WPS5424
Policy Research Working Paper 5424
Distributions in Motion
Economic Growth, Inequality, and Poverty Dynamics
Francisco H. G. Ferreira
The World Bank
Latin America and Caribbean Region
Office of the Chief Economist
September 2010
Policy Research Working Paper 5424
Abstract
The joint determination of aggregate economic the observation that growth, changes in poverty, and
growth and distributional change has been studied changes in inequality are simply different aggregations of
empirically from at least three different perspectives. information on the incidence of economic growth along
A macroeconomic approach that relies on cross the income distribution. This paper reviews the evolution
country data on poverty, inequality, and growth rates of attempts to understand the nature of growth incidence
has generated some interesting stylized facts about the curves, from the statistical decompositions associated
correlations between these variables, but has not shed with generalizations of the OaxacaBlinder method, to
much light on the underlying determinants. "Meso" and more recent efforts to generate "economically consistent"
microeconomic approaches have fared somewhat better. counterfactuals, drawing on structural, reducedform,
The microeconomic approach, in particular, builds on and computable general equilibrium models.
This papera product of the Office of the Chief Economist, Latin America and Caribbean Regionis part of a larger
effort in the department to understand the dynamics of poverty and income distribution. Policy Research Working Papers
are also posted on the Web at http://econ.worldbank.org. The author may be contacted at fferreira@worldbank.org.
The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development
issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the
names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those
of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and
its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent.
Produced by the Research Support Team
Distributions in Motion: Economic Growth, Inequality, and Poverty Dynamics
Francisco H. G. Ferreira1
Keywords: Poverty and inequality dynamics; growth incidence curves.
JEL Classification: D31, I32
1
The author is the World Bank's Deputy Chief Economist for Latin America and the Caribbean. This paper was
commissioned as a chapter for the Oxford Handbook of the Economics of Poverty, edited by Philip Jefferson. I am
grateful to the editor, to Stefan Dercon, Stephan Klasen and Maria Ana Lugo for comments on and helpful
conversations about an earlier version. I am also grateful for comments from seminar participants at the Paris
School of Economics, the Katholieke Universiteit Leuven, the Universities of Bari and Göttingen, and the Canazei
Winter School on Inequality. I am solely responsible for any remaining errors. The views expressed in this paper are
those of the author, and they should not be attributed to the World Bank, its Executive Directors, or the countries
they represent.
2
1. Introduction
The dynamic relationship between economic growth, inequality and poverty has always commanded
considerable attention among economists. The nexus between growth and development on the one
hand, and the distribution "of the whole produce of the earth" on the other has been central to the
discipline at least since David Ricardo's (1817) Principles of Political Economy.
In the second half of the Twentieth Century, this relationship was approached from a number of
different perspectives. Drawing on the seminal work of W. Arthur Lewis (1954) and Simon Kuznets
(1955), one strand of the literature has investigated whether income inequality follows a particular
dynamic process as economies grow. Lewis saw the process of economic development as largely driven
by the transfer of productive resources from backward, lowproductivity sectors (such as subsistence
agriculture) to highproductivity sectors such as modern plantation agriculture or industry. As labor
moved from the poor, but relatively egalitarian backward sectors towards the richer, but more unequal
modern sector, Kuznets expected inequality first to rise and then to fall, as the share of workers in the
original sector declined. The timeseries data on income inequality that was available to Kuznets in the
1950s was extremely restricted. It came from Germany, the United States and the United Kingdom. But
in those countries, an "inverted U" pattern for inequality could indeed be identified, thus lending
support to the Kuznets hypothesis, which came to dominate a subfield of development economics for
many years to come.
In the 1990s, progress in two areas of economic theory the consequences of asymmetric information
and incomplete contracts for how credit and insurance markets function, and endogenous growth
theory combined to generate a fair amount of interest in another approach to the same broad issue.
Rather than asking how growth and development affected the distribution of income, a new literature
asked whether high initial levels of inequality (or poverty) might be detrimental for future growth. With
missing or imperfect credit markets and nonconvex production sets, individuals with low wealth might
be trapped in lowinvestment equilibria, leading to divergence between the rich and the poor. Societies
starting off with a greater proportion of its population in poverty (or greater inequality given a certain
mean) might generate less aggregate investment, or a less advanced occupational structure, and thus
lower growth rates.2 Other stories linking initial income distribution to subsequent growth involved
political economy channels. In one strand, higher inequality led the "median voter" to support higher
rates of distortionary taxation, leading to lower growth (see, e.g. Alesina and Rodrik, 1994; and Persson
and Tabellini, 1994). In another, taxation and public spending were seen instead as potentially efficient
mechanisms for correcting market failures, but greater inequality in wealth and political power led to
too little public investment (see, e.g., Bénabou, 2000, and Ferreira, 2001).
A considerable expansion in the availability of household survey data, particularly among developing
countries, took place in tandem with these theoretical developments. Greater data availability enabled
researchers to "test" the predictions of their theories on crosscountry data sets that included measures
2
See, e.g. Galor and Zeira (1993) and Banerjee and Newman (1993).
3
of economic growth, income inequality and, in some cases, poverty statistics.3 From the point of view of
validating a particular theoretical approach, the resulting empirical literature was not encouraging. As
timeseries of inequality statistics became available for more countries, evidence of an "inverted U"
Kuznets curve appeared to vanish, both when looking within countries over time (see Bruno et al, 1998)
and across countries at different levels of GDP per capita (Ravallion and Chen, 1997). Evidence of
causality from inequality to subsequent growth fared no better. Some early papers found a negative
effect of initial inequality on growth in crosscountry regressions (Alesina and Rodrik, 1994; Deininger
and Squire, 1998), but later studies cast doubt on the interpretation of that result by finding that, in a
panel specification, the effect of lagged inequality on growth appeared to be, if anything, positive
(Forbes, 2000).
The literature never converged to a consensus. It was not clear whether the panel specification yielded
econometrically superior results (because it eliminated possible endogeneity biases by using lagged
variables as instruments), or whether there was something substantively different about recent changes
in inequality, visàvis differences in "steadystate" initial levels of inequality. Banerjee and Duflo (2003)
argued that crosscountry data of the kind used in this literature was not capable of shedding much light
on the myriad nonlinear processes that might be linking inequality and growth. Voitchovsky (2009)
concludes a recent survey by noting that "the inconsistency of reported empirical findings could reflect
the gap between the intricacy of the relationship, as expressed in the theoretical literature, and the
simple relationships that are commonly estimated." (p.569)
To make matters worse, it seemed for a moment in the early 2000s as though even the relationship
between growth and poverty which had always been taken more or less for granted, at least among
economists was being questioned. Using quotes from policy circles, Dollar and Kraay (2002) noted that
although "The world economy grew well during the 1990s [...], there is intense debate over the extent to
which the poor benefit from this growth." (p.195). While some appeared convinced that growth is "a
rising tide that lifts all boats", others insisted that, in the 1990s, "the rich were getting richer, and the
poor were getting poorer".
In the early 2000s, then, one might have been forgiven for concluding that economists had not made
much progress in understanding the relationship(s) between growth and distribution since the days of
David Ricardo. Our best shot at a general theory of how structural change and economic development
affected the distribution of income the Kuznets hypothesis appeared to be rejected by more plentiful
data.4 Similar data appeared to generate contradictory or inconclusive results for tests of alternative
theories about the reverse channel of causation: from inequality to growth. And now there was even a
3
The history of this growth in data availability and a discussion of how comparable the different data sets are
are topics of considerable interest in and of themselves, but they fall beyond the scope of this paper.
4
To be fair, there was an alternative view of longterm inequality dynamics, associated with Jan Tinbergen, which
proved rather more robust. Tinbergen (1975) saw changes in earnings inequality as largely reflecting the evolution
of a "race" between technological progress which he saw as raising the demand for skills and the expansion of
formal education which raised the supply of skills. Strangely, this view appears to have been more popular with
labor economists than with development economists.
4
debate on whether growth reduces poverty... Do economists actually know anything about what
François Bourguignon (2004) christened "the povertygrowthinequality triangle"?
This paper reviews some of the recent empirical literature on this triangular relationship, and makes a
twopart argument. The first part is that, even if it has not yielded a clear confirmation of any particular
grand theory of how growth and distribution are connected, this literature has taught us a few things. I
summarize these lessons in terms of three basic "stylized facts", which do seem to be robustly
supported by the data.
