Munich Personal RePEc Archive

On the Distribution Dynamics of Human
Development: Evidence from theMetropolitan Regions of Bolivia
Mendez, Carlos
Kyushu University

24 June 2018

Online at https://mpra.ub.uni-muenchen.de/87571/
MPRA Paper No. 87571, posted 24 Jun 2018 15:55 UTC

On the Distribution Dynamics of
Human Development:
Evidence from the Metropolitan Regions of Bolivia
Carlos Mendez-Guerra
Kyushu University
Abstract

Bolivia has experienced large socioeconomic transformations in the last decades.
Among them, almost half of the population currently lives in the main metropolitan regions of the country. Motivated by the potential for growth and development
convergence in these regions, this article documents the evolution of human development disparities and convergence patterns over the 1992-2013 period. Using a distribution dynamics framework, this article evaluates both the transitional
dynamics and the long-run equilibrium of the cross-regional distribution of human development. Results from the transitional dynamics analysis suggest thatthe formation of multiple clusters of convergence is a salient feature of inequality
reduction in human development. On the other hand, results from the long-run
equilibrium analysis suggest that the process of regional convergence is characterized by the transformation of a trimodal distribution into a left–skewed unimodal
distribution. The article concludes emphasizing that the cross-regional distributionof human development in Bolivia is quite sticky at its left tail, and as a result theleast developed regions are still relatively far from achieving complete convergencein the long run.
JEL Codes: O47, O40, O15
Keywords: convergence, distribution dynamics, human development, Bolivia

1Introduction

Since the mid-1980s, Bolivia has experienced large political, social, and economic transformations.1 Among its social and demographic transformations, there has been a continuous
movement of population toward the most urban and metropolitan areas of the country. By theyear 2013, forty six percent of the total population are concentrated in the main metropolitan
regions2 of Bolivia (UNDP, 2016).
Given the notion that metropolitan regions within a country are more likely to share common technological and institutional environments,3 the neoclassical growth model would predict that these regions are expected to converge in terms of their living standards. Motivatedby this prediction and the observed socioeconomic progress of the metropolitan regions of Bolivia,4 this article documents the evolution of human development disparities and convergence
patterns over the 1992-2013 period. In particular, using the United Nations’ human development index at the municipal level, this article evaluates the process of regional convergencethrough the lens of a distribution dynamics framework (Quah 1997; Johnson 2005).
Results from the transitional dynamics analysis suggest that the formation (and merge) ofmultiple clusters of convergence is a salient feature of inequality reduction in human development. The 1992-2001 period appears to be characterized by three separate convergence clusters.
The 2001-2013 period, on the other hand, highlights the merge between the central cluster andthe high-development cluster identified in the previous decade. Given these dynamics, resultsfrom the estimated long-run distribution suggest that the process of regional convergence ischaracterized by the transformation of a trimodal distribution into a left–skewed unimodal distribution. This unimodal transformation, however, largely depends on the continuation of thehuman development dynamics observed in the 2001-2013 period.
The rest of paper is organized as follows. Section 2 briefly describes the distribution dynamics framework and data of the study. Section 3 presents the results of the transitional dynamics
and the long-run equilibrium analyses. Finally, Section 4 offers some concluding remarks.
2
2.1

Methodology and Data

Distribution Dynamics Framework

Building on the seminal work of Silverman (1986), Quah (1993, 1997) introduces the distribution dynamics framework as a modeling technique that describes the evolution of the entire
income distribution across countries. At its core, this framework characterizes the dynamics ofa system in terms of the transitional dynamics and long-run equilibrium of a non-parametric distribution function. Transitional dynamics are modeled via an estimated stochastic kernel, which
is a continuous state-space representation of a Markovian transition matrix. The long-run equilibrium is modeled via an estimated ergodic distribution, which is a continuous representation
1 For example, in the political domain, Bolivia celebrated its return to democracy in 1982, after a series of

