WPS7758
Policy Research Working Paper 7758
All That Glitters Is Not Gold
Polarization Amid Poverty Reduction in Ghana
Fabio Clementi
Vasco Molini
Francesco Schettino
Poverty and Equity Global Practice Group
July 2016
Policy Research Working Paper 7758
Abstract
Ghana is an exceptional case in the Sub-Saharan Africa with a high degree of accuracy and granularity. Looking
landscape. Together with a handful of other countries, at the results from 1991 to 2012, the paper documents
Ghana offers the opportunity to analyze the distributional how the distributional changes hollowed out the middle
changes in the past two decades, since four comparable of the Ghanaian household consumption distribution and
household surveys are available. In addition, different increased the concentration of households around the high-
from many other countries in the continent, Ghana’s est and lowest deciles; there was a clear surge in polarization
rapid growth translated into fast poverty reduction. A indeed. When looking at the drivers of polarization, house-
closer look at the distributional changes that occurred in hold characteristics, educational attainment, and access to
the same period, however, suggests less optimism. The pres- basic infrastructure all tended to increase over time the
ent paper develops an innovative methodology to analyze size of the upper and lower tails of the consumption dis-
the distributional changes that occurred and their drivers, tribution and, as a consequence, the degree of polarization.
This paper is a product of the Poverty and Equity Global Practice Group. It is part of a larger effort by the World Bank to
provide open access to its research and make a contribution to development policy discussions around the world. Policy
Research Working Papers are also posted on the Web at http://econ.worldbank.org. The authors may be contacted at
vmolini@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
All That Glitters Is Not Gold: Polarization Amid Poverty
Reduction in Ghana
Fabio Clementi1, Vasco Molini2,†, and Francesco Schettino3
1
University of Macerata, Macerata, Italy
2
World Bank, Washington DC, USA
3
Second University of Naples, Naples, Italy
Keywords: Ghana; consumption expenditure; poverty and inequality; polarization; relative distribution;
decomposition analysis.
JEL classification: C14; D31; D63; I32.
†
Corresponding author. E-mail addresses: fabio.clementi@unimc.it (Fabio Clementi), vmolini@worldbank.org
(Vasco Molini), francesco.schettino@unina2.it (Francesco Schettino).
Note: The authors acknowledge financial support from the World Bank. We thank Dan Pavelesku (World Bank)
for excellent assistance with data preparation. We also thank Christoph Lakner, Pierella Paci and Andrew
Dabalen (World Bank) for comments on an earlier version of the manuscript. Of course, we are the sole
responsible for all possible errors the paper may contain.
1 Introduction
Over the last two decades, several African countries experienced stable and sustained growth that did
not translate, nonetheless, into rapid poverty reduction. Compared to other regions, particularly in the
last decade, the growth elasticity of poverty of Sub-Saharan African (SSA) countries has been lower
than in the rest of developing world (Molini and Paci, 2015). The causes of this limited inclusiveness
are numerous, but typically scholars point to the excessive reliance of many SSA economies on a
limited basket of raw materials and the limited trickle down of this growth to households’
consumption.
At first glance, Ghana is an exception compared to the rest of Sub-Saharan countries. Ghana’s rapid
growth did translate into fast poverty reduction. Inequality increased over the last two decades (Cooke
et al., 2016; Aryeetey and Baah-Boateng, 2015) but, compared to other SSA countries, Ghana still
fares relatively well. When ranking SSA countries according to the average Gini index over the last 20
years Ghana occupies the bottom 20 percent of the Gini distribution and despite some deterioration, in
2012, it was still below the median and among the lowest of rapidly growing African economies
(Molini and Paci, 2015).
A closer look at the distributional changes occurred in the same period, suggests, however, less
optimism. Like many other developing countries (Clementi et al., 2014, 2015; Clementi and Schettino
2015) Ghana is experiencing a fast increase in polarization. Whereas inequality relates to the overall
dispersion of the distribution and provides clues to whether a society’s prosperity has been shared
broadly or not, polarization is concerned with the division of society into subgroups. In the context of
income distribution, this concept is typically equated with the “hollowing out of the middle”, a
situation where the society has a sizeable group of poor persons and there is also a non-negligibly
sized group of persons with very high income and, in contrast, the size of the group occupying the
center of the income distribution is rather low (see, for instance, Foster and Wolfson, 1992, and
Wolfson, 1994, 1997). Within each group there is increasing “identification”, which means income
homogeneity and often declining income inequality, while between the two groups we have instead
increasing “alienation” (Duclos et al., 2004). The combined effect of the forces of alienation and
identification between two significantly sized groups would tend to lead to effective opposition, a
situation that might give rise to social conflicts and tensions (Esteban and Ray, 1999, 2008, 2011).
The contribution of this paper is twofold. First, it uses a very intuitive yet little explored method, the
relative distribution, (Handcock and Morris, 1998, 1999) to analyze the recent distributional changes
occurred in the country. The strength of this method consists in providing a non-parametric framework
for taking into account all the distributional differences that could arise in the comparison of
distributions over time and space. In this way, it enables to summarize multiple features of the
2
expenditure distribution that would not be detected easily from a comparison of standard measures of
inequality and polarization. Second and most important, the paper develops within the relative
distribution framework a novel methodology to identify the drivers of distributional changes and
quantify their impact on the welfare distribution; the main value added being it enables a very granular
analysis of the distributional changes that an analysis based on standard inequality decompositions
would not allow.
The paper is organized as follows. Section 2 discusses the data and presents the methodology. Section
3 provides the results. Section 4 concludes.
2 Data and methodology
2.1 The Ghanaian household survey data
The data used in this paper come from the Ghana Living Standard Survey (GLSS), a nation-wide
survey conducted by the government-run Ghana Statistical Service that provides information for
assessing the living conditions of Ghanaian households.
The GLSS has emerged as one of the most important tools for the welfare monitoring system in
Ghana. It provides detailed information on approximately 200 variables, including several socio-
economic and demographic characteristics, and information on household consumption of purchased
and home-produced goods as well as asset ownership. Each of the waves is organized into 4 modules,
which are stored in the individual, the labor force, the household and the household expenditure files,
for which survey questionnaires are readily available.
The Ghana Statistical Service has conducted six rounds of the GLSS since 1987, thereby providing
over 20 years of comparable data. The second, third, fourth and fifth rounds were carried out,
respectively, in 1988, 1991/92, 1998/99 and 2005/06. Recently, data for the sixth round of GLSS have
also become available, so that the proposed case study paper will be one of the first studies using this
data set. However, only the last four rounds, from 1991/92 (GLSS-3) to 2012/12 (GLSS-6), have been
based on the same questionnaire and are therefore fully comparable.
The availability of comparable and extensive information represents a success on its own. Ghana is
one of the few countries in Africa that has produced comparable, high-quality household data covering
over two decades. This is an important achievement because the availability of such rich and
comparable information beginning in 1991, as well as the quality improvements of the surveys over
the years and the fact that they collect data on both the monetary and the non-monetary dimensions of
welfare, permit the establishment of an accurate picture of inequality and polarization over time,
including the drivers behind these phenomena.