The second part of the argument is that, while it has been useful in shedding light on those stylized
facts, the essentially "macroeconomic" approach followed by this literature is not particularly promising
if the objective is to gain a real understanding of the joint determination of growth, inequality and
poverty. Average income, poverty and inequality are all aggregate concepts: averages of incomes or
income gaps, measured in different ways, and with different weights along the distribution. Their
evolution over time economic growth, changes in poverty and changes in inequality are all jointly
determined by the individual income dynamics in that distribution. Because the three vertices of the
triangle are all defined over the distribution of income, they are mechanically related by a statistical
identity. But estimating relationships between the three objects or between two at a time is unlikely
to tell us much about the underlying processes, since it ignores that all three are driven by the
interaction of individual behaviors at the microeconomic level.
Of course, like much else in macroeconomics, the estimated relationships between poverty, inequality
and growth reveal interesting stylized facts regularities in the data that are informative of deeper
forces. The paper begins by reviewing the useful stylized facts that have arisen from the recent
"macroeconomic" or crosscountry literature (in Section 2). Section 3 briefly turns to what I term a
"mesoeconomic" approach, which uses somewhat more disaggregated data along the spatial and
sectoral dimensions within individual countries, to investigate the same "triangular" relationship.
In Section 4, I focus on an alternative microeconomic approach, which delves beneath the aggregate
measures of poverty, inequality and growth, and considers changes in the entire underlying distribution
of incomes. First, each of the three aggregate variables in the povertygrowthinequality triangle is
shown to be expressible as a different aggregation of the information contained in a full description of
growth along the income distribution the growth incidence curve (GIC).5 This allows us to argue that to
understand distributional dynamics, one needs to understand the determinants of the GIC. This has
generally been attempted by means of counterfactual decompositions of distributional change, which
range from the purely statistical, to those with greater economic content. Although that literature has
seldom been related to the macro and mesoeconomic approaches discussed above, and often uses a
different language, the paper argues that they are closely related in their essence. A fifth section offers a
few concluding remarks, and suggests possible avenues for future research.
One feature that all three approaches reviewed in this paper have in common is their respect for the
anonymity (or `symmetry') axiom of inequality and poverty measurement. This axiom requires that
5
The GIC was first defined in Ravallion and Chen (2003).
5
poverty and inequality measures (and therefore, evidently, their differences) be invariant to
permutations of the income vector. It implies that, when comparing distributions and their summary
statistics, the analyst must ignore the individual dynamics along the distribution: two identical
distribution functions = , for must yield identical inequality and poverty statistics (for a
given poverty line), regardless of changes in the identities of the occupants of each percentile p.
This is a standard axiom in the analysis of poverty and inequality, and it helps to considerably narrow the
scope of the paper. In particular, it means that we do not review work on economic mobility, or on
individual or household income dynamics. As panel data has become available in developing countries, a
number of recent studies have sought to shed light on the determinants of individual income or
consumption dynamics (e.g. Dercon, 2004; Lybbert et al., 2004). These studies have often focused on
the role of different asset classes (land, livestock, physical infrastructure) in promoting income growth;
on the effects and persistence of various uninsured shocks; and on the evidence for or against poverty
traps (e.g. Jalan and Ravallion, 2002). This is an important literature. Because they follow the same
individuals over time, such panelbased studies are generally better at identifying the causal effects of
exogenous shocks (possibly including policy shocks) on inequality and poverty than most of the work we
review in this paper. At the same time, they typically rely on small samples, which are not representative
of entire countries. They are not intended to, and generally cannot, assess the joint determination of
aggregate economic growth, and societal poverty and inequality rates, which is our focus here. They are
omitted from this review on that basis, but their superiority in terms of causal identification means that
there may be much to be gained from deeper thinking about how these different approaches
interrelate. We briefly return to this point in the concluding section.
2. The macroeconomic approach
What I call the macroeconomic approach to the relationships between poverty, inequality and growth
consists of crosscountry (panel or single crosssection) analysis of how those three variables or, more
often, two at a time, are related to one another. In order to understand this approach, it is useful to
start from a very simple accounting identity, which relates the incidence of poverty known as the
headcount index, H both to the mean and to the `shape' of the distribution of income.
Denote the Lorenz curve for a given distribution as L(p, ), where , and is a vector of
6
parameters that fully determines the functional form of the Lorenz curve. It is wellknown that the
derivative of the Lorenz curve at percentile p is given by the ratio of the income at that percentile (the
quantile function ), to the overall distribution mean:
, (1)
The headcount is simply the share of the population with incomes no higher than the poverty line,
. Therefore, evaluating equation (1) at p = H, and solving for H yields:
6
F(y) is the cumulative distribution of income: it gives the measure of the population with incomes lower than y,
for every y. The Lorenz curve is a related, but different concept. It gives the cumulative share of income that
accrues to the poorest p% of the population, for every p.
6
/ , (2)
Equation (2) is the fundamental identity in the "poverty growthinequality triangle". For a given poverty
line z, it relates the incidence of poverty to the mean of the distribution (inversely), and to the
parameters of the Lorenz curve. The Lorenz curve is deeply associated with the concept of inequality.7
Given a constant real poverty line z, the poverty headcount is therefore fully determined by the "shape"
of the distribution (given by the Lorenz curve) and its central location (given by the mean). Analogous, if
somewhat more complicated, identities relate other poverty measures to the distribution's mean and
Lorenz curve.8
It is straightforward to move from the fundamental identity of the triangle in levels, to its dynamic
counterpart. One simply differentiates equation (2) with respect to time. Denoting the time derivative
of variable x as dx, one obtains:
(3)
Equation (3) relates changes in poverty to the rate of economic growth ( / ), and to changes in
"inequality" or, more precisely, in the Lorenz curve ( ).9 It tells us that any change in poverty can be
mechanically decomposed into a growth component (the first term on the RHS), and a distribution
component (the second term). Since the Lorenz curve is always increasing and convex by construction
(so that 0, 0 ), equation (3) also tells us that the partial elasticity of poverty with respect to
growth ( ), is always negative: if there is no change in the Lorenz curve, an increase in mean
incomes must be accompanied by a decline in poverty. In other words: growth must lead to poverty
reduction, unless it is accompanied by substantial distributional change (which may be fairly, albeit
somewhat imprecisely, described as "increasing inequality").
The partial inequality elasticity ( ), on the other hand, cannot be signed a priori: changes in the
distribution may increase or reduce poverty, depending on how the Lorenz curve shifts, and on the
relative position of the poverty line.
7
The Atkinson (1970) theorem establishes that, given two distributions A and B such that , , with
the inequality holding strictly at least at one point, then any inequality index that satisfies the PigouDalton
transfer principle must take a higher value in distribution A than in B. The (strong) PigouDalton transfer principle
states that an inequality measure must rise in response to a transfer of income from a poorer to a richer person. It
is regarded as a key axiom for inequality indices.
8
The most widelyused family of poverty measures is the FosterGreerThorbecke class, .
The headcount is the FGT measure when 0. Other commonlyused members of the class take values of
1,2.
9
We are deliberately glossing over the empirically important question of whether one should measure economic
growth as the growth in mean household incomes (from a household survey), or by growth in some concept
obtained from national accounts data, such as GDP per capita. While the two should not differ systematically over
long periods of time, they have often been found to diverge considerably in the short and medium runs.
7
This decomposition of changes in poverty into growth and distribution components was first applied
empirically by Datt and Ravallion (1992) and Kakwani (1993). Using discrete time intervals, Datt and
Ravallion noted that equation (3) could be approximated by writing:
, , , , , (4)
Once again, the first term on the RHS of equation (4) corresponds to the growth component, and holds
the Lorenz curve constant, while the second term measures the redistribution component, while holding
mean income constant. The third term is a residual that arises from the pathdependence of the discrete
decomposition, and vanishes if the decomposition is averaged across the two possible orderings. Datt
and Ravallion (1992) applied this decomposition to India (19771988) and Brazil (19811988). Over these
periods, poverty fell in India, and stayed broadly constant in Brazil. In rural India, where the decline was
of 16%, the growth component accounted for some ten percentage points, and the redistribution
component for about six points (the residual was negligible). In Brazil, the very limited growth that did
take place during the 1980s contributed towards a reduction in poverty, but this effect was entirely
offset by increasing inequality.
This exercise has since been repeated for many countries. While results vary considerably reflecting
crosscountry differences both in growth performance and in inequality trends one may summarize
them as follows: when economic growth is high, the negative growth component tends to dominate the
decomposition, and leads to falling poverty (although rising inequality can slow this down).10 When
growth is small, as in the Brazilian example above, the distribution component can dominate, and
changes in inequality may make the difference between rising and falling poverty.
Besides computing the poverty decomposition for individual countries one at a time, as in equation (4),
one could try to estimate equation (3) on a crosssection of countries. Although it holds as an identity
for each particular country at each point in time, the partial elasticity terms ( and ) obviously
differ across countries and periods, as the distributions themselves change. For that reason; because
different inequality indices summarize the information in the Lorenz curve somewhat differently; and
because of measurement error, it would be possible to estimate equation (3) econometrically, say by
regressing changes in poverty on growth and changes in inequality (I): . Such a
regression would not have an R2 of one, and estimates of and would represent sample estimates of
the average values for those elasticities.
