POLICY RESEARCH WORKING PAPER 2'975
Policy Options for Meeting
the Millennium Development Goals
in Brazil
Can Micro-Simulations Help?
Francisco H. G. Ferreira
Phillippe C(. Leite
The World Bank
Development Research Group
Poverty Team
February 2003
POLIcY t RESEARCH WORKING PAI'PER 2975
Abstract
Ferreira and Leite investigate whether micr-o-siiMulation simulationis is based on a richer model of behavior in the
techniques can shed light on the types of policies that labor markets. It points to the importanice of combining
should be adopted by countrics wishiing to mcet their differenlt policy options, such as educational expansion
Millennium Developmenlt Goals. They compare two and targeted conditionial redistribution schemes, to
families of micro-simulations. The first family of micro- ensure that the poorest people in socicty are successfully
simulations decomposes required poverty changes into a reached. But the absence of market equilibria in these
chanige in the meani and a reductioll in inequality. statistical models, as well as the strong stability
Although it highlilghts the importance of inequality assumptiolIs which are implicit in their use, argue for
reduction, it appears to be too general to be of muchl usc extrenile caution in their interpretation.
for policymaking. The sccond family of micro-
This paper-a product of the Poverty Teamii, Development Research Group-is part of a larger effort in the group to
understand pro-poor policies. Copies of the paper are available free from rhe World Bank, 1 818 H Street NW, Washington,
DC 20433. Please contact Patricia Sader, room MC3-556, telephoic 202-473-3902, fax 202-S22-1 153, email address
psadcr 2@worldbank.org. Policv Research Working Papers are also posted on the Web at http://ecoii.worldbank.org. The
authors may be contacted at ffcrreira@ worldbank.org or pleiteQ?worldbank.org. February 2003. (39 pages)
The Policv Research Workiig P'aper seris disseminztes the findings of) ilork ni progress to encourage the exchange of ideas about
developnient issuies. An objectivc offthe series is to get the findizgs ouit qtickly, even if the presentatioiis are less thani filly polished. The
p(in [irs tarrv the inimes of thse authors .snid sboi,ld he cited accordingly. Thlt, findings, interpretations, anid conclusions expressed in tbi1i
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couinitries thley represenlt
Produced by thc Research Advisory Staff
Policy Options for Meeting the Milennium Develo?ment Goals in
Brazil: Can micro-simulations help?
Francisco H.G. Ferreira and Phillippe G. Leite2
JEL classification: C15, D31, I31, J13, J22
XThis paper draws on previous joint work by the authors with Fran9ois Bourguignon and Ricardo Paes de
Barros, to whom we are indebted, without implication. We are also grateful for very useful comments
received from Francois Bourguignon, Carmen Pag6s, Martin Ravallion and Andr6s Rodriguez-Clare.
2 The World Bank and PUC-Rio.
2
1. Introduction
In September 2000, the member states of the United Nations unanimously adopted a
document known as the Millennium Declaration. After consultations with a number of
international organizations within the UN system, as well as the RMF, the World Bank
and the OECD, the General Assembly recognized the Millennium Development Goals
(MDG) as integral components of the implementation of that Declaration. There are eight
such goals, each corresponding to a key development aim in one dimension of human
welfare. They are listed in Table 1. Associated with the eight goals, there are eighteen
specific targets, which quantify the broad goals in a measurable manner. Finally, there are
forty-eight indicators in total, each of them associated with a specific target. These are
meant to be monitoring variables, through the evolution of which progress towards the
goals can be evaluated. For a complete listing of goals, targets and indicators, see:
www.worldbank.org/mdci.
Table 1. The Millennium Development Goals
Goal Title
1 Eradicate Extreme Poverty and Hunger
2 Achieve Universal Primary Education
3 Promote Gender Equality and Empower Women
4 Reduce Child Mortality
5 Improve Maternal Health
6 Combat HIV/AIDS, rnalaria and other diseases
7 Ensure Environmental Sustainability
8 Develop a Global Partnership for Development
These goals and their associated collection of targets and indicators have already
succeeded, to a large extent, in at least one of their objectives, namely raising awareness
of the issues which they seek to address and focusing the mind of policy-makers -
national and international - on the need to secure measurable progress along various
dimensions of human welfare in a relatively short period of time: most targets specify
objectives which should be accomplished no later than 2015. As part of the effort, some
3
of the multilateral institutions have started monitoring programs, which compile and
present up-to-date information on how different countries and regions are doing with
respect to each target.
Based on the results of these periodic monitoring exercises, questions have begun to
be asked in a number of countries as to whether this or that goal can in fact feasibly be
reached by 2015. In some nations, debates about policies to help meet some of the goals
have entered the political arena. Intemationally, at least two UN agencies have teamed up
to simulate progress and requirements for countries to meet their First MDG Target,
namely to halve the incidence of extreme poverty which prevailed in 1990, by 2015.3
The purpose of this paper is to investigate whether modem micro-simulation
techniques can shed any light on some of the policy options available to countries which
want to meet some of their Millennium Development Goals. Throughout the article, we
argue for considerable circumspection: all of the simulations we present are essentially
statistical exercises. Although they differ in the extent to which agent behavior is taken
into account, none of them is based on models where prices are endogenously
determined, and thus none takes full account of market adjustments towards equilibrium,
or of subsequent agent responses.
Nevertheless we argue that, subject to the necessary caution and humility, some
valuable lessons can indeed be learned from micro-simulation-based social forecasting.
We apply our analysis to a single country - Brazil - and to three of the eight goals. Table
2 lists the five indicators which we include in this exercise. The numbers associated to
them in the Table are their official numbers in the Millennium Development Goals.
Table 2. Speciflc MDG Indicators Considered in This Paper
Goal 1: Poverty and Hunger 1. Proportion of the population below $1 per day
2. Poverty gap ratio
Goal 2: Primary Education 6. Net enrollment in primary education
Goal 3: Gender Equality 9. Ratio of girls to boys in primary, secondary and tertiary
education.
11. Ratio of women to men in wage employment in the
non-agricultural sector.
3This was a simulation exercise for Latin America, undertaken jointly by the UNDP and ECLAC,
alongside Brazil's IPEA. See ECLAC and UNDP, forthcoming, for a full report.
4
The paper is organized as follows. In the next section we present a simple "growth
and inequality" simulation, which yields all combinations of growth rates and "Lorenz-
convex" inequality reductions which are statistically consistent with achieving the MDG
Target 1: "Halving, between 1990 and 2015, the proportion of people whose income is
less than one dollar a day". We then argue that., while some useful insights can be derived
from this exercise, implications for policy are necessarily limited by the behavioral
paucity of the underlying analysis. Accordingly we turn, in Section 3, to an approach
which is structurally richer, by virtue of taking into account observed patterns of behavior
with respect to key agent decisions, such as educational attainment, occupational choice
and earnings. We find that this approach generates more detailed and specific
counterfactuals, which may be useful in guiding policy interventions. We warn, however,
that both the absence of endogenous price responses in the model and the strength of the
assumptions of behavioral stability which are maintained, imply that the simulation
results should not be understood as predictions.
2. Growth and Inequality: a Statistical Plerspective4
The first target associated with Millennium Development Goal number One is that
countries should halve, between 1990 and 2015, the proportion of their population living
in households with per capita expenditure or income levels equal to or less than one
dollar per day, measured in purchasing power parity terms. Since this is a poverty
reduction target, it makes sense to start thinking about it in terms of the two basic
manners in which the extent of poverty in any given distribution can be reduced: growth
in the mean and/or reduction in inequality.
A measure of poverty II in a given income distribution F(y) is always defined with
respect to a poverty line z, which separates thie poor from the non-poor. It is therefore
always the case that poverty is a functional of the distribution of income and of the
poverty threshold: rI = fl(F(y), z). As we just: saw, the Millennium Poverty Reduction
4This section draws heavily on ECLAC and UNDP, forthcoming. The methodology presented here was
developed originally for the preparation of that Report. Both authors were fortunate to work on the team
that prepared it, and are grateful to all other team members - especially Ricardo Paes de 'Barros - for their
guidance.
5
Target was formulated in terms of the poverty incidence indicator Po, so that this
functional is simply Po = F(z).5
In order to consider how economic growth and changes in inequality contribute to
changes in the incidence of poverty, Po, it is convenient to draw on the established result6
that:
L'(p) = F1 (P)
,ay
where L'(p) denotes the first derivative of the Lorenz Curve:
Y(P) P
L(p)= - | xf(x)dx= -F-'(pYp
Y O AY O
associated with the income distribution p = F(y). It immediately follows that:
L' )= F (O) = Z
lIly ily
Thus:
Po = L- (z/JUy)
This merely states that the incidence of poverty is completely determined by the
poverty line, the mean of the distribution, and its Lorenz Curve.7
This is useful for our investigation of reductions in extreme poverty, since we can
simulate the effects of economic growth as changes in mean income (y) and the effects
of inequality as changes in the Lorenz Curve, L(p), which is independent of the mean by
construction. In particular, for any poverty incidence rate P* < Po(F(y), z), there should
5 On the definition and properties of the Pa family, see Foster, Greer and Thorbecke (1984).
6See, e.g., Kakwani (1980) and Deaton (1997).