painful military dictatorships. In the economics domain, Bolivia started in 1985 the implementation of a series ofdeep structural reforms that aimed to end its hyperinflation crisis and foster macroeconomic stability.
2 Bolivia is administratively divided into nine departments. Of those nine, the urban and metropolitan regionsof the largest three departments (La Paz, Santa Cruz, and Cochabamba) concentrate forty six percent of the total
population. Although the other six departments also show a tendency toward urbanization, this study focuses only
on the metropolitan regions of the three largest departments of Bolivia.
3 For instance, compared to urban and rural differences within a country or high-income and low-income differences across countries, metropolitan regions within a country are expected to have a higher degree of homogeneity.
4 See UNDP (2016) for a complete report on the human development progress of these regions.

of a Markov chain equilibrium.
In what follows, I sketch5 more formally the main components of the distribution dynamics framework in the context of the variables of this article. First, denote pt (x) as the initial
cross-sectional distribution of human development6 at time t. Likewise, pt+s (y) is the human development distribution at some future time t + s. To model the evolution from time
t to time t + s, the literature typically assumes a first-order autoregressive process of a timehomogeneous Markov chain. That is,
ˆ ∞
=
p (x)
dx.
(1)
P(y | x)p (y){z }| t{z }
| {z }| t+s
0
Future Distribution

Transitional Operator Initial Distribution

Where the transition between the initial distribution, pt (x), and the future distribution,
pt+s (y), is mapped by a transitional probability operator, P(y | x), that is commonly referred in
the literature as the stochastic kernel.
Transitional Dynamics via the Stochastic Kernel
To estimate the stochastic kernel, most recent studies exploit the advantages of non-parametricstatistical methods. The first step in the estimation process is the definition of the stochastic
kernel as a conditional distribution
P(y | x) =pt,t+s (y, x),
pt (x)(2)

where pt,t+s (y, x) is an unconditional joint distribution. The next step is to specify this joint
distribution in terms of two kernel functions and a pair of smoothing parameters. A common
candidate for this endeavor is 
y − yi1 nx − xipt,t+s (y, x) =∑ Ky hy Kx hx ,nhy hx i=1
where y and x denote (relative) human development in each region at time t and t + s respectively, Ky and Kx denote Gaussian kernel functions, and hy and hx denote the smoothing parameters for y and x respectively. Following Magrini (1999, 2009) and Kar, Jha, and Kateja(2011), the optimal selection of the smoothing parameters is based on the minimization of theasymptotic mean integrated square error (AMISE). The final step is the specification of themarginal distributions. Similar to the estimation of the joint distribution, the marginal distributions (pt+s (y) and pt (x)) are estimated using a single Gaussian kernel function and a smoothing
parameter.7
Long-run Equilibrium via the Ergodic Distribution
To estimate the ergodic distribution, the approach of Johnson (2000, 2005) is implemented.
Considering the dynamics described in Equation 1, the long-run equilibrium of the system is
5 See Epstein, Howlett, and Schulze (2003) or Magrini (2004, 2009) for a more complete presentation.
6 For the rest of this analysis, the human development level of each region is expressed in relative terms. Thatis, the officially reported HDI level for each region is normalized by the cross-sectional average of the sample.
7 The smoothing parameter for each marginal distribution is also derived through the the minimization of theasymptotic mean integrated square error (AMISE).

given by the solution to the following problem:ˆ ∞p∞ (y) =P(y | x)p∞ (x)dx = p∞ (x).