This is not, however, what most papers in the macroeconomic approach have done. To avoid the
impression of estimating an identity, most studies have omitted either growth or changes in inequality
from the RHS of the regression. The vast majority estimate a regression of changes in poverty on
economic growth, with or without controls (X):
10
See Ahuja et al (1997) for a set of the decompositions of this sort applied to highgrowth East Asian economies
prior to the Asian crisis of 199798.
8
(5)
One of the first papers to estimate equation (5) on crosscountry data was Ravallion and Chen (1997).
Using a compilation of household survey datasets available at the World Bank, these authors assembled
a data set with householdsurveybased poverty measures and growth rates for 67 countries over the
period from 1981 to 1994. With no controls other than a countryspecific time trend, and using an
international poverty line of US$1 per day at 1985 PPP exchange rates, they found a central estimate for
the growth elasticity of poverty of = 3.1. Excluding the then transitioning economies of Eastern
Europe and Central Asia, the regression line went through the origin: the average rate of change in
poverty at zero growth in their sample was zero. This reflected the fact that they could find no
significant crosscountry correlation between changes in inequality and economic growth in their
sample.
Although the numbers have changed as the sample expanded, and different specifications have been
tried, those two basic results have been confirmed by the more recent literature. Dollar and Kraay
(2002) replaced the headcount index with an alternative, slightly unconventional (inverse) measure of
poverty: the average income of the poorest 20% of the population. Using a sample of 92 countries over
four decades, they could not reject a positive elasticity of 1.0: growth in the incomes of the bottom
quintile was, on average, equiproportional to growth in mean incomes. This result, which survived the
introduction of a number of controls, once again implied that changes in inequality were not
systematically correlated with economic growth. Ravallion (2007) find a slightly lower growth elasticity
for the poverty headcount than the earlier RavallionChen study, and a small negative but statistically
insignificant correlation between changes in the Gini coefficient and proportional changes in mean
income, in a sample of 80 countries. Kraay (2006) uses variance decompositions to understand the main
drivers of poverty changes in developing countries in the 1980s and 1990s. He finds that changes in
distribution account for 30% of the variance in changes in the headcount when all spells are considered,
versus 70% for growth in average incomes. When the sample is restricted to long spells, those
proportions change to 3% and 97% respectively.
In sum, the macroeconomic approach to the povertygrowth inequality triangle yields two basic stylized
facts:
(i) Economic growth and changes in inequality are uncorrelated, at least in the sample of countries
available to researchers for the two decades from 1980 to 2000.
(ii) Poverty generally declines as the economy grows. The longer the growth spells under
consideration, the larger the share of the variance in poverty that is accounted for by the growth
component.
Given equation (3), (ii) is clearly implied by (i). The empirical content of the Ravallion and Chen (1997)
and Dollar and Kraay (2002) results is that changes in inequality appear to be uncorrelated with growth,
at least for this sample a result that is related to the empirical rejection of the Kuznets hypothesis,
documented by Bruno et al. (1998). Equation (3) tells us nothing about that relationship. It decomposes
9
changes in poverty into growth and redistribution components, but says nothing about how inequality
and growth should be related. With the apparent demise of the Kuznets curve, and no conclusive result
about the possible effects of inequality on subsequent growth, there is no convincing theoretical reason
to expect a systematic relationship. And indeed, there does not appear to be one in the data.
This is not to say, however, that inequality does not matter for poverty reduction. In fact, it clearly
matters in two ways. The first is that, even if inequality is uncorrelated with economic growth on
average, there is substantial dispersion around that average. Inequality did rise in many countries, and
did fall in many others. In countries with rising inequality, the effect of growth on poverty was
dampened or even reversed, while in those where inequality fell, the decline in poverty for a given
growth rate was greater. The ensuing heterogeneity in poverty dynamics at any given growth rate was
substantial. As an illustration, Ravallion (2007) estimates that the 95% confidence interval around the
regression coefficient of growth in (headcount) poverty on growth in survey income or consumption
mean implies that a annual growth rate of 2% (roughly the average for developing countries in the
1980s and 1990s) is consistent with poverty reductions ranging from 1% to 7%.
The second way in which inequality matters for poverty reduction is through the dependence of the
growth elasticity of poverty reduction on initial inequality. Recall that the partial growth elasticity is
given by . Given the convexity of the Lorenz curve, it can be shown that if a distribution A is
robustly more unequal than a distribution B (in the sense that in the relevant range, then
for poverty rates that are not "unusually high", and . Obviously, this implies
that, if the real poverty line and the mean are the same in distributions A and B, then the partial growth
elasticity is higher (i.e. its absolute value is lower) in the more unequal distribution. Or, in other words:
economic growth always contributes towards poverty reduction but, even if there is no change in
inequality, its "povertyreducing power" is less in countries that are initially more unequal.
Figure 1, drawn from World Bank (2005), illustrates this point by plotting the partial elasticity of the
poverty headcount against the initial Gini coefficient for a sample of 65 countries during 19812005,
using a US$ 1aday poverty line. The result described above is clearly visible in the data: the growth
elasticity is strongest among lowinequality countries (with a value of approximately 4.0 for countries
with Ginis in the mid20s) and weakest among highinequality countries (approaching 1.0 for countries
with a Gini index around 60/100). World Bank (2005) shows that the relationship is robust to changes in
both the poverty index (e.g. to FGT(2)) and poverty line (e.g. to US$2perday). Interestingly, the partial
elasticity result carries though to the total empirical elasticity, which also slopes upwards when plotted
against initial inequality. See World Bank (2005) and Ravallion (2007). The robustness of this regularity
allows us to list it as the third stylized fact that arises from the recent macroeconomic literature on
growth, inequality and poverty dynamics:
(iii) The (absolute value of the) growth elasticity of poverty reduction falls with inequality. The larger
the initial inequality in a given country, the higher the growth rate needed to achieve the same
amount of poverty reduction.
10
3. The "mesoeconomic" approach
Beyond those three stylized facts about countrylevel correlations, however, the macroeconomic
approach to the povertygrowth inequality triangle has yielded relatively little. During the period of
study, inequality was uncorrelated with growth, so the crosscountry evidence is limited to pointing out
that growth leads to poverty reduction, and that it does so more effectively if initial inequality is lower.
But it tells us very little about which country characteristics or policy choices might contribute to faster
poverty reduction, through reductions in inequality and a correspondingly higher (total) growth
elasticity of poverty reduction. If there were no other way to investigate the relationship between
growth and distributional dynamics, the conclusion would presumably have to be: `since we do not
know much about the determinants of distributional change, and since on average growth lowers
poverty, let's focus on whatever policies (we believe) yield the highest average growth rates'.11
Fortunately, there are other data sets that permit an investigation of this relationship. The closest in
nature to the crosscountry approach is to look at poverty dynamics within large countries that combine
three data characteristics: (i) a sufficiently long timeseries of repeated crosssectional household
surveys; (ii) national accounts information on economic growth that is disaggregated both by sectors
(e.g. agriculture, industry, and services) and subnationally (e.g. by province or state); and (iii) sufficient
information on other timevarying poverty determinants (such as inflation rates, patterns of public
spending, and the like). With such data, one could adapt equation (5) to a panel of subnational units,
and write:
, , , (6)
Here, a subscript i denotes a subnational unit (call it a "state"), while t denotes a time period. J denotes
a broad sector of economic activity, such as primary (P), secondary (S) or tertiary (T); and denotes the
share of the sector J in the total output of state i at time t. Naturally, equation (6) is estimated using
discrete data on statelevel poverty and sector output growth, so it is more commonly written in the
form:
, , , (6')
This general specification is designed to shed light on a number of possible "economic determinants" of
the distribution component in equation (3). Differences in across sectors J can be informative of
whether the pattern of growth matters for poverty reduction. In almost every case where it was tried,
researchers have comfortably rejected the null hypothesis that the elasticities are the same across
11
This is reminiscent of Dollar and Kraay's (2002) conclusion: "In short, existing crosscountry evidence including
our own provides disappointingly little guidance as to what mix of growthoriented policies might especially
benefit the poorest in society. But our evidence does strongly suggest that economic growth and the policies and
institutions that support it on average benefit the poorest in society as much as anyone else." (p.219, emphasis
added).
