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1 LIS Working Paer Series No. 648 Relative income change and ro-oor growth Marek Kośny, and Gastón Yalonetzky Setember 2015 Luxembourg Income Study (LIS), asbl

2 Relative income change and ro-oor growth Marek Kośny Institute of Alied Mathematics, Wroclaw University of Economics 1 Gastón Yalonetzky Leeds University Business School 2 Abstract Most methods for the analysis of distributional change rely on the changes in the income of a articular grou of eole, taking either the situation of this grou in the revious eriod, or the average change in the oulation, as reference oint. By contrast, we roose a measure of distributional change based on the comarison of a grou s wellbeing standard against a richer grou, thereby caturing a notion of change in relative income, which embodies the influence of others wellbeing on the judgment of the grou s own situation. The indices, and related relative income change (RIC) curves, are based on ratios of generalized mean incomes between two grous, which render them closely related to Zenga s inequality measures and Lorenz curve comarisons, when arithmetic means are used. We consider both relative and absolute income cut-offs for the grou artitions. Differences and similarities between our measures of relative income change and the Growth Incidence Curve are also discussed. These are highlighted in an emirical illustration on Euroean countries. Key words: relative income, income distribution, ro-oor growth JEL Codes: I31, J30 1 Institute of Alied Mathematics, Wroclaw University of Economics, ul. Komandorska 118/120, Wrocław, Poland, marek.kosny@ue.wroc.l 2 Leeds University Business School, The University of Leeds, Leeds LS2 9JT, UK, g.yalonetzky@leeds.ac.uk 1

3 1. Introduction Analyzing the attern of changes in income distributions rovide further knowledge as to the effects of economic rocesses. Above and beyond stating whether the level of income inequality has increased or decreased, the main urose of these analyses is to identify areas in the distribution of income in which changes of a given tye have occurred. Of articular interest in these studies is the situation of the oor whether (and how) their incomes grow, and whether economic growth is rooor or not (see for instance Kakwani and Pernia 2000, Dollar and Kraay 2002, Kraay 2006, Son and Kakwani 2008, Foster and Szekely, 2008; Deutsch and Silber 2011; Ferreira, 2012). Yet an identification of the attern of changes in the distribution of income is not limited to the area of low incomes. No less imortant are other areas, including the richest and the middle class. Arguably, their mutual relations can affect the stability of society, and the rosects of social tension (e.g. see Acemoglu and Robinson, 2009; Esteban and Ray, 2011). Assessing a attern of changes in the distribution of income deends on the ercetion of changes in the level of income. Among the roosed methodologies, two main streams can be identified: the relative and the absolute aroach (see, resectively, Ravallion 2004, Duclos 2009). Broadly seaking, they are distinguished with resect to the oint of reference used for the assessment of change in income: whether absolute or relative growth is required for assessing the change as beneficial for a given grou. This distinction is closely related to the way overty and inequality are measured. When an analysis is concentrated on satisfying basic needs, absolute growth of income is worth considering. This is of rimary concern for the oorest countries, where a large roortion of the oulation receives an income below the subsistence minimum (see Duclos 2009,. 38). Relative deendencies gain imortance in the case of develoed countries (Layard et al. 2010). Ensuring their own hysical existence still remains the most imortant issue for a certain grou of the oorest. But the assessment of an individual s (or household s) own relative situation, in reference to the situation of others, becomes an imortant factor. This direct assessment of the relative situation of different income grous is the basis for the measures roosed in this aer; by contrast to other measures commonly used in emirical analyses. Our measures do not describe an income change at a articular osition of the income distribution (as, 2