7This fact has long been known, and indeed long been used to decompose observed changes in poverty into
components due to 'growth' and 'inequality'. There is no single 'right' decomposition, and at least three
approaches have been proposed, namely those due to Datt and Ravallion (1992), Kakwani (1993) and Tsui
(1996). See Ravallion (2000) for a survey. While the basic approach used in this Section falls squarely in
that tradition, it differs in at least one respect: since we are concerned with simulating the future - a form of
extrapolating out of sample - we construct and analyse sets of arbitrarily defined counterfactual
distributions, rather than focusing on decomposing poverty changes between well-defined specific actual
distributions.
6
exist (a number of) hypothetical distributions F*, with mean level gyt and Lorenz curve
L*(p), which would have a poverty incidence cf P* = L*H (z/l *).
In particular, consider a counterfactual income distribution F*(y*), where:
(1) y*' = (l+1)[(l-a)y + ajy], withOO.
This transformation corresponds to a distribution-neutral increase of [3% in everyone's
income level, coupled with a redistribution policy consisting of taxing lOOa% of
everyone's income, and then distributing the revenues equally across every person in the
population.
It is easy to see that the mean of the resulting counterfactual distribution would be P%
higher than in the original distribution:
(2) 9Y* = (l+P)py.
It is also true that the Lorenz curve of the new distribution would be thus
transformed:
(3) L*(p) = (l-a)L(p) + ap
And, consequently, that the Gini coefficiernt of the counterfactual distribution would
be a% lower than that for the original distribution8:
(4) G*(y) = (l-a)G(y).
Given these properties, we refer to the two-parameter (a, P) class of transformations
of an income distribution, which is given by (1), as Lorenz-convex transformations.9 This
is clearly a restrictive set of transformations, but it is analytically convenient. For this
reason, they have been used before in the literature. They underlie, for instance, the
Kakwani (1993) decompositions.
The values of a and P can be chosen so that equations (2) and (3) hold exactly,
satisfying P* = L*'-'(z/pLy*). The target poverty incidence rate P* can then be written as a
functional of the original income distribution, of the relevant poverty line, and of the
simulation parameters a and ,B:
(5) P* = PO(a , F(y), z)
8 See the Appendix for a proof.
9 Analogously, we call any process that leads from L(p) to L*(p), defined as in (3), for 0 < a < 1, a
"Lorenz-convex inequality reduction".
7
Since a and f3 can be chosen independently, there is in fact one degree of freedom in
the choice of simulation parameters. In other words, given an arbitrary value of either a
or P (subject to 0 < a < 1, p > 0), there will exist a (positive or negative) value of the
other parameter such that (5) holds. One can thus define an isopoverty set for the
distribution F(y), for each target poverty incidence P*, with respect to poverty line z, as
the set of a, 1 pairs that would lead from F(y) to another distribution with poverty rate P*.
Formally:
(6) I(P*, F(y), z) = {( a, 1) Po(a, 1, F(y), z) = P*}
When plotted on a, 13 space, we will refer to it as the P* isopoverty curve. In the
specific case of the MDG poverty reduction target, P* is simply one half of the poverty
incidence rate Po which prevailed in the country in 1990. In this case, any combination of
a rate of inequality reduction (a) and a rate of economic growth (1) which belongs to I
will halve the 1990 incidence of poverty with respect to the extreme poverty line z.
Figure 1 below plots the isopoverty curve for the Brazilian Millennium Development
Goal poverty target, which is defined on the basis of the poverty incidence estimated
from the 1990 national household survey Pesquisa Nacional por Amostra de Domicilios
(PNAD).10 Using a purchasing power parity exchange rate and a thirty-days month, the
international U$1/day poverty line was converted to Brazilian Reais at R$22.11 per
person per month, in 1999 prices." The proportion of the Brazilian population living in
households with total per capita income levels below that line in 1990 was 7.46%. This
implies that the MDG poverty reduction target for Brazil would be to reach an extreme
poverty incidence of 3.73% by 2015.
'° The PNAD is Brazil's main nationally representative household survey. It is fielded annually, except in
Census years (such as 199 1), and covers the entire country, except the rural areas of the states of Acre,
Amapa, Amazonas, Para, Rondonia and Roraima. Its sample size in 1990 (1999) was 72,084 (91,546)
households. Although there is no better data set for either 1990 or 1999 in Brazil, see Ferreira, Lanjouw and
Neri (forthcoming) for a discussion of its shortcomings in measuring incomes, particularly in rural areas.
" The international "one-dollar per person per day" poverty line, which originated from the World Bank
Research Department, was originally used in 1990 and was expressed in 1985 prices. The World Bank later
updated it to U$1.08/day, in 1993 prices. To obtain the monthly poverty line in 1999 Brazilian Reais, we
computedz=U$1.08 * 30 * (I/PPP93) * Brazil's CPI (September 1999, with base September 1993) = 32.4
* 56.1243 * 38.30 = 22.11. The reader is warned that two of these numbers are measured with considerable
error: PPP exchange rates - which aim to calculate cost-of-living adjusted exchange rates across countries -
are based on a necessarily incomplete survey of product and service prices. Additionally, Brazilian inflation
rates were very high in 1993, so that the choice of base month in that year (i.e. the precise point in time for
which the PPP exchange rates were valid) matters considerably for the final 1999 poverty line. Our choice
of September 1999 (the PNAD reference month) implies a lower poverty line than using an average CPI for
1993 (as reflected in the World Bank's World Development Indicators (2002) figure for 1998).
8
Figure 1 plots the combination of cumulative rates of growth in mean per capita
incomes from 1990 to 2015 (J, on the horizontal axis) and the cumulative rates of
Lorenz-convex inequality reduction (aL, on the vertical axis) which would achieve that
target. Table 3 isolates three specific points, for analysis. The first of these is the vertical
intercept of the isopoverty curve. It tells us that one way to halve the poverty incidence
prevailing in 1990 would be to rely exclusively on inequality reduction: with zero growth
in mean incomes, the poverty reduction target would be reached with a 3.4% cumulative
decline in the Gini coefficient (through a Lorenz-convex shift of the Lorenz curve).This
would imply a fall in the Gini coefficient from 0.61 to 0.59. Alternatively, the same
poverty incidence (3.7 1%) could be reached with no movement in the Lorenz curve,
through an accumulated per capita growth rate of 50% - corresponding to an average
annual rate of 1.64% over the 25-year period - at the horizontal intercept of the curve.
F%= 1 BUzP8 MDG ovy e
4
335
7.
2.5
1.5
0.5I -
.0.
43 1 1~~~~~~~3% bbI0%pf~
In between these "pure strategies", there lies a continuum of combinations of
inequality reductions and accumulated rates of economic growth which would be
consistent with halving Brazil's 1990 poverty incidence. One such point, which might be
of interest, is the one arising from the historical performance of the country between 1990
and 1999. Over these nine years, Brazil's mean income in the PNAD grew at an average
9
annual rate of 1.02%, and the Gini coefficient fell at an average annual rate of 0.43%. As
the last row in Table 3 indicates, had this decline in the Gini been attained through a
Lorenz-convex inequality reduction, this pattern would have led to a halving of the
incidence of poverty in just under seven years. With a cumulative growth in mean income
of 7.35% and a Lorenz-convex fall in inequality of 2.94% (which corresponds to less than
two points of the Gini), the Brazilian extreme poverty headcount would have fallen to
3.38%, by 1997.
Table 3: Three points on Brazil's MDG Isopoverty Curve
Growth (P%) Inequality Reduction (a%) ji Headcount Gini
1990 232.66 7A6% 0.6119
1999 9.56 3.74 254.90 5.29% 0.5889
2015* 0 3.40 232.66 3.71% 0.5911
50 0.00 348.99 3.71% 0.6119
Historical per year (P=1.02%;ao=0.43%):
1997* 7.35 2.94 249.77 3.38% 0.5939
Sourm: PNAD/IBGE 1990, PNAD/IBGE 1999 and author's calculation
Notes: z = RS22.11 per person per month, in 1999 valus, which coresponds to USI/person/day.
*Denotes simulated distributions.
Yet, the actual observed incidence of extreme poverty in 1999 was 5.29%, despite the
fact that accumulated growth in the PNAD mean income since 1990 was actually 9.56%,
and that the 1999 Gini coefficient was 3.74% smaller than in 1990. How can this be? It is
simply an indication that the reduction in the Gini coefficient was not the result of a
Lorenz-convex inequality reduction. The shift of the Lorenz curve between 1990 and
1999 was not a perfect convex combination between the 1990 Lorenz curve and the line
of perfect equality, as implied by (3). This can be clearly seen in Figure 2, which was
truncated at the median in order to facilitate visualization of the lower tail. In this picture,
the lowest (thick) Lorenz curve is that for 1990. The solid thin line is the simulated
Lorenz curve corresponding to a convex transformation such as equation (3), with a =
0.0294. The dotted curve is the actual 1999 Lorenz curve. It can be seen that the factual
reduction in inequality was not as beneficial to the bottom of the distribution as a Lorenz-
convex transformation would have been.
