 7.0 percentage points (75.4%).

4 Conclusions

This study investigates the extension of the classical monetary poverty measurement to a two-dimensional approach, trying to refine the current link with material deprivation that is a direct poverty measurement. It broadens the classical one-dimensional disposable income model and makes it applicable to other monetary variables, for example monetary con- sumption, via the distribution function due to the fact that the poverty risk rate coincides with the value of this distribution function evaluated on the poverty threshold. Building from here, a two-dimensional poverty risk rate (income-consumption) based on the cen- troid determined by the respective one-dimensional thresholds is defined. This rate is seen

Fig. 3 At-risk of poverty rates (x-axis) and severe material deprivation (y-axis) by region, year 2017. Source: Prepared by the authors based on data presented in Table 7

Table 8 At risk of poverty rates and sensitivity (%) by degree of urbanisation, year 2017. Source: Prepared by the authors based on LCS anonymised microdata

Degree of urbanisation SMD rate Yd,60 Yidc,60

Arop.R Se. Arop.R Se.

1. Cities 6.0 19.2 63.3 21.1 68.0 2. Towns and suburbs 4.9 22.1 61.4 23.4 65.0 3. Rural areas 3.7 25.9 68.4 24.9 75.4 Total 5.1 21.6 63.8 22.6 68.7

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to show a stronger association in terms of correlations with material poverty than the two one-dimensional variables it is based on.

In this context the join distribution of monetary income and consumption at micro data level is explored, paying special attention to the left side of the distribution based on the two poverty thresholds that determine the centroid (yline,60,cline,60). The analysis of the two-dimensional poverty risk rate (income-consumption) makes it possible to determine two typologies. On the one hand, of those individuals whose consumption is more clearly linked to their income, both those who are located below both poverty thresholds (area I), and those whose levels of income and expenditure are above the two poverty lines should be considered (area IV). On the other hand, of those individuals with a less clear asso- ciation between income and consumption that, additionally, allow us to consider another two different situations: the first consists of individuals who have a low level of equivalent income but whose levels of monetary expenditure are above the consumption poverty line (that is, area II), which could conceal situations of consumption financed by means of pre- viously accumulated wealth, debts, family assistance or even informal economy activities, which would mean an infra declaration of income and that such individuals could not be really in a situation of material deprivation; the second would consist of individuals with a low level of monetary expenditure but whose income levels are medium–high since, in this case, they are to be found above the income poverty line (that is, area III), who are normally individuals facing debt service, usually a mortgage linked to home purchase. The interpretation of the latter situation provides an additional reason for the incorporation, with monetary variables, of the expenses and/or income related with net wealth as carried out in this study.

At this point we explore whether a linear combination of monetary income and con- sumption may offer a refinement of the classical approach to the monetary poverty. Since expenditure on housing is determinant in households in the first income quintile, and with the restriction of using empirical information based on official sources of statistics, the solution applied is to consider in the EU-SILC area the equivalised income characterized by expenditure on housing, with and without imputed rents.

The area under the curve obtained for Yd, Yid, Ydc and Yidc in 2017 are 0.82, 0.84, 0.83 and 0.84, respectively. These results are between 0.8 and 0.9 and can be considered as excellent (Mandrekar 2010) particularly in the cases of Yid and Yidc since they offer a slight improvement of the AUC compared to the classical Yd. Concerning the temporal dimension, which covers the decade 2008-2017, the associations measured via the cor- relation coefficients between severe material deprivation and the risk of poverty rates for this period offer better coefficients being obtained with the characterized income adding imputed rents, Yidc. The internal test at micro level, meanwhile, also throws up the result that, once again, Yidc has a greater sensitivity than the classical Yd (+ 10.8 percentage points in 2011) while the specificity and accuracy are always rather similar (around 80%). As far as the spatial dimension is concerned, the internal test is carried out via the analysis of the sensitivity of the indicator to severe material deprivation; when using the characterized income adding imputed rents Yidc this value increases in most of the autonomous commu- nities reaching the maximum intersection of 100% in some regions. On the other hand, the external test is carried out with the results obtained in the seventeen Spanish autonomous communities at the NUTS level and leads to the conclusion that the characterized income Yidc also increases the coefficient of determination and correlation with material depriva- tion. The results achieved are also more consistent when an analysis by degree of urbanisa- tion is carried out, particularly in the cases of rural areas and cities. We can therefore con- clude in this case that, from an empirical point of view, the poverty risk rate obtained using

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the equivalent characterized income adding imputed rents Yidc is an indicator that succeeds in refining the good results of the classical poverty risk indicator, in both its temporal and spatial dimensions.

Notwithstanding the good results achieved there are also some opportunities and limita- tions to be considered. The case presented in this study focuses the analysis in a country of the European Union and, at this stage, the conclusions should be limited to a context of complementary rather than substitutability of the classical Yd, which is an international standard. In addition, the applied approach is exclusively focused on monetary poverty var- iables in order to better measure the effect of the refinement, but it could also be extended by adapting the percentage p introduced in Eq.  (1) instead of considered it as a constant parameter defined by convention, 60% in the European Union, or by introducing other mul- tidimensional indicators to measure the poor, not only in developed countries (García-Pérez et al. 2016) but also by the different regions (Jurado and Pérez-Mayo 2012) and, especially, if regional purchase parities were applied to the equivalence scales. Influence of risk fac- tors of income poverty and severe material deprivation (Verbunt and Guio 2019) is another element that could be taken into consideration for widening the analysis. Finally, to be able to conclude a joint monetary income and consumption analysis it would be very interesting to have empirical data containing the two-dimensional patterns of households/individuals together with a direct measure of poverty, particularly severe material deprivation.

This study allows us to continue a line of research that seeks to improve the measure- ment of monetary poverty from a multidimensional perspective (Santos and Villatoro 2018), on this occasion by integrating the two visions of monetary poverty based on income and consumption according to UNECE, and also laying the foundations of a poten- tial conceptual convergence between residual income and characterized income indicators, with the consequent improvement of them.

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