1. Introduction. 2. The modified Gini index
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1 . ntroducton The n coeffcent s a popular and wdel-used ndex for measurng nequalt (Lerman and Ytzha, 984. Evdence for the OECD countres ndcates that there has been a sgnfcant and wdespread ncrease n ncome nequalt durng the past 20 ears (Chapell et al., 2009; OECD, When nequalt 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 sstems do serve to redstrbute ncome towards the poor (Chapell et al., We argue that the redstrbuton role plaed b the government through the provson of publc servces s sgnfcant, and should be taen nto consderatons when calculatng the n ndex (see also Stac, 978. eglectng publc, n-nd benefts when measurng ncome mght gve an ncomplete pcture of the dstrbuton of economc nequalt (Aaberge et al., 200 because n-nd benefts such as educaton, health nsurance, and other publc servces actuall consttute approxmatel one-half of the welfare state transfers n developed countres (Atnson et al., 2002; arfnel et al., We suggest a smple, practcal modfcaton to the tradtonal n ndex that can be calculated usng the aggregate data publshed for each countr. Let us assume two countres wth the same n ndex, one where the government provdes more n- nd benefts (educaton, healthcare, socal servces, securt, etc. than the government of the other provdes. We argue that the actual level of nequalt wll be lower n the countr whch provdes more n-nd benefts. Snce the dstrbuton of n-nd benefts s based toward the low ncome famles, the tradtonal n ndex that does not consder the redstrbuton generated b 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. olan (98 found that the value of non-cash benefts (such as medcal servces, housng and educaton appeared relatvel stable across ncome groups, fallng onl margnall as ncome rose. olan and Russell (200 loo at a range of non-cash benefts n reland, ncludng the free schemes, such as free travel, free electrct etc. The found that the medcal card scheme was strongl concentrated towards the bottom end of the dstrbuton wth 6 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., (200 showed that ncluson of noncash ncome (educaton and healthcare reduces nequalt b 5-25 percent. He used detaled data regardng the allocaton of the publc n-nd benefts among the dfferent ndvduals n the econom. Ths approach maes t almost mpossble to generalze for all countres and dfferent ears. Ths paper offers a generalzaton of ths approach that uses aggregate data that s avalable for each countr. n the next secton, we present the calculaton approach of the modfed n (M. Then, we llustrate our approach usng recent data for the n ndex for the OECD countres and conclude the paper n the last secton. 2. The modfed n ndex Let us consder ( as the accumulated ncome of the percentle. n that case the n ndex would be:
2 2 0 ( 2 d n ( ( where represents the percentle of the households wth ncome less than the ncome of the th household, and represents the total number of households. ow, let us add the provson of publc servces and assume that, where s the total n-nd benefts provded b the government. n ths case ŷ wll be: where the S represents the servces that the government provdes as a share of the total net ncome n the econom. S d ( 2 0 (2 As can be seen n equaton 2 and the llustraton n fgure, the modfed n ndex s a smple nterpolaton, whch uses the tradtonal n and the share of publc n-nd benefts n the total net ncome of the econom. The modfed n ndex s alwas lower then the tradtonal n. The larger the share of the publc n-nd benefts, the lower the modfed n. t converges to the tradtonal n ndex when no government nnd benefts are provded. S S (
3 Fgure : Lorenz curve: Regular vs. modfed n ( Modfed Lorenz Curve Lorenz Curve n the next secton, we show the results comparng the modfed to the tradtonal n for the OECD countres. 