3
As a measure of well-being we will use household consumption for 1991/92 (GLSS-3), 1998/99
(GLSS-4), 2005/06 (GLSS-5) and 2012/13 (GLSS-6). In that, we depart from the literature using
income as a measure of well-being. Our choice is mainly motivated by measurement issues, which
play a very relevant role in the case of Ghana and have to do with the quality of the income measures
that one can obtain from the GLSS data. In economies where agriculture is an important and
established sector, consumption has indeed proven preferable to income because the latter is more
volatile and more highly affected by the harvest seasons, so that relying on income as an indicator of
welfare might under- or over-estimate living standards significantly (see, for instance, Deaton and
Zaidi, 2002, and Haughton and Khandker, 2009). On the theoretical ground, as consumption gives
utility to individuals, the analysis of its distribution should be the most natural approach to study well-
being. Income matters insofar as it gives access to consumption, which is the ultimate source of
individual welfare. Consumption is a better measure of long-term welfare also because households can
borrow, draw down on savings, or receive public and private transfers to smooth short-run
fluctuations. The GLSS collects sufficiently detailed information to facilitate estimates of the total
consumption of each household. It relies on consumption per adult equivalent1 to capture differences
in need by age and economies of scale in consumption. Scales of consumption by age and sex are
computed by the Ghana Statistical Service.
The GLSS is based on a two-stage (non-stratified) sample design. Therefore, when the data are
analyzed, sampling weights are used to account for the survey design. Besides, to enhance
comparability of consumption data over the four waves, all expenditures have been deflated across
both space2 and time and expressed in 2005 constant prices – as well as converted, when necessary,
from Ghanaian second cedi (GHC) to Ghanaian third cedi (GHS), i.e. for GLSS-3 to GLSS-5.
A summary of distributional statistics obtained from the GLSS data sets is given in Table 1. Besides
the growth of the real mean and median consumption expenditures, the most notable feature is the
picture that emerges across different indicators of inequality. The consumption shares of the poorest
percentiles of the population decreased between approximately 0.9 and 1.4 % a year in the period
examined, in contrast to what is observed for the richest percentiles, whose shares experienced average
yearly increases of around 0.2 %. Inequality in household consumption was initially constant, but
widened considerably between 1998/99 and 2005/2006 – a jump of about 7 % in the Gini’s coefficient
and 20 % in the Theil’s index.3 Inequality has remained constant at the higher level after 2005/06, but
1
We use adult equivalent scales because also the official consumption, poverty and inequality figures are
expressed in adult equivalent terms.
2
The price deflator differs across the ten regions in which Ghana is divided and within each region by urban and
rural areas.
3
Running a simple t-test of the difference between Gini and Theil indices from the 1998/99 and 2005/06 samples
yields a p-value of around zero, which confirms the finding that points to increasing inequality over the 1998-
2005 period at any of the usual significance levels.
4
the trends in the shares of consumption of the bottom and top quintiles have continued in the same
direction.
However, the narrative about inequality is more nuanced than the summary measures suggest. The
summary measures of inequality analyzed above only partially capture the changes at various points of
the consumption distribution. The results of a simple inter-quantile analysis can provide more detailed
information on the changes occurring at all points of the distribution (see Table 2). They show that the
ratio of average consumption among the top 10 of the distribution to the average consumption among
the bottom 10 had risen considerably even before 1998/99, suggesting that the more well-off had
benefited more than the poorest decile from the economic growth in 1991-98. Over the years, the
consumption levels of the top and the bottom of the distribution continued to diverge at a steady rate
so that the gap expanded by 30 % over the full period.4 The divergence was widening because the
bottom 10 was being left behind, rather than because the top 10 was gaining disproportionally
compared with the rest of the population. The average consumption of the 90-th percentile rose little
relative to the median, while the average consumption of the bottom 10 had deteriorated by nearly 20
% by 2005/06. The bottom 10 appears to be losing ground also compared with other households in the
bottom 25, who are also losing ground to the median but only half as quickly.
These preliminary findings denote a clear tendency towards rising polarization in household
consumption over the period. The notion of “polarization” commonly refers to the case where there is
a significant number of individuals who are very poor but there exists also a non-negligible share of
the population that is quite rich. Such a gap between the poor and the rich implies evidently that there
is no sizeable middle class.5 As we will see later when applying relative distribution methods, the
distributional changes that occurred between 1991/92 and 2012/13 hollowed out the middle of the
Ghanaian household consumption distribution and increased the concentration of households around
the highest and lowest deciles, hence leading to an increase of polarization.
2.2 Relative distribution methods
2.2.1 Basic concepts
4
The gap between 90-th and 10-th deciles is probably a lower bound of the real one. In general, household
surveys do not contain good estimates of upper percentiles of welfare (Alvaredo and Piketty, 2010). When using
consumption to rank welfare, as it is normally done in low/er middle income countries, the situation is further
aggravated. Consumption is very accurate in capturing the well-being of poorer people, yet it is rather imprecise
in capturing that of people living in upper percentiles.
5
In this paper we will analyze the median-based approach to the measurement of polarization. Since it
subdivides the population into two subgroups – those above the median and those below the median, respectively
– we refer to this as the case of “bi-polarization”. For a detailed explanation of the main differences not only
between the study of inequality and that of polarization, but also between the concept of bi-polarization and that
of “multi-polar” polarization, see e.g. Chakravarty (2009, ch. 4), Deutsch et al. (2013) and Chakravarty (2015).
5
To address the question of the “hollowing out of the middle” in Ghana, we use relative distribution
methods. Developed by Handcock and Morris (1998, 1999), these techniques based on the relative
distribution powerfully assist in the description of distributional change and enable counterfactual
comparison of location-adjusted distributions.
Basically, relative distribution methods can be applied whenever the distribution of some quantity
across two populations is to be compared, either cross-sectionally or over time.6 For our purposes, the
relative distribution is defined as the ratio of the density in the comparison year to the density in the
reference year evaluated at each decile of the consumption distribution, and can be interpreted as the
fraction of households in the comparison year’s population that fall into each tenth of the reference
year’s distribution.7 This allows us to identify and locate changes that have occurred along the entire
Ghanaian household consumption distribution.
To formalize, let:
m
I c i 1 y
1
pit 0 t
j
c 0 i , i 1, ,10, (1)
m j 1
be the proportion of households in year t’s comparison sample falling into each decile and:
n
I c i 1 y
1
pi0 0 0
j
c 0 i , i 1, ,10, (2)
n j 1
be the proportion of households in year 0’s reference sample falling into the same deciles, where m
and n reflect the comparison and reference sample sizes and:
1 if the event S is true
I S (3)
0 otherwise
denotes the indicator function. The cut points c0[i-1] and c0[i] for each interval are estimated as deciles
of the reference sample, hence the proportion of the sample from the reference distribution falling into
each decile is exactly 1/10. The relative distribution is given by the proportion of year t’s households
6
Here we limit ourselves to illustrating the basic concepts behind the use of relative distribution methods.
Interested readers are referred to Handcock and Morris (1998, 1999) – but see also Hao and Naiman (2010, ch. 5)
– for a more detailed explication and a discussion of the relationship to alternative econometric methods for
measuring distributional differences. A method very similar in spirit to the relative distribution one has recently
been developed by Silber et al. (2014).
7
To keep the notation simple and the graphical displays informative, we will focus throughout the paper on
group-level data from underlying continuous distributions. We will also assume that discretization is based on
decile ranges with respect to the reference year’s distribution. By extending the fundamental concepts of the
relative distribution approach to the grouped data context, Handcock and Morris (1999, ch. 11) allow the analysis
of discretized distributions to retain the tractability and interpretability of its continuous counterpart based on
ungrouped data. For an application of relative distribution methods to ungrouped samples, see e.g. the Brazilian
and Nigerian case studies by, respectively, Clementi and Schettino (2015) and Clementi et al. (2014, 2015).
