HETEROGENEOUS GROWTH AND REGIONAL(DI)CONVERGENCE IN BOLIVIA:A DISTRIBUTION DYNAMICS APPROACH
Carlos Mendez-Guerra
Kyushu University
 RESUMEN: Bolivia ha experimentado altas tasas de crecimiento
económico en la última década y media. Este rápido crecimiento, sinembargo, varía considerablemente a través de sus regiones administrativas.
Considerando este contexto de crecimiento heterogéneo, el presenteartículo documenta la evolución de las disparidades del ingreso per cápita
y los patrones de convergencia de las regiones de Bolivia en el periodo
1988-2014. En particular, utilizando un enfoque de distribución dinámica,
el presente artículo evalúa el equilibrio de largo plazo y la dinámica detransición de la distribución del PIB per cápita regional. Los resultados
principales muestran un patrón claro de divergencia regional para elperíodo 1988-2000. En contraste, en el período 2000-2014 se encuentra uncomplejo patrón de (di) convergencia: la distribución de largo plazo está
caracterizada tanto por un proceso de convergencia desde la cola superiorcomo por un proceso de divergencia alrededor de la cola inferior. En
general, la evolución de la forma externa de la distribución del PIB regional
y su dinámica intra-distribucional sugieren que el proceso de crecimiento
regional en Bolivia podría ser caracterizado por al menos dos clubes deconvergencia. Adicionalmente, estos clubes son identificables en períodos
de alto y bajo crecimiento nacional.

*

Lecturer and Researcher, Faculty of Arts and Sciences, Kyushu University, Japan.
Email: mendez.carlos@artsci.kyushu-u.ac.jp

Economía coyuntural, Revista de temas de coyuntura y perspectivas, vol.2, núm. 4., pp. 81- 108.
http://doi.org/10.5281/zenodo.1211814

81 ECONOMÍA COYUNTURAL PALABRAS CLAVE: crecimiento regional, convergencia, distribución
dinámica, Bolivia
 ABSTRACT: Bolivia has experienced high economic growth rates in the last
decade and a half. This fast growth, however, varies largely across its
administrative regions. Considering this heterogeneous-growth context,
this article documents the evolution of income disparities and convergence
patterns of the Bolivian regions over the 1988-2014 period. In particular,
using a distribution dynamics approach, this article evaluates both the longrun equilibrium and the transition dynamics of the cross-sectional
distribution of regional GDP per capita. The main results show a clear
pattern of regional divergence for the period 1988-2000. In contrast, the2000-2014 period points to a much more complex pattern of(di)convergence: the long-run equilibrium distribution is characterized byboth a process of convergence arising from the top and a process ofdivergence near its bottom tail. Overall, the evolution of the external shapeof the distribution and the intra-distribution dynamics suggest that theprocess of regional growth in Bolivia may be characterized by at least two
convergence clubs. Moreover, these clubs are identifiable in periods ofboth low and high national growth.
 KEY WORDS: regional growth, convergence, distribution dynamics, Bolivia
 CLASIFICACIÓN JEI: O40, O47
 Recepción: 05/09/2017
Aceptación: 15/11/2017
1. Introduction
The convergence hypothesis is one of the central topics in the literature of
economic growth and development. Since the late 1980s, there has been an
explosion of empirical studies trying to test this hypothesis, first in the context
of cross-countries income differences (Baumol 1986; Barro & Sala-i-Martin
1992a; Barro 2015; among others) and later in the context of regional income
differences within countries (Barro & Sala-i-Martin 1991, 1992b; Magrini
1999, Royuela, & Garcia, 2015; among others). From a methodological point82