4 for examle, in the case of the Growth Incidence Curve, 3 which assesses the relative change in income for a given quantile) or a change in income of a grou of eole in comarison to the average change in the overall oulation (see, for examle, second-order ro-oorness; Duclos 2009,. 50). Our roosed measures reflect the change in the relative situation of two grous, telling us whether the situation of the first of them has imroved relative to the other. We argue that this aroach hels to incororate interactions between these grous. The increase in income of any erson has an imact on the others, esecially grous with similar incomes. For examle, if eole s own welfare assessments take into account the situation of others, then, arguably, the relative situation of the oorer grou (esecially slightly oorer) deteriorates in the case of an income increase in the richer grou. In this framework, an increase in the income of the oorer is, in fact, of relatively lesser worth, if the income of someone wealthier increased much more. Such a relative assessment of grous situation is of articular imortance in the case of countries with a high level of income inequality, but has also been emhasized as a otential roblem in the form of cometitive consumerism and its effect on subjective wellbeing (e.g. see Layard, 2011). Additionally, an imrovement in the situation of a grou of the richest eole, in comarison with the oorest, but also those with an average income, could mean the risk of rising social tensions and a decrease in the stability of the existing system (e.g. see Acemoglu and Robinson, 2009). Focusing on grous of eole is a key feature of our roosed measures. In contrast to analyses based on the Growth Incidence Curve, where only the situation of individuals corresonding to quantiles of a given order is actually considered, the roosed aroach is based on a direct comarison of the situation of grous, which can be exlicitly defined. In the case of the analysis of the relative situation of the oor, the comared grous are the oor and the non-oor. However, these grous can be distinguished within the oulation from the oint of view of any criteria: if adequately defined, they may, in articular, reflect the sociological concet of reference grous. This grou-oriented aroach does not necessarily mean a lack of interest in the income distribution inside these grous. Admittedly, we may want to account for the roblem of distribution of overty in our assessment of a growth attern. An equal treatment of oor eole in every osition in the income distribution would imlicitly assume a linear and continuous nature of overty, but the intensity of the overty exerience does not 3 See Ravallion and Chen (2003). 3

5 have to be a linear function of a overty ga. Desite an arbitrary (contractual) character of overty lines, 4 one could osit the existence of some thresholds below which living standards decrease substantially. This actual nature of overty is recognized in an extension to our roosed measure of a relative income change, in which we weigh oor incomes in a manner akin to Atkinson s inequality measures based on generalized means (Atkinson, 1970). As this rocedure rioritizes the wellbeing of the oorest, the roosed measures relate to the concet of inclusive growth (see Ali and Son 2007,. 12), the inability to articiate in subsequent asects of social life constitutes the thresholds discussed above. 5 Our measure of relative income change (RIC) comutes the difference in relative income between two eriods, where the relative income is defined by the income of the oor divided by the income of the non-oor, and the two grous are defined by a ercentile threshold. Additionally, we roose a RIC curve which lots the RIC index against each of the ossible grou-slitting ercentiles. We study the roerties of both the RIC measure and the RIC curve, and find that the latter s behaviour is closely related to the Lorenz inequality ordering. Likewise, our RIC curve is closely related to Zenga s family of inequality indices (Zenga, 2007). The aer is organized as follows. Section 2 introduces our measures of RIC, followed by the RIC curves, an extension emhasizing the exerience of the oorest among the oor, and an extension based on alternative definitions of the grous. We include a thorough discussion around the measures and curve s fulfilment of desirable roerties. Section 3 outlines the similarities and differences between the RIC framework and related methods. Section 4 develos the emirical illustration carried out for three grous of Euroean countries. Section 5 concludes. 4 Poverty lines are defined arbitrarily both if they are related to some summary statistics of income in the oulation (e.g. mean or median) and when they are defined as absolute values. A subsistence minimum can be given as an examle of the latter. According to the definition of this scale, nobody with a lower income should survive. Therefore, accounting for the sense of overty is given in the form of quasi-continuous weights, not defined for thresholds. 5 Kakwani and Son (2008) also weigh income growth rates by measures of overty intensity to construct their overtyequivalent growth rates. 4