6
whose consumption expenditures fall into each decile estimated from the reference distribution,
divided by the proportion in the reference year:
pit
g t i , i 1, ,10. (4)
pi0
When the fraction of the comparison population in a decile is higher (lower) than the fraction in the
reference year, the relative distribution will be higher (lower) than 1. When there is no change, the
relative distribution will be flat at the value 1. Therefore, in this way one can distinguish between
growth, stability or decline at specific points of the consumption distribution.
2.2.2 The location/shape decomposition of the relative distribution
One of the major advantages of this approach is the possibility to decompose the relative distribution
into changes in location, usually associated with changes in the median (or mean) of the distribution,
and changes in shape (including differences in variance, asymmetry and/or other distributional
characteristics) that could be linked to several factors such as, for instance, polarization. The
decomposition can be represented in the following terms:
0L t
pi pi
g i
t
0
0L
, i 1, ,10, (5)
pi pi
Location effect Shape effect
where:
n
I c i 1 y
1
pi0 L 0 0L
j
c0 i , i 1, ,10, (6)
n j 1
denotes the proportion of households in each estimated decile range of the original reference
distribution whose consumption expenditures have been median-adjusted by an additive shift to yield
identical centers of the comparison and reference distributions, while the shapes of the two
distributions remain the same.8
In formal notation, the median-adjusted reference variable is Y Y , where Y denotes the year 0’s
0L 0
8 0
consumption variable and the value ρ is the difference between the medians of the comparison and reference
distributions. Median adjustment is preferred here to mean adjustment because of the well-known drawbacks of
the mean when distributions are skewed. A multiplicative median shift can also be applied. However, the
multiplicative shift has the drawback of affecting the shape of the distribution. Indeed, the equi-proportionate
changes increase the variance and the rightward shift of the distribution is accompanied by a flattening (or
shrinking) of its shape – see e.g. Jenkins and Van Kerm (2005).
7
The first ratio term in the right hand side of Equation (5) is an estimate of the “location effect”, i.e. the
pattern that the relative distribution would have displayed if there had been no change in distributional
shape but only a location shift of the consumption distribution over time. When the median-adjusted
and unadjusted reference populations have the same median, the ratio for location differences will
have a uniform distribution. Conversely, when the two distributions have different median, the
location effect is increasing (decreasing) in i if the comparison median is higher (lower) than the
reference one.
The second term (the “shape effect”) represents the relative distribution net of the location effect and is
useful to isolate movements (re-distribution) occurred between the reference and comparison
populations. For instance, one could observe a shape effect with some sort of (inverse) U-shaped
pattern if the comparison distribution is relatively (less) more spread around the median than the
median-adjusted reference distribution. Thus, it is possible to determine whether there is polarization
of the consumption distribution (increases in both tails), “downgrading” (increases in lower tail),
“upgrading” (increases in the upper tail) or convergence towards the median (decreases in both tails).
The graphical display provides a useful visual summary of the relative size and nature of the three
components of the decomposition in Equation (5).
2.2.3 Relative polarization indices
Another relevant feature of these methods is that one can use summary measures to quantify the
observed pattern of changes. Morris et al. (1994) and Handcock and Morris (1998, 1999) developed a
measure of polarization that captures the degree to which there is divergence from, or convergence
toward, the center of the distribution, and is thus ideally suited to addressing the question of the
“hollowing of the middle”. For group-level data, the median relative polarization index (MRP) takes
the form (Morris et al., 1994, p. 217; Handcock and Morris, 1999, p. 190):
1
Q i
4 2 1 g t i Q ,
MRP
Q2
Q 2 Q2
(7)
i 1
where g t i , i 1, , Q , are the relative proportions in (4) and the adjustment by 1/2 establishes the
mid-point for each group. The expression for a decile aggregation is easily obtained from Equation (7)
by setting Q 1 0 . The index varies between -1 and 1. It takes the value of 0 when there has been no
change in the distribution of household consumption relative to the reference year. Positive values
signify relative polarization (i.e. growth in the tails of the distribution) and negative values signify
relative convergence toward the center of the distribution (i.e. less polarization).
8
The median relative polarization index can be decomposed into the contributions to distributional
change made by the segments of the distribution above and below the median, enabling one to
distinguish “upgrading” from “downgrading”. For grouped data, the lower relative polarization index
(LRP) and the upper relative polarization index (URP) are calculated as:
1
Q 2 i
8 2 1 g t i Q ,
LRP
Q2
Q 2 Q2
(8)
i 1
1
Q i
8 2 1 g t i Q .
URP
Q 2 i Q Q 2 Q2
(9)
2 1
They have the same theoretical range as the MRP and decompose the overall polarization index in the
following way (Handcock and Morris, 1998, 1999):
1
MRP LRP URP . (10)
2
To test the hypothesis of no change with respect to the reference distribution, i.e. that the three indices
have a statistically significant difference from zero, we use the asymptotic distribution of the estimates
under the non-parametric null hypothesis that the reference and comparison distributions are identical.
Under this hypothesis, the distribution of the group-level estimates of the MRP is asymptotically
normal with a mean equal to 0 and a variance equal to (Morris et al., 1994, p. 218):
11 1
Var MRP . (11)
3 m n
Distributional approximations for the LRP and URP are similar. The variance in both cases is
approximately (Handcock and Morris, 1999, p. 170):
51 1
. (12)
3 m n
Therefore, given a chosen significance level, the p-value for testing the null hypothesis H0 :RP 0
against the alternative that one of the three indices is different from zero can be calculated as:
RP
p-value 1 , (13)
Var RP
9
where is the standard normal distribution function and RP denotes the median, lower or upper
polarization index.
In practice, the normal approximations will be very good for sample sizes of 50 or more. As the
sample sizes in our study (m and n) are typically on the order of thousands, the distributional
approximations involved are excellent.
2.3 Blinder-Oaxaca type decomposition of location and shape differences
In this section we present a novel method for analyzing the effects of covariates on the observed
distributional changes due to both the location and shape shifts. Novel because in the original relative
distribution framework, the method proposed to measure the impact of polarization drivers does not
provide intuitive results and it is of limited use for policy making purposes. By contrast, our method
that combines the relative distribution approach and the regression based decompositions, can produce
an easily interpretable set of results.
In the relative distribution setting, the exploration of the distributional impacts of changes in
covariates requires that the overall relative density is adjusted for these changes using the technique
described in Handcock and Morris (1999, ch. 7). This technique partials out the impact of changes in
the distribution of the covariates – the “composition effect” – and the modifications in the conditional
distributions of household consumption expenditure given the covariate levels – the “residual effect”.
Conceptually, this parallels the traditional regression-based decomposition that separates changes in
covariates (the X’s) from changes in the “returns” to the covariates (the regression coefficients, or β’s).
However, the covariate adjustment technique proposed by Handcock and Morris does not provide a
simple and intuitively accessible way of dividing up the changes exclusively due to a location shift or
shape differences into the contribution of changes in the distribution of each single covariate and that
of the changing “returns” to the covariates; also, differently from what happens in the classical
regression decomposition approach, its drawback is making it difficult to summarize the contributions
above into a single value as, for example, the estimated coefficients obtained by the regression
procedure would make it possible to quantify.
The framework we propose integrates the spirit of the relative distribution approach and recent
developments from the regression-based decomposition literature. This can be regarded as an
extension of the covariate adjustment technique developed by Handcock and Morris and can be used
to quantify the impact of an arbitrary number of covariates on distributional differences due to both
location and shape shifts, so as to identify the key drivers of these changes.