HETEROGENEOUS GROWTH AND REGIONAL…|83

of view, the analysis of economic convergence can be broadly classified into
two kinds of frameworks. Those that evaluate convergence based on single
summary measures (for instance, beta or sigma convergence‡‡) and those that
evaluate convergence based on the shape and dynamics of the entire income
distribution§§.
When comparing the pros and cons of these frameworks, most survey
studies point that summary measures such as beta convergence could belargely uninformative due to its emphasis on the behavior of a representative
economy that convergences smoothly to a unique steady state. (De la Fuente
1997, 2000; Durlauf, Johnson, & Temple, 2005). The distribution dynamics
approach, on the other hand, provides valuable information on the behaviorof the entire cross-sectional income distribution. As it evolves over time, bothchanges in its external shape and changes in its intra-distribution dynamics
permit the study of heterogeneous behavior the emergence of multiple
convergence clubs (Durlauf & Quah, 1999; Magrini 2004, 2009).
In the Bolivian context, convergence in GDP per capita acrossregions*** has been mostly studied using classical summary measures.
Interestingly, research findings appear largely inconclusive given the series ofcontradictory results that are reported even for similar time spans and sample
compositions. For example, the work of Evia at al. (1999) reports conditionalbeta divergence for the 1976-1992 period. Contrary to these results, Sandoval(2003) reports conditional beta convergence for the 1980-1992 period. Morerecently, Sorucco (2012) studies the 1990-2010 period and reports conditional‡‡See Sala-i-Martin (1996) for an overview of the classical approach to convergence analysis.
§§See Magrini 2009 for an overview of the alternative approach to convergence analysis.

***Bolivia is conformed by nine administrative regions, also known as departments. In the restof the paper, the terms regions and departments are used interchangeably .

83 ECONOMÍA COYUNTURAL(and absolute) beta divergence. Kuscevic-Montero and Rivera-del-Rio (2013),
on the other hand, report conditional beta convergence for the 1998-2011
period. In an attempt to clarify these contradictory results, the work of
Caballero-Claure and Caballero-Martinez (2016) points that although thewhole 1990-2011 period is characterized by a lack of conditional convergence,the 2000-2010 sub-period shows some evidence of conditional convergence.
Given the informational problems of the classical summary measuresof convergence, the seemingly contradictory results found in the Bolivian
context, and the large growth differences across regions and over time,††† ––amore flexible convergence framework may be worth exploring. Hence themain objective of this paper is to implement the distribution dynamics
approach suggested by Quah (1993, 1996a, 1996b, 1997). From amethodological standpoint, this is a promising alternative that handles boththe informational problems of classical summary measures and theheterogeneous growth patterns that characterize the behavior of the Bolivian
regions. This non-parametric framework studies the evolution of the entire
distribution of income across regions through the estimation of kernel
densities, ergodic (long-run) distributions, and stochastic kernels.
To achieve this objective, this paper first documents the high degreeof growth heterogeneity over time and across regions. For instance, the 19882000 period is characterized by relatively slow growth in national GDP per
capita (a geometric annual average of 1.41 percent) and increasing regional
disparities. The 2000-2014 period, however, is characterized by faster national†††See Machicado, Nina, & Jemio (2012) for a detailed survey of the heterogeneous growth

patterns that characterize the behavior of the Bolivian regions.

84

HETEROGENEOUS GROWTH AND REGIONAL…|85

growth (a geometric annual average of 2.44 percent) and decreasing regional
disparities‡‡‡.
Next, for each of the previously described growth regimes, the paper
evaluates both the long-run equilibrium and the transitional dynamics of thecross-regional distribution of GDP per capita. Compared to the initial
distribution, the long-run equilibrium for the 1988-2000 period ischaracterized by a wider dispersion with thicker tails. The transition dynamics
of the stochastic kernel confirm this process by pointing to the shift of density
mass from the middle to the tails. Overall, these dynamics suggest a patternof distributional divergence with the formation of two regional clubs locatednear both tails of the distribution.
In contrast, the 2000-2014 period points to a much more complex
pattern of (di)convergence. The long-run equilibrium is characterized by botha process of convergence arising from the top and a process of divergencelocated at the bottom of the distribution. Although the convergence process
seems to be stronger§§§ than the divergence process, the mode of distribution
is still below the national average and there is a notoriously thick left tail.
Consistent with this observation, the transition dynamics suggest theformation of at least two convergence clubs, one near the left tail and anotherjust below the national average.
Overall, this paper contributes to the regional growth literature inthree ways. From a methodological point of view, it is the first study that
implements a complete distribution dynamics analysis in the Bolivian‡‡‡It is worth noticing here that the decrease in regional disparities during the 2000-2014

depends fundamentally on the exclusion of the department of Tarija.
§§§This is particularly true when the department of Tarija is excluded from the analysis.

