International Convergence in Well-Being Indicators

International Convergence in Well-Being Indicators

Vanesa Jorda • Jose Marıa Sarabia

Accepted: 19 February 2014� Springer Science+Business Media Dordrecht 2014

Abstract We re-examine the concept of beta-convergence in living standards across

countries during the period 1980–2012. In this study, well-being is assessed using the

Human Development Index (HDI) which considers income aspects as well as social

indicators, thus reflecting the multidimensional nature of this process. The existence of

sigma convergence is evidenced in this study and hence beta convergence, as a necessary

condition, is also pointed out. However, the linearity of this process has been questioned.

Therefore, we apply a semiparametric specification of this process to the HDI and each of

its intermediate indices. These models allows for nonlinearities in the estimation of the

convergence speed. Our results reveal that absolute convergence in human well-being is

satisfactorily represented by the conventional linear specification. However the income and

education indices show nonlinear patterns. We also include structural variables to capture

differences in the steady-state (conditional convergence). Under this model, convergence

speed of all indicators is higher and the convergence process seems to be linear only for the

health index.

Keywords Well-being � Beta-convergence � Sigma-convergence � Semiparametric

regression � Human Development Index

1 Introduction

The study of convergence has risen to prominence among academics since the presentation

of the classical works of Solow (1956, 1957) and Swan (1956). Several papers have tried to

V. Jorda � J. M. Sarabia (&)Department of Economics, University of Cantabria, Av. los Castros SN, 39003 Santander, Spaine-mail: [email protected]

V. Jordae-mail: [email protected]

123

Soc Indic ResDOI 10.1007/s11205-014-0588-8

determine if there is a long-run tendency towards equalisation, a question that lies in the

heart of the convergence debate.

According to the Solow–Swan neoclassical growth model, if countries only differ in

their level of capital, poor countries tend to grow faster than developed nations due to the

assumption of diminishing returns of capital. This theory is the so called absolute beta-

convergence, which assumes that all economies in the world converge to the same steady

state. Much of the existing literature on convergence hypothesis (see e.g. de la Fuente

1997; Islam 2003; Sala-i-Martin 1996) supports the existence of divergence among world

economies. Therefore, it is concluded that the currently rich nations are expected to be

even wealthier in the future, hence leaving developing countries behind. Note however that

economies usually differ in technology, population growth and human capital. Therefore,

differences in the structural parameters would result in different steady states. This concept

is called conditional beta-convergence in the classical literature, which has been evidenced

by numerous studies (see e.g. Barro and Sala-i-Martin 1990, 1992; Sala-i-Martin 1996),

thus pointing out that when taking the structural characteristics into account, poor countries

converge to their own steady state faster than the advanced economies.1

The concept of sigma-convergence has also been widely studied given its close rela-

tionship with the concept of beta-convergence. It is assumed that there is sigma convergence

if the dispersion of per capita income decreases over time, whereas beta-convergence is

evidenced when poor countries grow faster than wealthy nations. To achieve sigma-con-

vergence, the growth rate of developing countries needs to be higher than those observed for

rich countries. In this sense, it is said the beta-convergence is a necessary condition for

sigma-convergence. It could be also possible that the poor countries grow so fast that they

leave the initially rich nations behind until the point to increase the dispersion of the variable

under study. As a consequence, we would observe sigma-divergence along with beta-

convergence patterns, thus revealing that beta-convergence is not a sufficient condition for

sigma-convergence (Sala-i-Martin 1996). Previous studies conclude the existence of sigma

divergence across world economies for the second half of the last century (Decancq et al.

2009; Milanovic 2005; Pritchett 1997; World Bank 2006), revealing that inequality across

countries tends to increase over time.

Conventionally, the specification of absolute beta-convergence focuses on testing a

common linear trend between growth rate of per capita income and the initial level of

output. This regression is augmented with structural variables for testing conditional beta-

convergence. A negative sign of the coefficient on initial per capita income is interpreted as

a support for convergence across countries. However, many authors have questioned the

assumption of linearity (Durlauf et al. 2001; Fiaschi and Lavezzi 2007; Huang 2005),

concluding the existence of multiple growth regimes associated with different levels of

development.

Traditionally, income variables have played a main role in the measurement of quality of

life. However, there is a discontent with the hegemony of per capita GDP as an indicator of

well-being since there are other relevant dimensions which are imperfectly captured by

purely economic variables. There is by now nearly consensus that development is a mul-

tidimensional concept, which, in addition to income, also should consider social indicators.

This line of argumentation has gained prominence among academics over the last decades,

thus resulting in many attempts to synthesize different aspects of well-being, in a composite

1 This specification of convergence has been criticized for the so-called Galton’s fallacy problem and theinability to reflect the existence of multiple poles that might lead to multiple stable steady state equilibrium(See, e.g. Quah 1993, 1996).

V. Jorda, J. M. Sarabia

123

index which offers a more comprehensive perspective of such a process than per capita

income alone.

In 1979, David Morris from the Overseas Development Council designed the Physical

Quality Life Index (Morris 1979) constructed by a weighted average of infant mortality,

literacy rate and life expectancy at age one. Becker et al. (2005) developed an indicator

which combined income and longevity for measuring well-being inequality. More recently,

there have been many attempts to construct a composite index centred on the notion that

development entails more than just economic aspects (see e.g. Alkire and Foster 2010;

Bilbao-Ubillos 2013; Edgier and Tatlidil 2006; Fakuda-Parr et al. 2009; Grimm et al. 2008;

Morrison and Murtin 2012).

This line of thinking has induced academics to test the convergence hypothesis in other

dimensions such as health and education. A theoretical framework of convergence in life

expectancy is developed in Mayer-Foulkes (2003), concluding the existence of conver-

gence clubs, whereas global convergence is found to be weak. This result is confirmed in

Sab and Smith (2001), who also point out the existence of strong absolute and conditional

convergence in education. Mazumdar (2003) tests the existence of convergence in five

dimensions of well-being, including calorie intake, life expectancy, infant mortality, per

capita GDP and adult literacy rate, concluding divergence in all variables except for

income among the advanced economies.

A natural extension of these works is to test the hypothesis of convergence in an

aggregate index of quality of life, considering jointly social factors and economic indi-

cators. Note that this approach makes it possible to draw general conclusions regarding the

evolution of cross-country patterns of quality of life. There have been many attempts to test

whether a catching-up process in human well-being has taken place in the last decades (see

e.g. Konya and Guisan 2008; Mayer-Foulkes 2010; Noorbakhsh 2006), concluding that

living standards have converged slowly over the last 30 years. Nevertheless, some authors

questioned the linearity of this process. Mayer-Foulkes (2010), using series of superposed

transitions and quantile regression, concluded that complex relations of divergence and

convergence exist in the components of the HDI. In fact, nonlinear parametric models,

such as the quadratic specification, have been also proposed as a possible approximation of

this phenomenon (Mazumdar 2002, 2003). Note, however, that the parametric approach

requires making a priori assumptions about the evolution of the convergence speed, thus

the model might present misspecification bias. We opt for a semiparametric specification

which lets the data describe by themselves the convergence/divergence process, thus

offering a complete and continuous panorama of the distributional patterns of well-being.

Through the more flexible methodology of partially linear models (PLM), this work

aims to provide a reappraisal of the convergence process in terms of quality of life, using

the Human Development Index (HDI) as an indicator of this phenomenon, for the period

1980–2012. Note that this is the first study that uses the HDI with the changes introduced in

2010, which are argued to reveal a complete new situation in several aspects of human

development (Klugman et al. 2011). This fact will allow us to compare our estimates with

previous results, in order to investigate if the recent modifications applied to this indicator

have affected the conclusions regarding the process of convergence in well-being.

According to the results obtained by Martınez (2012), the new version of the HDI presents

higher levels of inequality than its predecessor and similar inequality trends are observed

for both definitions except for leftist indices such as the Kolm measure. The previous result

would be related to the concept of sigma-convergence, but nothing is said about the

consequences of the modification of the HDI on beta-convergence patterns.

International Convergence

123

Having reached this point, it should be emphasised that considering the hypothesis of

convergence in a composite indicator presents some shortcomings that should be taken into

account (Mazumdar 2003). In fact, these are the same criticisms that are attached to any

multidimensional indicator of well-being, namely the arbitrarily of the weights and the lack of

meaningfulness of the resulting indicator. Therefore, we also adopt a dimension-by-dimen-

sion approach to obtain more detailed conclusions regarding convergence in living standards.

The rest of the paper is organised as follows. Section 2 describes the characteristics of

the HDI as an indicator of well-being. Section 3 relates the convergence hypothesis to the

non-income variables. A detailed explanation of the data used and the methodology

applied is presented in Sect. 4. Section 5 explores the hypothesis of sigma-convergence

and presents the evolution of global well-being inequality over the last three decades. Beta-

convergence is tested in Sect. 6 using non-parametric techniques. Finally, Sect. 7 includes

some conclusions and discusses possible policy implications.

2 Measuring Development: Beyond Income

Since it was launched in 1990, the HDI attracts a large amount of attention from the media,

academics and policymakers. The HDI was designed following the Sen’s capability

approach (Sen 1988, 1989, 1999) which considers development as a process of enhancing

individuals’ choices. This new paradigm of development was presented in the first Human

Development Report which stated:

Human development is a process of enlarging people’s choices. In principle, these

choices can be infinite and change over time. But at all levels of development, the

three essential ones are for people to lead a long and healthy life, to acquire

knowledge and to have access to resources needed for a decent standard of living.

(UNDP 1990, p. 10).

To materialise this eminently subjective concept into a single number, three dimensions

were proposed, which were considered essential to measure the complex reality of human

development. Therefore, the HDI is made up of three intermediate indices, using country-

level data on income, health and education, which reflect achievements in each dimension

respect to the subsistence value and the historical maximum value observed.