10
In detail, we decompose the component relative distributions that represent differences in location and
shape by applying a procedure recently proposed by Firpo et al. (2009) for the decomposition of wage
differentials. The method is based on running unconditional quantile regressions to estimate the impact
of changing the distribution of explanatory variables along the entire distribution of the dependent
variable and using the traditional Blinder (1973) and Oaxaca (1973) decomposition framework to
decompose differentials at selected quantiles of the consumption distribution.
To estimate the unconditional quantile regression, we have first to derive the re-centered influence
function (RIF) for the τ-th quantile of the dependent variable distribution – consumption, in our case –
which can be shown as (Firpo et al., 2009; Essama-Nssah and Lambert, 2011; Fortin et al., 2011):
q f q , c q ,
RIF c; q , FC
C
(14)
q 1 , c q ,
fC q
where qτ is the sample quantile and fC(qτ) is the density of consumption C at the τ-th quantile. In
practice, the RIF is estimated by replacing all unknown quantities by their observable counterparts. In
the case of (14) unknown quantities are qτ and fC(qτ), which are estimated by the sample τ-th quantile
of C and a standard non-parametric kernel density estimator, respectively. Firpo et al. (2009) show that
the unconditional quantile regression can be implemented by running a standard OLS regression of the
estimated RIF on the covariates X:9
RIF C; q , FC X x
E X , (15)
where the coefficient βτ represents the approximate marginal effect of the explanatory variable X on
the τ-th unconditional quantile of the household consumption distribution. Applying the law of iterated
expectations to the above equation, we also have:
q E X RIF C; q , FC X x
E E X .
(16)
This yields an unconditional quantile interpretation, where βτ can be interpreted as the effect of
increasing the mean value of X on the unconditional quantile qτ.10
9
This can be performed using the Stata’s command rifreg, which is available for download at
http://faculty.arts.ubc.ca/nfortin/datahead.html.
10
As discussed in more detail by Fortin et al. (2011), one important reason for the popularity of OLS regressions
in economics is that they provide consistent estimates of the impact of an explanatory variable, X, on the
population unconditional mean of an outcome variable, Y. This important property stems from the fact that the
conditional mean, E Y X x , averages up to the unconditional mean, E Y , due to the law of iterated
11
Using unconditional quantile (RIF) regression, an aggregate decomposition for location and shape
differences can then be implemented in a spirit similar to the Blinder-Oaxaca decomposition of mean
differentials as follows:
ˆt c
ˆ0
ˆt c ˆt
ˆt
X
ˆt ,
I (17)
where the total difference in consumption at the same quantile τ of the year t’s comparison and year
0’s reference distributions,
ˆ t , is decomposed into one part that is due to differences in observable
characteristics (endowments) of the households,
ˆ t , one part that is due to differences in returns
X
(coefficients) to these characteristics,
t
ˆ , and a third part – for which no clear interpretation exists –
that is due to interaction between endowments and coefficients,
t
ˆ . In particular, once the RIF
I
regressions for the τ-th quantile of the comparison and reference consumption distributions have been
run, the estimated coefficients can be used as in the standard Blinder-Oaxaca decomposition to
perform a detailed decomposition into contributions attributable to each covariate. The aggregate
decomposition can be generalized to the case of the detailed decomposition in the following way:11
K K
K
ˆt Xt X0
k
k
ˆ0
,k
ˆt
ˆ0
ˆt
,k
ˆ0 X 0
,k k X kt X k0 ˆ
,k
t
ˆ0 ,
,k (18)
k 1
k 1
k 1
ˆt
ˆt
ˆt
X I
expectations. As a result, a linear model for conditional means, E Y X x X , implies that
E Y E X , and OLS estimates of β also indicate what is the impact of X on the population average of Y.
When the underlying question of economic and policy interest concerns other aspects of the distribution of Y,
however, estimation methods that “go beyond the mean” have to be used. A convenient way of characterizing the
distribution of Y is to compute its quantiles. A quantile regression model for the τ-th conditional quantile qτ(X)
postulates that q X X . By analogy with the case of the mean, βτ can be interpreted as the effect of X on
the τ-th conditional quantile of Y given X. Unlike conditional means, however, conditional quantiles do not
average up to their unconditional population counterparts, i.e. q Y E X q X E X , where qτ(Y) is
the unconditional quantile. As a result, the estimated βτ cannot be interpreted as the effect of increasing the mean
value of X on qτ. RIF regression offers instead a simple way of establishing a direct link between unconditional
quantiles of the distribution of Y and household characteristics X because of (16), which says that the conditional
expectation of (15) – the expected value of the RIF – is equal to the unconditional quantile of interest.
11
Following Jones and Kelley (1984), we focus here on the so-called “threefold” decomposition, which uses the
same reference distribution for both ˆ t but introduces the interaction term
ˆ t and
X
ˆ t . Equations (17) and (18)
I
can also be written by reversing the reference and comparison distribution designation for both
t
ˆ and
ˆ , as t
X
well as by allocating the interaction term to either
ˆ t or
X
ˆ t so as to implement a “twofold” decomposition.
However, while these various versions are used in the literature, using one or the other does not involve any
specific estimation issue (Fortin et al., 2011). Hence, for the sake of exposition, we shall utilize the
decomposition introduced in the text for the rest of our analysis.
12
ˆ and
where k represents the k-th covariate and ˆ are the estimated intercept and slope coefficients,
,k
respectively, of the RIF regression models for the comparison and reference samples.12
Specifically, since we use an additive median shift to identify and separate out changes due to location
differences in the consumption distribution, the decompositions above are carried out using the
medians (τ = 0.5) of the location-adjusted and unadjusted reference populations, so that the total
difference to be decomposed according to (17) and (18) is:
ˆ 0L c
0.5
0L
ˆ0.5 c0
ˆ0.5 , (19)
where ρ denotes the difference between the medians of the year t’s comparison and year 0’s reference
distributions (see footnote 6). As location-adjustment is performed by adding ρ to every household
consumption expenditure of the original reference population to match its median with that of the
comparison population, without altering the shape, the decomposition of the differential (19) can be
operated once and its results assumed to hold simultaneously across the entire relative distribution
representing changes exclusively due to a location shift. For what concerns the shape shift, the
differentials to be decomposed are instead as follows:
ˆt c
ˆ0L , 0.1,,0.9,
ˆt c (20)
where the quantiles cτ are estimated as deciles of the comparison and location-adjusted distributions –
the latter having the median of the comparison sample but the shape of the reference one.
Notice that the differentials (20) represent horizontal distances, or decile gaps, between the
distributions involved in the decomposition exercise, whereas the idea underlying the relative
distribution framework typically focuses on vertical ratios, or relative proportions. Hence, the
“declining middle class” scenario would suggest that negative differentials
ˆ t are to be expected for
deciles below the median, whereas for those above the median the total differences given by (20)
should be positive. Intuitively, this is because in this case the population shifts from the center of the
consumption distribution to the upper and lower deciles, so that the cut-off points identifying the
12
Notice that in order to decompose the total difference
ˆ t according to (18) it is also necessary to estimate two
counterfactual consumption distributions, namely, the distribution that can be obtained by combining the
distribution of characteristics of the comparison sample with the returns for households’ observable
characteristics of the reference sample, X t ˆ 0 , and the distribution obtained by combining the distribution of
characteristics of the reference sample with the returns for households’ characteristics of the comparison sample,
t
X , where X represents the covariates mean. This can be done automatically within Stata by invoking
0
Jann’s (2008) oaxaca8 command, which is the routine used in this study to perform empirical applications of
Equation (18).