10
Figure 2: Truncated Lorenz Cur'ves for Brazil; actual and simulated
0.13 13
0.12
0.1 ' /
0.09
0.08
0,0
0.07 4 4
0.045'i9
0.03 ' -/
0.02
0.01
0 D 6 10 IS 20 25 30 35 40
0 5 ~~~~~~~~~p
-Y90~~--Y97 ' ' Y99
Figure 3: Log Incone Differences per Percentle, 1990-1999; actual and simulated
1.3
0.1
0. 9 20 30 405
.0.3
49.5
- 1Y*7>0) X99 Ro90
11
This can be seen even more clearly a few levels of integration below the Lorenz
curve. Figure 3 plots the differences in the logarithms of income for each percentile,
between two pairs of distributions. The dotted line refers to the difference between the
simulated distribution F*(a=0.0294, P=0.0735) and the actual 1990 distribution, whereas
the solid line refers to the difference between the actual 1999 and the actual 1990
distributions. Although both distributions have lower Gini coefficients than the 1990
distribution, it is apparent that those distributions are obtained from the 1990 one through
rather different processes. In particular, it is clear that the actual changes at the bottom of
the distribution were very different from the simple arithmetic simulation implied by
equation (3): instead of the large proportional gains predicted by (1), the bottom three or
four percentiles suffered considerable losses.
These differences should not come entirely as a surprise. The simulation of a
counterfactual income distribution through the application of equation (1) is a simple
arithmetic procedure. There is no guarantee whatsoever that it would be consistent either
(a) with household behavior in various realms, such as fertility or occupational decisions,
which can affect the distribution of income; or (b) a general equilibrium of the markets in
the economy.
The exercise described in this section does serve one useful illustrative purpose. It
establishes that - at least for a country as unequal as Brazil - inequality reduction could
in principle be a very effective path towards the eradication of extreme poverty and the
meeting of the poverty reduction MDG. A simple two-point reduction in the Gini
coefficient (from 0.61 to 0.59) over the entire twenty-five year period could achieve the
goal, even without any economic growth. Conversely, the accumulated rate of economic
growth needed to meet the target at constant inequality is 50%. While the average annual
growth rate implied by this number (1.64%) is not high, it nevertheless lies above the rate
observed historically in the 1990s. In other words, the inclination of a country's
isopoverty curve can provide some guidance as to the statistical trade-off between the
growth and inequality reduction rates required to reduce poverty.'2
12 Note that this refers only to the statistical trade-off between growth and inequality. Economically, it is
quite possible that there be additional trade-offs or, conversely, that some inequality reduction might
facilitate growth.
12
Undertaking a similar exercise for eighteen countries in Latin America and the
Caribbean, ECLAC and UNDP (forthcoming) find that only seven countries"3 in the
sample would meet their MDG poverty targets if their growth and inequality trends
during the 1990s were replicated in 2000-2015. Another six countries would miss the
target by 2015, but would thereafter eventually halve the incidence of extreme poverty on
the basis of their performance in the 1990s.14 Finally, a hard core of five: countries where
either negative economic growth rates or increasing inequality in ithe 1990s, or a
combination of both, implied rising extreme poverty during that decade, would of course
never meet the MDG target under the assumption that their performances in the 1990s
would extend indefinitely into the future.'5 Turning to consider alternative scenarios, the
report found that isopoverty curves in the region were almost universally "flat", implying
that the poverty-reduction impact of a percentage-point reduction in the Gini coefficient
(under the maintained Lorenz-convexity assumption) was equivalent to that of many
percentage points in accumulated economic growth.
The very fact that the poverty-reduction impact of economic growth is relatively
weak in Latin America is itself associated with the region's high level of inequality (see,
for instance, Bourguignon, 2002). The international evidence strongly suggests that, with
everything else constant, inequality reduces the growth elasticity of poverty reduction, so
that an additional percentage point in the growth rate has a lower effect on (most) poverty
measures in a high-inequality country, than in a more egalitarian one. See Ravallion
(1997). Since Latin America is a highly unequal region (and Brazil a highly unequal
country), economic growth there translates into lower rates of poverty reduction than
elsewhere. This has an important additional implication: going beyornd the statistical
decomposition reported here, it is likely that reducing inequality will not only reduce
poverty directly now, but also that it will augment the future effects of economic growth
on poverty.
The general implication is that policies aimed directly at reducing inequality may
have high returns in terms of poverty reduction both now and in the future, provided they
3 Argentina (pre-crisis), Chile, Colombia, the Dominican Republic, Honduras, Panarma amd Uruguay.
"4 Brazil, Costa Rica, El Salvador, Guatemala, Mexico and Nicaragua. The Brazilian result differs from
ours because those authors assumed a constant inequality rate during the 1990s.
15 Bolivia, Ecuador, Paraguay, Peru and Venezuela.
13
do not have high efficiency costs. In the particular case of Brazil, Table 3 revealed that
the growth rate required to halve extreme poverty from its 1990 level without any
inequality reduction would be 60% higher than the rate actually observed in the 1 990s. It
also indicated that, in the absence of any economic growth, blanket untargeted
redistribution would require a substantial additional fiscal effort (of some 3.4% of GDP).
The clear implication is that whichever growth rate can be achieved in the next twelve
years should be complemented by redistribution policies which are more directly targeted
to the poor. In this way, they can contribute more to poverty reduction, at a lower fiscal
cost.
The simple simulation exercise reported in this Section can not take us much further
than this. While it was useful in deriving these general conclusions, the exercise has clear
limitations. *The Brazilian 1990-1999 experience, as illustrated by Figures 2 and 3,
provides a good example of how flawed the assumption of Lorenz-convexity can be in
approximating real distribution dynamics. The changes in a distribution of household
incomes are the complex outcome of a number of underlying economic and social
phenomena, such as changes in the productive endowments available to workers in the
economy; changes in retums to worker characteristics; changes in participation decisions;
changes in family composition; and so on. In the next section, we turn to an empirical
model of household income determination which seeks to incorporate some of these key
dimensions, in the hope that it can provide more specific policy guidance.
3. Behind the Mean and the Lorenz Curve: can a little microeconomics
help?
One reason why a simple transformation of the Lorenz Curve such as that implied by
equation (1) can perform poorly in approximating actual observed changes is that
household incomes are not random numbers drawn from some statistical law defined over
the population. Rather, they are determined by the combination of labor and other
incomes accruing to various household members, and thus depend on their individual
occupational decisions, on the human and physical assets they own, and on the rates at
14
which the markets remunerate -those assets. A simple descriptive model of household
income determination might therefore be given by the following four blocks'6:
Block I: Household Income Aggregation
(7) y~~~h [ id.-k#h +DI
This identity simply defines a household's income per capita from the sum of labor
incomes across occupations (indexed by j) and across household members (indexed by i).
yo denotes all non-labor incomes accruing to the household, and nh is household size. IJ is
an indicator variable that takes the value one if household member i participates in
occupation j, and zero otherwise.
Block II: Earnings Equations
(8) Log yhji = X, 4 i +
Equation (8) is a standard Mincerian earnings equation. In what follows, four such
equations are estimated separately. One is for age group 10-15, which is used only in the
simulation of a specific policy (Bolsa Escola) such as it exists now.'Another one is for
the age group 10 -18. Two are estimated for those aged 19 and older: one for own-
account workers ("conta-pr6prias") and employers; and another for wage-earning
employees.17 In all cases, workers were assigned to the sectors of their principal
occupation. The vector X, as is customary, contained characteristics both of the worker
and of the job. In this case, X included years of schooling (year dummies), age, age
squared, age interacted with schooling, a gender dummy, race (white, non-white),
formality status, and spatial variables (region of the country, urban/rmral). The exact
specification and results for the 19-and-older group (for the under- 18 group) are reported
in Table Al (Table A2) in the Appendix.
16 This model is adapted from Bourguignon, Ferreira and Lustig (1998). Unlike those authors, we do not
model fertility decisions, since simulations of that aspect of behavior would be difficult in this particular
application. Note, however, that the effects of education which operate through the conditional distribution
of family sizes can be substantial. See also Ferreira and Leite (2002).
17 Dummies are included to distinguish between "com carteira", "sem carteira" and public servants.
15
Block III: Occupational Structure
ez, r,
(9) Pi -- where s, j oc. categories. For those aged 19 or older.
eZIY' +XeZIYj
j¢s
Pk e(Z hY +Y {atk + WI .fi*
(10) Pi Ee(Z,.,+Y,a,+Wg.o,) For those aged 10-18.