Since 2010, the HDI of the country i in year t is constructed using a geometric mean of

the three intermediate indices as follows:

HDIit ¼ Ihealthit � IEducation

it � IIncomeit

� �1=3:

The health index (Ihealthit ) is measured by life expectancy at birth (LE), which is con-

sidered an indicator of longevity. This indicator is standardised according to the following

expression:

Ihealthit ¼ LEit � LEmin

LEmax � LEmin

;

where the minimum is the so-called level of subsistence fixed at 20 years, and the upper

bound is the maximum value observed between 1980 and 2011,2 that is 85 which

2 The upper bounds of all sub-indicators have been redefined in order to avoid the practice of cappingvariables at the top of the distribution. Consequently, the new bounds has lead an increase in the variabilityof the intermediate indices and hence in the HDI.


123

corresponds to Japan in 2011. It should be noted that life expectancy only measures years

of life, but no insights about the quality of these years are made. Notwithstanding its

limitations, life expectancy is the sole variable that has not been changed since the HDI

was launched, due to the scarcity of data on health indicators for long temporal periods

(Klugman et al. 2011).

The education index (IEducationit ) comprises two variables, expected years of schooling

(EYS) and mean years of schooling (MYS). These indicators replaced gross enrolment

ratios and literacy rates in 2010, since they were considered to have higher discriminatory

power than their predecessors (Klugman et al. 2011). The education component is, then,

computed with the geometric mean, given by:

IEducationit ¼ MYSit �MYSmin

MYSmax �MYSmin

� �� EYSit � EYSmin

EYSmax � EYSmin

� �� 1=2

:

MYS and EYS have lower bounds of zero given that societies would survive without

education. The maximum corresponds to Czech Republic in 2005 with 13.1 expected years

of schooling, whereas MYS variable has a fixed maximum of 18 years, which is achieved

in several developed countries. These variables have been introduced in 2010 substituting

adult literacy rate and the combined gross enrolment ratio. These indicators were con-

sidered uninformative since no discrimination across countries is provided, especially in

the developed nations whose literacy rates are superior to 95 %. Then, the introduction of

these variables has increased the variability of the education index and hence the dispersion

of the HDI, being consistent with the results obtained by Martınez (2012).

Income is represented by Gross National Income (GNI) per capita measured in PPP

2005 US dollars, to make incomes comparable across countries and over time. It should be

noted that income is regarded as the mean to acquire goods and services, concept which is

different to how much is produced in a particular economy. Thus, per capita GDP has been

replaced by per capita GNI in 2010, given that such a variable represents the economic

reality of countries more accurately, in terms of the capability approach, due to the con-

sideration of international aid and foreign remittances. The intermediate index of income

(IIncomeit ) is computed as follows:

IIncomeit ¼ ln GNIitð Þ � ln GNIminð Þ

ln GNImaxð Þ � ln GNIminð Þ ;

where the maximum value is 107,721 (per capita GNI for Qatar in 2011), whereas the

minimum value is fixed at the level of subsistence which is 100 US$. Logarithmic

transformation was introduced in 2001 with the objective to reflect that income is con-

ceived as a mean to purchase goods and services, thus the concavity of the logarithmic

function characterises impact of diminishing returns of income on well-being.

In spite of its popularity, the HDI has been highly criticised [see Kovacevic (2010) for a

review] on the grounds of construction (Kelley 1991), selection of variables (Srinivasan

1994; Alkire 2002), arbitrary weighting scheme (McGillivray and White 1993; Noo-

rbakhsh 1998), and redundancy with its components (Cahill 2005; McGillivray 1991;

Ravallion 1997).

Some authors argue that the HDI omits important aspects of well-being that should be

incorporated in the index. Among them, we emphasise democracy (Domınguez et al.

2011), social cohesion (Bilbao-Ubillos 2011), personal safety (Bilbao-Ubillos 2013) and

environment (Briassoulis 2001; Neumayer 2001; Sagar and Najam 1998). Distributional

aspects have also been proposed for its consideration in the construction of the index


123

(Alkire and Foster 2010; Hicks 1997; Seth 2010) since inequality in the different aspects of

well-being has a deep impact on the progress of a particular country. Conversely, some

authors have suggested removing the income component from the HDI (Anand and Sen

2000).

Concerning the construction of the HDI, two main criticisms need to be addressed. An

equal weight scheme seems to be arbitrary hence not based on social choice nor normative

arguments. Notwithstanding this subjective format, statistical methods (principal compo-

nents analysis) have been applied to determine the weights supported by the data, con-

cluding that the simple average is empirically justified (Ogwang and Abdou 2003). On the

other hand, the traditional simple average is considered problematic since the components

of the index are regarded as perfect substitutes, thus implying that the marginal rate of

substitution is constant. This axiom can lead to incongruent results, in the sense that the

maximisation of the HDI in a society may lead to corner solutions, promoting one

dimension and disregarding others (Klugman et al. 2011). The formula introduced in 2010

marks a conceptual change concerning the relationship between the three dimensions given

that some degree of complementarity is also considered.

Several studies point out that there is a high rank correlation of the HDI and its under-

lying components, reflecting a problem of redundancy in the information provided by the

composite index. This result implies that ‘‘assessing inter-country development levels on

any one of these variables yields similar results to those that the index itself yields’’

(McGillivray 1991, pp. 1462). Therefore, the HDI would not provide us with comple-

mentary information than the traditional indicator of development, i.e. per capita GDP,

provides. Note that the previous statement would lead to the loss of the relevance of this

study. Since there is apparently no difference between income and human development, the

conclusions reached by previous studies on the convergence hypothesis would apply.

However, it has been concluded that the distributions of income, health, education and the

HDI are remarkably different (McGillivray and Markova 2010; McGillivray and Pillarisetti

2004; Pillarisetti 1997), also pointing out different evolutions over time. This result

emphasises the point that the consideration of a growth-centred approach or a more com-

prehensive definition of human development strongly affects our assessment of progress

hence our conclusions about convergence might be also altered.

The criticisms exposed before suggest that the HDI is not an ideal indicator of well-

being. However, the assessment of quality of life is complex, abstract and difficult to

synthesise. Independently of its limitations, the HDI seems to be the most adequate alter-

native to perform cross-country analyses of well-being since it has homogeneous available

data for a wider period of time and for more countries than other related indices.

3 Convergence in Well-Being

The concept of convergence in well-being is essentially studied using inequality measures

of the composite indicators (see e.g. Decancq et al. 2009; McGillivray and Markova 2010;

McGillivray and Pillarisetti 2004). There is a common result which indicates that well-

being levels are converging over the time but at slow rate:

For most of the past 40 years human capabilities have been gradually converging.

From a low base, developing countries as a group have been catching up with rich

countries in such areas as life expectancy, child mortality, and literacy. A worrying

aspect of human development today is that overall state of converging is slowing—


123

and for a large group of countries divergence is becoming the order of the day.

(UNDP 2005, pp. 25).

Since the concept of beta convergence was derived from the Solow model, its theo-

retical framework is especially suitable for income. The principal mechanism behind the

convergence hypothesis is the assumption of diminishing returns of capital. Accordingly,

the vast majority of the papers that test convergence in living standards focuses on income

variables whereas social aspects of development are assumed to play little role. However,

there have been few attempts to test the convergence hypothesis in a more comprehensive

indicator per capita GDP (Mazumdar 2002; Noorbakhsh 2006; Konya and Guisan 2008;

Konya 2011; Mayer-Foulkes 2010), thus extrapolating the concept of diminishing results to

the non-income dimensions of the HDI.

According to Noorbakhsh (2006), the concept of diminishing returns can be ‘‘equally

applicable’’ to the educational variables and health indicators of the HDI but with some

peculiarities. Diminishing returns were derived from the mobility of the capital in the pure

economic model. In contrast, for non-income aspects, they are linked to the assumption

that investment returns in education and health diminish with the level of investment. In a

country with low levels of primary education, relatively less investment is necessary to

increase the mean years of schooling than in a developed nation, since tertiary education is

the most expensive type of education. Therefore, investment returns to increase the mean

years of schooling and the expected years of schooling will be higher in countries with low

levels of education. Moreover, given the nature of the educational indicators considered in

the HDI, which are basically quantitative variables that do not account for the quality of

education, they have upper limits that make plausible the existence of a convergence

process across countries.

Similarly, for the health dimension, it is supported that investment returns in health are

higher in countries with low life expectancy, since less amount of investment is needed to

improve health levels in countries with high rates of mortality. In fact, according to the last

report of millennium development goals (MDG), a large proportion of the deaths of

children under five could be saved through low-cost prevention and treatment measures

(United Nations 2012). Moreover this type of medical research is easily exported to other

countries, whereas advanced medical technology is more difficult to be implemented in

developing countries mainly due to lack of suitable personnel which also increases the

amount of investment (Mazumdar 2000).

4 Data and Methodology

We use the most recent available data from International Human Development Indicators

(UNDP 2012) on the HDI and its three components for 132 countries in the period

1980–2012 with different data frequency. For the period 1980–2005 we have 5-year

intervals and from 2005 to 2012 the data has annual frequency. Originally, our data

comprised only 105 countries, covering less than the 75 % of global population. We had

non-available data for 26 countries for one or more years before 1995. In order to offer

comparable results across periods and to not restricting the sample considerably, missing

values have been estimated. The estimation is based on two complementary methodologies

which jointly provide feasible and consistent results according to the sample: piecewise

cubic Hermite interpolating polynomial (PCHI) and the average rate of change, which is


123

used when PCHI offers unfeasible estimates or out of range results. After this procedure,

our dataset covers over 90 % of the world population during the whole period, including

132 countries whose indicators of income, health and education are available for thirteen

points of time.