6 2. Measure of relative income change Let be the income quantile for ercentile in eriod. 6 With we can slit the oulation into two contiguous, non-overlaing grous: a bottom grou (with incomes such that ) and a to grou (with with incomes such that ). Then we can define, resectively, the bottom and the to means: Then our measure of relative income change (RIC) between eriods and is defined as follows: (1) Note that, the relative size of the oorer grou, remains the same across eriods. Hence we are not using, for instance, an absolute overty line to divide the two grous in either eriod. We will consider this alternative as an extension in a section below. quantifies the absolute change in the average income of the oorer grou measured in relative terms as a ratio of the richer grou s average income. Besides, as long as, then clearly. Positive values of indicate an imrovement in the relative situation of the oorer grou. By contrast, being a relative measure, holds no information regarding the absolute situation of both grous. This means that even in the case of a decrease in overall income, the change can be considered favourable to the oor, e.g. if the decline among the richer is starker. The behaviour of can be further described by listing a set of roerties fulfilled by the index: Axiom 1. Scale invariance: if every value of is multilied by the same scalar in both eriods and then the value of remains unaffected. 6 In the next section of the aer, income will be used as a roxy for welfare. But it could be relaced with exenditure or any other measure of welfare (see Slesnick 1998). On a broader discussion on the alication of non-income variables see Grosse et al. (2008). 5

7 Axiom 2. Poulation rincile: Relicating every individual by the same number in both eriods does not change the value of. Axiom 3. Anonymity: No information excet for the income is taken into account when assessing the distributional change. Axiom 4. Focused monotonicity: if a erson who remains in the oorer grou in both eriods exeriences an increase in income between and. Axiom 5. Sensitivity to Pigou-Dalton transfers between individuals from different grous: if distribution is obtained from distribution by a Pigou-Dalton transfer involving a erson in ercentile in eriod together with a erson in ercentile in the same eriod. 7 Axiom 6. Insensitivity to Pigou-Dalton transfers within individuals belonging in the same grou: if distribution is obtained from distribution by a Pigou-Dalton transfer involving a erson in ercentile in eriod together with a erson in ercentile in the same eriod, such that either or. Axiom 4 through 6 summarize the main traits of sensitivity to distributional change exhibited by. whenever eole from the richer grou transfer income to eole in the oorer grou between the two eriod; whereas is insensitive to similar transfers when the two eole involved belong to the same grou. In the extensions further below we roose a modified version of which is also sensitive to intra-grou transfers in order to: 1) rioritize the wellbeing of the oorest among the oor; and 2) derioritize the wellbeing of the richest among the rich The RIC curve If we lot against across its whole domain we derive the RIC curve. Like the Growth Incidence Curve the RIC curve is helful in the analysis of ro-oor growth. In articular, the RIC curve enables detection of the size of the bottom segments of the oulation that benefit the most and least vis- 7 Note that fulfills this roerty even when one of the eole involved changes grou status in eriod as a consequence of the income transfer. 6

8 a-vis their richer comlementary counterarts. The differences between the Growth Incidence Curve and the RIC curve will be exlored further in section 3. The RIC curve satisfies axioms of scale invariance, anonymity and oulation rincile. In relation to the above axioms 5 to 6, the RIC curve behaves the following way: Axiom 7. Sensitivity to Pigou-Dalton transfers (between individuals from either different grous or within the same grou): if distribution is obtained from distribution by a Pigou-Dalton transfer. Note that the RIC curve does not satisfy the axiom of focused monotonicity since, deending on the choice of, the same individual exeriencing and increase in income may find himself either in the bottom grou or in the to one. Note also that axiom 7 is coherent with axioms 5 and 6. That is, when the Pigou-Dalton transfer involves ercentiles then, and. In fact, whenever, i.e. when the RIC curve is never negative and at least ositive for one value of, then distribution is less unequal than distribution according to any Lorenz-consistent inequality index. As the following roosition states: Proosition 1: if and only if for any Lorenzconsistent inequality index. Proof: Let be the Lorenz curve of distribution evaluated at ercentile, with being the mean of distribution. Then it is straightforward to show that: [ ] [ ]. Hence if and only if, i.e. if there is Lorenz dominance of over which imlies, and is imlied by, for any Lorenz-consistent inequality index Extensions: Prioritization of the oorest Placing a higher weight on the incomes of the oorest among the oor is a common trait of many overty measures, including the Watts index and any member of the Foster-Greer-Thorbecke family in which the normalized overty gas are raised to a ower higher than one. This way of 7