11
sectors. For China, Ravallion and Chen (2007) found that the (absolute) elasticity of poverty with respect
to agricultural growth was greater than that for any other sector. In India and Brazil, on the other hand,
growth in the tertiary (services) sector was more "propoor" than growth in either industry or
agriculture (Ravallion and Datt, 2002; Ferreira et al. 2010). can also vary across states (or provinces),
and those differences may be driven by various "initial conditions" at the state level. Ravallion and Datt
(2002) found that the elasticity of poverty with respect to nonagricultural growth did differ across the
states of India, and was higher in states with greater initial farm productivity and literacy rates. Ferreira
et al. (2010) found similar results for Brazil, where industrial growth had a greater povertyreducing
effect in states with higher initial levels of human capital (proxied by lower infant mortality rates and
higher average years of schooling in the adult population) and of worker empowerment (as measured by
initial unionization rates). They also found that the sectoral growth elasticities varied over time, at least
in part in response to changes in the policy regime, such as trade liberalization and price stabilization
measures.
The time varying controls ( ), which are usually introduced in lagged differences to alleviate
endogeneity concerns, can also be informative. The national inflation rate is generally included as one
such control, and it is often significant. Controlling for the composition of growth, statelevel fixed
effects, and a number of other covariates, lower inflation reduced poverty in both India and Brazil.
Statelevel spending, on the other hand, was effective in reducing poverty in India, but not in Brazil. The
growth of federal spending on social assistance and social insurance over the study period, however,
had a pronounced povertyreducing effect in Brazil. In fact, one way to interpret the Ferreira et al.
(2010) decomposition of poverty changes between 1985 and 2004 is that the full four to fivepoint
reduction in the headcount over the period can be attributed to expansions in federal redistribution
programs, with all other "poverty determinants" the level and composition of growth, changes in
inflation, changes in statelevel spending, etc. essentially canceling one another out.
The budding "mesoeconomic" approach to the study of poverty dynamics has added to the
macroeconomic approach in at least two ways. First, it has confirmed at a national level some of the
broad findings from the crosscountry literature. Two such results are (i) that lower inflation contributes
to poverty reduction, after controlling for the growth rate and other covariates; and (ii) that high levels
of initial inequality, in assets or incomes, are correlated with lower subsequent poverty reduction.12
Second, by exploring spatial and temporal variation in the sector composition of economic growth,
these papers show that not all growth is the same. Some kinds of growth reduce poverty more than
other kinds, and it is not always the same kind. Which types of growth have the greatest impact on
poverty depends on the country in question, as well as on spatial differences in economic structure and
historical distribution.
12
On the crosscountry association between inflation and poverty, see Easterly and Fischer (2001) and Romer and
Romer (1999). On asset inequality and growth see Deininger and Olinto (2000), in addition to the references cited
in the introduction.
12
This of course implies that, for policymakers or researchers interested in any particular country, relying
on the three stylized facts in Section 2 is not enough. Individual growth processes can be made more or
less "propoor" and, depending on the objectives13 of the policy maker, certain tradeoffs between
higher average growth and higher growth for the poor may become relevant. These results should really
come as no surprise, except perhaps to the most hardened representativeagent macroeconomist.
"Economic growth" is nothing but an average taken across the proportional output increases across
firms (or sectors) and government agencies across the economy. Or, if one approaches it from the
income account, it is an average taken across proportional income increases across all households
(adjusting from public goods, retained earnings, and measurement error). It should be perfectly plain
that policies that allocate resources and opportunities differently across these sectors, firms and
households will likely affect both the distribution and the average of future incomes. In fact, perhaps
more can be learned from examining how the underlying distribution of incomes changes over time,
including in response to shocks and policy changes, than from repeated estimations of how one or more
vertices in the triangle related by equation (3) affect the other ones. This microeconomic approach to
growth and distributional dynamics is the subject of the next section.
4. The microeconomic approach
The final level of work on the link between the dynamics of mean incomes (growth), poverty and
inequality investigates this at the microeconomic level. These are studies that do not rely on summary
measures of poverty or inequality as their primary data, but are based instead on full distributions of
income or consumption expenditures, from representative household (or, in some cases, labor force)
surveys. As noted in the introduction, this paper focuses on studies that investigate distributional
dynamics under the anonymity axiom, and hence rely on repeated crosssection, rather than panel,
data.
The natural starting point for these studies although the term had not yet been coined when a number
of them were written is the growth incidence curve (GIC). Defined (by Ravallion and Chen, 2003) as the
quantilespecific rate of economic growth between two points in time as a function of each percentile p
in [0, 1], it can be written as follows, in continuous or discrete time:
(7)
(7')
The discretetime version in equation (7') makes it clear that the GIC is simply the proportional
difference between the quantile function at each percentile of the income distribution.
If we define economic growth as the proportional change in the mean of the income distribution, then
growth can be expressed as a function of the growth incidence curve. By changing the integration
variable, note that: . Then it follows that:
13
His or her "social welfare function", to use a slightly older language.
13
(8)
Equation (8) simply reminds us of the obvious fact that average income growth is a weighted sum of
growth rates along the income distribution, weighted by each individual's initial income level.14 It is also
easy to show that changes in poverty can also be expressed in terms of the GIC, for a large class of
poverty measures.15 Poverty measures that satisfy the symmetry, monotonicity, focus and additive
decomposability axioms can be written as:
, (9)
Where z denotes the real poverty line as usual, and , denotes the individual poverty function.
Wellknown examples of this class include the FosterGreerThorbecke family of measures, which is
obtained when , , , and the Watts index, from , .
Differentiating (9) with respect to time, while holding z constant and using the standard notation in this
paper16, we have:
, (10)
,
Where and .
The first term on the RHS of equation (10) tells us that changes in poverty arise from income changes
along the distribution (given by the growth incidence curve), multiplied by how sensitive the particular
poverty measure in use is to changes at each point of the distribution (given by the function ).
Because of the focus axiom, there is a second term in (10), which captures changes in upper limit of the
integral in (9) which might arise as a result of the changes in the distribution of incomes. This term is
multiplied by the sensitivity of the poverty measure at the poverty line.
It turns out that there are a number of inequality indices whose changes over time can also be
straightforwardly expressed as functions of the growth incidence curve. Consider, for example, the class
of populationsubgroup decomposable relative inequality measures. These are indices that aggregate
functions of relative incomes across the distribution, where `relative income' refers to an absolute
income divided by the mean.17 Write such a class in general terms as:
(11)
14
The fact that the standard measure of economic growth weighs proportional changes in the incomes of the
wealthy much more heavily than proportional changes in the incomes of the poor has long been remarked upon.
See e.g. Ahluwalia and Chenery (1974) and Klasen (1994).
15
This analysis follows Kraay (2006).
16
While this notation is still probably clearest for the paper as a whole, note the possible confusion between two
uses of the operator d in (10). When it appears within an integral, it denotes the integrating variable. When it
appears alone, it denotes a timederivative.
17
Such measures are "relative inequality measures" by construction. They satisfy the scale invariance, rather than
the translation invariance, axiom.
14
Wellknown examples of this class of inequality measures include the Atkinson family, when
1 , and the Generalized Entropy Class when
1 . Differentiating (11) with respect to time yields:
(12)
Equation (12) is equally intuitive to interpret. At its core are differences between income growth in each
percentile, and the growth in mean income, . If everybody's income rises in exactly the
same proportion, then that term vanishes, and relative inequality remains unchanged. If individual
growth rates differ along the distribution, then they will contribute to changes in the aggregate
inequality index, in a manner which depends on how sensitive the index is to relative incomes at each
particular percentile p: .
Equations (8), (10) and (12) indicate that economic growth (at least when measured as the growth in
mean household income), changes in poverty and changes in inequality are ultimately just different
ways of aggregating the information contained in the growth incidence curve. Each of the three
concepts is driven by changes in individual incomes, at the microeconomic level. Because they seek to
capture different features of distributional change, they weight those individual changes differently:
Economic growth weighs growth in individual incomes by their original income relative to the mean.
Poverty measures weigh them according to how sensitive they are to income shortfalls from the poverty
lines. And inequality measures weigh them depending on their basic individual "distance" measure.
This fact is more than a simple mathematical curiosity. It highlights the fact that the three "corners" of
the poverty growth inequality triangle are so deeply related to one another because they are, in fact,
variant forms of aggregation of information about the incidence of growth on the initial income
distribution. Identities such as equation (3), which relates changes in a particular poverty measure (the
headcount index) to changes in the mean and the Lorenz curve, arise from this common origin shared by
the three concepts.