To shed light on the well-being convergence process over the last three decades two

methodologies have been applied in this study. As a starting point, we calculate four

inequality measures which reveal the evolution of dispersion of national levels of well-

being over the study period. Therefore, in the first step we analyse the so called sigma-

convergence, not only using the classical indicator (i.e. the variance) but also considering

the Gini, Theil’s Entropy and the Atkinson indices. All measures indicate the amount of

dispersion of well-being distribution across countries, however different weighting

schemes are applied for each part of the distribution3 depending on the measure consid-

ered. The Theil index is a special case of the generalised entropy measures when the

sensitivity parameter is set to 1 (Cowell 2011). Such a parameter determines the weight

assigned to the upper tail, which in the case of the Theil index the same weight to all

countries, independently of its level of development. The Atkinson index is interpreted as

the proportion of total income that would be required to achieve an equal level of welfare.

This inequality measure also includes a parameter which is called inequality aversion

parameter, since it adjusts the index to be more sensitive to the lower tail as the parameter

increases (Atkinson 1970). The expressions of the Gini, the Theil and the Atkinson indices

are, respectively, the following:

GðtÞ ¼ 1

2n2lðY ðtÞÞXn

i¼1

Xn

j¼1

YðtÞi � Y

ðtÞj

��; ð1Þ

T ðtÞ ¼ 1

n

Xn

i¼1

YðtÞi

lðY ðtÞÞ logYðtÞi

lðYðtÞÞ

!

; ð2Þ

and

AðtÞe ¼ 1� 1

n

Xn

i¼1

YðtÞi

lðY ðtÞÞ

!1�e2

4

3

5

11�e

; ð3Þ

where xðtÞi denotes HDI or one of its intermediate indices for the country i at time t, l is the

arithmetic mean of the indicator under study, n is the number of countries, and finally, e is

the inequality aversion parameter of the Atkinson index.

Consequently, our analysis provides a broad picture of the evolution of inequality over

the last 30 years which allows us to determine whether distances between countries have

been reduced in terms of well-being. As stated before, a necessary condition for sigma

convergence is that beta-convergence also takes place, thus implying that developing

countries increase their levels of HDI relatively faster than the advanced nations.

The hypothesis of absolute beta-convergence is evidenced when there is a negative

relationship between the value of a variable at the beginning of the period and its growth

rate, which conventionally is tested using the following model:

3 The inclusion of other measures to determine the dispersion of the distribution, responds to the problemspresented by the variance, which is ‘‘unsatisfactory in that were we simply to double everyone’s incomes(and thereby double mean income and leave the shape of the distribution essentially unchanged)’’ (Cowell2011, 27).


123

_yi ¼ aþ byi0 þ eit; ð4Þ

where yi0 is the logarithm of the HDI or any intermediate index which are denoted as Yit,

_yi ¼ ð1=TÞ ln ðYit=Yi0Þ is the growth rate of Yit and, finally, eit is the unexplained residual.

Positive values of the b parameter imply divergence, whereas negative values reveal

evidence of a catching-up process between developing and developed countries. Equation

(4) assumes that all countries of the sample converge to the same steady state. However,

nations have different structural features which lead to a multiple steady state equilibrium

(Sala-i-Martin 1996), which is related to the so-called conditional convergence hypothesis,

traditionally specified as an augmented regression of Eq. (4):

_yi ¼ aþ byi0 þ x0idþ eit; ð5Þ

where the matrix xi contains structural variables which are constant in the steady state. In

this study, a battery of conditioning variables is included along with regional dummy

variables for Latin America and the Caribbean and Sub-Saharan Africa.4 In particular, we

have included trade and foreign direct investment (FDI) both indicators as a percentage of

the GDP. According to Mayer-Foulkes (2010), these two variables are seen as indicators

of globalisation and technological change. As a measure of institutions, we have con-

sidered the Economic Freedom of the World (EFW) Index, which seems to represent

adequately the quality of national institutions with respect to economic performance

(Berggren 2003; De Haan et al. 2006).5 As domestic determinants of the expansion of

well-being, we have included public expenditures on health and on education as a per-

centage of the GDP. Domestic investment is expected to have a positive effect on

economic and human well-being which is measured with the variable gross capital for-

mation in relative terms to the GDP. Finally, following Noorbakhsh (2006), the number

of mobile lines (per 100 people) has been also considered to measure the level of

infrastructure. All variables have been drawn from World Development Indicators

Database (World Bank 2013) except the EFW index, which has been provided by

Gwartney et al. (2013).

It should be, however, noted that a number of studies have challenged the assumption of

linearity of income convergence. Using nonlinear specifications, it has been concluded that

the catching-up process is not adequately represented as a linear trend, thus classifying

countries into different groups which exhibit different convergence patterns (Azomahou et al.

2011; Durlauf 2001; Durlauf et al. 2001; Liu and Stengos 1999). Along this line, a gener-

alisation of the process of convergence in well-being is considered in Mazumdar (2002), who

includes quadratic and logarithmic terms to represent nonlinearities in the convergence

speed. Having reached this point, it is important to recall that parametric specifications

require making a priori assumptions about the functional form of the relationship under study.

On the other hand, Mayer-Foulkes (2010) performed quantile regressions to study non-

linearities in convergence in a number of indicators of quality of live. Note that this meth-

odology provides a restricted view of the process of convergence, given that it assumes

common distributional patterns within each quantile, not allowing for variability in the

4 We include only dummies for these two regions since they show remarkable different convergencepatterns than the rest of the world being characterized as the most unequal regions (see e.g. Chotikapanichet al. 2009).5 A number of studies demonstrated that there is a positive relationship between the EFW index and humanwell-being, see e.g. Goldsmith (1997), Gwartney and Lawson (2004), Gwartney et al (2010), Norton (1998).


123

direction and the intensity of this process.6 Therefore, we consider a more flexible model

which allows the data to describe by themselves the path of the convergence or divergence

process. Following the notation in Eqs. (4) and (5), we specify a semiparametric partially

linear regression (Wand 2005; Ruppert et al. 2003) for testing absolute and conditional beta-

convergence, given respectively by the following expressions:

_yi ¼ f ðyi0Þ þ git; ð6Þ

_yi ¼ f ðyi0Þ þ x0idþ git; ð7Þ

where yi0 denotes Yi0 expressed in natural logarithms, git is the error term identically and

independently distributed with mean 0 and variance r2g, and f(y0) is an unknown unidi-

mensional smooth function f ðY0Þ ¼ E _yjY0½ � which is represented by a linear combination

of polynomial functions, regression parameters and radial basis functions which need to be

chosen to be numerically stable. Therefore, the smooth function in Eq. (6) is expressed as a

radial basis function of degree three:

f ðY0Þ ¼ b0 þ b1yi0 þXK

k¼1

uk yi;0 � kk

�� 3;

where bi for i = 0, 1 are the so-called fixed effects. The unknown vector of parameters

u ¼ u1; u2; . . .; uKð Þ0 follows a Normal distribution with mean 0 and variance r2uR0, being K

the number of bases, and kk are fixed knots calculated as qk ¼ k þ 1=K þ 2ð Þ;8 k ¼ 1; . . .;K. Note that if uk = 0 for all k, then the semiparametric model used in this

study turns out to be the linear specification of beta-convergence, since the last term

disappears.

The estimation is based on the so-called penalized spline smoothing, which minimizes

the following expression:

minb;u

y�Hhk k2þk3h0Dh; ð8Þ

where h = [b, u] is the parameter vector, H is a matrix that contains the polynomial basis

functions and the k radial basis functions, k3h0Dh is called roughness penalty since it

penalises fits that are too rough (Ruppert et al. 2003). The first parameter k[ 0, estimated

by restricted maximum likelihood, determines the amount of smoothing, thus controlling

the trade-off between roughness and goodness of fit. Finally, D is a block identity penalty

matrix whose first two elements are zero given that the fixed effects (intercept and linear

term) are not penalised.

The solution of the optimisation problem in Eq. (8) is the estimator matrix:

h ¼ ðH0Hþ k3DÞ�1Hy where y ¼ Sky;

being Sk ¼ H0ðH0Hþ k3DÞ�1H the so called hat matrix.

We also compute a test to analyse the adequacy of the semiparametric models with

respect to the linear specifications in Eq. (4) and (5) respectively (Crainiceanu and Ruppert

6 Note that Mayer-Foulkes (2010) focuses on the dimensions of the HDI rather than the composite indexand then no global conclusions can be achieved in terms of well-being since these different componentsshow different convergence patterns. In fact, as stated in this paper ‘‘Each human development componentfollows its own set of transitions’’, Mayer-Foulkes (2010, pp. 28).


123

2004). Assuming that u is identically and independently distributed with mean 0 and

variance G ¼ r2uI, the null hypothesis u1 = u2 = … = uk is equivalent to r2

u ¼ 0:

H0 : r2u ¼ 0;

Ha : r2u [ 0:

Note that if the null hypothesis is no rejected, convergence in human development is

correctly represented by the conventional linear model. Otherwise, a more flexible semi-

parametric approximation is required.

We use the restricted log-likelihood ratio test (RLRT) expressed as follows:

RLRT ¼ supHa[H0

RELðh; r2e ; kÞ � sup

H0

RELðh; r2e ; kÞ;

where REL is the restricted maximum likelihood for the non-restricted model (PLM) and

the restricted specification (parametric model) respectively.

The computation of RLRT7 is relatively simple, however the derivation of its distri-

bution under the null has to be bootstrapped since the observations of the dependent

variable are not independent under the alternative. Therefore, the asymptotic probabilistic

theory does not hold.

5 Well-Being Inequality and Sigma Convergence

As a preliminary analysis, in this section we investigate sigma-convergence in the HDI and

each of its intermediate indices. This concept of convergence assumes that dispersion from

the cross-country mean tends to decrease over time (Barro 1991; Barro and Sala-i-Martin

1992). In the empirical literature, the variance of the logarithm of the variable under con-

sideration is the most commonly used measure of dispersion. We also have considered three

additional measures of inequality: the Gini [Eq. (1)], the Theil [Eq. (2)] and the Atkinson [Eq.