9 roceeding is meant to cature several related asects of the overty exerience, including low incomes limiting or even recluding articiation in a social life, negative imacts on health status due to lack of healthcare and roer food, etc. While an increase in the income of the oorest is unconditionally considered ro-oor, in the case of other distributional changes the answer does not need to be so obvious. For examle, the oorest can feel more derived as a result of the increase in the income of the richer oor (who are still oor after the change). Moreover, such a change in the distribution of income in some situations may cause an absolute worsening of the situation of the oorest, the growth of the urchasing ower of the oor as a whole can result in an increase in rices of some basic goods. Such mechanisms, however, are not necessarily reflected in the usual measures. In order to rioritise the situation of the oorest members of the oulation, we roose a weighted analogue of relying on generalized means. Hence we follow an aroach akin to Foster and Szekely (2008), which in turn draws insiration from Atkinson s inequality indices (Atkinson, 1970). For this urose we start by defining the bottom and to generalized means: [ ] [ ] Then we redefine the measure of RIC as a function of the two arameters and : (2) Now we consider the following axiom of rioritization of the oorest among the oor: 8

10 Axiom 8. Prioritization of the oorest among the oor: if distribution is obtained from distribution by a Pigou-Dalton transfer involving a erson in ercentile in eriod together with a erson in ercentile in the same eriod. It turns out that we can derive a whole family of RIC measures which lace higher weight on the oorest incomes by focusing on the indices, i.e. with. Proosition 2 identifies the sub-domain of for which satisfies axiom 8, in addition to axioms 1 through 5, lus an amended version of axiom 6 (since now is only insensitive to within-grou Pigou- Dalton transfers among the richer grou): Proosition 2: satisfies axiom 8 if and only if. The roof is straightforward Extensions: Prioritization of the oorest and de-rioritization of the richest We can also combine a rioritization of the oorest among the relatively oor grou with a derioritization of the wealthiest among the relatively rich grou. With this urose we comlement axiom 8 with axiom 9: Axiom 9. De-rioritization of the wealthiest among the rich: if distribution is obtained from distribution by a Pigou-Dalton transfer involving a erson in ercentile in eriod together with a erson in ercentile in the same eriod. Finally, Proosition 3 identifies the sub-domains of and for which satisfies axioms 8 and 9, in addition to axioms 1 through 5. Now the combined fulfilment of axioms 8 and 9 relaces the satisfaction of axiom 6. In other words, axiom 6 is incomatible with the joint axioms 8 and 9: Proosition 3: satisfies axioms 8 and 9 if and only if. The roof is straightforward Extensions: Alternative divisions of the grous In the revious sections our RIC measures define the oor and the non-oor in relative terms, by setting a ercentile cut-off. Alternatively we can also identify the oor and the non-oor in absolute terms, using a 9

11 redetermined overty line,, from the admissible domain of income. Then we can construct measures akin to the aforementioned. However, generally, the measures based on absolute overty lines will differ, from those based on ercentile cut-offs, in that their value does not only deend on the changes in the income shares of the two grous, as is the case of in (1) for instance, but also on the changes in the overty and non-overty headcounts. For examle, we can roose an index as an alternative to. In order to do so, firstly, we define the overty headcount in eriod :. We also need to redefine the bottom and to means in terms of the headcounts: Finally, we define the index: (3) It is easy to show that satisfies the same axioms as. Moreover we can define a similar RIC curve by lotting against the domain of and derive results similar to Proosition 1. Perhas more interesting in is its straightforward decomosition into changes in the share of income accruing to the oor and changes in the overty headcount: (4) Where: (a) and is the share of total income held by the oor in eriod. (b). (c) (d) 10