J
This block models the structure of occupations in the labor force by means of two
similar discrete choice models - specifically, two multinomial logits - which estimate
the probability of choice of each occupation as a function of a set of family and personal
characteristics. Table A3 contains the specification and results for those aged 19 or older,
with inactivity and unemployment as the base category. The other occupational
categories are self-employment ("conta-pr6pria'); formal private sector employment
("com carteira"); informal private sector employment ("sem carteira"); public service;
and being an employer. Table A4 presents the specification and results for those aged 10-
18, for whom the choice of occupations is modeled differently: a young person may not
attend school (base category), attend school only and not work in the market; or both
attend school and work in the market. 8
Note that the occupational choice model for adults is written in reduced form,
since it does not include the wage rate (or earnings) of the individual (or of its family
members) as explanatory variables. Instead, his or her productive characteristics (and the
averages for the household) are included to proxy for earning potential. This approach is
adopted to maintain the econometrics of joint estimation (with Block II) tractable. The
model for 10-18 year-olds, on the other hand, is estimated as a structural model, with the
predicted earnings from the earnings equation reported in Table A2 included as wi in the
18 We do not place any emphasis on the possible interpretations of equations (9))4l 0) as reduced forms of
utility-maximizing behavioral models. Instead, we interpret them as parametric approximations to the
relevant conditional distributions; that is to say, as descriptions of the statistical associations present in the
data, under some maintained assumptions about the functional forms of the relevant joint multivariate
distributions. See Bourguignon, Ferreira and Leite (2002a) for a more detailed statistical discussion of this
kind of counterfactual analysis.
16
RHS for all youngsters, as a measure of potential earnings.19 Other incomes accruing to
the family - but not to the child - are also included, and denoted by Y-j.
Block IV: The Distribution of Education
(11) OPM(e I a,r,g,s): P(e,|M)= D[cc(e,)-Mg]- D[c(e,, })-M.6]
This block models an individual's choice of final educational attainment (in terms
of years of schooling), as a function of his or her age (a), race (r), gender (g) and spatial
characteristics (s), which are grouped in the matrix M. Unlike the choices underlying the
occupational structure of the population, educational choices follow a specific ordering
by years, and are therefore more appropriately represented by an ordered probit model
(OPM). This approach models the probabil:ity (conditional on M) that an individual
chooses education level ei as the difference between the cumulative normal distribution
('D) evaluated at cut-off points estimated for levels eq and eq I. The estirnation results for
(11), containing both the estimated values for o and the seventeen estimated cut-off
points, are given in Table A5.
Although it consists only of four basic equations, this model does seem rather more
complicated than the one presented in Section 2. There had better be a real gain in
understanding and insight, to compensate for the additional complexity. We argue that
this gain is real, and arises from the ability to simulate policy outcomes, which were
impossible to specify in the more general framework of the previous section. To illustrate
this point, we will use equations (7)-(l 1) to simulate the effects of three different
"policies" on the Brazilian distribution of household incomes. Since the purpose of the
19 The occupational choice model for this age group had to be structural because of the nature of the policy
intervention under study for these individuals: it must be able to predict changes in children's occupations
as a result of transfers conditional on school attendance, taking account of the opportunity costs of
schooling in terms of forgone earnings. Simultaneity concerns are alleviated by the fact that only predicted
-rather than actual - earnings are used on the RHS of the Multinomial logit model. Selection issues into the
sample for which the earnings equation is estimated are difficult to address. We follow 'Bourguignon et.al.
(2001) in being skeptical of the Lee (1983) model for multivariate selection bias correction. A bivariate
Heckman correction procedure was tried, but abandoned because (a) it was inconsistent with a trivariate
model of occupational choice, such as (10), and (b) the estimated coefficients of the Mills ratios had values
which were difficult to interpret. This part of the model draws heavily on Bourguignon, Ferreira and Leite
(2002b), where specification and estimation are discussed in greater detail.
17
exercise is forward-looking, we take the 1999 distribution as the base, on which we
implement the simulations.
Policy Scenario One is an increase in individual educational endowments.20 To
simulate this increase, we depart from the existing 1999 PNAD data base to construct a
2015 counterfactual data-base. If one had panel data, or even many repeated cross-
sections from which to construct pseudo-panels, one might try to analyze the educational,
fertility and occupational dynamics of different cohorts, and to predict how these cohorts
might behave in 2015. Such longitudinal data is not available to us and, even if it were,
we would still be faced with missing observations for the young in 2015.
Instead, we make some adjustments to the 1999 data base. For individuals aged 35 or
older, we predict education in the counterfactual (2015) data base, using equation (11)
and their actual residuals, but replacing their age by their age minus sixteen. The effect of
this operation is to replace each of these persons by individuals with identical observed
and unobserved characteristics, but with educational levels prevailing in the cohort which
was sixteen years younger in 1999.
For individuals aged 18 to 34 - i.e. those who would have been two to eighteen in
1999, we simulate an educational expansion which increases mean years of schooling in
the population (five years or older) at the same annual rate (2.34% p.a.) as was observed
between 1990 and 1999. This is done by shifting the cut-off points in the ordered probit
model from their estimated values (see Table A5) to the right by a constant, until the
average predicted mean years of schooling changed from 5.2 (as observed in 1999) to 7.5
= (1.0234)16*5.2. The educational positions of individuals aged 17 or younger were left
unchanged.2'
20 We do not simulate the actual policies which might lead to these increases in educational attainment,
such as additional expenditures on school inputs (such as teachers), adoption of school vouchers, and the
like. While that would be very interesting, it lies beyond the scope of this paper. We simulate merely the
impact (on occupations and incom es) of the outcomes of policies which might have generated such
increases.
21 This assumption greatly simplifies the analysis, since it allows us to separate the educational simulation
from the occupational choice problem of the young, to which we will turn in Scenarios Two and Three.
However, it is probably unrealistic to suppose that the educational preferences of the young would have
remained constant in a setting where adults were more educated. The impact-of this possible
underestimation of schooling amongst the young on household incomes is ambiguous: on the one hand,
those who acquired more education and dropped out of school would have been likely to be commanding
higher wages. On the other, a number of children would be earning less (from child labor), because of more
time spent studying.
18
These procedures generated counterfactual years of schooling for everyone in our
simulated 2015 database. We then feed these counterfactual educational attainments
through equations (8)-(9), generating a counterfactual occupational structure and a
counterfactual earnings distribution for the population. Once -these are aggregated
through equation (7), we have created a counterfactual household income distribution for
Brazil, which departs, from the 1999 distribution, and differs only in ways that reflect
well-specified changes in the conditional distribution of educational endowments.
In Table 4 and Figure 4, results of this simiulation are presented in twvo steps, in order
to highlight the composition of the effects. Table 4 compares three poverty and four
inequality measures for each counterfactual distribution, with those for the actual 1990
and 1999 distributions. Figure 4 plots the differences in the logarithms of mean income
per percentile between the counterfactual distributions and the actual 1999 distribution. In
both cases, the column (or curve) labeled "a & ,B" refers to the counterfactual distribution
where only the direct impact of changes in education on earnings (through equation 8) is
taken into account. The columnn (or curve) labeled "a, p & X" refer to the counterfactual
distribution where irnipacts on occupational choice are also included.
The simulated declines in poverty arising from this policy are not large. Mean
incomes do rise as a result of greater educational endowriients22 (and of greater induced
labor force participation, in the "a, 1 & X" simulation), but inequality behaves
ambiguously. Whereas the, Theil-T and E(2) fall from 1999 to both counterfactual
distributions, the Gini and the mean log deviation both rise. This is an example of the
inequality-increasing effect which some educational expansions can have when returns to
schooling are sufficiently convex.23 In this case, an increase in unemployment and/or
inactivity among the very poor actually causes a further increase in inequality (for two
measures) once -occupational effects are taken into account. This is very' much in line
u It is important to note, however, that the returns to education are being kept constant here. This is clearly
arbitrary, as changes in the relative supply of skills would in general affect the return structure. On the
other hand, this model sheds no light at all on the determinants of the demand for skills, and their prices
must be taken as exogenous. Hence, the only alternative in this kind of exercise is to provide some sort of
sensitivity analysis by simulating different counterfactuals for different arbitrary return structures. Due to
space constraints, we have chosen not to present such an analysis here, but see Ferreira and Leite (2002) for
an example.
23 See Almeida dos Reis and Paes de Barros (1991); Lam (1999) and Bourguignon et. al. (1998) for
discussions.
Table 4: Three Policy Scenarios: Simulation Results
1990 1999 2015 simulated
a&P a,j3&k X t a, ,X&t
Mean Income 232.66 254.90 279.10 282.49 255.70 255.78 283.84
Poverty measures
Poverty Headcount - FGT(O) 7.46% 5.29% 4.98% 5.02% 4.14% 3.87% 3.68%
Povety Gap - FGT(1) 2.97% 2.50% 2.40% 2.45% 1.91% 1.78% 1.73%
FGT(2) 1.83% 1.77% 1.73% 1.77% 1.30% 1.22% 1.20%
Inequality measures
Mean of logarithmic deviation - E(O) 0.7416 0.6934 0.7033 0.7065 0.6618 0.6545 0.6672
Theil index - E(l) 0.7663 0.7045 0.6959 0.6956 0.6947 0.6921 0.6836
Half e Coefficient of Variation Squared - E(2) 2.1286 1.5837 1.4922 1.4830 1.5692 1.5665 1.4649
Gini coefficient 0.6119 0.5889 0.5929 0.5933 0.5869 0.5855 0.5875
Net enrollment in primary education (6 to 15 years old) 0.8008 0.9343 0.9343 0.9343 0.9482 0.9464 0.9594
Ratio of girls to boys in primary education (0 to 8 ys) 1.0255 0.9646 0.9314 0.9314 0.9646 0.9608 0.9244
Ratio of girls to boys in secondary education (9 to 12 ys) 1.2695 1.3105 1.1460 1.1460 1.3106 1.3128 1.1414
Ratio of girls to boys in terciary education (13 or more ys) 1.0199 1.3042 1.3308 1.3308 1.3038 1.3038 1.3404
Ratio of women to men in wage employment 0.5550 0.7137 0.7137 0.7548 0.7137 0.7137 0.7548
Source: PNAD/IBGE 1990, 1999 and authores calculation
Key: a & 0: Policy Scenario One - Earnings effects only
a, P & X: Policy Scenario One - Eamings and occupational effects
r: Policy Scenario Two
t: Policy Scenario Three - Transfers Only
a, P, x & t: Policy Scenario Three - Complete
with the result in Ferreira and Paes de Barros (1999) that increases in extreme poverty in
urban Brazil between 1985 and 1996 were largely due to an occupational effect at the
very bottom of the distribution.