(3)] indices, whose evolution over the last three decades is presented in Fig. 1. To facilitate

the comparison of results, inequality has been normalised to be 100 in 1980.

Convergence trends are observed for each component although the intensity of this

process varies across dimensions. The dispersion of the educational indicator decreases

continuously during the entire period, thus experiencing the greatest fall of inequality,

ranged from 35 to 60 % depending on the inequality measure analysed. Such convergence

has its origin in the increase of the mean years of schooling, which has been doubled in the

last 40 years, thanks to the efforts in education performed in developing countries, espe-

cially in Asia (Morrison and Murtin 2012; World Bank 2006). Even when notable

achievements have been accomplished in developing countries in terms of education, it

should be noted that, this trend can be interpreted as an artificial convergence pattern due to

the upper limit that characterizes the educational variables included in the HDI (Neumayer

2003; McGillivray and Pillarisetti 2004).

In line with previous investigations, the fall of health inequality has been remarkably

lower, ranging from 15 to 30 % over the last three decades (McGillivray and Markova

2010). A process of divergence is observed in this dimension during the nineties decade as

7 For a detailed explanation of the procedure for testing the null hypothesis of non-significance of thevariance component in linear mixed models with one variance component see Crainiceanu and Ruppert(2004). In that paper the finite and asymptotic distribution of the RLRT is derived to provide consistentresults.


123

a consequence of the rapid extension of AIDS in Sub-Saharan Africa (Becker et al. 2005;

Neumayer 2003), effect partially offset by the decrease in infant mortality (Deaton 2004).

This trend is also driven by the health crisis in most Eastern European countries derived

from social upheaval, alcohol and tobacco consumption (McMichael et al. 2004; Moser

et al. 2005). Conversely, much more egalitarian distribution is observed for the second half

of the study period, mainly due to the enhancement of life expectancy in East and South

Asia and in the North of Africa (Goesling and Firebaugh 2004).

Income inequality has received by far more attention than the other dimensions. It is

well-known that cross-country inequality has increased over the second half of the last

century (see e.g. Milanovic 2005; Pritchett 1997; World Bank 2001). In spite of the success

of Asia which rapidly converged to the incomes of developed countries in the last 30 years,

the failure of Africa in the eradication of poverty has led to the increase of income

disparities. Notwithstanding this trend, income inequality across countries has been

reduced by about 10 % over the last 30 years, thanks to the strong convergence process

that took place in the last decade. According to Decancq (2011), the fall of unweighted

income inequality over the last decade would reveal that the financial crisis has affected to

wealthiest countries more than proportionally.

In line with previous studies, our results reveal the presence of a global convergence

process in living standards during the study period (Decancq et al. 2009; Martınez 2012;

McGillivray and Markova 2010).8 Taking the study period as a whole, it is observed that

40

50

60

70

80

90

100

110

120

1980 1985 1990 1995 2000 2005 201040

50

60

70

80

90

100

110

1980 1985 1990 1995 2000 2005 2010

60

70

80

90

100

110

120

130

1980 1985 1990 1995 2000 2005 2010

70

80

90

100

110

120

1980 1985 1990 1995 2000 2005 2010

Education indexHDI

Health index Income index

Variance Gini Theil Atkinson

Fig. 1 Inequality in the HDI and its components (1980 = 100)

8 Note that in Decancq et al. (2009) the sensibility of the results to different trade-offs between dimensionsis investigated in relation to the evolution of multidimensional inequality in well-being convergence.Actually, multidimensional inequality is beyond de scope of this paper. In any case, it should be stated that if


123

inequality in human development decreased about 20 % according to the Gini index and

about 40 % for the Theil and the Atkinson indices over the last three decades. However,

two phases are clearly distinguishable. A stagnation term is observed from 1980 to 2000

which is derived from the slight increase of disparities in income and health during that

period, which was offset by the strong fall in disparities in education. Conversely, the last

decade of the study period is characterized by a sharp process of convergence in quality of

life, given that all components of the HDI reduced its inequality levels considerably.

Note however that the patterns described previously do not apply for the variance

because, as an absolute indicator, it does not take into consideration the mean of the

distribution. It should be stated that, for variables that show sharply positive or negative

trends over time, the coefficient of variation would provide more realistic reflection of the

convergence or divergence process (Kenny 2005). In fact, a number of papers consider

relative measures of well-being inequality to study sigma-convergence (Marchante et al.

2006; Ferrara and Nistico 2013; Konya and Guisan 2008; Noorbakhsh 2006), which is also

convenient in this case since the mean of the HDI has increased considerably over the last

decades, from 0.433 in 1980 to 0.621 in 2012 (UNDP 2013). We have calculated per-

centage change of coefficient of variation which is called the rate of sigma-convergence

(O’Leary 2001). Therefore, negative values indicate convergence in the sense of sigma,

whereas positive trends point out divergence patterns. Table 1 shows the growth rate of the

coefficient of variation for the countries included in the sample, calculated for each

dimension of the HDI and the index itself in the whole period and within each decade.

As for the other inequality measures, once the mean is taken into account, countries

converge in the sense of sigma, which implies that the dispersion tends to decrease over the

time. However, different patterns are presented across dimensions. Whereas a continuous

decrease is observed for the dispersion of the education indicator, inequality in income and

health is characterised by some fluctuations. Focusing on the evolution of inequality in the

composite index, it is concluded that, as in the case of education, a smooth linear process of

convergence has taken place over the last three decades. These dynamics point out that

uneven behaviours of different aspects of development are hidden when studying con-

vergence in well-being composite indices. Notwithstanding this fact, it is also important to

remark that convergence in the considered indicators of quality of life has taken place

mainly during the last decade in all cases.

At this point, it could be relevant to decompose the Theil index in two components:

inequality within-regions and inequality between-region in order to study the patterns of

sigma convergence more in detail (for the regions and the countries included see

‘‘Appendix’’). Among the inequality measures used in this study, the Theil index is the

only additively decomposable indicator.9 This measure can be expressed in terms of the

inequality within regions (which is a weighted average of the inequality within each

region) and inequality between regions (which represents the level of inequality that would

be if there were no differences within regions) using the following expressions (Cowell

2011):

Footnote 8 continuedwe apply unidimensional inequality measures to the HDI, we are assuming some degree of substitution andcomplementarity among dimensions since the composite indicator follows a Cobb–Douglas type function.9 The Atkinson index is decomposable but not additively, and then an interaction term is involved. The Giniindex can be additively decomposable if there is no overlapping between groups, but since we are con-sidering a regional classification, this is not the case.


123

TB ¼Xnr

i¼1

sr

lr

lT

� �log

lr

lT

� �;

TW ¼Xk

j¼1

sr

lr

lT

� �Tr;

where, sr is the proportion of countries included in the region (given that we are measuring

unweighted inequality), lr and lT are, respectively, the mean of the region and the global

mean of the variable under study. Finally, Tr is the Theil index of the region.

The evolutions of both components over the study period are presented in Fig. 2. In

terms of education we see that both types of inequality decreased steadily during the last

30 years, thus resulting in a decrease of educational disparities. Disparities in health

presented an ascending pattern from 1980 to 2000 which was mainly driven by differences

between regions which increased by 25 % in the first 20 years. In contrast, inequality

within-regions presented a decreasing trend except for the second half of the eighties.

Income inequality within-region reported an ascending pattern from 1980 to 2000, while

differences between regions remained rather constant. These dynamics resulted in the

increase of overall income disparities observed previously. Consequently, the last decade,

is characterised by the fall of both components. Similar trends are reported for disparities

in human development. Inequality within regions decreased continuously over the last

three decades, while an increase of the differences across regions is observed during the

nineties, followed by a decade of convergence. Since we observed a decreasing pattern of

global inequality in well-being over the whole period (see Fig. 1), it can be concluded that

the decrease in the within- region component offset the increase in disparities between

regions during the nineties.

It should be emphasized that even when different patterns are observed across

dimensions there are also common features that should be highlighted. First, differences

between regions dominate global inequality, representing more than the 75 % of overall

disparities in all cases. This result would indicate that the regions considered are homo-

geneous groups, and hence the bulk of inequality comes from disparities between these

territories. Secondly, the within-region component decreased substantially in for all indi-

cators considered, thus indicating that there was a process of convergence within the

borders of the regions, which became even more homogeneous groups at the end of the

study period. Third, a decrease in the differences between regions is observed except for

income whose inequality levels between these territories remained constant. The fall of this

component would imply that additionally to the convergence observed within regions, the

differences across them were also reduced. To sum up, a process of convergence in the

HDI is observed within regions and at the same time, differences across regions have been

also reduced, thus resulting in a global convergence process in quality of life.

Table 1 Rate of sigma-convergence

1980–1990 1990–2000 2000–2011 1980–2011

HDI -0.0723 -0.0270 -0.1197 -0.2054

Education Index -0.1379 -0.1030 -0.1483 -0.3414

Health Index -0.0451 0.0325 -0.1227 -0.1351

Income Index -0.0040 0.0201 -0.0853 -0.0706


123

6 Beta-Convergence in Well-Being

Table 2 presents the estimation results of absolute convergence according to Eq. (6) using

as dependent variable the growth rate of the HDI and its intermediate indices. For com-

parative purposes, we also present the conventional linear estimation of beta-convergence

[Eq. (4)]. According the parametric estimates, all dimensions show statistically significant

negative coefficients of yi0, thus suggesting a negative relationship between the growth rate

of the considered indicators and their value in 1980. In line with previous studies, the

magnitude of the coefficient is relatively low, but significantly higher than the convergence

rates reported by previous studies with similar time spans (Noorbakhsh 2006; Konya and

Guisan 2008, Mayer-Foulkes 2010). Since this is the first study that uses the new version of

the HDI, the previous result would suggest that the changes applied to the HDI in 2010 not

only changed the method to assess well-being levels. These modifications also reported

different convergence patterns that are more intense under the new normative framework.