85 ECONOMÍA COYUNTURAL
context****. Next, it applies this framework to two different sub-periods withthe purpose of highlighting the nature of regional convergence patterns under
different growth regimes. Finally, from the point of view of the results, itemphasizes that the process of regional convergence is complex and henceclassical summary measures such as beta-convergence or sigma-convergence
fail to identify the formation of regional convergence clubs in the Bolivian
context.
The rest of the paper is organized as follows. Section 2 describes the
distribution dynamics framework and database of the study. Section 3
discusses some central facts related to heterogeneous growth and regional
disparities in Bolivia. Section 4 presents the results of the distribution
dynamics analysis. Finally, Section 5 offers some concluding remarks.
2. Methodology and Data
This section briefly summarizes the distribution dynamics framework
developed by Quah (1993, 1996a, 1996b, 1997)††††. This non-parametricframework studies the evolution of the entire distribution of GDP per capita
across regions and over time. The study of transitional dynamics is typicallysummarized by a stochastic kernel‡‡‡‡ and the study of long-run (steady-state)equilibrium is summarized by the shape of the ergodic distribution. As a result,the joint study of the evolution of the shape of the distribution and the intradistribution dynamics provides valuable information regarding the persistence****Although other studies, such as Caballero-Claure and Caballero-Martínez (2016), estimate

basic kernel densities at different points of time, they do not estimate stochastic kernels andergodic distributions. As argued by Magrini (2004, 2009), a complete study or distribution
dynamics involves estimating kernel densities, stochastic kernels, and ergodic distributions.
††††For a more comprehensive presentation of this methodology, see Epstein, Howlett, andSchulze (1999, 2003), Magrini (2004, 2009) and the appendix in Bianco (2016).
‡‡‡‡The stochastic kernel is the continuous-time equivalent of a transition probability matrix.

86

HETEROGENEOUS GROWTH AND REGIONAL…|87

of regional inequality, polarization or stratification patterns, and the formationof convergence clubs.
Let 𝑓𝑡 (𝑥) denote the initial distribution of relative§§§§ GDP per capita
across regions at time 𝑡. Also, let 𝑓𝑡+𝑠 (𝑦) denote the distribution of relative
GDP per capita at some future time 𝑡 + 𝑠. Then one of the simplest forms ofmodeling the evolution of a distribution is to assume a time-homogeneous
Markov chain. Similar to a first-order autoregressive process, the dynamics ofthe distribution at time 𝑡 + 𝑠 is given by a transition probability operator, 𝐺(⋅), and the initial distribution at time 𝑡:∞

𝑓𝑡+𝑠 (𝑦)=∫⏟0𝐹𝑖𝑛𝑎𝑙 𝐷𝑖𝑠𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛

𝐺(𝑦|𝑥)𝑓𝑡 (𝑥)
𝑑𝑥. (1)⏟⏟
𝑇𝑟𝑎𝑛𝑠𝑖𝑡𝑖𝑜𝑛 𝑂𝑝𝑒𝑟𝑎𝑡𝑜𝑟 𝐼𝑛𝑖𝑡𝑖𝑎𝑙 𝐷𝑖𝑠𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛

The transition probability operator (𝑦|𝑥) , which is know as thestochastic kernel in the economic growth literature (Durlauf & Quah, 1999;
Quah, 1997), maps the transition from time 𝑡 to time 𝑡 + 𝑠. Among otheruseful properties of this operator, Johnson (2005) shows that∞

∫ 𝐺 (𝑦|𝑥)𝑑𝑦 = 1.
0

Furthermore, this operator is also a conditional density that can becalculated as
𝐺(𝑦|𝑥) =𝑓𝑡,𝑡+𝑠 (𝑦, 𝑥),
𝑓𝑡 (𝑥)§§§§Relative means that GDP per capita of each reagion is normalized by the national

average.

87(2) ECONOMÍA COYUNTURAL
where 𝑓𝑡,𝑡+𝑠 (𝑦, 𝑥) is a joint density, which in turn can be estimated using nonparametric methods.
The general form of the kernel estimator for the joint density is𝑛1
𝑦 − 𝑦𝑖𝑥 − 𝑥𝑖𝑓𝑡,𝑡+𝑠 (𝑦, 𝑥) =∑ 𝐾𝑦 () 𝐾𝑥 (),
𝑛ℎ𝑦 ℎ𝑥ℎ𝑦ℎ𝑥𝑖=1where 𝑦 and 𝑥 denote relative GDP per capita of each region at time 𝑡 + 𝑠
and 𝑠 respectively, 𝐾𝑦 and 𝐾𝑥 denote kernel functions, and ℎ𝑦 and ℎ𝑥 denotethe smoothing parameters or variable bandwidths of 𝑦 and 𝑥 respectively.
Although there are different kernel functions in the literature, Silverman(1986) and Wand and Jones (1995) show that the kernel estimator is not very
sensitive to any particular functional choice. Given that most papers in thegrowth literature have adopted a bivariate Gaussian form (Andrade et al. 2004;
Epstein et al. 2003; Quah, 1997), this paper also follows this convention.
Thus, the kernel estimator becomes𝑛2