Figure 4: Log Differences Between Counterfactual 2015 and Actual 1999
Diistributions
0.8 . .. . ...... ..................... ..........
0.7
0.6 ^
0.5 -
0.4 -
03
0.2-
0.1
0
v 10 20 30 40 50 60 70 s0 90 Io0
-0.1I... -.
Percentis
As a result of these effects, the incidence of extreme poverty in Brazil in the
simulated distribution falls only from 5.3% to around 5.0% - well short of the Millennium
target of 3.73%. The FGT (1 and 2) measures fall even less, proportionately. The
imnplication is that educational expansions in the scale experienced in Brazil in the 1 990s
are unlikely to be sufficient - on their own -- to canry the country through to meeting its
MDG first target. Since education is often pointed to as something of a distributional
panacea, this is not an entirely irrelevant finding for policy makers.
Why is it that the simulated expansion in -education had such a small effect on
poverty'? The main - but not the only - reason appears to be the flatness of the returns to
schooling at very low levels of education (1-4 years), which the poorest: people in society
tend to have. In Figure 5 we plot (in the solid line) the complement to the cumulative
distribution of years. of schooling among the poor in Brazil in 1999 - i.e. the bottom
5.29% of the population. The dotted line labeled "20 15" plots the counterfactual
21
distribution of schooling for the same individuals, under Policy Scenario One. Using the
same horizontal scale, we graph our estimate of the returns to education in Brazil in 1999:
the coefficients on year dummies, in a regression of log wages on schooling and all the
controls in Table Al, except for the interaction terms between age and education. This
model was estimated jointly for employees and self-employed. It shows that almost 80%
of the poor (by the international poverty line) in 1999 had four or fewer years of
schooling. Even after the counterfactual expansion simulated under Policy Scenario One,
still nearly 70% of that group had four or fewer years of schooling. Marginal returns to
additional schooling at those levels are very low. The results of the simulation in Column
3 of Table 4, where there are no occupational effects, indicate that these returns are
insufficient to make much of a dent in poverty, by any of the three measures reported
there. Colurnn 4 indicates that the occupational effect actually contributes to a marginal
increase in poverty. This is because the incidence of male unemployment increases with
schooling in Brazil and, among the poor, this effect turns out to dominate the increases in
female labor force participation due to greater education.
Figure 5: Actual and Counterfactual Distributions of Education (1-F(e)) among the 1999 Poor, and
Returns to Schoollng
1.00 2.5
0.90
0.80 2.0
0.70 /
0.60 15=
0.50-
0.40 1.0 1
0.30
0.20 0.5
0.10
0.00 0.0
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Years of schooling
- 1999 ' ' 2015 R-turnstoeducaton- 6ghhandsdelo
22.
There are a number of important caveats, of course. Returns are being assumed
constant - as is the constant term in (8), which might rise with economic growth that
arises from other sources. The impact of greater schooling among adults on the demand
for education by their children is not taken into account.24 Perhaps most importantly,
gains in per capita incomes through reductions in fertility - which are not being simulated
here - can be substantial. In a separate study (Ferreira and Leite, 2002) where it was
possible to estimate the impact on household incomes of the reduction in the number of
children in households - both directly through reductions in the per capita denominator
and indirectly through further increased female labor force participation - this turned out
to be substantial. In the simulation most closely comparable to this one, it accounted for
just under a quarter of the overall educational impact.25
On the other hand, there is no guarantee that the pattern of technical change will
allow returns to low skills to rise much, in response to a decline in their supply. Nor has
economic growth generally been known to deliver rapid rates of poverty reduction in
Latin America. And even if we allowed for an additional fifty percent decline in poverty,
due to fertility effects even larger than those estimated in Ferreira and Leite (2002), this
would still only have changed the proportional decline in Po arising from this policy from
6% to 9%. All in all, it might be wise to pay some heed to the finding that, under
reasonable assumptions, educational expansions - however desirable in themselves - will
not eradicate poverty in Brazil on their own.
Table 4 also contains infornation about the other four targets listed in Table 2. The
row entitled "Poverty Gap - FGT(1)" contains the second indicator under Goal 1:
Poverty and Hunger. Like P0, this measure also falls very little as a result of the simulated
Policy Scenario One. Towards the bottom of the Table, the row on '"Net enrollment in
private education" shows considerable actual progress between 1990 (80%) and 1999
(93%). Policy Scenario One, as simulated above, does not affect enrollment rates in 2015
- because it does not alter occupational choices among children. It affects only the
24 Although this impact is incorporated in Policy Scenario Three below and although it wouldn't affect
incomes in 2015 in any case, except through the labor earnings of under- 1 8s.
25 Fertility effects could be simulated there because that was a pure "comparative statics" exercise, with no
cohort linkages between the counterfactual and the base distributions. Here, with only sixteen years
separating 1999 from 2015, a sensible simulation of fertility effects would have had to take cohort effects
into account. As discussed, the absence of panel or pseudo-panel data prevents us from undertaking cohort
analyses in this exercise.
23
distribution of education among adults. This is why the two columns corresponding to
Policy Scenario One show no change in net enrollment from 1999. We will return to this
indicator in the other two simulations.
The next three rows in Table 4 give the ratios of female to male students enrolled
in each of the three levels in the Brazilian education system, in accordance with indicator
#9 (Goal 3) in Table 2. Between 1990 and 1999, women increased their enrollment
advantage over men in both the secondary and tertiary levels, but lost in the primary
level. Given that repetition rates are higher for males in primary school (see
Bourguignon, Ferreira and Leite, 2002b) this might simply reflect a larger number of
male grade-repeaters in primary school. Alternatively, it might signal some deeper trend
among young girls. An investigation of this issue goes beyond the scope of this paper, but
would deserve attention among those concemed with meeting the gender equality goal in
Brazil. If one assumes that gender equality is really the goal, the female advantage at the
secondary and university levels is cause for concem. Are Brazilian men becoming an
undereducated substratum of the population? Can the causes of higher rates of drop-out
among men - which may be related to child-labor, drug-trafficking and violence - be
combated somehow?
Finally, the row entitled "ratio of women to men in wage employment" approximates
the indicator #11, under Goal 3. It is only an approximation because we have not
confined the analysis to the non-agricultural sectors. Once again, the historical gain in
female employment in the 1990s is rather remarkable, as the ratio climbs from 56% to
71%. Looking forward to 2015, the occupational response to the educational gains
simulated under Policy Scenario One would further increase this ratio to just over 75%.
Since an educational expansion appears to be insufficient to meet the MDG poverty-
reduction goals, largely because it fails to raise incomes at the very bottom of the
distribution, we tum next to a consideration of more direct redistribution. Policy Scenario
Two consists of an increase in targeted transfers. Here, rather than simulating a lump-sum
transfer to the poorest households in the sample - which would have ignored the practical
problems of identifying and reaching them - it seemed more interesting to simulate an
existing transfer program, which has received considerable attention and has recently
24
been expanded as a Federal program, namely the Bolsa Escola.26 This is done by adding
conditional cash transfers of T = R$15 per child per month (up to a maximum of R$45
per household) to all households whose children between the ages of 6 and 15 are in
regular attendance at a public school, provided that the household's pre-transfer income
per capita level is less than Y° = R$90 per month."
The conditional nature of the transfer is not innocuous in terms of the estimation
procedure. There are now five different rectuced-form utility levels in the associated
multinomial logit model, to be estimated by (10). These are given by (12), with j = 0
denoting occupational category "not attending school"; j =1 denoting "attending school
and working", and j = 2 denoting "attending school only". Notation in that equation is
exactly as in (10), and M is a part-time adjustment factor for the potential wage of
children who both work and study (see Bourguignon et. al., 2002b). Since the standard
estimation procedure for a multilogit model involves estimating the differences between
parameter values (e.g. al - ao or P2 - Po), the introduction of incomes which are
asymmetric across categories requires additional identification assumptions to enable the
estimation of (12). The assumption we make is that individuals working on the market
and not going to school (j = 0) have zero domestic productivity. Under this assumptions,
the occupational choice model for the young, given by equations (10) and (12) was
estimated both for 10-15 year-olds and for 10-18 year-olds (for reasons which will soon
become apparent), and the results are presented in Table A4.