It should be also noted that the speed of convergence differs across dimensions. In line

with Mayer-Foulkes (2010) and Neumayer (2003), the educational dimension has seen the

most intense process of convergence, with rates close to 4 %. In contrast, income shows

the lowest reduction in the gap between developed and developing countries. Conse-

quently, even when little advance have been achieved in income levels, significant

improvements in non-income dimensions and human well-being have been accomplished.

This result points out the relevance of considering non-income dimensions in the study

of convergence hypothesis, since their distributional patterns differ substantially from

income.

0.0000

0.0050

0.0100

0.0150

0.0200

0.0250

0.0300

0.0350

0.0400

1980 1985 1990 1995 2000 2005 20100.0000

0.0100

0.0200

0.0300

0.0400

0.0500

0.0600

0.0700

0.0800

1980 1985 1990 1995 2000 2005 2010

0.0000

0.0050

0.0100

0.0150

0.0200

0.0250

1980 1985 1990 1995 2000 2005 20100.0000

0.0050

0.0100

0.0150

0.0200

0.0250

0.0300

0.0350

0.0400

1980 1985 1990 1995 2000 2005 2010

Education indexHDI

Health index Income index

Within Between

Fig. 2 Decomposition of the Theil index in within- and between-region inequality components


123

According to the results of the RLRT test, the null hypothesis of linearity is rejected for

the income and education indices (see the last row in Table 2), given that the bootstrapped

p values are practically equal to zero. As a result, we might conclude that the convergence

process has been nonlinear for both indicators. This conclusion would imply that, using

parametric models, the convergence speed is overestimated or underestimated for some

levels of income and education. These dynamics are observed from Fig. 3 which shows the

estimated function f(yi0) with the corresponding 95 confidence interval for absolute con-

vergence. The parametric counterpart (yi0) and its confidence bands are also plotted.

Education shows a decreasing and convex pattern which approaches to a linear trend for

medium and high educational standards. In contrast, the speed of convergence is under-

estimated for less educated countries given that the parametric estimates lies below the

confidence bands of the PLM model. The fact that the speed of convergence is higher in

countries with low educational standards could be related with the promotion of primary

education by Millennium Development Goals. One of the main concerns of this global

partnership is to achieve universal primary education. Then, the efforts undertaken by the

international community would have focused on this type of education, thus accelerating

convergence in this part of the educational distribution.

The income dimension presents a high convergence speed for low developed countries,

whereas a stagnation phase is observed for medium developed economies, which seems to

turn into convergence for the most advanced nations. This conclusion is also found in other

studies of global income convergence (see e.g. Dobson et al. 2003), also being consistent

with the well-known fact of the twin-peaked income distribution (Quah 1993, 1996).

Previous studies point out that the income distribution has evolved from a unimodal

distribution (in the decades of sixties and seventies) to a bimodal shape (in 2000). This

change reflects two different dynamics of medium developed countries. On the one hand a

number of medium developed nations converged to the poorest economies, while the rest

converged to the wealthiest countries (Sala-i-Martin 2000). These two opposite trends

Table 2 Parametric and Semiparametric estimations. Absolute convergence

Variable HDI Education index Health index Income index

Parametric specification

yi0a -0.0196***

(0.0017)-0.0402**(0.0037)

-0.0147***(0.0023)

-0.0126***(0.0038)

Constant 0.0191***(0.0011)

0.0334***(0.0020)

0.0154***(0.0018)

0.0119***(0.0025)

Adj. R2 0.5325 0.6860 0.2732 0.1313

Semiparametric specification

f(yi0) Fig. 2a Fig. 2c Fig. 2e Fig. 2g

Smoothing parameter 564 2.084 2.497 1.014

RLRT testb 0.0000(1.0000)

19.7747(0.0000)

0.2115(0.1926)

19.0775(0.0000)

Number of observations: 132 countries

The dependent variables are de average growth rate of the variables in columns

*** Significance at 1 % level; ** significance at 5 % level; * significance at 10 % level. Standard errors inparenthesisa Bootstrapped standard errors (based on 999 simulations)b Bootstrapped p value in parenthesis (based on 10,000 simulations)


123

seem to balance in the aggregate, thus explaining the flat shape of the convergence speed

for medium income countries. Therefore, an important part of the linear estimated trend

lies outside the nonparametric confidence interval, thus indicating that the conventional

specification to test beta-convergence would mask nonlinearities which are actually cap-

tured by the semiparametric model. On the other hand, semiparametric estimates reveal

that the speed of convergence of the health index and the HDI follow linear trends which

are analogous to the conventional convergence models since the parametric estimations lie

inside the confidence bands in both cases.

We have augmented Eqs. (4) and (6) with a set of conditioning variables which capture

the existence of specific characteristics in each country thus allowing for the existence of

different steady states. Estimated results for conditional convergence [Eqs. (5) and (7)] are

presented in Table 3. From the parametric models, it is observed that the estimates of the

speed of convergence increase substantially when structural variables are included. This

raise is particularly evident in the case of health and education, whose speed of convergence

under the conditional framework is almost double the rate of absolute convergence.10 It

-1.5 -1.0 -0.5

-0.0

050.

000

0.00

50.

010

0.01

50.

020

0.02

50.

025

HDI

HDI in 1980 (in log)

aver

age

grow

th r

ate

-3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0

0.00

0.02

0.04

0.06

0.08

Education Index

Education index in 1980 (in log)

aver

age

grow

th r

ate

-1.2 -1.0 -0.8 -0.6 -0.4 -0.2

-0.0

050.

000

0.00

50.

010

0.01

50.

020

Health Index

Health index in 1980 (in log)

aver

age

grow

th r

ate

-2.0 -1.5 -1.0 -0.5 0.0

0.00

0.01

0.02

0.03

0.04

Income Index

Income index in 1980 (in log)

aver

age

grow

th r

ate

(d)

(b)

(c)

(a)

Fig. 3 Nonparametric estimation of f(yi0) according to Eq. (6). In each case yi0 represents the naturallogarithm of the HDI or its intermediate indices. The solid blue line corresponds to the estimate of f(yi0) andthe dashed curves delimit the 95 % confidence bands. The solid green line represents the classical linearestimation of beta-convergence. (Color figure online)

10 The acceleration of the convergence process under the conditional framework is a common result in theliterature (see Noorbakhsh (2006) and Konya and Guisan (2008) for examples related to convergence inhuman well-being). Note that the absolute model implies that all countries converge to the same steady state,


123

should be also noted that, as in the case of the unconditional model, we observe higher rates

of convergence than those of reported by previous studies (Noorbakhsh 2006; Mayer-

Foulkes 2010), thus reinforcing the hypothesis that the changes applied to the HDI in 2010

have modified the concept of development and the evaluation of levels of quality of life, and

consequently, its distribution has been also affected.

We have included all the conditioning variables only in the model for the HDI, which

tests the hypothesis of convergence in well-being. Instead, for each individual component,

we only include the auxiliary variables that have influence on the particular dimension. In

the case of the educational component we have considered as conditioning variables the

public expenditure on education and the dummies for Sub-Saharan Africa and Latin

America. Both dummies are significantly negative, thus indicating that educational levels

in the steady state are lower in the countries that belong to these regions. Public expen-

diture in education would also show a positive effect on convergence in education, a result

that emphasizes the role of the public policies in the expansion of educational levels.

For the health dimension, the dummy variables have been also included along with the

public expenditure in health as a percentage of the GDP. The signs of the dummies are the

same as in the case of education, also suggesting that the health levels in the steady state

are lower in Latin American and African countries. The role of the public services in health

is significant and the sign of the coefficient indicates that it has a positive influence in the

enhancement of life expectancy.

For the Income component, we have included several conditioning variables since this

dimension is related with trade, FDI, domestic investment, and the EFW index. According

to the value of the coefficient on the EFW index and consistently with previous investi-

gations (Gwartney and Lawson 2004; De Haan et al. 2006), the quality of institutions

seems to have a positive and highly significant effect on the increase of income. Similarly,

there is a positive relationship between gross capital formation and economic growth. In

the case of trade as a percentage of the GDP we have obtained a negative coefficient value

which is in line with the results presented by Slaughter (2001). Note that the effect of trade

openness on economic growth is far from consensual. Some authors argue that there is a

positive relationship (see e.g. Frankel and Romer 1999), while others found a negative link

in a number of country case studies (Greenaway et al. 1998; Wacziarg and Welch 2008).

Staying in the middle, some studies have pointed out a conditional relationship which

depends on structural and geographical variables of the countries involved in international

trade agreements (Lundberg and Squire 2003; Rodrik et al. 2004). On the other hand, FDI

seems to have no effect on income growth, a result that was also obtained in previous

studies (Mayer-Foulkes (2010)). The rationale behind the null effect of external invest-

ments seems to be the low stock of capital in some developing countries. According to

Borensztein et al. (1998), FDI potentiates economic growth only when the host economy

has enough absorptive capability of advanced technologies. As observed for the other

dimensions, dummy variables are found to be negative since income levels at the steady

state are lower in these to regions.

For the model of the HDI that would test the hypothesis of convergence in human

well-being, we observe a significant relationship between the composite index and all

indicators that were significant for individual dimensions. Then, FDI is the sole variable

Footnote 10 continuedwhile the consideration of structural variables allows for the existence of multiple steady state equilibrium.Then, only countries that share these characteristics are converging to the same steady state, and this processshould be faster than universal convergence.


123

Ta

ble

3P

aram

etri

can

dS

emip

aram

etri

ces

tim

atio

ns.