1 𝑦−𝑦𝑖1 𝑥−𝑥𝑖 2
1
1
1
)
− (
− (
)
2 ℎ𝑦
𝑓𝑡,𝑡+𝑠 (𝑦, 𝑥) = ∑ [𝑒𝑒 2 ℎ𝑥 ].
𝑛
√2𝜋ℎ𝑦
√2𝜋ℎ𝑥
𝑖=1

Although the kernel estimator is not very sensitive to a particularkernel function, the choice of bandwidths ℎ𝑦 and ℎ𝑥 has a significant impact
on the density estimates (Henderson & Parmeter, 2015; Li & Racine, 2007).
Finding optimal bandwidths is a challenging exercise since it requires finding
a balance between variance and bias in the estimation. A small bandwidth
reduces the variance at the cost of increasing bias, similarly a large bandwidth
reduces the bias at the cost of increasing the variance. To handle this tradeoff, this paper follows Kar, Jha, and Kateja (2011) and Magrini (1999, 2009)88

HETEROGENEOUS GROWTH AND REGIONAL…|89

in the derivation of optimal bandwidths using a selection algorithm that isconstructed based on the minimization of the asymptotic mean integrated
square error (AMISE)*****.
Finally, the marginal kernel of 𝑥 can be estimated as𝑛

1 𝑥−𝑥𝑖 2
11− ()
𝑓𝑡 (𝑥) = ∑ [𝑒 2 ℎ𝑥 ].
𝑛
√2𝜋ℎ𝑥
𝑖=1

Similar to the bivariate case, a variable bandwidth ℎ𝑥 is adopted. This
selection not only attempts to handle the variance-bias trade-off, but also
should reduce the effects of outliers in the density estimation (Magrini, 2009).
Finally, Equation 1 can also be used to estimate an ergodic (long-run
equilibrium) distribution. As 𝑠 → ∞, the ergodic distribution 𝑓∞ (𝑦) becomes
the solution to the following problem∞

𝑓∞ (𝑦) = ∫ 𝐺 (𝑦|𝑥)𝑓∞ (𝑥)𝑑𝑥 = 𝑓∞ (𝑥).

(3)0This long-run equilibrium distribution plays a central role in theanalysis of regional convergence. At any point of time, the distribution
𝑓𝑡+𝑠 (𝑦) may reflect disequilibrium due to short-run external shocks. In thelong-run, however, the ergodic distribution, 𝑓∞ (𝑦), remains invariant and alltransitionary effects disappear. Moreover, if 𝑓∞ (𝑦) shows a tendency towards
a unique point of mass or mode, then it is indicative of distributional
convergence. On the other hand, if 𝑓∞ (𝑦) shows a divergent tendency
towards bimodality (or multimodality), then it is indicative of polarization (or*****By its composition, the AMISE function incorporates a variance-bias trade-off. Thus, its

minimization is a reasonable criteria for obtaining optimal bandwidths.

89 ECONOMÍA COYUNTURAL
stratification). Furthermore, the existence of clear multiple modes in a longrun equilibrium distribution are also indicative of convergence clubs (Galor,
1996).
Finally, the database for the analysis is from the National Institute of
Statistics of Bolivia (INE)†††††. Real GDP per capita for each department isconstructed using prices of 2014. In an attempt to control for national andregional business cycle effects, potential GDP has been computed using the
Hodrick–Prescott (1997) decomposition. Furthermore, to control for otheraggregate shocks that might affect all departments, relative GDP per capita
for each region is computed as potential GDP per capita divided by thepotential national average‡‡‡‡‡. Finally, to facilitate the interpretation of the
distribution dynamics results, relative GDP per capita is presented in natural𝑙𝑜𝑔 terms. This transformation simply re-scales GDP differences relative tothe national average. As such, given the properties of logarithms, the national
average now takes a vale of zero at each time period.
3. The Facts: Regional Growth and Disparities
Since the late 1990s, Bolivia has experienced rapid economic growth. As
shown in Figure 1, this phenomenon has characterized not only thenationwide average, but almost all its regions.§§§§§ Besides the national average,
Figure 1 also includes three representative regions:****** Tarija, La Paz, andBeni, which are ordered based on their GDP per capita. Although at different†††††The