But if that is the case, then statistical and econometric analysis of the growth incidence curve should
prove a sensible way to explore the dynamic relationship between growth, poverty and inequality,
under the anonymity axiom. In order to investigate what share of the change in poverty, inequality, or
growth, may be associated with a particular economic event (such as a demographic change, a
macroeconomic shock, or a structural transformation) one might for instance seek to decompose the
GIC into a component that corresponds to the change that can be attributed to the event in question,
and a residual component, as follows:
(13)
15
Where denotes a counterfactual income distribution, which would be obtained by the exclusive
application of the event to , all else constant. If such a counterfactual could be empirically
estimated, then the first term on the RHS of (13) would give the corresponding counterfactual growth
incidence curve. This term could be substituted into equations (8), (10) or (12), to generate the resulting
counterfactual growth, poverty and inequality change arising from the policy. The second term on the
RHS of (13) simply measures the residual component of the GIC: changes in income distribution that
were not caused by the policy or other object of investigation.
Of course the great challenge is, as usual, that of identification: how does one compute a meaningful
causal estimate of ? In a limited set of cases, such as when estimating the impact of a randomly
assigned policy intervention with no diffuse spillovers, the usual experimental methods can be used to
construct such a causally interpretable counterfactual. Another (tantalizing) possibility would be to
"import" causal estimates (say, of the effect of a weather shock) from panel data analysis, into the
construction of a counterfactual GIC. In most other cases whether one is interested in understanding
the effect of endogenous changes in fertility rates on inequality, or the effect of a currency devaluation
on poverty a causal interpretation of (13) is extremely difficult.18
That crucial caveat notwithstanding, there is actually a wellestablished literature on the nature (if not
causes) of distributional change that basically revolves around estimating statistical decompositions like
(13), and using them as suggestive descriptions of the factors that drive poverty and inequality
dynamics. Most of the original contributions to this literature Juhn, Murphy and Pierce (1993),
DiNardo, Fortin and Lemieux (1996), Bourguignon, Fournier and Gurgand (2001) were written before
Ravallion and Chen (2003) defined the GIC, and therefore do not use that language. But they all use the
"active ingredient" of equation (13), namely the idea of decomposing the overall change in income
distribution into two or more steps demarcated by counterfactual income distributions.
4.1 Decomposing distributional change using statistical counterfactuals
The pioneering paper was perhaps Juhn, Murphy and Pierce's (JMP, 1993) attempt to decompose
changes in the US wage distribution between 1963 and 1989 into a term attributable to changes in
observable worker characteristics (such as educational attainment), a term corresponding to changes in
market returns to those characteristics, and another component associated with changes in both the
distribution of and the returns to unobservable worker characteristics. These authors extended the
classic decomposition of differences in mean earnings between different population subgroups (men
and women, blacks and whites) due to Oaxaca (1973) and Blinder (1973), by incorporating changes in
the distribution of residuals into the analysis. Like Oaxaca and Blinder, their analysis was based on the
standard Mincer earnings equation (for individual i at time t):
(14)
18
For an illuminating discussion of the role of counterfactuals in assessing the causal effects of policies on
inequality, including a discussion of the separation between individual heterogeneity and uncertainty, see Cunha
and Heckman (2007).
16
Denoting the cumulative distribution of residuals at time t by  , they constructed two
counterfactual income distributions:
, , , (15)
And , , , (16)
Although JMP do not use this language or notation, their analysis can be written in terms of a
decomposition of the growth incidence curve between 1963 (t=0) and 1989 (t=1) as follows:
(17)
The first term on the RHS of (17) was interpreted as the "returns component" of the decomposition,
since the only differences between and arise from the change in the coefficients (see
equation 15). The second term on the RHS of (17) was interpreted as the component due to changes in
unobserved characteristics, since the only differences between those two quantile functions arise from
a rankpreserving transformation of the residuals i.e. from replacing each residual in the t=0
distribution with the residual with identical rank in the t=1 distribution (see the last term in equation
16). The third term in (17) corresponds to changes in the joint distribution of observed characteristics
(X), and was obtained residually.
JMP sought to explain the secular increase in earnings inequality in the US in the period from the mid
1960s to the late 1980s. On the basis of the above decomposition although without mentioning
"growth incidence curves" they concluded that very little of the increase was accounted for by
changes in the distribution of observed worker characteristics, including years of schooling. From around
1979 onwards, a substantial share of the increase in the 9010 earnings differential could be attributed
to increases in the returns to observable characteristics, chiefly formal education. But throughout the
entire period, the most important component of the change in inequality was changes in unobserved
worker characteristics, and their remuneration. The authors attributed this to increasing returns to
unobservable aspects of human capital, such as the ability to adapt to new technologies, which are only
imperfectly correlated with formal schooling.
Even though this analysis, only briefly summarized here, can certainly lay no claim to identifying the
exact causes of changes in the US wage distribution, it was nevertheless an influential piece of statistical
evidence in the academic debate. In fact, another pioneering paper in the literature estimating
counterfactual income distributions was motivated, at least in part, as a response to some of the
findings by Juhn et al. (1993). Dinardo, Fortin and Lemieux (DFL, 1996) sought to investigate whether
changes in labor market institutions in particular the declines in the real value of the minimum wage
and in the rate of unionization had also contributed to rising inequality in the United States. Instead of
working with the quantile function , these authors expressed their decomposition in terms
of the primal density function, f(y).
17
When data is available on both income y and a set of covariates X, the density function is simply the
marginal of the joint distribution , . Using the definition of a conditional distribution, DFL write
that identity as:
 (18)
Where g() denotes the conditional distribution of y on X, is the joint distribution function of
observed covariates (X), and ... represents the operation of integrating over every element of the
vector X. Counterfactual density functions can then be generated either by simulating an alternative
conditional distribution function  , or by constructing the appropriate counterfactual joint
distribution of covariates, . The first procedure can be seen as a generalization of importing the
estimates of the parameters from another year, as in equation (15) above. The Mincer equation used
by Juhn, Murphy and Pierce (1993) is a representation of the conditional distribution of y on X, under a
loglinear functional form assumption. The more general version of the corresponding counterfactual
distribution would have a density given by:
 (19)
The second procedure constructing a counterfactual joint distribution of covariates yields an
alternative counterfactual marginal distribution:
 (20)
How is a counterfactual income distribution, such as those in equations (19) or (20), constructed in
practice? Consider first equation (20). If the desired counterfactual is of the sort: "what would the wage
distribution be if people had the characteristics of the population at t=1, but were paid according to the
conditional distribution at t=0?", then a reasonable approximation would be to use:
(21)

where 
is a reweighting function, which reweights the sample observed at t=0, with the
weights from t=1. Then, in essence,  is simply obtained by a
kernel density estimation of the density function of y, on a sample that has been reweighted by the
ratio of population weights in t=1 to t=0.
DiNardo, Fortin and Lemieux (1996) used this procedure (including some more complex variations on
the same basic theme) to investigate whether changes in the composition of the population say, in
terms of its ethnic, educational or demographic makeup could account for some of the increase in US
wage inequality over the period of study. One compositional change which did seem to account for
some of the increase in the earnings gap was the decline in the share of the population that was
unionized suggesting that changes in labor market institutions did have a role to play in the period's
distributional dynamics. They also found that the persistent decline in the real value of the minimum
wage had a negative effect on earnings in the lower tail, particularly for women.
18
Once a counterfactual density function like (19) or (20) has been constructed, the overall change in
the distribution of incomes can be decomposed into the part accounted for by these specific changes,
and a residual term, as follows:
(22)
The decomposition in (22), which has been termed a generalized OaxacaBlinder decomposition, is
obviously analogous to the decomposition of GICs in equation (13). The latter can be uniquely obtained
from (22) by integrating each density function to obtain cumulative distribution functions, inverting
those to obtain the quantile functions, and then dividing the quantile function at t=0.
The basic idea of the generalized OaxacaBlinder decompositions is to "break up" the complex and
multilayered processes behind distributional change into individual building blocks e.g. changes in
returns, changes in personal characteristics, changes in labor market institutions so that a sense of
their relative importance can be gauged. The counterfactuals can be constructed in different ways:
relying on specific functional forms and on importing parameters estimated for one year into another, as
in JMP; using nonparametric reweighting methods, as in DFL: or indeed using a combination of the two.
The same basic idea has been extended in various directions, including the analysis of changes in the
distribution of household incomes (as opposed to the simpler wage distributions studied by JMP and
DFL), and the comparison of distributions across countries, rather than time periods.19
Although mechanically one could apply a decomposition such as (13) or (22) to any distribution, whether
of wages or of household incomes, the choice of the conditional distribution linking y to the covariates X
is likely to differ substantially depending on the nature of the distribution under study. For a distribution
of wages or earnings, the Mincerian equation, or some nonparametric equivalent, clearly embodies the
relevant features of the conditional distribution. If one were after causal parameters, one might want to
correct for sample selection bias into employment, but if the objective is to provide an estimate of the
conditional distribution of wages for workers actually employed, even the simple OLS estimate (in the
parametric case) might suffice. When y denotes household incomes, however, there are other linkages
between observed characteristics (X) and final incomes (y). Individual characteristics affect the very
composition of households both through choice of partner and through fertility decisions. They affect
occupational decisions within the household both who works and who doesn't, and the choice of
sector and formality status. And they clearly still affect earnings in the usual way, depending on returns
in different sectors and occupations.
