Munich Personal RePEc Archive

Heterogeneous Growth and Regional(Di)Convergence in Bolivia: A
Distribution Dynamics Approach
Mendez-Guerra, Carlos
Kyushu University

30 August 2017

Online at https://mpra.ub.uni-muenchen.de/81060/
MPRA Paper No. 81060, posted 13 Sep 2017 07:35 UTC

Heterogeneous Growth and Regional(Di)Convergence in Bolivia:
A Distribution Dynamics Approach
Carlos Mendez-Guerra*
Kyushu University
August 30, 2017
Abstract
Bolivia has experienced high economic growth rates in the last decadeand 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 andconvergence patterns of the Bolivian regions over the 1988-2014 period. In
particular, using a distribution dynamics approach, this article evaluates
both the long-run equilibrium and the transition dynamics of the crosssectional distribution of regional GDP per capita. The main results show
a clear pattern of regional divergence for the period 1988-2000. In contrast,
the 2000-2014 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
shape of the distribution and the intra-distribution dynamics suggest thatthe process of regional growth in Bolivia may be characterized by at least
two convergence clubs. Moreover, these clubs are identifiable in periodsof both low and high national growth.

JEL Codes: O40, O47
Keywords: regional growth, convergence, distribution dynamics, Bolivia*

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

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 ofcross-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 point 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 (forinstance, beta or sigma convergence ) and those that evaluate convergence based
1on the shape and dynamics of the entire income distribution .
2

When comparing the pros and cons of these frameworks, most survey
studies point that summary measures such as beta convergence could be largely
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 theother hand, provides valuable information on the behavior of the entire crosssectional income distribution. As it evolves over time, both changes in its external
shape and changes in its intra-distribution dynamics permit the study ofheterogeneous behavior the emergence of multiple convergence clubs (Durlauf& Quah, 1999; Magrini 2004, 2009).
In the Bolivian context, convergence in GDP per capita across regions has
3been mostly studied using classical summary measures. Interestingly, researchfindings appear largely inconclusive given the series of contradictory results thatare reported even for similar time spans and sample compositions. For example,
the work of Evia at al. (1999) reports conditional beta divergence for the 19761992 period. Contrary to these results, Sandoval (2003) reports conditional beta
convergence for the 1980-1992 period. More recently, Sorucco (2012) studies the
1990-2010 period and reports conditional (and absolute) beta divergence.
1

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.
3
Bolivia is conformed by nine administrative regions, also known as departments. In the rest of the paper,
the terms regions and departments are used interchangeably .
2

2

Kuscevic-Montero and Rivera-del-Rio (2013), on the other hand, reportconditional 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 the whole 1990-2011 period is characterized by a lackof conditional convergence, the 2000-2010 sub-period shows some evidence ofconditional convergence.
Given the informational problems of the classical summary measures of
convergence, the seemingly contradictory results found in the Bolivian context,
and the large growth differences across regions and over time, ––a more flexible
4

convergence framework may be worth exploring. Hence the main objective of
this paper is to implement the distribution dynamics approach suggested by
Quah (1993, 1996a, 1996b, 1997). From a methodological standpoint, this is apromising alternative that handles both the informational problems of classicalsummary measures and the heterogeneous growth patterns that characterize thebehavior of the Bolivian regions. This non-parametric framework studies theevolution of the entire distribution of income across regions through theestimation of kernel densities, ergodic (long-run) distributions, and stochastic
kernels.
To achieve this objective, this paper first documents the high degree ofgrowth heterogeneity over time and across regions. For instance, the 1988-2000
period is characterized by relatively slow growth in national GDP per capita (ageometric annual average of 1.41 percent) and increasing regional disparities.
The 2000-2014 period, however, is characterized by faster national growth (ageometric annual average of 2.44 percent) and decreasing regional disparities .
5

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 is characterized
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 the4

See Machicado, Nina, & Jemio (2012) for a detailed survey of the heterogeneous growth patterns thatcharacterize the behavior of the Bolivian regions.
5
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.

3

middle to the tails. Overall, these dynamics suggest a pattern of distributional
divergence with the formation of two regional clubs located near both tails of the
distribution.
In contrast, the 2000-2014 period points to a much more complex patternof (di)convergence. The long-run equilibrium is characterized by both a processof convergence arising from the top and a process of divergence located at thebottom of the distribution. Although the convergence process seems to bestronger than the divergence process, the mode of distribution is still below the6national average and there is a notoriously thick left tail. Consistent with thisobservation, the transition dynamics suggest the formation of at least two
convergence clubs, one near the left tail and another just below the national
average.
Overall, this paper contributes to the regional growth literature in three
ways. From a methodological point of view, it is the first study that implements
a complete distribution dynamics analysis in the Bolivian context . Next, it
7

applies this framework to two different sub-periods with the purpose ofhighlighting the nature of regional convergence patterns under different growth
regimes. Finally, from the point of view of the results, it emphasizes that theprocess of regional convergence is complex and hence classical summary
measures such as beta-convergence or sigma-convergence fail to identify theformation 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

