Explaining and Comparing

Transcription

1 ACES EU CENTERS OF EXCELLENCE GRANT AY DELIVERABLE GWU Explanng and Comparng AY Practcal Modfed Gn Index Amr Shoham (wth M Malul, Danel Shapra)

2 Practcal Modfed Gn Index M Malul, Danel Shapra and Amr Shoham Abstract The Gn ndex s the most common method for estmatng the level of ncome nequalty n countres. In ths paper we suggest a smple modfcaton that taes nto account the moderatng effect of n-nd government benefts. Unle other studes that use mcro level data that s rarely avalable for many countres or over a perod of tme, the proposed modfed Gn ndex could be calculated usng just the regularly avalable data for each country. Such data ncludes the orgnal Gn coeffcent, government consumpton expendtures, GDP and total tax revenue as a percentage of GDP. Ths modfed verson of the Gn ndex allows us to calculate the level of nequalty more precsely, and mae better comparsons between countres and over tme. Key words: Inequalty, Gn ndex, n-nd benefts, government consumpton JEL Classfcaton: H1, I3 2

3 1. Introducton The Gn coeffcent s a popular and wdely-used ndex for measurng nequalty (Lerman and Ytzha, 1984). Evdence for the OECD countres ndcates that there has been a sgnfcant and wdespread ncrease n ncome nequalty durng the past 20 years (Chapell et al., 2009; OECD, 2008). When nequalty s measured n terms of dsposable ncome, the rse was more modest than t s when comparng maret ncomes, whch ndcates that the tax and socal transfer systems do serve to redstrbute ncome towards the poor (Chapell et al., 2009). We argue that the redstrbuton role played by the government through the provson of publc servces s sgnfcant, and should be taen nto consderatons when calculatng the Gn ndex (see also Stac, 1978). Neglectng publc, n-nd benefts when measurng ncome mght gve an ncomplete pcture of the dstrbuton of economc nequalty (Aaberge et al., 2010) because n-nd benefts such as educaton, health nsurance, and other publc servces actually consttute approxmately one-half of the welfare state transfers n developed countres (Atnson et al., 2002; Garfnel et al., 2006). We suggest a smple, practcal modfcaton to the tradtonal Gn ndex that can be calculated usng the aggregate data publshed for each country. Let us assume two countres wth the same Gn ndex, one where the government provdes more nnd benefts (educaton, healthcare, socal servces, securty, etc.) than the government of the other provdes. We argue that the actual level of nequalty wll be lower n the country whch provdes more n-nd benefts. Snce the dstrbuton of n-nd benefts s based toward the low ncome famles, the tradtonal Gn ndex that does not consder the redstrbuton generated by n-nd benefts wll be based upward. Sefton (2002) shows that poorer households receve a greater proporton of non-cash welfare benefts than rcher households. Nolan (1981) found that the value of non-cash benefts (such as 3

4 medcal servces, housng and educaton) appeared relatvely stable across ncome groups, fallng only margnally as ncome rose. Nolan and Russell (2001) loo at a range of non-cash benefts n Ireland, ncludng the free schemes, such as free travel, free electrcty etc. They found that the medcal card scheme was strongly concentrated towards the bottom end of the dstrbuton wth 61 percent of medcal card spendng gong towards the bottom 30 percent of the ncome dstrbuton. Callan and Keane (2009) showed that the overall pattern of redstrbuton through publc health and educaton s pro-poor. Aaberge et al., (2010) showed that ncluson of noncash ncome (educaton and healthcare) reduces nequalty by percent. He used detaled data regardng the allocaton of the publc n-nd benefts among the dfferent ndvduals n the economy. Ths approach maes t almost mpossble to generalze for all countres and dfferent years. Ths paper offers a generalzaton of ths approach that uses aggregate data that s avalable for each country. In the next secton, we present the calculaton approach of the modfed Gn (MGINI). Then, we llustrate our approach usng recent data for the Gn ndex for the OECD countres and conclude the paper n the last secton. 4

5 2. The modfed Gn ndex Let us consder y( ) as the accumulated ncome of the percentle. In that case the Gn ndex would be: 1 Gn 1 2 y( ) d (1) 0 y I 1 y( ) N I 1 I I 1 where represents the percentle of the households wth ncome less than the ncome of the N th household, and N represents the total number of households. Now, let us add the provson of publc servces and assume that Iˆ I G N, where G s the total n-nd benefts provded by the government. In ths case ŷ wll be: yˆ G ( Iˆ ) I 1 N N Iˆ I G 1 I 1 G I NI G 1 I y SG 1 SG 1 where the G SG represents the servces that the government provdes as a share of the total net I ncome n the economy. GINI ˆ 1 GINI 1 2 yˆ( ) d (2) 0 1 SG As can be seen n equaton 2 and the llustraton n fgure 1, the modfed Gn ndex s a smple nterpolaton, whch uses the tradtonal Gn and the share of publc n-nd benefts n the total net ncome of the economy. 5

6 The modfed Gn ndex s always lower then the tradtonal Gn. The larger the share of the publc n-nd benefts, the lower the modfed Gn. It converges to the tradtonal Gn ndex when no government n-nd benefts are provded. 6

7 Fgure 1: Lorenz curve: Regular vs. modfed Gn y () Modfed Lorenz Curve Lorenz Curve In the next secton, we show the results comparng the modfed GINI to the tradtonal Gn for the OECD countres. 7