Bourguignon, Fournier and Gurgand (2001) and Bourguignon, Ferreira and Lustig (BFL, 2005) combine
the parametric and semiparametric approaches described above to the more complex problem of
decomposing changes in household income distributions. They note that the vector of household
covariates (X) includes endogenous variables such as family size and individual occupation, which are
19
In this paper, we focus on the extension to household income distributions. But see Donald, Green and Paarsch
(2000) for a comparison of wage distributions between Canada and the US, using a hazardfunctionbased
estimator of cumulative distributions; and Bourguignon, Ferreira and Leite (2008) for a comparison of household
income differences between Brazil and the US.
19
likely affected by or correlated with other elements in the vector, such as individual levels of
education, gender and ethnicity. They propose to separate out (as distinct statistical "building blocks")
the effects of changes, say, in the distribution of education on the distribution of income through the
different mechanisms: changes in family composition (through changes in fertility), changes in
occupational structure, and changes in earnings. To do so, they treat the "endogenous covariates" of
interest chiefly fertility and occupational choices differently from other covariates, and estimate
their own conditional distributions on a narrower subset of "exogenous" variables. In other words, they
partition the vector X into two subvectors V and W, where V includes variables such as the number of
children in the household, occupation of work and, in some cases, years of schooling. And they replace
the overall joint distribution of X with the corresponding product of conditional distributions and a
reducedorder joint distribution of W. If, for simplicity, , , then equation (18) can be re
written as:
 ,  ,  (23)
In practice, the case studies in Bourguignon, Ferreira and Lustig (2005) generally use parametric
methods to construct counterfactual conditional distributions, g( ) and h( ). The conditional distributions
of individual earnings on their covariates are estimated by standard Mincer equations, separately by
sector of activity, for initial and terminal years. The conditional distribution of observed occupations
(e.g.: unemployment, inactivity, formal employment, informal employment, selfemployment) is
estimated by means of a discretechoice model, such as a multinomial logit or probit. In some of the
case studies, specifications differ for household heads and other household members, to introduce
some measure of intrahousehold interdependence. Similar discrete choice models are used to estimate
the conditional distribution of family size (or, more specifically, the number of children in each
household) on observed family characteristics. 20
After these statistical models of conditional distributions have been estimated for each relevant year in
the decomposition (at least one initial and one terminal year), a set of counterfactual income
distributions is constructed by importing the relevant set of parameters from one year into another. For
example, to simulate the counterfactual distribution corresponding to Brazil's situation in 1976, but with
occupational choice parameters from 1996, the coefficients from the occupational choice multinomial
logit from 1996 would be imported into 1976, and used to reallocate workers across sectors in the 1976
sample.21 Those workers who are counterfactually "moved", say from unemployment into informal
wage employment, are then counterfactually ascribed the earnings that their characteristics would earn
in that sector, given the sectorspecific coefficients from a Mincer equation (and a residual drawn from
the empirical distribution for the sector).
20
See also Hyslop and Maré (2005) for a "less parametric" application of these decompositions to the distribution
of household incomes, which closely follows DiNardo, Fortin and Lemieux (1996).
21
Reallocating workers on the basis of importing coefficients of a multinomial logit require drawing pseudo
residuals from the appropriate Weibull distribution, subject to the constraint that they be consistent with the
originally observed choice. See Bourguignon and Ferreira (2005) for details on this, and the entire BFL
methodology.
20
These and a host of analogous manipulations generate a set of counterfactual income distributions,
. For each one, counterfactual poverty and inequality measures can be computed, and compared
to the initial and final distributions actually observed. As an illustration, the results for just such a set of
comparisons for the distributional change between 1976 and 1996 in Brazil are presented in Table 1,
which is taken from Ferreira and Barros (2005), one of the case studies in Bourguignon, Ferreira and
Lustig (2005). The columns of Table 1 list the mean, four inequality, and three poverty measures (for two
different poverty lines) for each actual and counterfactual distribution. The first two rows are for the
actual distributions observed in 1976 and 1996. Each of the subsequent rows is for a counterfactual
distribution, denoted by the Greek letters corresponding to the estimated coefficients that are imported
from 1996 into 1976 in each case.
But just as the counterfactual distributions can be used to compute scalar summary measures of
inequality and poverty, they can also be used to construct quantile functions, and to compute the GIC
decomposition in equation (13). Four such "full distribution" decompositions are depicted, for the same
study of Brazil between 1976 and 1996, in Figure 2.
In this figure, the solid dark line is an approximation of the actual growth incidence curve between 1976
and 1996.22 Each of the other curves, identified by a set of Greek letters, corresponds to the
counterfactual GIC obtained from comparing a counterfactual income distribution with the actual 1976
distribution. In each case, the counterfactual income distribution was constructed by importing a set of
parameters (denoted by the corresponding Greek letters) from a model estimated in 1996, to the 1976
model, and microsimulating the resulting changes. So in Figure 2, for example, the line denoted "s and
s" gives the counterfactual growth incidence attributable only to changes in the returns in all Mincer
equations. The next line, which also includes s, combines those changes in returns with changes in
occupational choices (estimated using multinomial logits). The line that also includes further
incorporates behavioral changes associated with fertility choices. Finally, the line that includes
" , , s, s, and s", adds the changes in educational attainment, from a multinomial logit that
estimates the conditional distribution of years of schooling on a set of exogenous variables such as race,
age, gender, and region of residence. Critically, when the GIC represents a combination of effects, as in
each of these cases, they are made internally consistent. For example, if a person in the 1976 sample is
ascribed a new level of education by the simulation arising from importing the parameters, then
that new level of education carries through to the person's new occupational choice, decision on
fertility, and earnings determination.
In the Brazil case study which I have used to illustrate this approach, the decompositions summarized in
Table 1 and in Figure 2 suggest that three main economic forces combine to explain changes in income
levels, poverty and inequality i.e. in Brazil's "povertygrowthinequality triangle" between 1976 and
1996. The first is a shift in the occupational structure towards greater unemployment and informality,
and towards fewer hours worked within the informal sector by less educated workers. This effect was
responsible for the pronounced income losses in the first decile of the distribution, and the
22
The writing preceded the definition of GICs, and the authors calculated the log differences in incomes for each
percentile, which approximates their growth rates.
21
corresponding increase in bottomsensitive poverty measures. Contemporaneously, levels of education
increased throughout the Brazilian population, leading both to higher endowments of human capital
being sold on the labor market, and to marked reductions in desired fertility. These two effects of the
educational expansion would have contributed to higher incomes across the distribution. However, in a
context of macroeconomic stagnation, the labor markets were unable to absorb the greater levels of
education at the going wages, and returns to education fell. This third force essentially cancelled out the
gains from the education expansion, leading to an income distribution that was little changed (above the
first decile) between 1976 and 1996.
Bourguignon, Ferreira and Lustig (2005) also contain methodologically similar studies for Argentina,
Colombia, Indonesia, Malaysia, Mexico and Taiwan (China). Although the decomposition techniques
were very similar across these studies, each country case was unique in terms of the real economics
underlying distributional change. In Taiwan, a large increase in female labor force participation
contributed to a reduction in earnings inequality (because the women entrants had middling wage
rates), but an increase in the inequality of household incomes (because they were predominantly
married to highearning men). In Mexico, rising female labor force participation was also a key part of
the story, but the pattern was a mirror image of the Taiwanese experience: women entered both at the
bottom and at the top of the wage distribution, leading to higher earnings inequality, but contributing to
a decline in household income inequality (primarily because of the resulting increase in incomes for the
poorest households). Part of the attraction of this version of the GIC decomposition using statistical
counterfactuals is its versatility, and the ensuing ability to capture a wealth of different economic forces
underpinning distributional change.
But, of course, it also has its limitations. The whole family of GIC decompositions using statistical
counterfactuals suffers, for instance, from path dependence: the order in which the decomposition is
undertaken affects the size of each individual component. In terms of equation (22), for instance:
. This is a property that the generalized OaxacaBlinder
decompositions inherit from their parent. In the original OaxacaBlinder decomposition too, the returns
component was different if the difference in the vectors was weighted by the characteristics of blacks
(say), than if it was weighted by the characteristics of whites. The problem carries through to all
decompositions of the form of (13) or (22). Fortunately, it can be addressed relatively easily, either by
showing the results for all different paths of decomposition or, more formally, by taking the appropriate
average (which turns out to be a Shapley value) across all of them, as shown by Shorrocks (1999).