26 Note, however, that the purpose of simulating Policy Scenario Two is to investigate the effects of
redistributing current income. Our counterfactual therefore corresponds to a program ofiredistribution
which starts in 2015. We do not model the likely impacts of the earlier existence of such a policy (say,
during 1999-2015) on additional schooling, or anything else. This is therefore not an ex-ante evaluation of
Bolsa Escola. For that, please see Bo urguignon et. al. (2002b) instead. Other studies describing early
versions of the program, and trying to assess their impacts include Rocha and Sab6ia (1998), Sant'Ana and
Moraes (1997) and World Bank (2001).
27 These monetary values are kept identical to those adopted in the 2001 law which introduced the Federal
Bolsa Escola program, under the Projeto Alvorada. Since our counterfactual 2015 distribution uses 1999
Reais as units of account, this should not be a problem. Note also that administrative targeting of the
benefit does not actually rely on monthly income (of R$90 or less). Instead, in practice a household living
standards questionnaire (often supplemented by a visit by a social worker) is used to ge:nerate a score,
which is calibrated to bear some resemblance to the inccme means-test. In our simulations, however, we do
use the PNAD total income variable for the means-test. This follows Bourguignon, Ferreira and Leite
(2002b).
25
Uj (0) = Z,.0 + aoY, + POw, + v10
ui (1) =Zi.r, + a, ()r, + T) +,8l3ww + v,l if Y s + Mw; < YO
(12) U,(1)=Z,-.y,+ailY,+A,wi+vi, if 1Y,+ Mw, >Y°
U,(2)=Z,. 2+a2(Y,+T)+fi 2w1+v,2 iflY Y°
One interesting benefit of estimating this structural model for the young is that it
allows us not only to simulate the effect of Bolsa Escola transfers on incomes, but also on
the occupational structure among the young. After all, one objective of conditional cash
transfer programs such as this one, Progresa in Mexico28 or PRAF in Honduras, is to
encourage human capital accumulation by rewarding school attendance. While this issue
is discussed in more detail in Bourguignon, Ferreira and Leite (2002b), we present the
main results for the 10-15 age group below, in Table 5. This table contains two
occupational transition matrices - one for all households and one for poor households
only. Each cell (i, j) in any one of these matrices gives the proportion of people moving
from (actual) occupational category i to (counterfactual) occupational category j. The
matrix converts the initial (1999) marginal occupation distribution (in the last column)
into the counterfactual (2015) marginal distribution (in the bottom row).
Table 5: Simulated effect of Bolsa Escola on schooling and working status (all children 10-15 years old)
AR Households
Not Studying Working and Studying Studying Total
Not Studying 64.1% 12.3% 23.7% 6.0%
Working and Studying - 98.8% 1.2% 16.8%
Studying - - 100.0% 77.2%
Total 3.8% 17.4% 78.8% 100.0%
Poor Households
Not Studying Working and Studying Studying Total
Not Studying 38.7% 20.1% 41.2% 8.7%
Working and Studying - 99.2% 0.8% 30.1%
Studying - - 100.0% 61.2%
Total 3.4% 31.6% 65.00/0 100.0%
Source: PNAD/IBGE 1999 and authors calculation
28 Due to the random nature of village selection in the first stage of its beneficiary selection design,
Progresa - which has been renamed "Oportunidades " and is ongoing in Mexico - has been
comprehensively evaluated. See, for example, Parker and Skoufias (2000) and Schultz (2000).
26
It can be observed that the simulated impact of this transfer scheme is to reduce the
number of children not enrolled in school by 36% among all households, and by over
60% among poor households. About a third of these individuals will attend school but
also keep working in the market. The remaining two thirds would counterfactually only
attend school. Movement from the "working and studying" category to the "studying
only" category is negligible in both groups. The impact of Policy Scenario Two on
incomes can be gauged from Table 4 (column 5), and from Figure 4 (t line). The small
change in mean income reported here is a result of the fact that our model is not an
equilibrium one, and we have not increased taxation anywhere to pay for the transfers.
Even under this unrealistic "manna from heaven" assumption, the increase in the mean is
negligible, due to the small size of the actual Bolsa Escola transfers.29 Their targeting is
effective, however, so that even these small transfers reduce inequality by much more
than Policy Scenario One, according to every measure but the E(2), which is very
sensitive to top incomes. All three poverty measures also fall considerably. The incidence
measure Po reaches 4.14%, much closer to the MDG target than under Policy Scenario
One. Once again, however, it appears that the Bolsa Escola policy by itself - even if fully
implemented in every state of the Federation, and with an administrative targeting
scheme which successfully identified those families living under the R$90 means-test -
would not suffice to meet the MDG poverty reduction target for Brazil.
As a natural next step we simulate, as Policy Scenario Three, a combination of the
previous two policies: an educational expansion identical to Policy Scenario One, and a
transfer scheme with exactly the same criteria and means-test as Bolsa Escola. This time,
however, we solve for the transfer amount, so as to meet the MDG poverty reduction
target. In other words, we construct a counterfactual income distribution applying the
model (7)-(12) to the original 1999 PNAD data set, iterating upwards on the value of the
per-child transfer T (in equation 12), until the poverty incidence Po for the counterfactual
distribution reaches or falls below 3.73%.30 Remarkably, the value of the individual per-
29 As noted by one of the referees, the simulation of Policy Scenario One suffers from the same lack of
fiscal closure, since we do not account for the need to pay for the costs of additional schooling.
30 To be consistent, this combination required that the years of schooling variables for both youngsters and
their parents which are used in the simulation of (10) be adjusted to reflect gains in educational
endowments arising from Policy Scenario One. Similarly, parental occupation variables had to be adjusted
to account for changes induced by the simulated occupations in (9).
27
child transfer which enables the counterfactual distribution to reach the poverty target
was exactly T = R$15, just as in the current program. However, the transfer design in our
Policy Scenario Three differs from the current Bolsa Escola design in two ways: first,
there is no household transfer ceiling; second, youngsters in the 16-18 age range are also
eligible.31
The results for poverty and inequality are given in the last two columns of Table 4,
and by the "ac, ,, x & t" line in Figure 4. Column 6 in Table 4 (labeled "t") corresponds
to the counterfactual distribution under the modified transfer scheme (i.e. as in t, but
expanded to 16-18 year-olds, and with no benefit ceiling), without the educational
expansion. It shows that the expansion of the original Bolsa-Escola design further
reduces both poverty and inequality, bringing the Po indicator to 3.87% - very close to the
MDG target. When an educational expansion as described under Policy Scenario One is
then further combined with this transfer scheme, poverty incidence finally falls to 3.68%,
just below the MDG target. The poverty gap ratio and FGT (2) also fall substantially
from 1990, but by less than 50%.
In terms of inequality, the counterfactual Gini coefficient under Policy Scenario
Three is almost unchanged with respect to the actual 1999 coefficient. Most of the
poverty-reduction effect came from changes at the very bottom of the distribution, as can
be seen from the more pronounced fall in the mean log deviation, which is more sensitive
to these incomes, and from the "a, 3, X & T" line in Figure 4. This line shows clearly that
the largely proportional gains from Policy Scenario Three accrue exactly to the bottom
five percent of the population - exactly the group which was overlooked by the
educational expansion under Policy Scenario One.
Gains elsewhere in the distribution, and particularly from the second quintile
upwards, are much more like those from Policy Scenario One. This is because the
transfer component of Policy Scenario Three is well targeted, as in the real Bolsa Escola
program, and hence has almost no impact above that range of the income distribution.
31 The maximum transfer to a single household was R$150, indicating that ten children in this household
attended school in the counterfactual distribution. The average transfer per household, among those
receiving positive transfers (6,838,017 households in the expanded sample), was R$36.70. Note also that
the inclusion of 16-18 year-olds corresponds roughly to the extension of the benefit to secondary schools,
which many commentators have suggested. See World Bank (2001) and Camargo and Ferreira (2001).
28
The transfers do, however, have a sizeable impact on the schooling decisions of those
children at which they are aimed. Table 6 below is a counterfactual transition matrix
analogous to Table 5, but for 10-18 year-olds. Now that the transfers are combined with
higher schooling levels for both students (parlicularly at the higher ages;) and parents, the
number of children entering school is even higher than before: over 50% among all
households, and 65% among the poor.
Table 6: Sirmlated effect of Bolsa Escola on sdooling and mrking stats (all childin 10-18 jU old) after simuations
All Households
Not Studying Working and Studying Studying Total
Not Studying 45.8% 26.90/o 27.3% 14.2%
Woeking and Studying - 95.3% 4.70/o 22.3%
StU4* - 1.9% 98.0% 63.6%
Total 6.5% 26.3% 67.2% 100.0%
Poor Households
Not Studying Woking and Studying Studying Total
Not Studying 36.50 30.6% 32.80/o 15.4%
Working and Stuying 96.8% 3.2% 31.2%
Studying 0.6% 99.4% 53.4%
Total 5.6% 35.2%o 59.1% 100.0%
Swa PNADIBGE 1999 and auSs calolain
Mobility from the "working and studying" category to the "studying only"
category is also higher than before, but still not substantial. Interestingly, the
educational gains which are incorporated into this counterfactual mean that it is now
possible to have people moving in the reverse direction: from studying only to both
working and studying. This arises because one does not lose one's entitlement to the
transfer, and the multinomial logit model indicates that, with the additional education
level, this individual would most likely now also be working.