Condit

ional

conver

gen

ce

Var

iab

leE

du

cati

on

index

Hea

lth

index

Inco

me

index

HD

I

OL

Sa

PL

MO

LS

aP

LM

OL

Sa

PL

MO

LS

aP

LM

f(y i

0)

-0

.049

05

**

*(0

.00

65

1)

Fig

.2d

-0

.032

65

**

*(0

.00

33

8)

Fig

.2f

-0

.021

27

**

*(0

.0

03

58

)F

ig.

2h

-0

.037

14

**

*(0

.00

25

5)

Fig

.2b

Inte

rcep

t0

.03

53

6**

*(0

.00

22

9)

-0

.00

02

7(0

.00

17

8)

0.0

27

74

**

*(0

.00

21

6)

-0

.00

17

8*

(0.0

009

7)

-0

.004

60

(0.0

067

6)

-0

.02

01

1**

*(0

.00

67

6)

-0

.017

40

**

*(0

.00

27

0)

-0

.011

59

**

(0.0

05

09

)

Tra

de

-0

.000

03

*(0

.00

00

1)

-0

.00

00

3*

(0.0

00

01

)-

0.0

00

02

**

(0.0

000

1)

-0

.000

02

**

(0.0

00

01

)

FD

I0

.00

01

0(0

.00

02

3)

0.0

00

30

(0.0

00

17

)-

0.0

00

05

(0.0

004

1)

-0

.000

02

(0.0

00

09

)

EF

W0

.00

26

6**

*(0

.00

08

0)

0.0

02

82

**

*(0

.00

05

4)

0.0

01

17

**

*(0

.00

04

5)

0.0

01

30

**

*(0

.00

03

2)

Gro

ssca

pit

alfo

rmat

ion

0.0

00

31

*(0

.00

01

8)

0.0

00

07

**

*(0

.00

00

9)

0.0

00

12

*(0

.00

00

7)

0.0

00

12

**

(0.0

00

05

)

Mo

bil

e0

.000

07

**

*(0

.00

00

3)

0.0

00

07

**

*(0

.00

00

2)

Pu

bli

cex

pen

dit

ure

ined

uca

tio

n0

.00

09

0*

(0.0

00

53

)0

.000

47

**

(0.0

002

1)

0.0

00

41

**

(0.0

001

7)

0.0

00

31

*(0

.00

01

7)

Pu

bli

cex

pen

dit

ure

inh

ealt

h0

.00

04

5**

*(0

.00

01

5)

0.0

00

27

*(0

.00

01

5)

0.0

00

10

**

(0.0

002

0)

0.0

00

14

*(0

.00

01

7)

Lat

inA

mer

ica

-0

.003

37

**

*(0

.00

09

5)

-0

.00

14

8**

*(0

.00

08

2)

-0

.000

13

(0.0

003

8)

-0

.00

02

0(0

.00

06

4)

-0

.002

11

**

(0.0

010

2)

-0

.00

22

5**

(0.0

01

14

)-

0.0

01

41

**

*(0

.00

05

1)

-0

.001

68

**

*(0

.00

05

8)

Su

b-S

ahar

anA

fric

a-

0.0

05

24

**

(0.0

02

37

)-

0.0

03

98

**

*(0

.00

09

4)

-0

.008

23

**

*(0

.00

12

2)

-0

.00

82

6**

*(0

.00

07

6)

-0

.004

50

**

*(0

.00

16

3)

-0

.00

40

5**

*(0

.00

12

7)

-0

.004

50

**

*(0

.00

09

9)

-0

.004

48

**

*(0

.00

07

0)

Sm

ooth

ing

par

amet

er3

.458

41

8.4

0.6

51

90

.614

4

Ad

j.R

20

.73

10

0.6

07

10

.40

17

0.7

69

1


123

Ta

ble

3co

nti

nued

Var

iab

leE

du

cati

on

index

Hea

lth

index

Inco

me

index

HD

I

OL

Sa

PL

MO

LS

aP

LM

OL

Sa

PL

MO

LS

aP

LM

RL

RT

test

b3

.34

78

(0.0

152

)0

.00

00

(1.0

00

0)

14

.77

8(0

.00

01

)1

2.6

66

3(0

.00

00

)

Nu

mb

ero

fo

bse

rvat

ion

s:1

32

cou

ntr

ies

Th

ed

epen

den

tv

aria

ble

sar

eth

eg

row

thra

teo

fv

aria

ble

sin

colu

mns

**

*S

ign

ifica

nce

at1

%le

vel

;*

*si

gn

ifica

nce

at5

%le

vel

;*

sign

ifica

nce

at1

0%

lev

el.

Sta

nd

ard

erro

rsin

par

enth

esis

aB

oo

tstr

app

edst

andar

der

rors

(bas

edo

n9

99

sim

ula

tio

ns)

bB

oo

tstr

app

edp

val

ue

inpar

enth

esis

(bas

edon

10,0

00

sim

ula

tions)


123

that seems to be no related with the enhancement of quality of life. Similar to the

results presented by Noorbakhsh (2006), the coefficient associated with trade is nega-

tive. The inverse relationship between openness and well-being seems to be driven by

its negative correlation with the income component. Negative coefficients are also

found for the dummy variables. Since we found empirical evidence that Latin America

and Sub-Saharan Africa would present lower levels of income, health and education at

the steady state, the levels of human development would be also lower. Congruently

with the regression results of individual dimensions, the rest of variables are signifi-

cantly positive.

According to the results of the RLRT test, the health component is the sole dimension

that is adequately represented by the conventional linear specification (see the last row in

Table 3), given that the bootstrapped p value is almost cero. In contrast, the null hypothesis

of linearity is rejected in the cases of income, education and human well-being. Using

parametric models for testing the convergence hypothesis in these indicators will over-

estimate or underestimate the convergence rate for some parts of the distribution.

To analyse how conditional convergence speed evolves with the level of development,

nonparametric estimates for each dimension are presented in Fig. 4. Conditional conver-

gence patterns tend to be similar to the absolute ones (see Fig. 3) but with higher slopes. In

-1.5 -1.0 -0.5

-0.0

100.

000

0.00

50.

010

0.01

50.

020

0.02

5

HDI

HDI in 1980 (in log)

aver

age

grow

th r

ate

-3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0

0.00

0.02

0.04

0.06

0.08

Education Index

Education Index in 1980 (in log)

aver

age

grow

th r

ate

-1.2 -1.0 -0.8 -0.6 -0.4 -0.2

-0.0

050.

000

0.00

50.

010

0.01

50.

020

0.02

5

Health Index

Health Index in 1980 (in log)

aver

age

grow

th r

ate

-1.5 -1.0 -0.5 0.0

-0.0

2-0

.01

0.00

0.01

0.02

0.03

0.04

Income Index

Income Index in 1980 (in log)

aver

age

grow

th r

ate

(a)

(d)

(b)

(c)

Fig. 4 Nonparametric estimation of f(yi0) according to Eq. (7). In each case yi0 represents the naturallogarithm of the HDI or its intermediate indices. The solid blue line corresponds to the estimate of f(yi0) andthe dashed curves delimit the 95 % confidence bands. The solid green line represents the classical linearestimation of beta-convergence. (Color figure online)


123

the case of education, we observe higher convergence speed for primary education, but the

change in the slope is less pronounced under the conditional model. Income dimension

presents high rates of convergence for poor countries as well as for wealthy nations, while

medium developing countries show a flat shape that again indicates the absence of con-

vergence, thus reinforcing the hypothesis of a convergence clubs pattern. As concluded by

the RLRT test, the convergence process of the HDI seems to be nonlinear in this case.

Medium developed countries slowed down the convergence speed, which can be derived

from the stagnation phase that we observed for the income dimension. Note that the

parametric estimation of convergence in human well-being and income lies completely

below the semiparametric estimates, non-overlapping in any case. This result along with

the higher slope observed for the convergence process in the least educated countries

would highlight the fact that semiparametric models report different convergence patterns

than those obtained using the classical linear specification. If the nonlinearities are ignored,

our estimates of convergence speed would be underestimated for some parts of the dis-

tribution, also distorting the design of international strategies to achieve convergence. Note

that some authors argue that more efforts are needed from donor countries and interna-

tional aid agencies to accelerate the process of convergence in lees developed countries

(Noorbakhsh 2006). This conclusion is also supported by our results, but according to the

semiparametric estimates, medium developed countries should be also considered as

possible recipients of these funds or other expansive policies, given the deceleration of

convergence in well-being observed in these countries.

7 Conclusions

In this paper we re-examine the hypothesis of beta-convergence in well-being across

different economies during the period 1980–2012. The HDI is used as an indicator of such

process, which considers education and health as essential as income in the measurement

of well-being. Specifically, we analyse the concepts of sigma-convergence, which assumes

that dispersion of living standards tends to decrease over time; and beta-convergence,

which implies a negative relationship between the initial levels of a particular indicator and

its growth rate. Conversely to previous studies which estimate parametric models focused

on a linear trend, we opt for a flexible semiparametric approach. This specification does not

require making a priori assumptions about the model specification thus letting the data state

by themselves how the convergence rate evolves as the level of human well-being

increases. For comparative purposes, the parametric model is also estimated and structural

variables are included to capture differences in the steady-state, which is associated with

the concept of conditional beta-convergence.

Our results point out that the gap between developed and developing countries has been

substantially reduced in a wide range of indicators of quality of life. The educational

dimension shows the greatest reduction, around 60 %, followed by health whose inequality

levels have fallen about 30 %, and finally, the income dimension only reduced its

inequality in 10 % over the study period. These trends have resulted in a much more

egalitarian distribution of human well-being than 30 years ago. We decompose the Theil

index in two components, which represent inequality within and between regions. This

analysis reveals that disparities in well-being are dominated by differences across regions,

which represent more than the 75 % of overall disparities. A decrease in inequality within-


123

region is observed along with the fall of differences across regions, thus resulting in a

global process of convergence in quality of life.