A more serious limitation relates to the issue of causality, discussed earlier. The fundamental problem is
that counterfactual income distributions are statistical constructs that do not necessarily correspond to
a meaningful economic counterfactual. This too can best be understood in the simple terms of the
original OaxacaBlinder decomposition. We may value a decomposition that tells us that x% of the
difference in earnings between blacks and whites is associated with differences in characteristics
between those two groups, while (100x)% is due to differences in returns to those characteristics. But
we understand that the counterfactual used to compute x, namely the earnings that blacks (whites)
would receive if their characteristics were remunerated with the returns normally associated with
whites (blacks), does not correspond to an economic equilibrium. Analogously, most counterfactual
22
income distributions discussed in this subsection e.g. the income distribution that would attain in
Brazil if the only change since 1976 were the change in returns to schooling observed by 1996 do not
correspond to tenable economic equilibria. Just as in the case of the original OaxacaBlinder
decompositions, there is some value in decompositions based on counterfactuals that are statistically
welldefined, even if they do not correspond to a tenable equilibrium and cannot therefore be
interpreted causally.
Nevertheless, some recent research has attempted to construct GIC decompositions where the
counterfactual distributions may correspond more closely to a tenable equilibrium, and where the
ensuing distributional changes might, therefore, be interpreted as suggestive of causality. The next sub
section briefly reviews three (rather different) approaches to this quest.
4.2 Towards GIC decompositions based on economic counterfactuals.
In order for a counterfactual distribution to correspond to an equilibrium allocation, every outcome in
the datagenerating process for each individual must be consistent with the equilibrium behaviors of all
other agents in the economy. One approach to constructing such a counterfactual, therefore, would be
to have a full structural model of behavior for the economic agents involved, and to use such a model to
simulate the effects of a particular policy or shock. As an example, consider the model of education,
fertility and labor supply estimated by Todd and Wolpin (2006) for the Mexican villages where the
Progresa conditional cash transfer program was introduced in 1997. It was not the authors' objective to
decompose changes in the distribution of income in that rural economy into a component due to the
Progresa transfers and another (residual) component due to all other changes. Instead, their objective
was to use the results of the experimental evaluation of the program which yielded credible causal
estimates of the effect of the transfers on household incomes by comparing outcomes between
randomly assigned treatment and control villages to validate their structural behavioral model.
But if the model succeeded in its objective, so that its predictions of the effects of the transfers on
household incomes, accounting for labor supply, enrollment and fertility responses, are correctly
validated by the treatment effect estimates from the experimental evaluation, then a distribution of
income obtained from simulating the model would be an economically meaningful counterfactual.
Under such a "true model", changes in poverty, inequality or growth computed from the corresponding
growth incidence curve would indeed be causally and not just statistically attributable to the
Progresa program. 23
The feature of the Todd and Wolpin (2006) study which lends particular credibility to its modelbased
construction of an economic counterfactual GIC is the existence of credible estimates of program impact
from an experimental evaluation. What happens, though, when one is interested in estimating the
effect (on poverty, inequality and growth) of some economywide policy that is not assigned to specific
groups, and cannot be evaluated by experimental or quasiexperimental methods? Examples of such
23
See also Attanasio, Meghir and Santiago (2004) and Bourguignon, Ferreira and Leite (2003) for alternative
models of the effects of conditional cash transfers on household incomes, accounting for behavioral responses.
23
policies include trade reform, exchange rate devaluations or revaluations, economywide labor market
reforms, etc.
Growth incidence curve decompositions based on economic counterfactuals have been tried for such
"economywide" policies as well, although the standards of empirical identification are probably lower
than in the case of wellevaluated assigned programs. Let us briefly review two approaches. In the first,
exemplified by Ferreira, Leite and WaiPoi (2010), the treatment of general equilibrium relationships is
extremely reducedform. These authors attempt to estimate the effect of a trade liberalization episode
on the distributions of wages and household incomes and thus on poverty and inequality in Brazil,
between 1988 and 1995.
The authors combine the twostage regression approach of Goldberg and Pavcnik (2005) with a
parametric GIC decomposition in the style of Juhn, Murphy and Pierce (1993). They construct a panel of
industries over time, and regress three industrylevel dependent variables (wagepremia, skillpremia
and employment levels), which they obtain from estimating Stage 1 regressions (24) and (25) below, on
(arguably) exogenous trade policy variables (such as changes in tariff rates and industryspecific
exchange rates).
ln wij X ij I ij * wp j ( I ij * S ij ) sp j ij (24)
e Z i s
Pr j s P s ( Z i , ) (25)
e Z i s e
Zi j
js
Equation (24) is an individuallevel earnings regression, augmented by industry ( I ij ) and skill (Sij) dummy
variables. The coefficients wpj and spj are correspondingly interpreted as industry and industryskill
wage premia. A panel of such "premia coefficients" (as well as estimates of the constant term 0 in eq.
25) across industries j and years t is regressed on the trade policy variables, as noted above: these are
the Stage 2 regressions. Once they have been estimated, the coefficients from the secondstage
regressions are used to predict "trademandated" changes in wpj, spj, and 0j , for actual or
counterfactual values of changes in the exogenous trade policy variables. These predicted firststage
coefficients are in turn imputed back into (24) and (25), to generate counterfactual occupation and wage
distributions analogous to those in JMP or BFL.
Inequality and poverty statistics can be computed for each of these counterfactual distributions, and
compared with the actual (pre and postliberalization) distributions, in an attempt to isolate the
contribution of the policy to the overall changes. Equation (13) can also be computed for each
percentile, showing a full graphical comparison of the actual GIC between 1988 and 1995, and the
counterfactual GIC attributed only to the trademandated effects of the liberalization. This
decomposition is shown in Figure 3, drawn from Ferreira et al. (2010). In this figure, the thick upper line
is the actual wage growth incidence curve for Brazil between 1988 and 1995, and the dashed line that
matches it closely from the first quintile upwards is the counterfactual GIC obtained from the simulation
exercise just described. The line is interpreted in the paper as a lowerbound for the effects of trade
24
liberalization on wage inequality in Brazil. The authors also show that this inequalityreducing effect is
almost entirely due to employment reallocation across industries (changes in 0), rather than to changes
in wage or skill premia.
The second approach goes into further detail in the modeling of the general equilibrium (or
macroeconomic) relationships that link the behavioral responses of different firms and individuals to a
particular shock or policy change, and to one another. Rather than relying on a reducedform
relationship between a set of observed exogenous variables (such as changes in tariff rates) and a set of
industrylevel shifters (as above), studies in this second approach estimate a full macroeconomic (or
computable general equilibrium) model. This "macro model" (for short) is used to generate a set of
"linkage aggregate variables", such as vectors of wage rates and employment levels, for certain
combinations of sectors and types of workers (e.g. wages and employment for highskilled workers in
the informal sector in urban areas).
These variables are then used to connect the macro model to a set of earnings and occupation
equations similar to (24) and (25) above estimated on household (or labor force) microdata. A
convergence algorithm is used to ensure that the counterfactual distributions of employment choices
and wage rates add up to the aggregate simulations from the macro model. At the microlevel, the
simulation generates counterfactual occupation and income distributions and growth incidence curves
much as in the Bourguignon et al. (2005) or the Ferreira et al. (2010) exercises. Behind these
counterfactual GICs now lies a full macroeconomic or computable general equilibrium model. To the
extent that one trusts the capacity of those models to accurately predict the effects of policies on the
general equilibrium of the economy, these GICs are also economically meaningful counterfactuals.24
That, however, is not a trivial caveat...
5. Conclusions
Income distribution dynamics have long been of interest to economists. As the availability of household
survey data for developed and (particularly) developing countries expanded in the 1990s, so did their
ability to investigate distributional change empirically. The crosscountry (or "macroeconomic")
literature that sought to exploit international variation in poverty and inequality changes, economic
growth and covariates, offered no support for the "grand theories" linking development and
distribution. The evidence did not appear particularly supportive of the Kuznets hypothesis, and was
inconclusive about the possible effects of initial (or lagged) inequality and poverty on subsequent
growth.
That literature did, however, generate three robust stylized facts about growth and distribution in the
last couple of decades of the Twentieth Century: (i) there was no statistically significant crosscountry
correlation between economic growth and changes in inequality; (ii) so economic growth was strongly
24
See the various chapters in Bourguignon, Bussolo and Pereira da Silva (2008) for a set of examples of this
"macromicro" approach.
25
and negatively correlated with changes in poverty. However, (iii) the higher a country's initial level of
inequality, the higher the growth rate needed to obtain a given amount of poverty reduction.