The total annual cost of the transfers disbursed under the counterfactual Policy
Scenario Three would have been approximately R$ 3 billion, always in 1999 prices.
This amount excludes any administrative costs, as well as the costs of implementing
the educational reform policies underlying the increases in schooling simulated as in
Policy Scenario One. It corresponds to 0.31 % of the Brazilian GDP in 1999.
29
4. Conclusions
In this paper, we have sought to investigate whether micro-simulation techniques
can shed any light on the kinds of policies which might help countries reach their
Millennium Development Goals. Rather than trying to cover many countries
superficially, the approach we adopted was to test a richer set of approaches for a
single country. We picked Brazil, with which we are most familiar. We started out in
Section 2 with a simple statistical procedure, based on different combinations of
growth rates and inequality reductions which would be consistent with the poverty
reduction target. This exercise suggested that, at least for a country as unequal as
Brazil, the MDG poverty reduction target could be attained through a modest
reduction in inequality, but would require a growth rate well above the recent
historical average if the Lorenz curve remained unchanged. Unless Brazil's growth
performance improves considerably over the next decade (with respect to the 1990s),
then some amount of redistribution will be required to ensure that the Millennium
Development Goal poverty reduction target is met. Additionally, if that redistribution
were to be accomplished through a universal lump-sum transfer - rather than through
more targeted interventions - its financing would imply a sizable additional fiscal
effort.
While this is a useful general policy message, the 'statistical' approach adopted in
Section 2 was too aggregated for thinking about specific policies, be they for
education, labor markets, redistribution schemes, or what have you. Additionally, the
underlying assumption of the specific form in which inequality was reduced in that
particular simulation - which we called Lorenz-convex inequality reduction - turned
out to be strong. In Brazil, the fall in the Gini coefficient actually observed between
1990 and 1999 - in conjunction with the observed growth rate - would have been
enough to more than meet the MDG. Nevertheless, the country's observed poverty
incidence in 1999 was still well above the target - because the shift in the Lorenz
curve which generated that reduction in the Gini was nothing like the simulated one.
This persuaded us of the need to employ a structurally richer model of household
income determination, which was presented in Section 3, and included parametric
30
models for earnings, occupational and educational distributions, conditional on a
number of observed individual and household characteristics. On the basis of these
estimated models, we simulated three different policy scenarios on the 1999 PNAD
data base, attempting to construct plausible outcomes for 2015. Policy Scenario One
consisted of an increase in the schooling levels of the population, calibrated to be
consistent with the increases observed over the 1990s. Policy Scenario Two was the
federal Bolsa Escola program, as currently designed, as if it were functioning
country-wide. Policy Scenario Three was a combination of the previous two, with a
limited expansion in the coverage of the transfer benefit.
Throughout, we attempted to keep the limitations of the exercise and the strength
of the assumptions underlying it at the forefront. Even in these simulations, which
take existing behavioral patterns into account to a much greater extent, we are unable
to predict how prices - and the prices of skills in the labor market in particular - will
respond to the changes we simulate. Or indeed to all the other myriad changes which
we do not simulate, and have no idea about. This abstraction from equilibrium
responses is a general characteristic of simulations in the Oaxacat (1973); Blinder
(1973) family.32 But it is less problematic when used in the context for which it was
originally designed, namely to decompose changes that have already happened and
been observed into different effects. In the present context, when a single structure is
observed and used to construct an entire counterfactual in the future, the limitations
are very serious indeed.
Nevertheless, some of the findings from our Section 3 simulations were
interesting. First, an expansion in schooling levels appears to be unlikely to reduce
extreme poverty by very much, because returns to an additional year of schooling at
very low levels of education are too small. Educational expansions are enormously
beneficial to society as a whole, but their impacts on the poorest of the poor are likely
to be indirect, and could take a very long time to be felt. If policy-makers in a country
like Brazil were serious about reducing the incidence and severity of extreme poverty,
it seems almost certain that they should rely on some form of redistribution.
32 See DiNardo, Fortin and Lemieux (1996) and Bourguignon, Ferreira and Leite (2002a) for discussions.
31
In that context, a conditional cash-transfer program, like Bolsa Escola or
Progresa, designed with incentive considerations very much in mind, would appear
to be a natural candidate. Our simulations indicate that, whereas a program like Bolsa
Escola might not be sufficient in isolation and in their current format, it might be a
very important tool in meeting the Millennium Development Goals, if combined with
a set of sustained policies aimed at expanding educational attainrnents. Our Policy
Scenario Three, which could be described as a Bolsa Escola extended to secondary
school and without household ceilings, combined with an educational expansion at
the pace which was observed historically in Brazil during the 1990s, does generate a
counterfactual distribution where the incidence of poverty is below the MDG target
for the country. And because it is narrowly targeted to the poor, its fiscal
requirements are an order of magnitude smaller than those of a universal lurnp-sum
redistribution scheme such as that implied by equation (1) in Section 2: 0.3% - rather
than 3% - of GDP.
Of course, because prices might change; because occupational structures might no
longer be governed by the parametric relationships estimated in 1999; and because of
a million other unforeseen events, these are not predictions. Our scenarios are not
intended - and should never be taken - as detailed policy blueprints. But they may,
perhaps, be useful as an indication of the broad types of policies which policy makers
might want to focus on, if they are interested in reducing extreme poverty in unequal
middle-income countries.
It turns out that the extreme poor in these countries are hard to reach through
"blunt" policy instruments like generalized educational expansions. Distribution-
neutral economic growth - which certainly is good for the poor - also needs to be of
some magnitude to translate into the absolute income increments needed to raise
those at the very bottom of the distribution above the relevant poverty lines. If such
copious growth is for some reason not immediately forthcoming, "sharper" tools -
like fiscally affordable targeted conditional redistribution programs - can become
very useful complements to broad-based educational and income expansions.
32
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Appendix.
Equation (4) can be obtained as follows. We know that the Gini Coefficient is given by:
G(Y) = 21 IY-Y
It follows from (1) that: y* - y1*y = (jl+0)(1-a)jyj- yjj
Thus: 1 Iyi"j - I = (1+0)(1-a)y_jy - yjI
Dividing through by 2n2(1+I3)1Ay:
(2n2A,*)-l yj* - yj*F l (2n2(l+J),ty'(l+I)(i-a)XXIyi yji
which yields equation (4).
