Social security effects on income distribution: a counterfactual analysis for Brazil
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Social security effects on income distribution: acounterfactual analysis for BrazilRodrigo Leandro de Moura a b , Jaime de Jesus Filho c , Paulo Srgio Braga Tafner d & LigiaHelena da Cruz Ourives b ea Applied Economic, Brazilian Institute of Economy, Getulio Vargas Foundation , 60 Baro deItambi Street, Office 809, Rio de Janeiro , 22231-000 , Brazilb Graduate School of Economics, Getulio Vargas Foundation , Rio de Janeiro , Brazilc Department of Economics , University of Chicago , Chicago , IL , USAd Directory of Macroeconomic Policy & Studies, Institute of Applied Economic Research , Riode Janeiro , Brazile Economic Policy Secretariat, Ministry of Finance , Braslia , BrazilPublished online: 18 Oct 2012.
To cite this article: Rodrigo Leandro de Moura , Jaime de Jesus Filho , Paulo Srgio Braga Tafner & Ligia Helena da CruzOurives (2013) Social security effects on income distribution: a counterfactual analysis for Brazil, Applied Economics Letters,20:7, 631-637, DOI: 10.1080/13504851.2012.725922
To link to this article: http://dx.doi.org/10.1080/13504851.2012.725922
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Social security effects on income
distribution: a counterfactual
analysis for Brazil
Rodrigo Leandro de Mouraa,b,*, Jaime de Jesus Filhoc, Paulo SergioBraga Tafnerd and Ligia Helena da Cruz Ourivesb,e
aApplied Economic, Brazilian Institute of Economy, Getulio VargasFoundation, 60 Barao de Itambi Street, Office 809, Rio de Janeiro 22231-000,BrazilbGraduate School of Economics, Getulio Vargas Foundation, Rio de Janeiro,BrazilcDepartment of Economics, University of Chicago, Chicago, IL, USAdDirectory of Macroeconomic Policy & Studies, Institute of AppliedEconomic Research, Rio de Janeiro, BrazileEconomic Policy Secretariat, Ministry of Finance, Braslia, Brazil
Oneofthereasonsfortheexistenceofsocialsecuritysystemsis that theyfunctionas an income redistributionmechanism (Diamond, 1977).Nevertheless, there isno obvious consensus about this social security property. We test it to theBrazilian case and try to answer an additional question: is the trend of socialsecurity systems increasingly progressive or regressive? We conclude that thechanges inBrazilianSocial Security legislation reduced inequalitybetween1987and 1996, but only for the elderly. For the other age groups, there is a stabletrend. Results for the period between 1996 and 2006 reveal that the Braziliansystem is neutral for all cohorts.
Keywords: social security; income distribution; counterfactual distribution
JEL Classification: H55; C14; D31
The Brazilian social security system follows a Pay-As-
You-Go (PAYG) retirement system in which each gen-
eration of workers provides financial support for the
preceding generations retirees and pensioners. Due to
a peculiar financial design, PAYG is vulnerable to
demographic and labour market developments.
Indeed, there is a consensus that PAYG systems pro-
duce an increasing burden on every nations budget.
Many modern societies have witnessed a worsening
situation in their social security systems. In Brazil, for
example, social security deficit has reached 5% of
Gross Domestic Product (GDP), one of the highest in
the world. This highlights the fact that the Brazilian
system seems to be heading towards insolvency in the
future. This has, in fact, been the subject ofmuch public
discussion. Proposals for reform of the social security
system in Brazil range from a simple invalidation of
male/female age differential as a rule for benefit pay-
ments to a complete institutional change in the direc-
tion of a funded system.If social security is an advantageous contract for a
certain group of people, in particular the poorest ones,
then there isaprogressive incomedistribution.1There isa
wide range of literature that regards social security
*Corresponding author. E-mail: email@example.com or firstname.lastname@example.orgProgressivemeans when social security achieves a better income distribution.