But economic growth, changes in inequality and changes in poverty are actually just three different
aggregations of information about individual income dynamics. They are therefore jointly determined
(by the general equilibrium of the economy), and macroeconomic estimates of the reducedform
relationships between them however useful in identifying empirical regularities were never likely to
shed much light on the fundamental factors underlying distributional change.
Two alternative approaches have been more successful in doing that. The first, which I have called
"mesoeconomic", uses subnational panel data on poverty and on economic growth rates disaggregated
by sector, to investigate the role of different growth patterns and initial conditions on poverty
reduction. The second approach, which is microeconomic in nature, investigates distributional change at
a fully disaggregated level, by decomposing changes in the growth incidence curve. These
decompositions have not resolved the identification problems inherent in studying distributional
dynamics either. The first crop of studies in this tradition are essentially generalizations of the Oaxaca
Blinder decomposition to a fulldistribution, dynamic setting. The counterfactual income distributions on
which they rely suffer from the usual problems of equilibriuminconsistency and path dependence.
Nevertheless, they have succeeded in shedding some light on the nature of distributional change in
countries ranging from Indonesia to the United States, in a set of quite informative ways. These studies
have employed various different methods, parametric and otherwise. They have generally focused on a
set of key factors, including (i) the dynamics of the distribution of educational attainment; (ii) changes in
the returns to education (and, less prominently, other covariates); (iii) changes in the structure of
occupations, including female labor force and the extent and nature of the informal sector(s); (iv) the
links between education, labor force participation, and demographic change; (v) changes in labor
market institutions, including unionization and minimum wages. Although the topics are often similar
across countries, as the number of studies expands, one interesting result has been just how different
each country's specific story is.25 It appears that the basic pieces of the income distribution dynamics
puzzle can be combined in a multiplicity of ways.
A second crop of growthincidence based studies attempts to get nearer to a causal interpretation of the
GIC decompositions, by deriving counterfactual income distributions from models of behavior, or of the
general equilibrium of the economy. This paper briefly summarized a few such studies, which were
remarkable, if for nothing else, at least for their methodological diversity ranging from oldfashioned
CGEs linked to microsimulations, to fully structural models of dynamic household behavior.
Despite this great methodological diversity, there are some shared findings and areas of common
ground in the multifaceted literature on the povertygrowthinequality triangle. Growth is good for the
poor, and it is particularly good when it is the incomes of the poor that are growing...26 This is most likely
25
See, for example, the concluding chapter in Bourguignon, Ferreira and Lustig (2005).
26
When the incomes of the poor grow faster than those of the nonpoor, inequality generally declines, and
poverty mechanically falls by more than if growth was uniformly distributed.
26
to happen when growth takes place in the areas where the poor live, and in the sectors where they
work. They are better able to benefit when their initial endowments of human capital, land, and political
power are greater. But contemporaneous policy choices can also make a great deal of difference to how
the poor share in economic growth. Both marketfriendly policies (such as farmgate price liberalization
in China and trade liberalization in Brazil) and stateled redistribution (such as investments in public
education in various countries, and welltargeted cash transfer schemes in Brazil and Mexico) have
contributed to faster poverty reduction. At the individual country level, in other words, there is a
plethora of policy choices that naturally affects the endowments and growth opportunities of people all
along the income distribution. These policies naturally affect the incidence and average rate of growth
simultaneously, and thus jointly determine the evolution of the povertygrowthinequality triangle.
The microeconomic literature that seeks to empirically describe this joint determination process is still in
its infancy, and there is considerable scope for more work on building counterfactual distributions that
are consistent with economic equilibria possibly by striving for a middle ground between the fullscale
complexity of structural models of dynamic household behavior and the adhoc rigidities of computable
general equilibrium models.
Another direction with potentially high research payoffs is to learn from and draw more on the
literatures on individual income dynamics and on socioeconomic mobility. As noted in the introduction,
all of the literature reviewed in this paper falls under the aegis of the anonymity axiom, and relies
essentially on repeated crosssections. However, a number of concepts highlighted here, including that
of the GIC, would remain relevant in a panel data context, subject to interesting adjustments. Grimm
(2007) defines a variant of the GIC, termed the "individual growth incidence curve (IGIC)", which follows
the same individual over time, and is defined as the income growth rate for each individual as a function
of their percentile in the initial distribution. Whereas the RavallionChen GIC is the relevant one for
changes in inequality when the symmetry or anonymity axiom is upheld, Grimm's IGIC tells us about
individual income trajectories over time, and thus about economic mobility. Scope remains for further
interesting work on how the GIC and the IGIC relate, and on whether the IGIC provides as much of a
unifying basis for mobility measurement as we have shown that the GIC does for inequality
measurement.27 Similarly, and as indicated earlier, there is probably much to be learned from combining
the sort of growth incidence analysis reviewed in this paper with the insights on how various shocks and
policy changes affect individual income trajectories, from the more causal literature on individual
income dynamics.
27
On the measurement of various concepts of mobility, see Fields and Ok (1996).
27
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Table 7: Simulated Poverty and Inequality for 1976, Using 1996 coefficients.
Mean Inequality Poverty
p/c Z = R$30 / month Z = R$ 60 / month
Income Gini E(0) E(1) E(2) P(0) P(1) P(2) P(0) P(1) P(2)
1976 observed 265.101 0.595 0.648 0.760 2.657 0.0681 0.0211 0.0105 0.2209 0.0830 0.0428
1996 observed 276.460 0.591 0.586 0.694 1.523 0.0922 0.0530 0.0434 0.2176 0.1029 0.0703
Price Effects
for wage earners 218.786 0.598 0.656 0.752 2.161 0.0984 0.0304 0.0141 0.2876 0.1129 0.0596
for selfemployed 250.446 0.597 0.658 0.770 2.787 0.0788 0.0250 0.0121 0.2399 0.0932 0.0490
for both 204.071 0.598 0.655 0.754 2.190 0.1114 0.0357 0.0169 0.3084 0.1249 0.0673
only, for both 233.837 0.601 0.664 0.774 2.691 0.0897 0.0275 0.0129 0.2688 0.1040 0.0545
All (but no ) for both 216.876 0.593 0.644 0.736 2.055 0.0972 0.0303 0.0143 0.2837 0.1114 0.0590
Education for both 232.830 0.593 0.639 0.759 2.691 0.0779 0.0234 0.0110 0.2531 0.0953 0.0488
Experience for both 240.618 0.600 0.664 0.771 2.694 0.0851 0.0265 0.0125 0.2592 0.1000 0.0525
Gender for both 270.259 0.595 0.649 0.751 2.590 0.0650 0.0191 0.0090 0.2160 0.0797 0.0404
Occupational Choice Effects
for both sectors (and both 260.323 0.609 0.650 0.788 2.633 0.0944 0.0451 0.0331 0.2471 0.1082 0.0671
heads + others)
for both sectors (only for 265.643 0.598 0.657 0.757 2.482 0.0721 0.0231 0.0119 0.2274 0.0867 0.0454
other members)
for both sectors 202.325 0.610 0.649 0.788 2.401 0.1352 0.0597 0.0402 0.3248 0.1466 0.0902
Demographic Patterns
d only, for all 277.028 0.574 0.585 0.704 2.432 0.0365 0.0113 0.0063 0.1711 0.0554 0.0264
d , , , , for all 210.995 0.587 0.577 0.727 2.177 0.0931 0.0433 0.0321 0.2724 0.1129 0.0677
Education Endowment Effects
e only, for all 339.753 0.594 0.650 0.740 2.485 0.0424 0.0136 0.0073 0.1593 0.0567 0.0287
d, e for all 353.248 0.571 0.584 0.688 2.320 0.0225 0.0078 0.0049 0.1131 0.0359 0.0173
e , d , , , , for all 263.676 0.594 0.600 0.727 1.896 0.0735 0.0374 0.0296 0.2204 0.0913 0.0561
Source: Based on "Pesquisa Nacional por Amostra de Domicílios" (PNAD) of 1976 and 1996.
Source: Ferreira and Paes de Barros (2005).
32
Figure 1: Empirical partial growth elasticities of poverty reduction against initial Gini index:
(LDCs in 19812004, poverty headcount, z = US$1 a day).
Source: World Bank (2005)
Figure 2: A Generalized OaxacaBlinder decomposition of the GIC for Brazil, 19761996
Source: Ferreira and Paes de Barros (2005)
33
Figure 3:
Observed and counterfactual wage growth incidence curves, 198895,
all trademandated changes from 2nd stage
110%
90%
70%
50%
%
30%
10%
10%
30%
0 10 20 30 40 50 60 70 80 90 100
percentiles
Source: Authors' calculation from PNADs. g (p) g 2(p) g 3(p)
Source: Ferreira, Leite and WaiPoi (2010)