6This is particularly true when the department of Tarija is excluded from the analysis.
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 and ergodic distributions. As
argued by Magrini (2004, 2009), a complete study or distribution dynamics involves estimating kernel
densities, stochastic kernels, and ergodic distributions.
74

by Quah (1993, 1996a, 1996b, 1997) . This non-parametric framework studies the8evolution of the entire distribution of GDP per capita across regions and overtime. The study of transitional dynamics is typically summarized by a stochastic
kernel and the study of long-run (steady-state) equilibrium is summarized by
9

the shape of the ergodic distribution. As a result, the joint study of the evolutionof the shape of the distribution and the intra-distribution dynamics provides
valuable information regarding the persistence of regional inequality,
polarization or stratification patterns, and the formation of convergence clubs.
Let 𝑓𝑓" (𝑥𝑥) denote the initial distribution of relative

10

GDP per capita

across regions at time 𝑡𝑡. Also, let 𝑓𝑓"'( (𝑦𝑦) denote the distribution of relative

GDP per capita at some future time 𝑡𝑡 + 𝑠𝑠. 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 of the
distribution at time 𝑡𝑡 + 𝑠𝑠 is given by a transition probability operator, 𝐺𝐺(⋅), andthe initial distribution at time 𝑡𝑡:
𝑓𝑓"'( (𝑦𝑦)./012 4/("5/67"/80

=

?

@

𝐺𝐺(𝑦𝑦|𝑥𝑥)𝑓𝑓" (𝑥𝑥);510(/"/80 <=>51"85 A0/"/12 4/("5/67"/80

𝑑𝑑𝑥𝑥.

(1)

The transition probability operator 𝐺𝐺(𝑦𝑦|𝑥𝑥) , which is know as thestochastic kernel in the economic growth literature (Durlauf & Quah, 1999; Quah,
1997), maps the transition from time 𝑡𝑡 to time 𝑡𝑡 + 𝑠𝑠 . Among other usefulproperties of this operator, Johnson (2005) shows that?

@

𝐺𝐺 (𝑦𝑦|𝑥𝑥)𝑑𝑑𝑦𝑦 = 1.

Furthermore, this operator is also a conditional density that can be calculated as
𝐺𝐺(𝑦𝑦|𝑥𝑥) =𝑓𝑓","'( (𝑦𝑦, 𝑥𝑥),𝑓𝑓" (𝑥𝑥)(2)

where 𝑓𝑓","'( (𝑦𝑦, 𝑥𝑥) is a joint density, which in turn can be estimated using nonparametric methods.

The general form of the kernel estimator for the joint density is
8

For a more comprehensive presentation of this methodology, see Epstein, Howlett, and Schulze (1999,
2003), Magrini (2004, 2009) and the appendix in Bianco (2016).
9
The stochastic kernel is the continuous-time equivalent of a transition probability matrix.
10
Relative means that GDP per capita of each reagion is normalized by the national average.

5

1𝑓𝑓","'( 𝑦𝑦, 𝑥𝑥 =𝑛𝑛ℎI ℎJ

0
/LM

𝐾𝐾I

𝑦𝑦 − 𝑦𝑦/𝑥𝑥 − 𝑥𝑥/
𝐾𝐾J
,
ℎI
ℎJ

where 𝑦𝑦 and 𝑥𝑥 denote relative GDP per capita of each region at time 𝑡𝑡 + 𝑠𝑠

and 𝑠𝑠 respectively, 𝐾𝐾I and 𝐾𝐾J denote kernel functions, and ℎI and ℎJ

denote the smoothing parameters or variable bandwidths of 𝑦𝑦 and 𝑥𝑥

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
the growth 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 becomes
1𝑓𝑓","'( (𝑦𝑦, 𝑥𝑥) =
𝑛𝑛

0
/LM

1

2𝜋𝜋ℎI

𝑒𝑒

R

M IRIT W
S UV

1

2𝜋𝜋ℎJ

R

M JRJT W
UX
.

𝑒𝑒 S

Although the kernel estimator is not very sensitive to a particular kernel
function, the choice of bandwidths ℎI and ℎJ has a significant impact on thedensity 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 thevariance at the cost of increasing bias, similarly a large bandwidth reduces thebias at the cost of increasing the variance. To handle this trade-off, this paper
follows Kar, Jha, and Kateja (2011) and Magrini (1999, 2009) in the derivation of
optimal bandwidths using a selection algorithm that is constructed based on theminimization of the asymptotic mean integrated square error (AMISE) .
11

Finally, the marginal kernel of 𝑥𝑥 can be estimated as
1𝑓𝑓" (𝑥𝑥) =
𝑛𝑛

0

/LM

1

2𝜋𝜋ℎJ

𝑒𝑒

R

M JRJT W
S UX.