35
Table Al: Micerian Equation for adults (above 18 years old)
Self-employed and Enployer Employees: Formal, infonnal and public servauts
Coefficient Std P>Izl Coefficient Std P>kz
R2 0.52 0.59
#obs 39,071 81,918
Yeas ofachoolmg
1 0.0805 0.0281 0.0040 -0.0086 0.0158 0.5840
2 0.1646 0.0245 0.0000 40.0465 0.0131 0.0000
3 0.2202 0.0245 0.0000 -0.0332 0.0130 0.0100
4 0.3603 0.0251 0.0000 -0.0089 0.0128 0.4880
5 0.4145 0.0327 0.0000 0.0024 0.0156 0.8760
6 0.4470 0.0368 0.0000 0.0052 0.0177 0.7710
7 0.5210 0.0392 0.0000 -0.0214 0.0188 0.2540
8 0.5732 0.0393 0.0000 0.0416 0.0192 0.0300
9 0.5296 0.0548 0.0000 0.0302 0.0229 0.1860
lo 0.6555 0.0505 0.0000 0.0495 0.0234 0.0350
lI 0.8045 0.0482 0.0000 0.2230 0.0228 0.0000
12 0.9970 0.0890 0.0000 0.4566 0.0316 0.0000
13 1.0622 0.0756 0.0000 0.4579 0.0337 0.0000
14 1.0457 0.0796 0.0000 0.5351 0.0343 0.0000
15 1.3055 0.0697 0.0000 0.6911 0.0331 0.0000
16 1.4778 0.0758 0.0000 0.8992 0.0380 0.0000
17 1.7109 0.0986 0.0000 0.9884 0.0468 0.0000
Age 0.0526 0.0024 0.0000 0.0468 0.0013 0.0000
Agp2 -0.0006 0.0000 0.0000 -0.0006 0.0000 0.0000
Intemclion beween age and schooling 0.0005 0.0001 0.0000 0.0014 0.0001 0.0000
Male 0.6702 0.0110 0.0000 0.4595 0.0046 0.0000
White 0.2250 0.0106 0.0000 0.1368 0.0048 0.0000
Am
Urbansnetcpolilaa -0.1539 0.0109 0.0000 -0.1971 0.0048 0.0000
RwW -0.4709 0.0145 0.0000 -0.3768 0.0075 0.0000
Occupation
selfemployri -0.8164 0.0141 0.0000
Fonral -0.0260 0.0077 0.0010
Infonn l -0.4102 0.0085 0.0000
Region
Noshb -0.1356 0.0181 0.0000 -0.0844 0.0093 0.0000
Notbeast -0.4507 0.0128 0.0000 -0.3696 0.0059 0.0000
South -0.1220 0.0138 0.0000 -0.0783 0.0062 0.0000
Ce.it.w. -0.0044 0.0160 0.7840 -0.0199 0.0068 0.0040
Intaeep 4.4372 0.0634 0.0000 4.4388 0.0314 0.0000
Soetcr PNAThIBOE 1999 and authoes caleulation
36
Table A2: Earnings Equation for the Young
10 to 15 years old' 10 to 18 years old2
Coefficient Std P>jzl Coefficient Std P>IzI
n obs 2428 8637
R2 0.48 0.51
Dummy WS -0.2956 0.0335 0.0000 -0.1293 0.0147 0.0000
Years of schooling -0.0483 0.0192 0.0120 -0.0128 0.0085 0.1300
Age 0.1538 0.0118 0.0000 0.1464 0.0047 0.0000
Years of schooling2 0.0095 0.0020 0.0000 0.0042 0.0007 0.0000
Male 0.1590 0.0273 0.0000 0.2210 0.0140 0.0000
White 0.0844 0.0277 0.0020 0.0752 0.0144 0.0000
Urban non metroplitan 0.0341 0.0315 0.2800 -0.0815 0.0152 0.0000
Rural 0.0334 0.0393 0.3940 -0.1197 0.0205 0.0000
North -0.1806 0.0440 0.0000 -0.0720 0.0255 0.0050
Northeast -0.1984 0.0365 0.0000 -0.1941 0.0202 0.0000
South -0.0280 0.0403 0.4860 -0.0470 0.0183 0.0100
Center-West -0.1189 0.0397 0.0030 -0.0837 0.0196 0.0000
Log of means earnings by cluster 0.3725 0.0141 0.0000 0.3580 0.0097 0.0000
Intercept 1.3783 0.1745 0.0000 1.1375 0.0892 0.0000
Notes:
- Log of means earnings by cluster computed for children between 10 to 15
- Log of means earnings by cluster computed for children between 10 to 18
Source: PNAD/IBGE 1999 and authors calculation
Table A3: The Multinomial Logit Estimates for Participation Behavior and Occupational Choice for adults (above 18 years old)
Self-employed Formal Informal Public servants Employers
ME* P>Iz| MME P>|z| MM P>Iz| zM* P* ME* P>iz|
Pseudo RX 0.1798
#obs 210,000
Yearsofschooling - 0.000 - 0.000 - 0.121 - 0.000 - 0.000
Years of schooling2 - 0.730 - 0.416 - 0.000 - 0.008 - 0.058
Age - 0.000 - 0.000 - 0.000 - 0.000 - 0.000
Age2 - 0.000 - 0.000 - 0.000 - 0.000 - 0,000
Interaction between age and schooling - 0.000 - 0.000 - 0.000 - 0.000 - 0.000
Male 0.155 0.000 0.084 0.000 0.018 0.000 0.005 0.000 0.043 0.000
White 0.013 0.000 -0.008 0.060 -0.020 0.000 -0.009 0.000 0.017 0.000
Average endowments of age 0.000 0.000 0.000 0.000 -0.001 0.000 0.000 0.662 0.000 0.000
Average endowments of schooling 0.000 0.642 -0.003 0.000 -0.006 0.000 -0.001 0.000 0.002 0.000
#ofbouscholdsncmbcrbelowltyearsold 0.004 0.000 40.005 0.000 0.005 0.000 0.000 0.276 0.000 0.873
#of households mamber beween 19 and 64 yea old -0.011 0.000 0.006 0.000 -0.005 0.000 -0.001 0.278 -0.002 0.000
#ofhouseolds nemnberabove65yearsold 0.005 0.081 -0.026 0.000 -0.020 0.000 -0.003 0.109 0.009 0.000
Head of the household 0.186 0.000 0.190 0.000 0.070 0.000 0.046 0.000 0.053 0.000
2nd head of the household 0.031 0.000 -0.079 0.000 -0.074 0.000 0.006 0.001 0.016 0.000
Ifnotthehead,theheadisactive? 0.002 0.178 -0.030 0.000 -0.006 0.000 -0.005 0.000 0.010 0.000
Area
Urban non-metropolitan 0.021 0.000 -0.014 0.049 0.026 0.000 0.020 0.000 0.016 0.000
Rural 0.070 0.000 -0.105 0.000 0.015 0.000 0.009 0.000 0.018 0.000
Region
North 0.040 0.000 -0.176 0.000 -0.021 0.629 0.025 0.000 0.001 0.010
Northeast 0.068 0.000 -0.126 0.000 -0.020 0.000 0.014 0.000 0.003 0.001
South 0.026 0.000 0.016 0.000 40.015 0.000 0.002 0.348 0.002 0.047
Center-West 0.000 0.011 -0.065 0.000 0.018 0.000 0.021 0.000 0.007 0.000
ep"t - 0.000 - 0.000 - 0.000 - 0.000 - 0.000
Source: PNAD/IBGE 1999 and authors calculation
Note: ME*: Marginal Effect calculated from the estimated coefficients.
The marginal effects for age and education are omitted due to the interaction terms.
Table A4: The Multinomial Logit Estimates for Participation
Behavior and Occupational Choice for the Young
Working and Studying Studying
Pseudo-R' #obs ME* P>Izl ME* P>IZI
10 to 15 years old 0.2145 43418
Total household income 0.000 0.065 0.000 0.000
Earning's children (What) 0.002 0.001 -0.004 0.000
Total people by household 0.009 0.000 -0.007 0.196
Age - 0.000 - 0.000
Years of schooling 0.000 - 0.000
(Age-schooling)2 - 0.001 - 0.091
White -0.028 0.997 0.038 0.000
Male 0.101 0.000 -0.087 0.036
Max parenfs education -0.008 0.000 0.013 0.000
Max parent's age -0.001 0.403 0.001 0.000
Number of children (O to 5 years old) -0.001 0.000 -0.010 0.000
Rank of child 0.014 0.219 -0.014 0.546
Urban non metroplitan 0.031 0.015 -0.032 0.451
Rural 0.212 0.000 -0.219 0.000
North 0.093 0.000 -0.084 0.742
Northeast 0.094 0.000 -0.076 0.006
South 0.095 0.023 -0.117 0.000
Center-West 0.069 0.002 -0.075 0.026
Means of earnings by cluster -0.002 0.000 0.004 0.000
Intercept -0.729 0.000 1.216 0.000
10 to 18 years old 0.2557 65507
Total household income 0.00 0.07 0.00 0.00
Earning's children (What) 0.00 0.02 0.00 0.00
Total people by household 0.01 0.00 0.00 0.00
Age - 0.00 - 0.00
Years of schooling 0.00 0.00
(Age-schooling)2 - 0.00 - 0.01
White -0.02 0.55 0.02 0.00
Male 0.08 0.00 -0.08 0.61
Max parent's education -0.01 0.00 0.01 0.00
Max parent's age 0.00 0.00 0.00 0.00
Number of children (O to 5 years old) 0.00 0.00 -0.02 0.00
Rank of child 0.01 0.71 -0.02 0.00
Urban non metroplitan 0.03 0.24 -0.04 0.00
Rural 0.18 0.00 -0.22 0.00
North 0.04 0.00 -0.03 0.00
Northeast 0.06 0.00 -0.04 0.00
South 0.07 0.74 -0.10 0.00
Center-West 0.05 0.00 -0.06 0.01
Means of earnings by cluster 0.00 0.22 0.00 0.00
Intercept -0.77 0.00 1.31 0.00
Source: PNAD/IBGE 1999 and author's calculation
Note: ME*: Marginal Effect calculated from the estimated coefficients.
The marginal effects for age and education are omitted due to the interaction terms.
Table A5: Ordered Probit model (5 years old or more)
Coefficien Std P>IzI
Age group
5 to 10 -1.6811 0.0062 0.0000
11 to 18 -0.0218 0.0040 0.0000
Male -0.0405 0.0041 0.0000
White 0.3851 0.0045 0.0000
Area
Urban non-metropolitan -0.2275 0.0046 0.0000
Rural -0.8049 0.0061 0.0000
Region
North -0.0280 0.0083 0.0010
Northeast -0.2405 0.0054 0.0000
South -0.0121 0.0058 0.0380
Center-West 0.0541 0.0067 0.0000
Cut-off points
1 -1.4363 0.0065
2 -1.2189 0.0062
3 -0.9484 0.0060
4 -0.6563 0.0058
5 -0.1847 0.0058
6 0.0110 0.0057
7 0.1627 0.0057
8 0.3162 0.0057
9 0.5968 0.0058
10 0.7002 0.0058
11 0.8144 0.0058
12 1.4831 0.0063
13 1.5423 0.0064
14 1.6095 0.0065
15 1.6978 0.0067
16 2.1622 0.0082
17 2.6981 0.0126
Source: PNAD/IBGE 1999 and author's calculation
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