Regarding beta-convergence, the results obtained from the classical linear analysis at

least suggest weak absolute convergence in living standards over the last 30 years. It

should be worth noting that the convergence rates obtained in this study using the new

framework of the HDI, are unambiguously higher than those of reported by previous

studies. This finding is robust to the introduction of conditioning variables which leads to

higher rates of convergence speed. Consequently, the changes applied to the HDI in 2010

affected substantially the method to evaluate well-being, thus redefining the convergence

patterns of this indicator.

The results of the RLRT test point out that the process of convergence has been

nonlinear for some of the indicators considered. In particular, PLM models reveal that

whereas the absolute convergence process in human well-being is adequately represented

by a parametric trend, conditional convergence shows nonlinear patterns. In fact, semi-

parametric estimates show that convergence in well-being seems to be slowed down for

medium developed countries, whereas for the advanced economies, the convergence

process is again accelerated. Our results suggest that, even when little advances have been

achieved in income levels, significant improvements in non-income dimensions and human

well-being have been accomplished. This conclusion highlights the relevance of consid-

ering non-income dimensions in the study convergence hypothesis, since their distribu-

tional patterns differ substantially from income.

This study reveals that some degree of equalisation in well-being levels has taken place

in the last decades. However, the convergence process is being rather slow and hence the

action of international organisations is essential to achieve faster rates of convergence.

International cooperation in social policies plays also a crucial role in increasing well-

being levels in developing countries in the near future, thus moving on the direction MDG.

Given that less developed countries have a scarcity of technological and capital resources

(UNDP 2003; WHO 2003) more efforts are needed from donor countries and international

aid agencies (Noorbakhsh 2006). In fact, the fulfilment of a global partnership seems to be

the key in achieving the eight targets of MDG by 2015 (United Nations 2012). Note that

medium developed countries should also be considered as possible recipients of these

funds or other expansive policies, given the deceleration of convergence in well-being

observed for these nations. The role of the national governments is also important espe-

cially in expanding schooling rates. Their efforts to improve primary care are also deter-

minant to enhance the quality of life (Kenny 2005), thus encouraging a catching-up process

between developing countries and leader economies.

Acknowledgments The authors thank the Ministerio de Economıa y Competitividad (Project ECO2010-15455) and the Ministerio de Educacion (FPU AP-2010-4907) for partial support of this work. Authors aregrateful for the constructive suggestions provided by the reviewers, which improved the paper substantially.

Appendix: Regions and Countries Included

Western Europe, North America, and Oceania: Australia, Austria, Belgium, Canada, Denmark, Finland,France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Japan, Korea (republic of), Luxembourg,Malta, Netherlands, New Zealand, Norway, Portugal, Spain, Sweden, Switzerland, United Kingdom,United States

Arab States: Algeria, Bahrain, Egypt, Israel, Jordan, Morocco, Qatar, Saudi Arabia, Sudan, Syrian ArabRepublic, Tunisia, Yemen, United Arab Emirates


123

Appendix continued

East Asia and the Pacific: Brunei Darussalam, China, Fiji, Hong Kong, Indonesia, Kiribati, Lao People’sDemocratic Republic, Malaysia, Mongolia, Myanmar, Papua New Guinea, Philippines, Thailand, Tonga,Viet Nam

Europe and Central Asia: Albania, Armenia, Bulgaria, Cyprus, Estonia, Latvia, Lithuania, Moldova(Republic of), Montenegro, Romania, Russian Federation, Slovenia, Slovakia, Tajikistan, Turkey, Ukraine

Latin America and the Caribbean: Argentina, Belize, Bolivia (Plurinational State of), Brazil, Chile,Colombia, Costa Rica, Cuba, Dominican Republic, Ecuador, El Salvador, Guatemala, Guyana, Haiti,Honduras, Jamaica, Mexico, Nicaragua, Panama, Paraguay, Peru, Trinidad and Tobago, Uruguay,Venezuela (Bolivarian Republic of)

South Asia: Afghanistan, Bangladesh, India, Iran (Islamic Republic of), Nepal, Pakistan, Sri Lanka

Sub-Saharan Africa: Benin, Botswana, Burundi, Cameroon, Central African Republic, Congo, DemocraticRepublic of the Congo, Cote d’Ivoire, Gabon, Gambia, Ghana, Kenya, Lesotho, Liberia, Malawi, Mali,Mauritania, Mauritius, Mozambique, Namibia, Niger, Nigeria, Rwanda, Senegal, Sierra Leone, SouthAfrica, Swaziland, Tanzania (United Republic of), Togo, Uganda, Zambia, Zimbabwe

References

Alkire, S. (2002). Dimensions of human development. World Development, 30, 181–205.Alkire, S., & Foster, J. (2010). Designing the Inequality-Adjusted Human Development Index (IHDI).

Human development research paper, 2010/28. UNDP.Anand, S., & Sen, A. (2000). The income component of the Human Development Index. Journal of Human

Development, 1, 83–106.Atkinson, A. (1970). On the measurement of inequality. Journal of Economic Theory, 2, 244–263.Azomahou, T. T., Nguyen-Van, P., & Pham, T. K. C. (2011). Testing convergence of European regions: A

semiparametric approach. Economic Modelling, 28, 1202–1210.Barro, R. J. (1991). Economic growth in a cross section of countries. The Quarterly Journal of Economics,

106, 407–443.Barro, R. J., & Sala-i-Martin, X. (1990). Economic growth and convergence across the United States. NBER

working paper no. 3419.Barro, R., & Sala-i-Martin, X. (1992). Convergence. Journal of Political Economy, 100, 407–433.Becker, S. G., Philipson, T. J., & Soares, R. R. (2005). Quantity and quality of life and the evolution of

world inequality. American Economic Review, 95, 277–291.Berggren, N. (2003). The benefits of economic freedom. A survey. The Independent Review, 8, 193–211.Bilbao-Ubillos, J. (2011). The limits of Human Development Index: The complementary role of economic

and social cohesion, development strategies and sustainability. Sustainable Development. doi:10.1002/sd.525.

Bilbao-Ubillos, J. (2013). Another approach to measuring human development: The Composite DynamicHuman Development Index. Social Indicators Research. doi:10.1007/s11205-012-0015-y.

Borensztein, E., De Gregorio, J., & Lee, J. W. (1998). How does foreign direct investment affect economicgrowth? Journal of International Economics, 45(1), 115–135.

Briassoulis, H. (2001). Sustainable development and its indicators: Through a planner’s glass darkly.Journal of Environmental Planning and Management, 41, 409–427.

Cahill, M. B. (2005). Is the human development index redundant? Eastern Economic Journal, 31, 12–19.Chotikapanich, D., Grifiths, W., Rao, D.S.P., Valencia, V. (2009). Global Income Distribution and Inequality:

1993 and 2000. University of Melbourne research paper no. 1062.Cowell, F. A. (2011). Measuring inequality (5th ed.). New York: Oxford University Press.Crainiceanu, M. C., & Ruppert, D. (2004). Likelihood ratio test in linear mixed models with one variance

component. Journal of the Royal Statistical Society: Series B, 66, 165–185.De Haan, J., Lundstrom, S., & Sturm, J. E. (2006). Market-oriented institutions and policies and economic

growth: A critical survey. Journal of Economic Surveys, 20(2), 157–191.De la Fuente, A. (1997). The empirics of growth and convergence: A selective review. Journal of Economic

Dynamics and Control, 21, 23–73.


123

http://dx.doi.org/10.1002/sd.525

http://dx.doi.org/10.1002/sd.525

http://dx.doi.org/10.1007/s11205-012-0015-y

Deaton, A. (2004). Health in age of globalization., Washington, DC: Brookings Trade Forum, BrookingsInstitution.

Decancq, K. (2011). Measuring global well-being inequality: A dimension-by-dimension or multidimen-sional approach? Reflets et perspectives de la vie economique, 4, 179–196.

Decancq, K., Decoster, A., & Schokkaert, E. (2009). Evolution of world inequality in well-being. WorldDevelopment, 37, 11–25.

Dobson, S., Ramlogan, C., & Strobl, E. (2003). Cross-country growth and convergence: A semi-parametricanalysis. Economics Discussion Papers No. 0301, University of Otago.

Domınguez, R., Guijarro, M., & Trueba, C. (2011). Recuperando la dimension polıtica del desarrollohumano. Sistema, 220, 11–31.

Durlauf, S. N. (2001). Manifesto for a growth econometrics. Journal of Econometrics, 100, 65–69.Durlauf, S. N., Kourtellos, A., & Minkin, A. (2001). The local Solow growth model. European Economic

Review, 45, 928–940.Edgier, V. S., & Tatlidil, H. (2006). Energy as an indicator of human development: A statistical approach.

The Journal of Energy and Development, 31(2), 213–232.Fakuda-Parr, S., Lawson-Remer, T., & Randolph, S. (2009). An index of economic and social rights

fulfilment: Concept and methodology. Journal of Human Rights, 38, 195–221.Ferrara, A. R., & Nistico, R. (2013). Well-being indicators and convergence across Italian regions. Applied

Research in Quality of Life, 8(1), 15–44.Fiaschi, D., & Lavezzi, A. M. (2007). Nonlinear economic growth: Some theory and cross-country evidence.