3. Comparng the modfed n to the tradtonal n for the OECD countres n order to modf the n ndex, we need to evaluate the share of government n-nd benefts n the total net ncome n the econom (S. To ths end, we use three basc measures: DP, government consumpton expendtures ( and total tax revenue as a percentage of DP (T to gve: S DP( T where DP(-T s a prox for the total net ncome of the econom. t should be noted that ths s not exactl the total net ncome, because the DP ncludes the deprecaton. The S as presented here underestmates the effect of the n-nd benefts on the level of nequalt. f we had the accurate fgure, the change n the n would be even greater (Recall: M. S n addton, we assume that the n-nd benefts provded b the government are dstrbuted equall among all households n the econom. Ths assumpton further underestmates the effect of the n-nd benefts on the n ndex because t s more lel that the lower ncome percentles actuall receve a hgher share of the n-nd benefts (Callan and Keane 2009; olan, 98. n table we present the modfed n ndex vs-à-vs the tradtonal n for the OECD countres. We also present the n ranng change that results from the proposed modfcaton. Table : Ranng change when usng modfed n Countr n ranng n Year % of total ncome Modfed n Modfed ran Ran Sweden
4 Denmar Slovena orwa Slova Republc Belgum Czech Republc Fnland Hungar etherlands France celand Austra erman Luxembourg Swtzerland tal ew Zealand reece Span reland Canada Korea Poland Japan Estona Australa Unted Kngdom srael Portugal Unted States
5 Ture Mexco Chle n table, we see that there are sgnfcant transformatons n the ranng when usng the modfed n ndex nstead of the tradtonal n ndex. For example, we can see that tal moved up from the 27 th poston to the 7 th poston. Even though the level of nequalt accordng to the ncome dstrbuton s relatvel hgh, the n-nd benefts provded b the government sgnfcantl reduces the nequalt. Smlar results appear n the cases of Sweden, etherlands and ew Zealand. Accordng to the modfed n, Sweden s the countr wth the lowest nequalt n ncome dstrbuton, whle accordng to the standard n Sweden s raned 6 th. Conversel, we can see that the ranngs of Austra, Luxemburg, Swtzerland, Poland and Estona deterorate sgnfcantl because these countres provde a sgnfcantl smaller quantt of n-nd benefts to the publc. The medan decrease n the n ndex as a result of ncluson of the n-nd benefts s 5%. For comparson s sae, Aaberge (200 found that for European countres the change n n would be approxmatel 5-25% when usng hs more elaborate calculaton of n-nd benefts, whch s not ver dfferent than our results. However, unle the method proposed b Aaberge (200, our method maes t possble to calculate a modfed n wthout havng detaled data about the dstrbuton n-nd benefts, because t uses onl the avalable aggregate data that both developed and developng countres report annuall. 4. Concluson n ths paper, we present a smple modfcaton to the ndex that can be calculated smpl usng the common aggregate data avalable for each countr. Ths measure, whch taes nto consderaton the value of the n-nd benefts that the government provdes, allow us to better understand the nequalt 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 et been presented n the lterature. We beleve that the modfed n ndex can be used b polc maers and researchers around the world to assess the dfferences n nequaltes between countres as well as trends n the level of nequalt over tme more accuratel because t taes n-nd benefts nto account wthout needng access to complcated and rarel avalable data sets. 5. References Aaberge R., Langorgen, A., Lndgren, P., 200. The mpact of basc publc servces on the dstrbuton of ncome n European countres, n: Atnson A.B. and Marler E. (Eds, ncome and Lvng Condtons n Europe. Eurostat, European Unon. 5
6 Atnson, T., Cantllon, B., Marler, E. olan, B., Socal ndcators: The EU and Socal ncluson. Oxford Unverst Press, Oxford. Callan T. Keane C., on-cash benefts and the dstrbuton of economc welfare. Econ. Soc. Rev. 40(, Chapple S., Forster, M., Martn J.P., nequalt and Well Beng n OECD Countres: What Do We Know? OECD, Pars. arfnel,., Ranwater, L., Smeedng, T. M., A re-examnaton of welfare states and nequalt n rch natons: How n-nd transfers and ndrect taxes change the stor, J. Pol. Anal. Manage., 25, Lerman, R. Ytzha, S A note on the calculaton and nterpretaton of the n ndex, Econ. Letters, 5, olan, B., Russell, H., on-cash benefts and povert n reland. Polc Research Seres, o. 39, Dubln: The Economc and Socal Research nsttute. olan, B. 98. Redstrbuton of household ncome n reland b taxes and benefts. Econ. Soc. Rev. 3. OECD, rowng Unequal? ncome Dstrbuton n OECD Countres. OECD, Pars. Sefton, T., Recent changes n the dstrbuton of the socal wage. Case Paper 62, Centre for Analss of Socal Excluson. Stac, S., 978. The effect of drect government nvolvement n the econom on the degree of ncome nequalt: A cross-natonal stud. Am. Socol. Rev. 43,
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