Applied Economics Letters ISSN 13504851 print/ISSN 14664291 online # 2013 Taylor & Francishttp://www.tandfonline.com
Applied Economics Letters, 2013, 20, 631637
systems as good policy instruments for income distribu-tion in industrial countries,but there isnoclearconsensusabout that.2 In this article, we evaluate the distributiveproperty of public pensions (Diamond, 1977) and try toanswer an additional question: is the trend of socialsecurity systems increasingly progressive or regressive?To test the distributive pattern of the system, we
look closely at what would happen to per capita familyincome distribution in Brazil if there were the sameshare of beneficiaries and taxpayers as 10 years ago.We had two alternative approaches: (i) a simpleregression of wages and (ii) an estimation of densities.The advantage of the latter is the accountability ofincome distribution. In addition, it is possible to cal-culate various metrics of income inequality and com-pare them with the real ones. At this point, we followDinardo, et al. (1996) to disaggregate counterfactualdensities. Using this general procedure, we achieve amore precise analysis of changes of the progressivity(regressivity) in the social security system.This article uses data from the PNAD (Brazilian
National Household Survey) to analyse two sets ofpairwise years: 1987/1996 and 1996/2006. In fact,there were two important structural breaks in eachset: (i) the Constitution of 1988 altered social securityrules and (ii) the Social Security Reform in 2003altered the rules for civil servants. Only individualsaged over 18 years and reporting some income werekept in the sample.Figure A1 in Appendix shows that the share of
beneficiaries has increased in Brazil, from 12.81% in1987 to 18.53% in 2006. In turn, the share of taxpayershas remained almost stable over the past years.Table 1 indicates that the number of beneficiariesincreased from 10.10 million in 1987 to 16.13 millionin 1996 and 22.95 million in 2006. Pensions showed ahuge increment in terms of relative participation: from24.48% in 1986 to 36.10% in 2006.Section II explains the methodology. Section III
describes the results, and Section IV makes aconclusion.
Following Dinardo et al. (1996), the kernel density
estimate bfh of a univariate density f based on a random
sample of wages3 fWigni1 of size n, with weightsif gni1,
Pi i 1, is
where K(.) is a Gaussian kernel function and h is the
Silvermans (1986) rule of thumb bandwidth.
Estimation of counterfactual densities
Our methodology intends to answer the following
question: what would the density of wages have been
in 1996 if the share of beneficiaries and taxpayers had
remained at its 1987 level?4
Let us define b and c as the dummy variables for
beneficiaries and taxpayers, respectively. The variable x
includes individual attributes as dummies for schooling
years, age, race and marital status, dummy for whether
the individual is head of family, interaction dummy for
head of family and sex, total hours of work, place of
residence (urban or rural) and dummies for the states
where the individual lives. The variable t is the date,
which takes only two values in the comparisons and
includes years 1987, 1996 and 2006.The density of wages, ft(w), can be written as
ft w Z
dFw; b; c; xjtw;b;c;:x t
f wjb; c; x; twjb;c;x t
dFbjc; x; tbjc;x t dFcjx; tcjx t dFxjtxt
f w; twjb;c;x t; tbjc;x t; tcjx t; tx t
where x, b and c are the domains of definition ofthe individual attributes and F(.) is the distribution
function. The notation tw;b;c;x t represents the valuesof wages, share of beneficiaries, share of taxpayers and
all other individual attributes at date t. For example,
fw; twjb;c;x 96; tbjc;x 87; tcjx 96; tx 96 repre-sents the counterfactual density of wages in 1996 if
only the share of beneficiaries (variable b) had
remained at their 1987 level, while all other attributes
had been according to the wage schedule observed in
1996. We may write this counterfactual density as5:
2Gokhale and Kotlikoff (2002) show that social security may greatly increase the inequality in American wealth distribution.In turn, Liebman (2002) finds that social security redistribution is not related to income. Ferreira (2006) shows that retirementsand pensions increase the level of per capita household income inequality in Brazil. But the Brazilian evidence is still notconclusive.3Wages refer to logarithm of the sum of net earnings of all family members in per capita terms.4 In the explanation of the methodology, we always used these pairwise years.5We omitted domains for simplicity.