12 Since satisfies the same axioms as, when we use absolute overty lines then we can relate imrovements in our measure of ro-oor growth based on changes in relative income share to two key comonents: changes in the overty headcount and changes in the share of income held by the oor. Ceteris aribus, any reduction in the roortion of oor eole increases the value of, thereby reflecting a ro-oor growth exerience. Likewise, any increase in the share of income held by the oor, ceteris aribus, roduces the same effect in. Moreover, a reduction in the roortion of oor eole accomanied by an increase in the share of income held by the oor, for every choice of renders. That is, if distribution both first-order and Lorenz dominates distribution then the mean of the oor relative to the non-oor increases for every choice of overty line. However the reverse is not true, i.e. could still be ositive if either or (but not both simultaneously) is negative, as long as the other comonent is ositive and more than offsets the effect of the negative comonent on. 3. A numerical illustration In order to highlight some roerties and features of the roosed measures, we resent a numerical hyothetical illustration in Table 3.1. and denote the incomes of erson i in the initial and final eriod, resectively. one of three scenarios of change: We consider three alternative scenarios for the final income distribution: A, B or C. Final incomes in scenarios B and C are the same as in scenario A, with the excetions of (scenarios B and C) and (scenario C). The differences are highlighted in bold font. For each scenario we comute, together with the oular Growth Income Curve (GIC; Ravallion and Chen, 2003) for comarison. For scenarios A and C we also reort. Their resective values are in Table

13 Table 3.1. Emirical illustration: and GIC. i Initial income (x i 0 ) Final income (x i 1 ) Scenario A Scenario B Scenario C GIC ( ) Final income (x i 1 ) GIC Final income (x i 1 ) GIC ( ) Figure 1 resents the GIC and RIC curves for scenario A. The GIC shows all ositive growth rates that are smaller for higher initial incomes. Naturally, the RIC describes this situation with ositive and increasing values: the situation of the lower grou has imroved with resect to the uer grou, irresective of the ercentile choice for grou artition. Yet the RIC curve more directly shows that the relative benefits from income growth rise with. GIC RIC Fig. 1. GIC and RIC curves for scenario A. 12

14 Figure 2 shows the RIC curves for the three scenarios: RIC Scenario A Scenario B Scenario C Fig. 2. RIC curves for scenarios A, B and C. Scenario B differs from A only in the income of, which rises from 4 to 6.50; whereas in A income growth for is smaller, from 4 to Until the RIC curve of A is slightly above B, but then from onward a sike favouring B is rominent. This advantage over scenario A, due to the imrovement in the situation of the third erson, remains throughout until, but decreases as the size of the bottom grou increases (thereby rendering the income of the third erson relatively less imortant in the comutation of the overall mean). Scenario C differs from B only in the income of (101 in C against in scenarios A and B, in the final eriod). Comaring C against A, only the income growth situation of two individuals has changed, but in fact, such changes affect the situation of the others, by modifying the relative means of the two grous. The RIC curve of C is above A s between roughly and. During this interval, the gain in the third income contributes more to the bottom grou s mean than the gain in the 15 th income does to the to grou s mean. However ast, the relative contributions are reversed and the RIC of C falls below A s. Finally, once both the third and the 15ht erson belong to the oorer grou (i.e. for ), the RIC curve of C remains ermanently above A s. These dynamics cannot be easily observed in the individual aroach imlicit in the GIC curves, as it rules out any judgments of relative income or welfare measurement interactions across individuals/households. 13