Journal of Development Economics, 84, 271–290.Frankel, J. A., & Romer, D. (1999). Does trade cause growth? American Economic Review, 89, 379–399.Goesling, B., & Firebaugh, F. (2004). The trend in international health inequality. Population and Devel-

opment Review, 30(1), 131–146.Goldsmith, A. A. (1997). Economic rights and government in developing countries: Cross-national evidence

on growth and development. Studies in Comparative International Development, 32(2), 29–44.Greenaway, D., Morgan, M., & Wright, P. (1998). Trade reform, adjustment and growth: What does the

evidence tell us? Economic Journal, 108, 1547–1561.Grimm, M., Harttgen, K., Klasen, S., & Misselhorn, M. (2008). A Human Development Index by income

groups. World Development, 36, 2527–2746.Gwartney, J., & Lawson, R. (2004). Ten consequences of economic freedom. Policy Report, 268.Gwartney, J., Lawson, R., & Hall, J. (2010). Economic freedom of the world 2010 annual report. Van-

couver, BC: The Fraser Institute.Gwartney, J., Lawson, R., & Hall, J. (2013). Economic freedom of the world 2013 annual report. Van-

couver, BC: The Fraser Institute.Hicks, D. A. (1997). The Inequality-Adjusted Human Development Index: A constructive proposal. World

Development, 25, 1283–1298.Huang, H. C. (2005). Diverging evidence of convergence hypothesis. Journal of Macroeconomics, 27,

233–255.Islam, N. (2003). What have we learnt from the convergence debate? Journal of Economic Surveys, 17,

309–362.Kelley, A. (1991). The Human Development Index: ‘‘Handle with Care’’. Population and Development

Review, 17, 315–324.Kenny, C. (2005). Why are we worried about income? Nearly everything that matters is converging. World

Development, 33(1), 1–19.Klugman, J., Rodrıguez, F., & Choi, H.-J. (2011). The HDI 2010: New controversies, old critiques. Journal

of Economic Inequality, 9, 249–288.Konya, L. (2011). New panel data evidence of human development convergence from 1975 to 2005. Global

Business and Economics Review, 13, 57–70.Konya, L., & Guisan, M. C. (2008). What does the human development index tell us about convergence?

Applied Econometrics and International Development, 8, 19–40.Kovacevic, M. (2010). Review of HDI critiques and potential improvements. Human development research

paper no. 33. UNDP.Liu, Z., & Stengos, T. (1999). Non-linearities in cross-country growth regressions: A semiparametric

approach. Journal of Applied Econometrics, 14, 527–538.Lundberg, M., & Squire, L. (2003). The simultaneous evolution of growth and inequality. The Economic

Journal, 113(487), 326–344.Marchante, A. J., Ortega, B., & Sanchez, J. (2006). The evolution of well-being in Spain (1980–2001): A

regional analysis. Social Indicators Research, 76, 283–316.


123

Martınez, R. (2012). Inequality and the new Human Development Index. Applied Economics Letters, 19,533–535.

Mayer-Foulkes, D. (2003). Convergence clubs in cross-country life expectancy dynamics. In R. van derHoeven & A. Shorrocks (Eds.), Perspectives on growth and poverty (pp. 144–171). Tokyo: UnitedNations University Press.

Mayer-Foulkes, D. (2010). Divergences and convergences in human development. Human developmentresearch paper no. 2010/20. UNDP.

Mazumdar, K. (2000). Inter-country inequality in social indicators of development. Social IndicatorsResearch, 49, 335–345.

Mazumdar, K. (2002). A note on cross-country divergence in standard of living. Applied Economics Letters,9, 87–90.

Mazumdar, K. (2003). Do standards of living converge? A cross-country study. Social Indicators Research,64, 29–50.

McGillivray, M. (1991). The Human Development Index: Yet another redundant composite developmentindicator? World Development, 19, 1461–1468.

McGillivray, M., & Markova, N. (2010). Global inequality in well-being dimensions. Journal of Devel-opment Studies, 46, 371–378.

McGillivray, M., & Pillarisetti, J. R. (2004). International inequality in well-being. Journal of InternationalDevelopment, 16, 563–574.

McGillivray, M., & White, H. (1993). Measuring development? The UNDP’s Human Development Index.Journal of International Development, 5, 183–192.

McMichael, A. J., McKee, M., Shkolnikov, V., & Valkonen, T. (2004). Mortality trends and setbacks:Global convergence or divergence? The Lancet, 363(9415), 1155–1159.

Milanovic, B. (2005). Worlds apart: Measuring international and global inequality. Princeton: PrincetonUniversity Press.

Morris, M. D. (1979). Measuring the conditions of the world’s poor: The Physical Quality of Life Index.New York: Pergamon.

Morrison, C., & Murtin, F. (2012). The Kuznets curve of human capital inequality: 1870–2012. Journal ofEconomic Inequality. doi:10.1007/s10888-012-9227-2.

Moser, K., Shkolnikov, V., & Leon, D. A. (2005). World mortality 1950–2000: Divergence replacesconvergence from the late 1980s. Bulletin of the World Health Organization, 83(3), 202–209.

Neumayer, E. (2001). The Human Development Index and Sustainability—A constructive proposal. Eco-logical Economics, 39, 101–114.

Neumayer, E. (2003). Beyond income: Convergence in living standards, big time. Structural Change andEconomic Dynamics, 14, 275–296.

Noorbakhsh, F. (1998). The Human Development Index: Some technical issues and alternative indices.Journal of International Development, 10, 589–605.

Noorbakhsh, F. (2006). International convergence or higher inequality in human development? Evidence for1975–2002. WIDER research paper no. 2006/15.

Norton, S. W. (1998). Poverty, property rights, and human well-being: A cross-national study. Cato Journal,18, 233.

Ogwang, T., & Abdou, A. (2003). The choice of principal variables for computing human developmentindicators. Social Indicators Research, 64, 139–152.

O’Leary, E. (2001). Convergence of living standards among Irish regions: The roles of productivity, profitoutflows and demography, 1960–1996. Regional Studies, 35(3), 197–205.

Pillarisetti, J. R. (1997). An empirical note on inequality in the world development indicators. AppliedEconomic Letters, 4, 145–147.

Pritchett, L. (1997). Divergence, big time. Journal of Economic Perspectives, 11(3), 3–17.Quah, D. (1993). Galton’s fallacy and tests of the convergence hypothesis. Scandinavian Journal of Eco-

nomics, 95, 427–443.Quah, D. (1996). Regional convergence clusters across Europe. European Economic Review, 40,

1951–1958.Ravallion, M. (1997). Good and bad growth: The human development reports. World Development, 25,

631–638.Rodrik, D., Subramanian, A., & Trebbi, F. (2004). Institutions rule: The primacy of institutions over

geography and integration in economic development. Journal of Economic Growth, 9(2), 131–165.Ruppert, D., Wand, M. P., & Carroll, R. J. (2003). Semiparametric regression. London: Cambridge Uni-

versity Press.Sab, R, & Smith, S. C. (2001). Human capital convergence: International evidence (Vol. 1). IMF working

paper. International Monetary Fund.


123

http://dx.doi.org/10.1007/s10888-012-9227-2

Sagar, A. D., & Najam, A. (1998). The Human Development Index: A critical review. Ecological Eco-nomics, 25, 249–264.

Sala-i-Martin, X. (1996). The classical approach to convergence analysis. The Economic Journal, 106,1019–1033.

Sala-i-Martin, X. (2000). Apuntes de Crecimiento Economomico (2nd ed.). Barcelona: Antoni Bosch Editor.Sen, A. (1988). The concept of development. In H. Chenery & T. N. Srinivasan (Eds.), Handbook of

development economics (pp. 9–26). Amsterdam: Elsevier.Sen, A. (1989). Development as capabilities expansion. Journal of Development Planning, 19, 41–58.Sen, A. (1999). Development as freedom. Oxford: Oxford University Press.Seth, S. (2010). A class of distribution and association sensitive multidimensional welfare indices. The

Journal of Economic Inequality. doi:10.1007/s10888-011-9210-3.Slaughter, M. J. (2001). Trade liberalization and per capita income convergence: A difference-in-differences

analysis. Journal of International Economics, 55(1), 203–228.Solow, R. M. (1956). A contribution to the theory of economic growth. Quarterly Journal of Economics, 70,

65–94.Solow, R. M. (1957). Technical change and the aggregate production function. Review of Economics and

Statistics, 39, 312–320.Srinivasan, T. N. (1994). Human development: A new paradigm or a reinvention of the wheel? American

Economic Review, 84, 238–243.Swan, T. W. (1956). Economic growth and capital accumulation. Economic Record, 32, 334–361.UNDP. (1990). Human development report. Concept and measurement of human development. New York:

United Nations Development Program.UNDP. (2003). Human development report. Millennium development goals: A compact among nations to

end human poverty. New York: United Nations Development Program.UNDP (2005). Human Development Report. International cooperation at a crossroads: Aid, trade and

security in an unequal world. New York: United Nations Development Program.UNDP. (2012). International human development indicators. Retrieved from http://hdr.undp.org/en/

statistics/. Accessed March 28, 2013.UNDP. (2013). Human development report. The rise of the south: Human progress in a diverse world. New

York: United Nations Development Program.United Nations. (2012). The millennium development goals report. New York: United Nations.Wacziarg, R., & Welch, K. H. (2008). Trade liberalization and growth: New evidence. The World Bank

Economic Review, 22(2), 187–231.Wand, M. P. (2005). SemiPar: An R package for semiparametric regression. Working paper.World Bank. (2001). World development report 2000/2001: Attacking poverty. Oxford: Oxford University

Press.World Bank. (2006). World development report 2005/2006: Equity and development. Oxford: Oxford

University Press.World Bank. (2013). World development indicators database. Retrieved from http://data.worldbank.org/

data-catalog/world-development-indicators. Accessed November 15, 2013.World Health Organization (WHO). (2003). The world health report: Shaping the future. Geneva: World

Health Organization.


123

http://dx.doi.org/10.1007/s10888-011-9210-3

http://hdr.undp.org/en/statistics/

http://hdr.undp.org/en/statistics/

http://data.worldbank.org/data-catalog/world-development-indicators

http://data.worldbank.org/data-catalog/world-development-indicators

Date post:	21-Dec-2016
Category:	Documents
Upload:	jose-maria
View:	218 times
Download:	3 times

International Convergence in Well-Being Indicators

Documents