original database can be downloaded from the following website:
http://www.ine.gob.bo/index.php/producto-interno-bruto-departamental/productointerno-bruto-departamental-5 .
‡‡‡‡‡This average is the weighted national average reported by the National Institute of
Statistics (INE).
§§§§§
The only exception occurs in the region of Pando (See Appendix A) where GDP per
capita increased during the 1990s and then decreased in the 2000s.
******The performance of the remaining regions is shown in the Appendix A.

90

HETEROGENEOUS GROWTH AND REGIONAL…|91

initial levels, all regions show a pattern close to an exponential growth
performance.
Figure 1. Two Growth Regimes: Nationwide Average and Selected
Regions

Source: Author’s calculations using data from the Bolivian National Institute of Statistics(INE).

To focalize the analysis on the growth differences across regions andovert time, Table 1 summarizes the implications of the heterogeneous growth
patterns observed in the data. Considering the two sub-periods pointed by
Caballero-Claure and Caballero-Martínez (2016), the national average growthrate†††††† of the 2000-2014 period has been just above one percent higher than
the growth rate of the 1988-2000 period. Over a decade, however, this small††††††The growth rate is computed as a geometric average of potential GDP per capita ofeach region and the nationwide average.

91 ECONOMÍA COYUNTURAL
difference has had a large effect on the level of GDP per capita. Given the
average growth rate of the most recent period (2.44 percent), GDP per capita
in Bolivia would double in approximately 29 years.‡‡‡‡‡‡ This a much shortertime spam when compared to the 50 years that would be needed given thegrowth rate of the 1988-2000 period. Also, for most of the regions of
Bolivia,§§§§§§ the average growth rate of the 2000-2014 period has been higher
than that of the 1988-2000 period. In short, growth heterogeneity over timeis represented by two clear growth regimes. Also, most regions moved in the
direction of the national average, albeit at different speeds.
Table 1 not only points the growth differences over time, but mostimportantly, it highlights the implications of regional growth differences. For
instance, given the growth rate of the 2000-2014 period, the region of Tarija
would double its GDP per capita in only 10 years. Santa Cruz, on the other
hand, would need 70 years to achieve the same objective. Pando is an extreme
case where the continuation of a negative growth rate would imply halving its
GDP per capita in 46 years.

‡‡‡‡‡‡

This calculation is based on the simple “rule of 70”, which is commonly referred in
the economic growth literature.
§§§§§§The exceptions are the regions of Oruro and Pando.

92

HETEROGENEOUS GROWTH AND REGIONAL…|93

Table 1. Regional Growth Heterogeneity and Years to Double GDP
per capita

Source: Author’s calculations using data from the Bolivian National Institute of Statistics(INE).

Figure 2 compares the growth and income******* differences acrossregions. For comparison purposes, Figure 2 also includes the nationwide
average level of income (labeled as BOLIVIA). Both panels of the figuresuggest that in spite of rapid growth across most of the regions, there are stilllarge income differences among them. In particular, the region of Tarija clearly
diverges from the national average†††††††. By excluding this region from theanalysis, Panel (b) shows more clearly the dynamics of regional income. By
the end of the sample period, income differences among relatively rich regions(Santa Cruz, Oruro, and La Paz) are smaller compared to those of relatively
poor regions (Beni, Potosi, and Pando). This was not the case at the beginning*******Note that in this paper the words GDP and income are used interchangeably.

†††††††This extraordinary performance is largely due the extraction of natural resources, inparticular natural gas.

93 ECONOMÍA COYUNTURAL
of the sample period, when relatively middle-income regions used to have thesmallest income gaps.
Figure 2. Heterogeneous Growth and Regional Income Differences

Source: Author’s calculations using data from the Bolivian National Institute of Statistics(INE).