13
deciles below the median in the comparison distribution come before those of the reference
distribution along the consumption scale, while cut-off points for deciles above the median come after.
3 Results
3.1 Changes in the Ghanaian consumption distribution
To introduce the results obtained from using the methods and data described in previous sections, in
Figure 1(a) we present two probability density functions of the Ghanaian distribution of total
consumption expenditure.13 The solid line is the distribution of household consumption in 1991/92,
taken as the baseline throughout the analysis. The density drawn with the dotted line, which we will
treat as the comparison, is the distribution in 2012/13.14 Examining these two distributions, we see that
the reference or 1991/92 distribution has a slight right skewness, while the comparison distribution has
a larger median and variance.
However, the graphical display above does not provide much information on the relative impact that
location and shape changes had on the differences in the two distributions at every point of the
expenditure scale. It also does not convey whether the upper and lower tails of the consumption
distribution were growing at the same rate and for what reasons (i.e. location and/or shape driven). As
already pointed out in Subsection 2.2, this is exactly what relative distribution methods are particularly
good at pulling out of the data.
The relative density of total consumption expenditure of Ghanaian households between 1991/92 and
2012/13 is examined in Figure 1(b), showing the fraction of households in 2012/13 that fall into each
decile of the 1991/92 distribution.15 The graph offers the immediate impression that the proportion of
households in the upper deciles increased dramatically throughout the two decades, while the
13
To handle data sparseness, the two densities have been obtained by using an adaptive kernel estimator with a
Silverman’s plug-in estimate for the pilot bandwidth (see e.g. Van Kerm, 2003). The advantage of this estimator
is that it does not over-smooth the distribution in zones of high expenditure concentration, while keeping the
variability of the estimates low where data are scarce – as, for example, in the highest expenditure ranges.
14
Obviously, reversing the reference and comparison distribution designation will change the view provided by
the relative distribution graph and the displays of the estimated effects of location and shape shifts, because these
are defined in terms of the reference distribution scale. However, designating which distribution will serve as the
reference is a decision that must be made by the analyst, and in our application the natural choice was suggested
by time ordering. In addition, the relative polarization indices (measurements of the degree to which a
comparison distribution is more polarized than a reference distribution, and defined in terms of the relative
distribution of the comparison relative to the median-adjusted reference) are symmetric, meaning that they are
effectively invariant to whether the 1991/92 or 2012/13 consumption distribution is chosen as the reference – in
fact, swapping the comparison and reference distributions yields indices of the same magnitude and opposite
sign (Handcock and Morris, 1999, pp. 71-72; Hao and Naiman, 2010, pp. 88-89). Thus, reversing the reference
and comparison distributions designation will not alter our findings in a substantive way – if not for the fact that
polarization would now be analyzed in the reverse direction of time.
15
Throughout, we rely on the R statistical package reldist (Handcock, 2015) to implement the relative
distribution method.
14
proportion in the bottom and around the middle declined. Indeed, if we choose any decile between the
first and the seventh in the 1991/92 distribution, the fraction of households in 2012/13 whose
consumption rank corresponds to the chosen decile is less than the analogous fraction of households in
1991/92.
While the display of the relative distribution points to the dominant trend for the entire period, the
dominant trend may be masking some of the more subtle changes. To see these, we decompose the
relative density into location and shape effects according to Equation (5). Figure 1(c) presents the
effect only due to the median shift, that is the pattern that the relative density would have displayed if
there had been no change in distributional shape but only a location shift of the density. The effect of
the median shift was quite large. This alone would have virtually eliminated the households in the first
four deciles of the 1991/92 consumption distribution and placed a considerable fraction of them in the
top end of the 2012/13 distribution. Note, however, that neither tail of the observed relative
distribution is well reproduced by the median shift. For example, the top decile of Figure 1(c) is about
2.5, below the value of 3.6 observed in the actual data, and the bottom deciles of the same figure are
also substantially lower than observed.
These (and other) differences are explained by the shape effect presented in Figure 1(d), which shows
the relative density net of the median influence. Without the higher median, the greater dispersion of
consumption expenditures would have led to relatively more low-consuming households in 2012/13,
and this effect was mainly concentrated in the bottom decile. By contrast, at the top of the distribution
the higher spread worked in the same direction of the location shift: operating by itself, it would have
increased the share of households in the top decile of the 2012/13 consumption distribution by nearly
120%. In sum, once changes in real median expenditure are netted out, a U-shaped relative density is
observed, indicating that polarization was hollowing out the middle of Ghanaian household
consumption.
Relative distribution methods permit us to also analyze how re-distribution across households took
place over the entire time period. For each wave of the GLSS between 1991/92 and 2012/13, Figure 2
shows the shape effect of the household consumption relative density using 1991/92 as the reference
sample.16 Following the plot through each successive wave, one is offered with the immediate
impression that the fraction of households at both the top and bottom tails of the Ghanaian
consumption distribution increased consistently over the course of the last two decades, while the
fraction in the middle declined. Polarization, or the “hollowing out of the middle”, has been therefore
the consistent trend in distributional inequality for all the GLSS waves since 1991/92. Because this
period was also characterized by a sizable shift in location, viewed together these results indicate that,
16
The relative distribution, and therefore its shape effect, is by definition flat in the reference year (Morris et al.,
1994, p. 211).
15
in the course of the upswing in consumption expenditures, some households fell behind, while others
shifted toward the top, joining the ranks of those whose consumption put them in the top decile in
1991/92.
To summarize these changes, we present in Figure 3 the set of relative polarization indices computed
from the GLSS data using Equations(7)-(9).17 These indices track changes in the shape of the
distribution only, and they code the direction as well as the magnitude of the change. The overall index
(MRP) rises continuously and the rise is statistically significant from the outset, thus confirming the
visual impression from Figure 1(d). Decomposing the MRP into the contributions from the lower and
upper tails of the distribution, it also appears that “downgrading” dominated “upgrading” in the
polarization upswing – the value of the LRP is indeed always greater than that of the URP.
3.2 Temporal decomposition
To get a more compact picture of the timing and nature of the polarization trend described above, we
can break the 21-year period into 3 sub-periods – 1991-98, 1998-2005, and 2005-12 – and highlight
the changes that took place within each of them. The top three panels of Figure 4 show the relative
distribution for each sub-period. In contrast to the 21-year decile series, which takes 1991/92 as the
reference distribution for all waves, each panel here takes the beginning year of the sub-period for the
reference distribution and the end year for the comparison. The displays clearly point to the median
up-shift in household consumption expenditure as the dominant trend for each sub-period. These are
the images of a “rising tide that lifts all boats”, i.e. the effect of a location shift that was the most
influential contributor to the overall pattern during all sub-periods. The differences due to the median
shift – representing what the relative density would have looked like if there had been no change in
distributional shape – are plotted in the middle row panels of Figure 4. As expected, the strongest
effects were in the bottom deciles, confirming that more low-consuming households joined the ranks
of those whose consumption levels put them in the top half of the reference distributions. However,
once changes in location are netted out, there is also an indication of growing polarization that is not
evident in the overall relative distributions. The differences explained by the shape changes are
presented in the bottom row panels of Figure 4, where the median-adjusted relative distributions take
an approximate U-shape. Strong growth occurred in the fraction of households at the top and bottom
tails of the period-specific consumption distributions, while sizable declines occurred in the middle.
This polarizing trend seems nearly symmetric for the years 2005 to 2012, while throughout the 1990s
and up to the mid-2000s the growth in the lower tail of the distribution was noticeably stronger than in
the upper tail.