8 3. Comparng the modfed Gn to the tradtonal Gn for the OECD countres In order to modfy the Gn ndex, we need to evaluate the share of government n-nd benefts n the total net ncome n the economy (SG). To ths end, we use three basc measures: GDP, government consumpton expendtures (G) and total tax revenue as a percentage of GDP (T) to gve: G SG GDP( 1T) where GDP(1-T) s a proxy for the total net ncome of the economy. It should be noted that ths s not exactly the total net ncome, because the GDP ncludes the deprecaton. The SG as presented here underestmates the effect of the n-nd benefts on the level of nequalty. If we had the GINI accurate fgure, the change n the Gn would be even greater (Recall: MGINI ). 1 SG In addton, we assume that the n-nd benefts provded by the government are dstrbuted equally among all households n the economy. Ths assumpton further underestmates the effect of the nnd benefts on the Gn ndex because t s more lely that the lower ncome percentles actually receve a hgher share of the n-nd benefts (Callan and Keane 2009; Nolan, 1981). In table 1 we present the modfed Gn ndex vs-à-vs the tradtonal Gn for the OECD countres. We also present the Gn ranng change that results from the proposed modfcaton. 8

9 Table 1: Ranng change when usng modfed Gn Country Gn ranng Gn Year G % of total ncome Modfed Gn Modfed ran Ran Sweden Denmar Slovena Norway Slova Republc Belgum Czech Republc Fnland Hungary Netherlands France Iceland Austra Germany Luxembourg Swtzerland Italy New Zealand Greece Span Ireland Canada Korea Poland Japan Estona Australa Unted Kngdom Israel Portugal Unted States Turey Mexco Chle

10 In table 1, we see that there are sgnfcant transformatons n the ranng when usng the modfed Gn ndex nstead of the tradtonal Gn ndex. For example, we can see that Italy moved up from the 27 th poston to the 17 th poston. Even though the level of nequalty accordng to the ncome dstrbuton s relatvely hgh, the n-nd benefts provded by the government sgnfcantly reduces the nequalty. Smlar results appear n the cases of Sweden, Netherlands and New Zealand. Accordng to the modfed Gn, Sweden s the country wth the lowest nequalty n ncome dstrbuton, whle accordng to the standard Gn Sweden s raned 6 th. Conversely, we can see that the ranngs of Austra, Luxemburg, Swtzerland, Poland and Estona deterorate sgnfcantly because these countres provde a sgnfcantly smaller quantty of n-nd benefts to the publc. The medan decrease n the Gn ndex as a result of ncluson of the n-nd benefts s 15%. For comparson s sae, Aaberge (2010) found that for European countres the change n Gn would be approxmately 15-25% when usng hs more elaborate calculaton of n-nd benefts, whch s not very dfferent than our results. However, unle the method proposed by Aaberge (2010), our method maes t possble to calculate a modfed Gn wthout havng detaled data about the dstrbuton n-nd benefts, because t uses only the avalable aggregate data that both developed and developng countres report annually. 10

11 4. Concluson In ths paper, we present a smple modfcaton to the GINI ndex that can be calculated smply usng the common aggregate data avalable for each country. Ths measure whch taes nto consderaton the value of the n-nd benefts that the government provdes allow us to better understand the nequalty n ncome dstrbuton n the dfferent economes. To the best of our nowledge, our general approach toward ntegratng the n-nd benefts nto the ncome dstrbuton has not yet been presented n the lterature. We beleve that the modfed Gn ndex can be used by polcy maers and researchers around the world to assess the dfferences n nequaltes between countres as well as trends n the level of nequalty over tme more accurately because t taes n-nd benefts nto account wthout needng access to complcated and rarely avalable data sets. 11

12 5. References Aaberge R., Langorgen, A., Lndgren, P., The mpact of basc publc servces on the dstrbuton of ncome n European countres, n: Atnson A.B. and Marler E. (Eds), Income and Lvng Condtons n Europe. Eurostat, European Unon. Atnson, T., Cantllon, B., Marler, E. Nolan, B., Socal Indcators: The EU and Socal Incluson. Oxford Unversty Press, Oxford. Callan T. Keane C., Non-cash benefts and the dstrbuton of economc welfare. Econ. Soc. Rev. 40(1), Chapple S., Forster, M., Martn J.P., Inequalty and Well Beng n OECD Countres: What Do We Know? OECD, Pars. Garfnel, I., Ranwater, L., Smeedng, T. M., A re-examnaton of welfare states and nequalty n rch natons: How n-nd transfers and ndrect taxes change the story, J. Pol. Anal. Manage., 25, Lerman, R. Ytzha, S A note on the calculaton and nterpretaton of the Gn ndex, Econ. Letters, 15, Nolan, B., Russell, H., Non-cash benefts and poverty n Ireland. Polcy Research Seres, No. 39, Dubln: The Economc and Socal Research Insttute. Nolan, B Redstrbuton of household ncome n Ireland by taxes and benefts. Econ. Soc. Rev. 13. OECD, Growng Unequal? Income Dstrbuton n OECD Countres. OECD, Pars. Sefton, T., Recent changes n the dstrbuton of the socal wage. Case Paper 62, Centre for Analyss of Socal Excluson. Stac, S., The effect of drect government nvolvement n the economy on the degree of ncome nequalty: A cross-natonal study. Am. Socol. Rev. 43,