(3)

0

If a solution exists, then the shape of the ergodic distribution, p∞ (y), provides valuable information regarding the long-run convergence patterns of the economic system under study. To
compute this solution, this article uses the MATLAB functions developed by Magrini (2009).
2.2

Data

The dataset is from the 2016 Human Development Report for Bolivia.8 The United Nations
Development Program (UNDP, 2016) constructed a municipal-level Human Development Index (HDI) that covers 20 municipalities from the metropolitan regions of La Paz, Cochabamba,
and Santa Cruz. The temporal dimension of this dataset comprises four years: 1992, 2001,
2005 and 2013. The construction of this dataset required census data, household surveys, andadministrative records of public services.
To control for aggregate shocks that might affect all metropolitan regions, a relative (ratio)
measure of the HDI is used as the main unit of analysis. More specifically, the HDI of eachmunicipality was rescaled by the cross-sectional mean of each year. To facilitate the interpretation of the results, relative HDI of each municipality is presented in natural log terms. Thistransformation simply re-scales the HDI in a way that the sample average now takes a vale ofzero at each point in time.
Figure 1: Regional Mobility and Convergence across Regions

8 The report can be downloaded from the following website: http://www.bo.undp.org/content/dam/bolivia/docs/

undp_bo_IDH2016.pdf . Table 1 of the appendix has been used to construct the dataset of this study.

Figure 1 presents a graphical summary of the dataset at three points in time.9 First, thelocation of observations along the main scatterplot axes show a noticeable reduction in humandevelopment differences over time. Relative to the sample average of the year 1992, humandevelopment differences ranged between 17 percent below average (the case of Palca) and 20
percent above average (the case of Santa Cruz). By the year 2013, this range has noticeably
decreased. Human development differences ranged between 12 percent below average (thecase of Laja) and 7 percent above average (the case of Santa Cruz). The subperiod scatterplots
point that the 2001-2013 period shows the largest reduction in human development differences
across regions.
The slope of the fitted regression lines in Figure 1 suggests that regions with relatively
lower levels of development appear to be moving forward, whereas the regions with relatively
higher levels of development appear to be moving backward.10 Naturally, the outcome of these
dynamics is a process of convergence, which was most notorious in the 2001-2013 period.
Regions located above the dashed 45-degree line are those that improved their relative position
and regions located below are those that deteriorated their position, relative to its initial levelof human development. For instance, over the 1992-2013 period, the region of Tiquipaya
improved its relative position from 3 percent below average11 to 7 percent above average.12 On
the other hand, the region of El Alto deteriorated its position from 7 percent above average to 7
percent below average. Indeed, these patterns of forward and backward mobility appear to bea general characteristic of the development path of the regions in the sample.
Although the fitted regression lines of Figure 1 summarize—to some extent—the overall
convergence pattern across metropolitan regions, there are some key aspects of the convergence process that require further investigation. The distribution dynamics framework provides
valuable new insights regarding nonlinear dynamics and the formation of convergence clusters.
In addition, a more complete dynamic analysis should include both notions of transition andlong-run equilibrium. These two key features are presented in the next section.
3
3.1

Results

Transitional Dynamics

Figures 2 and 3 show the transitional dynamics of convergence through the lens of the estimatedstochastic kernel. One of the main features of the estimation is the graphical identification ofstagnation, transition, and clustering patterns. Building on top of the mobility patterns described in Figure 1, the stochastic kernel shows that the dynamics of convergence clusters (orclubs) is a salient feature of inequality reduction in human development across metropolitan
regions in Bolivia. Moreover, these cluster dynamics are different across the two decades of
the analysis.
9 Although, given the data availability, it is possible to work with four reference points and three sub-periods,

this article focuses only on two longer sub-periods that roughly cover two decades each.
10 Note that a backward movement in relative terms does not imply a backward movement in absolute terms.
11 This is the sample average of the year 1992, which in the scatterplot is normalized to zero.
12 This is the sample average of the year 2013, which in the scatterplot is normalized to zero.