Figure 3 documents the dynamics of income disparities. For thispurpose, first GDP per capita of each region is expressed in relative termswith respect to the national average. Then, different measures of dispersion
are calculated for each cross-section at each point in time.
For the 1988-2000 period, there is a clear increase in the dispersion ofincome. This finding is robust across different measures of dispersion. The
increasing income dispersion over this period has been reported in theliterature as lack of evidence of sigma convergence in Bolivia (CaballeroClaure & Caballero-Martinez, 2016; Kuscevic-Montero & Rivera-del-Rio,
2013; Sorucco 2012).
For the 2000-2014 period, however, the results are less evident. As
previously shown in Figure 2, the region of Tarija is a clear outlier. And since
typical measures of dispersion such as the standard deviation or the coefficientof variation are very sensitive to outliers, the measurement of dispersion via
94

HETEROGENEOUS GROWTH AND REGIONAL…|95

the interquartile rage seems more suitable in this case. By its construction, theinterquartile rage ignores the influence of extreme outliers. When using thisindicator, the 2000-2014 period shows a reduction in income dispersion
across regions. Consistent with this finding, Panel (b) indicates that once
Tarija is removed from the analysis, all indicators report a reduction in income
dispersion.
Figure 3. Regional Income Disparities over Time

Source: Author’s calculations using data from the Bolivian National Institute of Statistics(INE).

Given the growth heterogeneity across regions and over time, Figure
4 documents the degree of income mobility of the nine regions of Bolivia.
Similar to Figure 3, the income of each region is expressed in relative termswith respect to the national average. Moreover, the natural logarithm is taken
to rescale the distances from the national average‡‡‡‡‡‡‡. The dotted lines
represent the national average in each period. The solid (45-degree) line
represents the notion of lack of mobility relative to the level of income in theinitial period.

‡‡‡‡‡‡‡In this case, the national average takes a value of zero after this transformation.

95 ECONOMÍA COYUNTURAL
Considering the 1998-2000 period, five regions (Tarija, Pando, Oruro,
Cochabamba, and Potosi) moved upward, relative to their initial position.
From this group, the most notable case is Oruro, which used to be below thenational average at the beginning of the period and ended up above thenational average at the end of the period. In contrast, four regions (Santa Cruz,
La Paz, Chuquisaca, and Beni) moved backward. From this group, the largest
backward divergence occurred in Chuquisaca and Beni.§§§§§§§
Considering the 2000-2014 period, four regions moved forward andfive regions moved backward, relative to their initial position. A notable caseis Pando, which used to be above the national average at the beginning of theperiod and ended up below the national average at the end of the period. An
extreme outlier is Tarija, which shows the largest upward mobility in the wholecountry.

§§§§§§§

During this period, the growth rate of Beni and Chuquisaca has been close to zero(see Table 1). Thus, given the positive growth rate of the national average, these regions
experienced a reduction in their relative incomes.

96

HETEROGENEOUS GROWTH AND REGIONAL…|97

Figure 4. Regional Income Mobility

Source: Author’s calculations using data from the Bolivian National Institute of Statistics(INE).

97 ECONOMÍA COYUNTURAL
4. Distribution Dynamics
This section presents the results of the distribution dynamics frameworkdescribed in Section 2. To organize the findings, they are presented in two
parts. First, the estimation of the initial, final, and ergodic distributions
constitutes the first kind of dynamic analysis that help us understand theevolution of the external shape of the income distribution. Second, theestimation of the stochastic kernel is a complementary analysis that help us
understand the intra-distribution dynamics.
4.1. External Shape Dynamics
Panel (a) of Figure 5 shows a clear pattern of divergence for the period 19882000. The mass of density is shifting from the middle to the tails of the
distribution. Moreover, given these historical dynamics, the long-run
equilibrium (ergodic) distribution is even flatter with thicker tails and avanishing middle. As a result, the period 1988-2000 shows a clear pattern of
divergence towards the bottom and the top of the distribution.

98

HETEROGENEOUS GROWTH AND REGIONAL…|99

Figure 5. Initial, Final, and Ergodic Distributions

Source: Author’s calculations using data from the Bolivian National Institute of Statistics(INE).