632 R. L. de Moura et al.
Social security effects on income distribution 633
where Cbjc;x b; c; x is the reweighting functiondefined as
The difference between the actual 1996 density and
this counterfactual density represents the effect of
changes on the distribution of beneficiaries, ceteris par-
ibus all other factors. A way to estimate the reweighting
function of Equation 2 is by estimating a probit model
for each year separately, that is, to estimate
Prb 1jc; x; tbjc;x t 1 Fa0tGc; x 3
where (.) is a normal distribution function andG(.) is a
function of other attributes.The counterfactual distribution in cases b and c had
remained at the 1987 level, as shown:
where Ccjx c; x dFcjx; tcjx 87=dFcjx; tcjx 96. The same way as in (3), we obtain an estimate ofCcjx c; x estimating a probit model of the variable cagainst variable x.Finally, by altering b, c and x, the counterfactual
f w; twjb;c;x 96; tbjc;x 87; tcjx 87; tx 87
R R Rfwjb; c; x; twjb;c;x 96
dFbjc; x; tbjc;x 87
dFcjx; tcjx 87dFxjtx 87
R R Rfwjb; c; x; twjb;c;x 96
Cbjc;xb; c; x
dFbjc; x; tbjc;x 96
Ccjx c; x dFcjx; tcjx 96 Cx x dFxjtx 96
where Cx x dFxjtx 87=dFxjtx 96. Applyingthe Bayes rule, this ratio can be written as