Figure 2: Stochastic Kernel: Contour Plots

For the 1992-2001 period, the stochastic kernel (Figure 2 and 3 , Panel a) points to three
separate clusters of high density. Relative to the central cluster, located around the average
human development level of the year 2001, there is a low human development cluster locatedat about 10 percent below average. On the other side of the distribution, there is a high humandevelopment cluster located at about 14 percent above average. In addition, note that in Figure
2 (Panel a) the low human development cluster is mostly located above the 45-degree line (thatis, forward mobility) and the high human development cluster is mostly located below the 45degree line (that is, backward mobility). Thus, over time, both clusters are moving closer to thecentral cluster.
For the 2001-2013 period, the stochastic kernel (Figure 2 and 3 , Panel b) highlights themerge (convergence) between the central cluster and the high-development cluster identified
in the previous decade. The newly merged cluster is now located at about 3 percent above
the human development average of the year 2013. The relatively low development cluster,
on the other hand, is located at about 4 percent below the average of the same year. Overall,these transitional dynamics suggest that the convergence process arising from the bottom the
distribution is much more sticky compared to that arising from the top of the distribution.
Figure 3: Stochastic Kernel: Surface Plots

3.2

Long-Run Equilibrium

Figure 4 shows the long-run dynamics of convergence through the lens of the estimated ergodic
distribution. The main purpose of an ergodic distribution analysis is to clarify and magnify theeffects of the observed transitional dynamics.13 Overall, Figure 4 shows a process of convergence characterized by the evolution of a trimodal distribution (year 1992) into a left–skewed
unimodal distribution (ergodic estimation for the period 2001-2013). Moreover, similar to thetransitional dynamics findings, the two periods of analysis show two largely different convergence dynamics in the long run.
Panel (a) of Figure 4 shows the marginal distributions for the years 1992 and 2001, and thelong-run (ergodic) distribution associated to that time span. As expected, human development
differences are smaller in the long run. However, the asymmetric and bumpy shape of theergodic distribution may still suggest the existence of two convergence clubs. For one reason,
it is clear that in the year 2001 the human development distribution shows two density peaks.
And, to some extent consistent with this bimodality, the ergodic distribution still shows two
density concentrations: one located at about 12 percent below average and the other at about
about 2 percent above average.
Panel (b) of Figure 4 shows the the long-run (ergodic) distribution given the transitional
dynamics of the 2001-2013 period. Although there are no clear multiple density bumps in thelong run, the shape of the ergodic distribution is still largely asymmetric. Indeed, the distance
between the left tail and the mode of the distribution suggests that the least developed regionsof the sample are still relatively14 far from achieving convergence in the long run.
Figure 4: Initial, Final, and Ergodic Distribution

4

Concluding Remarks

This article has documented the reduction of human development disparities (as measured by
the United Nations’ human development index) across the metropolitan regions of Bolivia overthe 1992-2013 period. In particular, through the lens of a nonparametric density estimation
13 Note that the estimation of a long-run distribution should not be considered as a forecast of what will happen

in the future (Quah, 1997).
14 Relative to the level of convergence experienced by the most developed regions in the sample.

framework, the process of regional convergence has been characterized in terms of its transitional dynamics and long-run equilibrium.
Overall, there is a tendency toward regional convergence that is driven by both the forward mobility of the less developed regions and the backward mobility of the more developed
regions. However, the transitional dynamics analysis, via the estimated stochastic kernel, suggests that the formation of different convergence clusters is a salient feature of inequality reduction in human development. Furthermore, these clustering dynamics are notoriously different
across the two decades of the analysis. While the 1992-2001 period appears to be characterized
by the formation of three separate clusters, the 2001-2013 period highlights the convergence(merge) between the central cluster and the high-development cluster identified in the previous
decade.
The long-run equilibrium analysis, via the estimated ergodic distribution (and the observed
marginal distributions), suggests that the process of regional convergence is characterized by
the transformation of a trimodal distribution (year 1992) into a left–skewed unimodal distribution (ergodic estimation). This unimodal transformation, however, largely depends on thecontinuation of the human development dynamics observed in the 2001-2013 period. If, forinstance, the dynamics of the 1992-2001 period are taken as a more realistic input for thelong run, then the human development distribution is more likely to be characterized by two
convergence clubs. In any of these cases, it appears to be clear that the human development
distribution is quite sticky at the bottom, and thus the least developed regions are still relatively
far from achieving complete convergence in the long run.
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