17
Since the value of the three indices always equals 0 in the baseline year (Morris et al., 1994, p. 209),
polarization summaries for 1991/92 were not included in the graphical display.
16
The relative polarization indices, shown in Table 3, capture these changes well. The MRP index is
always positive and statistically significant (p-value = 0.00). Decomposing the MRP into the
contributions to distributional change made by the segments of the distribution above and below the
median, it appears that “downgrading” dominated “upgrading” in the polarization upswing over the
course of the first two sub-periods: the value of the lower relative polarization index (LRP) is indeed
greater than that of the upper relative polarization index (URP) – 0.26 vs. 0.17 and 0.27 vs. 0.11,
respectively – which is consistent with the visual impression from the shape shifts above. The values
of the indices in the 2005-12 period denote instead a nearly perfectly symmetric polarization in each
tail.
In sum, while often less noticeable in any single period when compared to the large swings in median
household consumption expenditure, the growth in polarization was a major contributor to the overall
changes in the Ghanaian consumption distribution since the early 1990s. Behind these shape shifts,
however, was probably a set of key drivers. The following section relies therefore on GLSS data to
examine how the changes above have been associated with consumption growth and, thereby,
identifies the main drivers behind the polarization upsurge.
3.3 The drivers of growing polarization in Ghanaian household consumption
The presentation of polarization results over the three sub-periods requires a considerable amount of
space. For the sake of brevity, we chose to present only part of the results and made an effort to
present the main findings in an abridged format. For example, we decided not to comment on the
econometric results of the unconditional quantile regression, and to place the decomposition tables in
the appendix, and regarding the polarization decomposition results, to focus our attention only on the
top percentiles results (top two and bottom two).
Overall this is not a big limitation since, as shown in panels (a) and (b) of Figure 5, the inter-quantile
analysis has detected a significant variation in the percentiles’ cut-offs (between deciles inequality,
measured by interquartile ratios) primarily among these deciles and a very limited one among the rest
of the distribution. Furthermore, the other component of polarization, the so-called “identification”
(measured by deciles’ coefficient of variation, CV) tended to be more accentuated in these deciles
rather in the central ones. Looking at sub-periods, it clearly emerges that, in 1991-98 and 2005-12, the
between component was compensated by a high identification component, thus neutralizing the
modification of inequality; differently, in the sub-period 2005-12 it appears both a sustained growth of
between component and an important reduction of identification component (growth of CV) especially
for what concern the 10-th and 90-th deciles.
17
Table 4 compares the counterfactual cut-off points (labelled with “c”) – the cut-offs of the reference
distribution augmented with the location effect between the two sub-periods – with the cut-offs of the
comparison distribution. In all three sub-periods, the cut-offs of the bottom percentiles of the
comparison distribution are significantly lower than those of the reference, indicating, as we discussed
in the previous subsection, lower relative polarization, whereas for the top percentiles the opposite
holds: the comparison distribution cut-offs are higher than the reference ones, indicating upper relative
polarization.
The Oaxaca-Blinder (OB) methodology (Oaxaca, 1973; Blinder, 1973), decomposes the difference
between cut-offs into that part that is due to group differences in the magnitudes of the determinants
(endowments effect) of consumption, on the one hand, and group differences in the effects of these
determinants (coefficients effect), on the other. Coefficient and endowment variations are aggregated
by groups of variables: primary, secondary and tertiary education are grouped into the education
attainment group; private, public and self-employment of household head are grouped into
employment category; the infrastructure index captures the access to basic services;18 urbanization and
residence in regions other than Upper East (urban and regional dummies having as baseline Upper
East); and household structure (household size and all other household characteristics). The interaction
term and the constant are also included so that the sum of all decomposition elements adds up to the
total differences between cut-offs. Below any decomposition graph, we present a table summarizing
the main variable trends for upper and lower polarization.
Recalling previous section results regarding 1991-98 sub-period, the polarization increased as testified
by the shifts leftward and rightward of the lower and upper cut-offs respectively. The polarization
decomposition shows how the combined effect of household composition, infrastructure index and the
constant increased the lower polarization while location effects and education tended to reduce the
effect. On the upper deciles nearly the same variables played a pro-polarization role (Figure 6).
Between 1991 and 1998 growth concentrated in urban areas and in few regions on the Coast or in the
immediate inland (Ashanti region) among households with relatively higher levels of education and
with access to a number of basic infrastructures. This group of households occupying the top two
deciles of the distribution distances itself from the rest of other groups determining an increase in the
upper polarization.
The 1998-2005 sub-period sees polarization growing. In this decade, Ghana experienced a boom in
cocoa production and exports. The cocoa boom generated, in the western and coastal areas, a high
demand for the workforce, but also for capital and infrastructure, and the skills of the workforce and
the rise in revenues even at lower levels translated into a higher demand for capital, infrastructure and
18
The infrastructure index is obtained by combining four variables through principal component analysis: access
to protected water, access to electricity, access to protected sanitation, and access to safe sources of cooking.
18
skills (Molini and Paci, 2015). These resources were relatively scarce, and the price effect and
variation in returns was, thus, substantial. In these areas, the cocoa boom had a positive impact on
poverty, but did not benefit everybody equally.
The drivers of polarization, both upper and lower, were very similar (Figure 7). Household
characteristics, educational attainment and basic infrastructures all tended to have pro-inequality
outcome and increased the tails size of the 2005 distribution, indeed more polarization. It is worth
noting the particular importance of changes in the household structure in explaining the upper
polarization. Top deciles were particularly benefitting from the demographic dividend stemming from
smaller families and lower dependency ratios. The only set of variables that countered this increase
were the location/urban ones. The cocoa boom and the relatively good performance of many rural
areas in the Central and Coastal part of the country such as Ashanti, Volta, Eastern, Western and
Central region (Molini and Paci, 2015) explains this positive distributional impact.
Finally, between 2005 and 2012, the upper polarization substantially stagnates. Compared to the
previous sub-period, the distributional changes of this sub-period are driven by a positive variation in
endowments and stagnation in the returns on covariates (see appendix). This seems to suggest that the
high returns obtained in the previous period encouraged households to invest in assets and human
capital. This clearly reduced their scarcity, but, at the same time, returns massively declined. The
greater availability of people in the nonfarm sector who had low levels of educational attainment
(typically primary school) determined a clear decline in their relative returns (Molini and Paci, 2015).
Differently from the previous period, urban and regional variables drive polarization (Figure 8).
Households residing in Greater Accra and the urban areas of Ashanti region performed well and
increased their relative economic advantage over the rest of the country. Interestingly, the drivers of
upper polarization are very similar to those playing a role in the 1991-98 sub-period. In addition to the
urban and regional variables, the infrastructure index, the employment variables and education had a
strong impact on polarization. As for 1998-2005, the variations in household composition benefit the
top percentiles and contribute significantly to the increase of polarization.
4 Concluding remarks
The topic of the increasing gap between the richer and poorer is gaining momentum thanks, in
particular, to the large attention that has been obtained in recent research on world inequalities (see e.g.
Stiglitz, 2012, 2014, Piketty, 2014, and Atkinson, 2015, inter alia). The overall idea that emerges is
that in the last 20/30 years both developing and developed countries went through dramatic
distributional changes that increased disparities.
19
The main contribution of our paper is proposing a tool that displays these changes but also identifies
and quantifies the underlying drivers. We focus our attention on polarization defined as the
combination of divergence from global and convergence on mean local incomes. The method
developed blends two different frameworks of distributional analysis: relative distribution (Handcock
and Morris, 1998 1999) and unconditional quantile regression (Firpo et al., 2009). The advantage over
other methodologies is that it allows to single out the different drivers of polarization at different
points of the consumption distribution.