Cx x Prtb 87jxPrtb 96jx
Prtb 96Prtb 87
fw; twjb;c;x 96; tbjc;x 87; tcjx 96; tx 96 R R R
fwjb; c; x; twjb;c;x 96 dFbjc; x; tbjc;x 87dFcjx; tcjx 96dFxjtx 96
Z Z Z
fwjb; c; x; twjb;c;x 96Cbjc;xb; c; x dFbjc; x; tbjc;x 96 dFcjx; tcjx 96
Cbjc;x b; c; x ; dFbjc; x; tbjc;x 87=dFbjc; x; tbjc;x 96
bPr b 1jc; x; tbjc;x 87
Prb 1jc; x; tbjc;x 96 1 b
Pr b 0jc; x; tbjc;x 87
Prb 0jc; x; tbjc;x 962
f w; twjb;c;x 96; tbjc;x 87; tcjx 87; tx 96
R R R
f wjb; c; x; twjb;c;x 96
dFbjc; x; tbjc;x 87dFcjx; tcjx 87dFxjtx 96
R R R
f wjb; c; x; twjb;c;x 96
Cbjc;x b; c; x dFbjc; x; tbjc;x 96Ccjx c; x dFcjx; tcjx 96dFxjtx 96
634 R. L. de Moura et al.
So, to infer the first ratio, we simply estimate a probit ofthe year against variable, and for the second ratio, wecalculate the proportion of observations in each year.Thus, the change in variables for the 1987 level will
be in the following order: benefits, contributions andother factors. This decomposition is called normaldecomposition, whose results will be shown in the fol-lowing section.6
Table 2 shows the Gini and Theils inequality indica-tors. From 1987 to 1996, the joint effect of share ofbeneficiaries and taxpayers change implies worsen-ing of inequality as we compare 96bc877 to 1996,where the Gini coefficient (Theil index) increasesfrom 0.5396 (0.5600) to 0.5581 (0.6037). In turn,from 1996 to 2006, the effect was almost neutral aswe compare 06bc96 to 2006.Table 4 summarizes the percentage change of the
Gini coefficient and Theil index of factual and coun-terfactual densities. In the sample of individuals over18 years old, the effect of benefits raises the Ginicoefficient (Theil index) by 3.30% (7.23%) when com-paring 1996 to 96b87 and raises it by 1.5% (1.49%)when comparing 2006 to 06b96. Since we have main-tained the share of beneficiaries constant at the baseyear level, we also consider the effect of fixing the
share of taxpayers in the base year (by comparing, as
an example, 96b87 to 96bc87 densities). Thus, the
effect of contributions is almost none from 1987 to
1996 (0.14% (Gini) and 0.54% (Theil)) and progres-
sive from 1996 to 2006 (-1.81% (Gini) and -3.86%(Theil)). By maintaining all social security rules con-
stant at the base year level (b and c at the 1987 level),
the effect of other factors8 is almost none from 1986 to
1996 and regressive for the next period.The social security structure change provided a raise
in inequality9 between 1987 and 1996. It means that
the system has become more regressive. In the last
decade (19962006), the joint effect is almost none
for inequality.However, the results can be altered if we have a
reverse order of the effects.10 Thus, we perform the
sequential decomposition in reverse order, that is,
altering x, c and b.Table 3 shows the results for the sequential decom-
position in reverse order and Table 4 displays the per-
centage change in the right column. If we consider the
effect of maintaining other factors constant at the base
year level, we find an increase in the Gini coefficient
(Theil index) of 4.58% (10.77%) from 1987 to 1996 and
a slightly lower raise in the next decade (1.06% (Gini)
and 1.46% (Theil)). In turn, social security changes
have little effect on the two decades as all other attri-
butes are constant at the base year level.
Table 2. Inequality indicators for densities (normal decomposition)
Measures 1987 1996 2006 96b87 96bc87 96bcx87 06b96 06bc96 06bcx96
Gini 0.5668 0.5581 0.5432 0.5403 0.5396 0.5386 0.5352 0.5451 0.5374Theil 0.6267 0.6037 0.5504 0.5630 0.5600 0.5560 0.5423 0.5641 0.5417
Table 3. Indicators for densities (sequential decomposition in reverse order)
Measures 1987 1996 2006 96x87 96xc87 96xcb87 06x96 06xc96 06xcb96
Gini 0.5668 0.5581 0.5432 0.5337 0.5351 0.5386 0.5375 0.5373 0.5374Theil 0.6267 0.6037 0.5504 0.5450 0.5480 0.5560 0.5425 0.5413 0.5417
6 In the next section, we too consider reversing the order of change in the variables.7 It represents the counterfactual density of wages in 1996 if only the share of beneficiaries (b) and taxpayers (c) had remained attheir 1987 level while all other attributes had been at their 1996 level. The same logic applies to 06bc96, 06b96 and 96bc87.8 The percentage can be easily verified by dividing, for example, 96bc87 by 96bcx87 from Table 2.9 The effect can be approximately measured as the sum of percentages of Table 8.10 To perform this decomposition, we apply the procedure described in the previous section, but in reverse order. Then, weestimate Cxjc;b x; c; b , Ccjb c; b and Cb b . We obtain an estimate of Cxjc;b x; c; b , applying the Bayes rule:bCxjc;b x; c; b bCbjc;x b;c;x bCcjx c;x bCx x bCcjb c;b bCb b . Ccjb c; b was estimated by a probit model. And Cb b was estimated as Cx x , replacingx with b.
Social security effects on income distribution 635
IV. Concluding Remarks
When individual attributes are constant at the baseyear level, the changes in Brazilian Social Securitylegislation reduced inequality between 1987 and1996, but only for the elderly. For the other agegroups, there is a stable trend. Results for the periodbetween 1996 and 2006 reveal that the Brazilian sys-tem is neutral for all cohorts.Therefore, we found out that social security systems
are not an effective mechanism for income redistribu-tion, as predicted by previous studies. In view of theresults obtained, we conclude that the Brazilian PAYGsystem generates a high cost for the Brazilian economy.
We are grateful for the comments made by all partici-pants of Latin American and Caribbean EconomicAssociation (LACEA) (2008) and NortheastUniversities Development Consortium (NEUDC)
(2009) conferences, EPGE and IPEA seminars and
XXXV Brazilian Economics Meeting. Any remaining
errors are our own responsibility.
Diamond, P. A. (1977) A framework for social securityanalysis, Journal of Public Economics, 8, 27598.