15 The recise scoe of the changes which result from an increase in the income level of given individuals deends, naturally, on the rioritization of eole within the grous. For examle, Figure 3 shows RIC curves for scenarios A and B with two choices of : RIC Scenario A (alfa=0.3, beta=1) Scenario C (alfa=1, beta=1) Scenario C (alfa=0.3, beta=1) Fig. 3. RIC curves with different values of for scenarios A and C. Note how a lower choice of flattens the RIC curve of C. This means that the growth in the income of the third erson is less imortant with a lower when the third erson is among the least oor of the oor (e.g. when ), however as more eole join the ranks of the bottom grou and the third erson is somehow sent to the rear, i.e. richer eole join in, then the contribution of the income change of the third erson increases. This latter increase is significant enough to comletely offset the effect of the growth in the income of the 15 th erson, to the oint that the RIC curve of scenario C with is never below the RIC curve of scenario A with the same (which features lower growth in the income of the 15 th erson). 4. Emirical results for some Euroean countries We now use, along with the GIC, in order to assess the attern of growth for some of the countries covered by the Luxembourg Income Study Database (2012). The available data generally come from national household budget surveys (excet for Denmark, where the data are taken from the tax register). The harmonization of national datasets is comleted before making the data available. 14

16 However, full harmonization is not ossible due to the differences between the analyzed countries (fiscal systems, education etc.). Such discreancies should not, however, significantly influence the resented results because the basic comarison between the oor and the non-oor is made within the same dataset (for a given country and year). The largest set of countries in this database is available for the so-called Wave 6 (around 2004). Wave 5 (around 2000) rovides the initial eriod reference oint. 8 The analysis is based on disosable income. Variable di denotes net income (gross income minus income taxes and mandatory ayroll taxes GI-(PAYROLL+V11) for gross datasets and net income GINET for net datasets) er household. Each household is assigned the erson weight in order to adjust for the structure of the oulation and the number of individuals in the household. A detailed descrition of the data and the recise definitions of variables (comonents and structure) are rovided by the LIS Data Centre on the roject website: htt:// GDP growth in the eriod under consideration was mediocre, both in advanced economies and in the whole world (see World Economic Outlook Database 2013). The burst of the dot-com bubble resulted in an economic slowdown after the raid growth of the late 1990s. The analysis was carried out taking into account the geograhical location of countries (this factor was widely considered, among others, during the next crisis which began in 2008). Countries from southern and northern Euroe, available in the LIS Database for selected years, were considered. Two countries from central Euroe (Luxembourg and Switzerland), whose economies largely deend on the financial sector, were also included. 8 Minimum 4-year distance between the beginning and the end of the analyzed eriod is required. Only datasets available in the LIS Web Tabulator were taken into account. We used average incomes corresonding to consecutive deciles grous. 15

17 GIC, RIC Italy GIC RIC GIC, RIC Greece GIC RIC GIC, RIC Sain GIC RIC Fig. 4. GIC and RIC curves between Wave 6 (around 2004) and Wave 5 (around 2000) for three southern Euroean countries. In the southern Euroean countries analyzed, differences in income between the oorest (first quintile of the income distribution) and the rest of the oulation decreased slightly, indicating a rooor change. In Italy and Greece, the RIC values (for the eriod ) decreased with income. This denotes the kind of change which is favourable not only for the oorest, but also for the richest in the oulation, as the distance between the richest and the middle-income grou has increased in the eriod analyzed. A different attern of changes was observed in Sain. Changes which are relatively favourable to the oorest (in relation to the rest of the oulation) were accomanied by a significant imrovement in the relative situation of the uer-middle-income grou (see the rising RIC curve for Sain in Figure 4). The strictly relative nature of this imrovement is emhasized by the negative values of the GIC, which means a decrease in nominal income. 16