For the 2000-2014 period, Panels (b) and (c) indicate a much more
complex pattern of (di) convergence. On the one hand, there is a process of
convergence arising from the top of the distribution. On the other, there is aprocess of divergence at the bottom of the distribution. This latter pattern
appears to be robust both to the inclusion (Panel b) and exclusion (Panel c)of the department of Tarija. Given the historical dynamics of the 2000-2014
period, the ergodic (long-run equilibrium) distribution also reflects thesepatterns of convergence from the top and divergence at the bottom. Although
the convergence process seems to be stronger than the divergence process,99 ECONOMÍA COYUNTURAL
the mode of distribution is still below the national average and there is anotoriously thick left tail when Tarija is excluded.
4.2. Intra-distribution Dynamics
Figure 6 and 7 show the intra-distribution dynamics of regional income. Panel(a) in both figures shows that for the 1988-2000 period the stochastic kernel
is mostly located around the 45 degree line. This is a sign of lack ofconvergence. In addition, consistent with Panel (a) of Figure 5, the density at
the center of the distribution is much lower than that of the extremes. Thus,
these internal dynamics suggest the emergence of two predominantconvergence clubs, both located near each tail of the distribution, and anotherless predominant––and vanishing––club located near the center.
Figure 6. Intra-distribution Dynamics: Stochastic Kernel (Surface
plots)

Source: Author’s calculations using data from the Bolivian National Institute of Statistics(INE).

100

HETEROGENEOUS GROWTH AND REGIONAL…|101

As expected, given the differences in growth rates, the intradistribution dynamics of the 2000-2014 period are largely different whencompared to those of the 1988-2000 period. First, when evaluating all regions(see Panel (b) of Figures 6 and 7), the department of Tarija is a clear outlier
that conforms a notoriously separated club. Second, when studying all regions
but Tarija, Panel (c) of Figure 6 indicates that there is a counter clockwise
rotation in the stochastic kernel.******** This rotation is a sign of convergence.
However, given the magnitude of the income differences, Panels (b) and (c)of Figure 7 suggest that all regions but Tarija appear to be moving toward two
broad convergence clubs: a relatively poor club (conformed by Potosi, Beni,and Pando) and a relative rich club (conformed by Chuquisaca, Cochabamba,
La Paz, Oruro, and Santa Cruz).
Figure 7. Intra-distribution Dynamics: Stochastic Kernel (Contour plots)

Source: Author’s calculations using data from the Bolivian National Institute of Statistics(INE).

********Because of the position of the axis, the counter clockwise rotation observed in Figure

6-Panel (c) is equivalent to the clockwise rotation observed in Figure 7-Panel (c).

101 ECONOMÍA COYUNTURAL
5. Concluding Remarks
The analysis of this paper documents the regional growth differences and theevolution of income disparities among the administrative regions(departments) of Bolivia. First, the 1988-2000 period shows a relatively slow
growth in GDP per capita and increasing regional disparities. In contrast, the2000-2014 period shows faster growth and decreasing regional disparities.
Next, through the lens of a distribution dynamics framework, thispaper evaluates the long-run equilibrium and transitional dynamics of thecross-sectional distribution of regional income. The (ergodic) long-run
equilibrium of the 1988-2000 period is characterized by a wider distribution
with noticeable thick tails. Furthermore, the transitional dynamics (stochastic
kernel) analysis highlights the shift of the density mass from the middle to thetails of the distribution. Overall, these dynamics suggest a pattern of
distributional divergence with the formation of two regional clubs at theextremes of the distribution and a vanishing middle.
The period 2000-2014, on the other hand, is characterized by acomplex pattern of (di)convergence: convergence from the top anddivergence at the bottom. Although the convergence process seems to bestronger, the mode of distribution is still below the national average and there
is a notoriously thick left tail. Consistent with this observation, the transitional
dynamics analysis suggests the formation of at least two convergence clubs,
one at the bottom and one just below the national average.
Finally, further research on regional convergence in Bolivia seems
promising in at least three fronts. First, regional analysis at the municipal level
could provide additional insights and statistical precision regarding theestimation of the long-run distribution and the formation of convergence102

HETEROGENEOUS GROWTH AND REGIONAL…|103

clubs. Second, the implementation of the new (panel-time series) convergencetest and clustering algorithm of Phillips and Sul (2007, 2009) could prove tobe highly complementary to the present distribution dynamics framework.
Finally, although there are some studies that suggest that spatial dependence
in Bolivia does not have a statistically significant effect on regional
convergence, those studies still suffer from the informational (and statistical)
limitations that characterize the classical regression approach. Further studies
that integrate

spatial dependence

into thedistribution dynamics

approach†††††††† could still provide a different and richer perspective in the
Bolivian context.
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Appendix A
Figure 8. Two Growth Regimes in Selected Regions

Source: Author’s calculations using data from the Bolivian National Institute of Statistics(INE).

Economía coyuntural, Revista de temas de coyuntura y perspectivas, vol.2, núm. 4. , pp. 81- 108.

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