Dinardo, J., Fortin, N. M. and Lemieux, T. (1996) Labormarket institutions and the distribution of wages,19731992: a semi-parametric approach, Econometrica,64, 100144.
Ferreira, C. R. (2006) Aposentadorias e distribuicao darenda no Brasil: uma nota sobreo perodo 1981 a2001, Revista Brasileira de Economia, 60, 24760.
Gokhale, J. and Kotliko, L. J. (2002) Simulating the trans-mission of wealth inequality, The American EconomicReview Papers and Proceedings, 92, 2659.
Liebman, J. B. (2002) Redistribution in the currentU.S. social security system, in The DistributionalAspects of Social Security and Social Security Reform,Chapter 1, (Eds) M. Feldstein and J. B. Liebman,University of Chicago Press, Chicago, pp. 148.
Silverman, B. (1986) Density Estimation for Statistics andData Analysis, Chapman & Hall, London.
Table 4. Increase/decrease in Gini coefficient and Theil index due to the effect of share of beneficiaries and taxpayers from a baseyear to a specific year
Normal decomposition Sequential decomposition in reverse order
18 Gini (%) 3.30% 0.14 1.50 -1.81 -0.26 -0.66 0.04 -0.02Theil (%) 7.23 0.54 1.49 -3.86 -0.56 -1.44 0.22 -0.07
1827 Gini (%) 1.37 1.06 -0.49 -0.61 0.01 0.03 -0.04 -0.01Theil (%) 1.07 2.40 -2.99 -3.27 0.02 0.14 -0.06 0.05
2837 Gini (%) 1.53 1.07 -1.06 -1.67 -0.13 -0.16 -0.11 -0.16Theil (%) 2.44 3.11 -4.60 -3.59 -0.33 -0.38 -0.25 -0.38
3847 Gini (%) 2.26 2.13 1.59 -0.04 -0.29 -0.20 0.06 0.12Theil (%) 5.71 5.33 2.07 -0.09 -0.73 -0.51 0.15 0.33
4857 Gini (%) 1.74 0.09 0.49 0.67 -0.09 -0.30 0.24 0.29Theil (%) 4.33 0.72 0.09 1.54 -0.22 -0.76 0.58 0.68
5867 Gini (%) 0.64 -1.73 -0.01 2.40 1.21 -2.61 -0.42 0.34Theil (%) 0.15 -3.87 -0.14 6.07 2.12 -4.58 -0.81 0.68
68 Gini (%) 5.85 25.20 -2.83 -0.58 1.24 -3.35 -0.65 0.39Theil (%) 7.92 65.28 -5.97 -1.69 1.67 -5.07 -1.20 0.74
Notes: 96x87 (06x96) represents the counterfactual density of wages in 1996 (2006) if only the other factors (x) had remained attheir 1987 (1996) level. 96xc87 (06x96) represents the counterfactual density of wages in 1996 (2006) if only x and the share oftaxpayers (c) had remained at their 1987 (1996) level. And 96xcb87 (06xcb96) represents the counterfactual density of wages in1996 (2006) if only x, c and the share of beneficiaries (b) had remained at their 1987 (1996) level.Increase/decrease in Gini coefficient and Theil index is calculated by dividing the ratio between factual indicator and counter-factual of benefit and tax for normal decomposition and the ratio between counterfactual indicator of other factors andcounterfactual of other factors, benefit and tax. For example, the 1996/96b87 ratio considers the increase in Gini/Theilcoefficient due to the effect of a change in the share of beneficiaries and taxprayers from 1987 to 1996. The 96x87/96xb87ratio considers the increase inGini/Theil coefficients due to the effect of a change in the share of beneficiaries and taxpayers from1987 to 1996, given the change in other factors.
636 R. L. de Moura et al.
Share of taxpayers
Share of beneficiaries
Fig. A1. Beneficiaries/taxpayers over 18 years old in the Brazilian population (%)Source: Elaborated by the authors based on PNAD data.
Social security effects on income distribution 637