18 GIC, RIC Finland GIC, RIC Denmark GIC RIC GIC RIC GIC, RIC Norway GIC, RIC Sweden GIC RIC GIC RIC Fig. 5. GIC and RIC curves between Wave 6 (around 2004) and Wave 5 (around 2000) for northern Euroean countries. A different direction of change in the situation of the oorest was observed in several northern Euroean countries. Figure 5 shows negative values for the RIC curve in the cases of Finland, Denmark and Norway. These negative values were observed also for higher values of, which indicates an increase in income inequality and the relative imrovement only in the situation of the wealthiest. The excetion among the Scandinavian countries was Sweden, whose RIC curve was consistently ositive. The highest values in its lower art suggest that the imrovement in the relative situation was the highest for the least affluent grou. In contrast to the other three country-cases, the robustly ositive values of the RIC curve in Sweden denote a reduction in Lorenz-consistent inequality. GIC, RIC Luxembourg GIC, RIC Switzerland GIC RIC GIC RIC Fig. 6. GIC and RIC curves between Wave 6 (around 2004) and Wave 5 (around 2000) for Switzerland and Luxembourg. 17

19 A different attern of change was observed in the case ofluxembourg and Switzerland, which is why they were analyzed as a searate, central Euroean grou. Their common feature is the large deendence of their economies on the financial sector. The distinctive feature of these countries (against those reviously analyzed, as well as others which are available in the LIS Web Tabulator) is a local decrease in income for the grou below the median (see GIC in Figure 6). In this situation, inference about attern of income growth on the basis of GIC can be confusing. Desite the increase in the income of the oorest grous (ositive values of GIC), the overall change should be considered anti-oor (negative RIC values) in relative terms. All RIC values for Luxembourg are negative and this indicates a relative imrovement only in the situation of the richest, whereas RIC values for Switzerland grew with the increase in income which denotes that the uer-middle-income grou is the most favoured. The results show that the use of RIC curves allows a relatively unambiguous assessment of the nature of changes in the distribution of income (such an identification can be much more difficult using GIC). It also allows for the assessment of changes in the relative situation of the richer and oorer grous. We observed, for three Scandinavian countries and Luxembourg, a deterioration in the situation of the oorer comared to the wealthier individuals (RIC takes only negative values) which imlies an increase in income inequality. Considering the otentially negative consequences of such changes (e.g. increase in social tensions), it is worth noting that these countries are characterized by very low levels of income inequality (according to LIS data, the value of the Gini coefficient for these countries is between 0.23 and 0.28), significantly lower than for the analyzed countries from the south of Euroe ( ). Verification of the hyothesis that these factors are interrelated, and eriods of economic downturn are characterized by ro-oor changes in countries with a relatively higher income inequality and anti-oor changes in countries with lower income inequality, would require a much broader analysis. 18

20 5. Conclusion Identifying a attern of changes in the income distribution can be a crucial element in the rocess of designing a social olicy. Ideally a distributional assessment should not just comly with some formal statistical requirements, but should also reflect individuals ercetions of distributional change including those ertaining to relative income. The roosed relative income measures are insired by Zenga s inequality index. The essential element of this aroach is the direct comarison of income across subgrous in the oulation. For a ro-oor assessment, the grous are made u of the oor and the non-oor. Such a direct comarison reflects the general idea of a reference grou; albeit, admittedly, in a restricted way as the basis of differentiation between grous is mainly uni-dimensional (e.g. income or another single measure of welfare). In addition to the relative income change index, we introduce a Relative Income Change (RIC) curve, while showing both how it relates to Lorenz inequality comarisons, and how it comlements and differs from the oular Growth Incidence curve. We also rovide several interesting extensions of the relative-income-change measurement framework. Firstly, we show how the RIC indices can be amended to rioritize the oorest among the oor, thereby caturing the non-linear relationshi between the overty ga and the actual situation of the oor. Likewise we show how the RIC indices can further be amended to de-rioritize, or enalize, income gains accrued by the richest among the rich. Finally, we roose a RIC index, and curve, based on grou artitions driven by absolute income cut-offs (e.g. absolute overty lines). We show that these indices are affected both by changes in the roortion of oor eole and in the share of income held by them. Thus this form of RIC index highlights that ro-oor distributional change can manifest in two different, but related, ways. A key feature of all these measures is their intuitive interretation. They reflect changes in the relative situation of the oor vis-a-vis the non-oor: ositive values denote a ro-oor develoment, while negative values reflect anti-oor scenarios. Finally, our roosals rovide a method to acknowledge and quantify otential externalities in the assessment of welfare across eole. In our framework, the income growth rate at one articular ercentile is not only intrinsically imortant, but also affects the relative shares of grous defined with 19