Ghana, almost unique among SSA countries, offers the opportunity to analyze the last two decades’
distributional changes, since four comparable household surveys are available. The country also
presents interesting specificities. Since 1991, poverty had declined very fast, inequality has not
increased dramatically and yet the country has seen a rapid surge in polarization. The results of our
analysis suggest that the distributional changes hollowed out the middle of the Ghanaian household
consumption distribution and increased the concentration of households around the highest and lowest
deciles.
Results on drivers of polarization indicate that although there is some heterogeneity across the various
sub-periods in particular in terms of magnitude, household characteristics, educational attainment and
access to basic infrastructures all tended to increase over time the size of the upper and lower tails of
the consumption distribution and as a consequence the degree of polarization. Urban rural and regional
variables started to have a strong impact on polarization only in the last decade; households residing in
Greater Accra and the urban areas of Ashanti region performed well and increased their relative
economic advantage over the rest of the country.
From a policy perspective, the pro-polarization impact of variables that tend to change slowly over
time is of particular concern. It is very unlikely that policy makers can find a quick fix to the problem
and any intervention will produce results only in the long run. This implies that the country needs to
start now to develop a strategy that, if not able to immediately reverse polarization, at least can
mitigate its impact. The creation of a modern social protection system, the expansion in the access to
basic services, the continued effort to expand primary and secondary education are all interventions
that can pay off and help the country to maintain its social cohesion.
20
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23
Tables
Table 1: Summary measures of Ghanaian household total consumption expenditure, 1991/92 to 2012/13.
1991/92 1998/99 2005/06 2012/13
Observations 4,523 5,998 8,687 16,772
Mean 459.91 568.45 736.80 883.48
Median 352.66 438.04 559.44 655.60
Consumption shares
Bottom 5 1.11 1.00 0.79 0.82
Bottom 10 2.71 2.42 2.08 2.13
Bottom 20 6.82 6.21 5.65 5.63
Top 20 44.78 44.47 46.59 46.94
Top 10 29.16 28.17 30.75 30.43
Top 5 18.52 17.41 19.95 19.17
Inequality measures
Gini 0.38 0.38 0.41* 0.41
Theil 0.25 0.25 0.30* 0.29
* Denotes statistically significant change from the previous period at the 5 % level (p-value < 0.05).
Source: authors’ own calculation using GLSS data sets.
24
Table 2: Inter-quantile consumption ratios by GLSS Wave, 1991/92 to 2012/13.
Wave p10/p50 p25/p50 p75/p25 p75/p50 p90/p10 p90/p50
1991/92 0.46 0.66 2.37 1.56 5.23 2.42
1998/99 0.41 0.63 2.60 1.64 6.00 2.48
2005/06 0.39 0.61 2.63 1.62 6.36 2.46
2012/13 0.39 0.62 2.68 1.66 6.73 2.65
Source: authors’ own calculation using GLSS data sets.
25
Table 3: Relative polarization indices by sub-periods, 1991/92 to 2012/13.
Index p-value
1998/99 to 1991/92
MRP 0.22 0.00
LRP 0.26 0.00
URP 0.17 0.00
2005/06 to 1998/99
MRP 0.19 0.00
LRP 0.27 0.00
URP 0.11 0.00
2012/13 to 2005/06
MRP 0.14 0.00
LRP 0.14 0.00
URP 0.14 0.00
Source: authors’ own calculation using GLSS data sets.
26
Table 4: Counterfactual Reference cut-offs vs. comparison cut-offs: by deciles and sub-periods.
Decile 1991c 1998 1998c 2005 2005c 2012
1-st 248.74 181.03 302.43 216.83 312.99 258.36
2-nd 296.69 246.72 368.12 304.00 400.17 357.47
8-th 704.60 803.14 924.54 1,011.40 1,107.56 1,242.97
9-th 940.64 1,084.86 1,206.26 1,377.14 1,473.31 1,738.20
Source: authors’ own calculation using GLSS data sets.
27
Figures
(a) (b)
(c) (d)
Figure 1: Changes in the Ghanaian household consumption distribution between 1991/92 and 2012/13. (a)
Kernel distributions. Expenditures in the upper tiers of the densities have been truncated for better presentation
of the graph, where the vertical lines denote the medians of the two survey waves. (b) Relative consumption
distribution. (c) The effect of the median difference in consumption growth. (d) The median-adjusted relative
consumption distribution (the effect of changes in distributional shape).
28
Figure 2: Median-adjusted relative consumption distribution series for Ghana, 1991/1992 to 2012/2013.
29
Figure 3: Relative polarization indices by wave. The number above each bar indicates the p-value for the null
hypothesis that the index equals 0.
30
(a) 1998/99 to 1991/92 (b) 2005/06 to 1991/92 (c) 2012/13 to 2005/06
(d) 1998/99 to 1991/92 (e) 2005/06 to 1991/92 (f) 2012/13 to 2005/06
(g) 1998/99 to 1991/92 (h) 2005/06 to 1991/92 (i) 2012/13 to 2005/06
Figure 4: Location and shape decomposition of the relative consumption distribution for Ghana by sub-periods.
The top row shows the overall change by sub-period, the middle shows the effect of the median shift (the shape-
adjusted relative distribution), and the bottom shows the effect of the shape changes (the median-adjusted
relative distribution).
31
16 0.6
14 0.5
12
100/10 0.4 10th
10
8 90/20 0.3 20th
6 100/20 0.2 90th
4 90/10 0.1 100th
2
0.0
0
1991 1998 2005 2012
1991 1998 2005 2012 -0.1
(a) (b)
Figure 5: (a) Inter-decile ratio by year, using couterfactual distributions; (b) coefficient of variation, by year and
decile.
32
400
300
Interaction
200
Constant
100
Urbreg
0 Infrastructure index
10th 20th 80th 90th
Employment Category
-100
Education attainment
-200
Household composition
-300
-400
Total Lower polarization Upper polarization
Urbreg --- +++
Infrastructure + +
Education -- ++
Employment - -
Household + ----
Constant ++++ ++
Figure 6: Blinder-Oaxaca type decompositions, 1991-98.
33
400
300
constant
200
Interaction
100
Urbreg
0 Infrastructure index
10th 20th 80th 90th
Employment Category
-100
Education attainment
-200
Household composition
-300
-400
Total Lower polarization Upper polarization
Urbreg --- ---
Infrastructure + +
Education ++ ++
Employment + -
Household ++ ++++
Constant + +
Figure 7: Blinder-Oaxaca type decompositions, 1998-2005.
34
500
400
300 Interaction
Constant
200
Urbreg
100
Infrastructure index
0
10 20 80 90 Employment Category
-100
Education attainment
-200 Household composition
-300
-400
Total Lower polarization Upper polarization
Urbreg ++++ ++
Infrastructure - +++
Education - ++
Employment - ++
Household -- ++++
Constant ++ ---
Figure 8: Blinder-Oaxaca type decompositions, 2005-12.
35
Appendix
Table A.1: Location effect RIF-regression results.
1991 1998 2005 2012
Number of obs 4,523 5,998 8,687 16,772
F( 25, 4497) 61.57 144.54 166.58 273.29
Prob > F 0.00 0.00 0.00 0.00
R-squared 0.27 0.29 0.32 0.32
Adj R-squared 0.26 0.29 0.32 0.31
Root MSE 241.33 322.80 413.75 500.16
Coef. P>z Coef. P>z Coef. P>z Coef. P>z
Household size -15.08 0.00 -21.83 0.00 -29.53 0.00 -33.16 0.00
Demographic Features
Share of Children -32.44 0.27 -79.78 0.02 -20.62 0.60 -32.67 0.41
Share of Care-Dependent Persons 9.47 0.76 -0.58 0.99 83.26 0.03 -16.22 0.70
Household Head Age -0.40 0.36 -0.57 0.24 -0.95 0.07 -1.18 0.03
Sex of Household Head -16.34 0.16 7.83 0.54 56.80 0.00 60.86 0.00
Share of Adult Males 139.49 0.00 122.12 0.00 110.30 0.00 213.38 0.00
Share of Adult Females 207.10 0.00 265.36 0.00 327.24 0.00 418.16 0.00
Socioeconomi Education
Up to Primary School 9.42 0.55 21.63 0.18 41.40 0.03 41.15 0.02
Features
Up to Secondary School 32.80 0.01 55.43 0.00 84.64 0.00 111.18 0.00
Higher than Secondary School 100.94 0.00 129.84 0.00 232.60 0.00 302.11 0.00
Private Workers 41.62 0.04 48.09 0.02 93.72 0.00 57.21 0.01
c Features
Public Workers 56.47 0.00 53.63 0.01 100.33 0.00 58.92 0.04
Non Agricoltural Self Employeed 57.42 0.00 44.95 0.00 117.33 0.00 132.62 0.00
Agricoltural Self Employeed 36.81 0.04 -7.08 0.65 6.11 0.75 10.02 0.61
Assets 40.53 0.00 78.13 0.00 78.43 0.00 117.91 0.00
Western -34.48 0.21 339.59 0.00 267.86 0.00 211.91 0.00
Central 65.31 0.02 152.87 0.00 261.49 0.00 146.10 0.00
Greater Accra -3.50 0.90 349.13 0.00 131.97 0.00 323.70 0.00
Volta 17.54 0.54 206.22 0.00 165.38 0.00 160.94 0.00
Other
Eastern 9.02 0.76 229.43 0.00 299.66 0.00 169.09 0.00
Ashanti 42.01 0.12 253.64 0.00 223.86 0.00 186.47 0.00
Brong Ahafo -29.55 0.28 248.58 0.00 173.82 0.00 187.04 0.00
Northern 7.51 0.79 146.83 0.00 162.93 0.00 59.73 0.00
Upper East -106.72 0.00 28.75 0.18 -5.44 0.82 89.90 0.00
Urban Area Residence 102.49 0.00 27.64 0.05 143.21 0.00 92.73 0.00
Constant 338.30 0.00 219.03 0.00 266.81 0.00 295.86 0.00
36
Table A.2: Location effect OB results.
1998-91 2005-1998 2012-05
Median predicted (1) 438.18 559.53 655.62
Median predicted (2) 352.69 438.18 559.53
Coef. P>z Coef. P>z Coef. P>z
Difference
85.49 0.00 121.36 0.00 96.09 0.00
Endowments
Household size 7.26 0.00 -1.53 0.17 3.92 0.00
Demographic Features
Share of Children -0.17 0.43 0.85 0.05 0.14 0.63
Share of Care-Dependent Persons 0.10 0.77 0.00 0.99 0.16 0.39
Household Head Age -0.30 0.41 0.12 0.56 -0.30 0.25
Sex of Household Head 0.51 0.21 1.25 0.54 -0.97 0.03
Share of Adult Males 2.10 0.00 2.36 0.00 0.25 0.46
Share of Adult Females 4.43 0.00 1.69 0.04 3.10 0.00
Socioeconomi Education
Up to Primary School 0.64 0.55 -0.67 0.20 2.32 0.04
Features
Up to Secondary School 0.39 0.29 1.18 0.04 0.92 0.13
Higher than Secondary School 2.30 0.00 0.78 0.13 3.05 0.00
Private Workers 0.57 0.11 2.18 0.03 2.89 0.00
c Features
Public Workers -2.22 0.00 -0.83 0.05 -0.71 0.08
Non Agricoltural Self Employeed 1.83 0.00 -1.52 0.01 6.74 0.00
Agricoltural Self Employeed 2.36 0.04 0.31 0.65 -0.07 0.77
Assets (see note) 11.05 0.00 12.20 0.00 23.96 0.00
Western -0.37 0.36 -3.06 0.08 -2.33 0.03
Central 0.79 0.16 -4.27 0.00 0.26 0.80
Greater Accra -0.11 0.91 -3.38 0.10 3.21 0.00
Volta 1.06 0.54 -14.02 0.00 1.99 0.00
Other
Eastern -0.34 0.76 6.69 0.00 -8.74 0.00
Ashanti 0.85 0.20 -2.60 0.11 6.22 0.00
Brong Ahafo 1.29 0.29 4.72 0.00 1.09 0.12
Northern -0.23 0.80 8.28 0.00 -3.27 0.00
Upper East 3.53 0.00 0.76 0.19 0.04 0.84
Urban Area Residence 2.69 0.01 0.65 0.12 17.60 0.00
Total 40.02 0.00 12.16 0.01 61.45 0.00
37
Table A.2: Continued.
Coefficients
Household size -42.27 0.07 -44.53 0.05 -21.26 0.39
Demographic Features
Share of Children -9.85 0.28 12.62 0.25 -2.44 0.83
Share of Care-Dependent Persons -0.40 0.82 4.20 0.10 -4.66 0.08
Household Head Age -7.63 0.80 -17.61 0.60 -10.72 0.76
Sex of Household Head 15.43 0.16 29.74 0.03 3.12 0.88
Share of Adult Males -3.67 0.67 -2.67 0.80 25.30 0.04
Share of Adult Females 14.82 0.20 17.06 0.23 25.64 0.10
Socioeconomi Education
Up to Primary School 1.39 0.59 3.60 0.44 -0.04 0.99
Features
Up to Secondary School 9.06 0.24 12.04 0.20 11.50 0.28
Higher than Secondary School 0.80 0.47 5.18 0.01 3.92 0.09
Private Workers 0.40 0.83 3.45 0.15 -4.41 0.25
c Features
Public Workers -0.37 0.91 4.30 0.17 -3.17 0.29
Non Agricoltural Self Employeed -2.33 0.53 15.84 0.00 2.83 0.56
Agricoltural Self Employeed -4.36 0.06 2.16 0.59 0.47 0.89
Assets (see note) -15.35 0.00 -0.04 0.98 0.81 0.12
Western 37.21 0.00 -7.90 0.04 -5.65 0.12
Central 9.07 0.02 12.56 0.00 -10.12 0.00
Greater Accra 41.40 0.00 -32.32 0.00 26.68 0.00
Volta 15.50 0.00 -5.83 0.24 -0.33 0.90
Other
Eastern 31.40 0.00 7.38 0.04 -17.52 0.00
Ashanti 33.44 0.00 -5.31 0.34 -6.28 0.25
Brong Ahafo 32.38 0.00 -5.43 0.03 1.21 0.70
Northern 13.18 0.00 1.03 0.62 -12.43 0.00
Upper East 7.34 0.00 -0.72 0.30 4.54 0.00
Urban Area Residence -24.47 0.00 40.81 0.00 -19.02 0.03
Constant -119.27 0.02 47.78 0.38 29.04 0.62
Total 32.83 0.00 97.41 0.00 17.01 0.04
Interaction
Total 12.64 0.01 11.79 0.02 17.63 0.00
38
Table A.3: Shape effect RIF-regression results.
39
Table A.4: Shape effect OB results
40