21 different criteria, and therefore ercetions of relative income change. The chosen criterion for grou artition does affect how the income growth exerience of any given ercentile contributes to the evaluation of relative income change; yet, as we show above, our RIC curves are helful in inointing the circumstances under which the exerience of ro-oor (or not) relative income change is robust to the varying artitioning criteria. Acknowledgements We would like to thank Jacques Silber and the anonymous referees for helful comments and suggestions. Marek Kos ny would like to acknowledge the financial suort of Polish National Science Centre (Grant No. 3804/B/H03/2011/40). Any remaining errors are our own. References Acemoglu, D. and Robinson, J. (2009) Economic origins of dictatorshi and democracy, Cambridge University Press. Ali, I., Son, H. (2007), Measuring Inclusive Growth, Asian Develoment Review, 24, Atkinson, A. (1970) On the Measurement of Inequality, Journal of Economic Theory, 2(3): Deutsch, J., Silber, J. (2011), On Various Ways of Measuring Pro-Poor Growth. Economics: The Oen-Access, Oen-Assessment E-Journal, 5, (htt://dx.doi.org/ /economics-ejournal.ja , ). Dollar, D., Kraay, A. (2002), Growth is Good for the Poor, Journal of Economic Growth, 7, Duclos, J.-Y. (2009), What is Pro-Poor?, Social Choice and Welfare, 32, Esteban, J. Ray, D. (2011), Linking conflict to inequality and olarization, American Economic Review, 101: Ferreira, F. (2012) Distributions in Motion: Economic Growth, Inequality, and Poverty Dynamics, chater 13 in Jefferson (editor), The Oxford Handbook of the Economics of Poverty, Oxford University Press. Foster, J., Greer, J., Thorbecke, E. (1984), A Class of Decomosable Poverty Measures, Econometrica, 52, Foster, J., Szekely, M. (2008) Is Economic Growth Good for the Poor? Tracking Low Incomes Using General Means, International Economic Review, 49(4): Grosse, M., Harttgen, K., Klasen, S. (2008), Measuring Pro-Poor Growth in Non-Income Dimensions, World Develoment, 36(6), Kakwani, N., Pernia, E. (2000), What is Pro-oor Growth?, Asian Develoment Review, 18(1), Kakwani, N., Son, H. (2008), Poverty Equivalent Growth Rate, Review of Income and Wealth, 54, Kraay, A. (2006), When is growth ro-oor? Evidence from a anel of countries, Journal of Develoment Economics, 80(1), Layard, R., Mayraz, G., Nickell, S. (2010) Does relative income matter? Are the critics right?, chater 6 in Diener, E., Kahneman, D., Lelliwell (editors), International Differences in Well-Being, Oxford University Press. Layard, R. (2011) Hainess: Lessons from a New Science, Second edition, Penguin. LIS Web Tabulator (2013), htt:// Luxembourg, LIS. Ravallion, M. (2004), Pro-Poor Growth: A Primer, World Bank Policy Research Working Paer, Ravallion, M., Chen S. (2003), Measuring ro-oor growth, Economics Letters, 78, Slesnick, D. (1998), Emirical Aroaches to the Measurement of Welfare, Journal of Economic Literature, 36, Son, H., Kakwani, N. (2008), Global Estimates of Pro-oor Growth, World Develoment, 36(6), Temkin, L. (1993), Inequality, Oxford University Press, Oxford. World Economic Outlook Database (2013), htt:// Washington D.C., International Monetary Fund ( ). Zenga, M. (2007), Inequality curve and inequality index based on the ratios between lower and uer arithmetic means, Statistica&Alicazioni, 1,