Similar to the bivariate case, a variable bandwidth ℎJ 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 ).

11

By its composition, the AMISE function incorporates a variance-bias trade-off. Thus, its minimization isa reasonable criteria for obtaining optimal bandwidths.

6

Finally, Equation 1 can also be used to estimate an ergodic (long-run
equilibrium) distribution. As 𝑠𝑠 → ∞, the ergodic distribution 𝑓𝑓? (𝑦𝑦) becomes

the solution to the following problem
𝑓𝑓? (𝑦𝑦) =?

@𝐺𝐺 (𝑦𝑦|𝑥𝑥)𝑓𝑓? (𝑥𝑥)𝑑𝑑𝑥𝑥 = 𝑓𝑓? (𝑥𝑥).

(3)This long-run equilibrium distribution plays a central role in the analysisof regional convergence. At any point of time, the distribution 𝑓𝑓"'( (𝑦𝑦) may
reflect disequilibrium due to short-run external shocks. In the long-run, however,

the ergodic distribution, 𝑓𝑓? (𝑦𝑦), remains invariant and all transitionary effects

disappear. Moreover, if 𝑓𝑓? (𝑦𝑦) shows a tendency towards a unique point ofmass or mode, then it is indicative of distributional convergence. On the other
hand, if𝑓𝑓? (𝑦𝑦)shows a divergent tendency towards bimodality (ormultimodality), then it is indicative of polarization (or stratification).
Furthermore, the existence of clear multiple modes in a long-run 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 is
12

constructed 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 foreach region is computed as potential GDP per capita divided by the potential
national average . Finally, to facilitate the interpretation of the distribution
13

dynamics results, relative GDP per capita is presented in natural 𝑙𝑙𝑙𝑙𝑙𝑙 terms.

This transformation simply re-scales GDP differences relative to the national
average. As such, given the properties of logarithms, the national average now
takes a vale of zero at each time period.

12

The original database can be downloaded from the following website:
http://www.ine.gob.bo/index.php/producto-interno-bruto-departamental/producto-interno-brutodepartamental-5 .
13This average is the weighted national average reported by the National Institute of Statistics (INE).

73. The Facts: Regional Growth and Disparities
Since the late 1990s, Bolivia has experienced rapid economic growth. As shownin Figure 1, this phenomenon has characterized not only the nationwide average,
but almost all its regions. Besides the national average, Figure 1 also includes
14

three representative regions: Tarija, La Paz, and Beni, which are ordered based
15on their GDP per capita. Although at different initial levels, all regions show apattern 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 and overt
time, Table 1 summarizes the implications of the heterogeneous growth patterns
observed in the data. Considering the two sub-periods pointed by CaballeroClaure and Caballero-Martínez (2016), the national average growth rate of the
16

14

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.
15
The performance of the remaining regions is shown in the Appendix A.
16
The growth rate is computed as a geometric average of potential GDP per capita of each region and thenationwide average.

8

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 difference has had alarge effect on the level of GDP per capita. Given the average growth rate of themost recent period (2.44 percent), GDP per capita in Bolivia would double inapproximately 29 years. This a much shorter time spam when compared to the17

50 years that would be needed given the growth rate of the 1988-2000 period.
Also, for most of the regions of Bolivia, the average growth rate of the 2000-201418

period has been higher than that of the 1988-2000 period. In short, growthheterogeneity over time is represented by two clear growth regimes. Also, mostregions 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 thecontinuation of a negative growth rate would imply halving its GDP per capita
in 46 years.
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).
17

This calculation is based on the simple “rule of 70”, which is commonly referred in the economic growth
literature.
18
The exceptions are the regions of Oruro and Pando.

9Figure 2 compares the growth and income differences across regions. For
19

comparison purposes, Figure 2 also includes the nationwide average level ofincome (labeled as BOLIVIA). Both panels of the figure suggest that in spite of
rapid growth across most of the regions, there are still large income differencesamong them. In particular, the region of Tarija clearly diverges from the national
average . By excluding this region from the analysis, Panel (b) shows more clearly20

the dynamics of regional income. By the end of the sample period, income
differences among relatively rich regions (Santa Cruz, Oruro, and La Paz) aresmaller compared to those of relatively poor regions (Beni, Potosi, and Pando).
This was not the case at the beginning of the sample period, when relatively
middle-income regions used to have the smallest 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 this purpose,first GDP per capita of each region is expressed in relative terms with respect tothe national average. Then, different measures of dispersion are calculated foreach 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 the literature
as lack of evidence of sigma convergence in Bolivia (Caballero-Claure &19
20

Note that in this paper the words GDP and income are used interchangeably.
This extraordinary performance is largely due the extraction of natural resources, in particular natural gas.

10

Caballero-Martinez, 2016; Kuscevic-Montero & Rivera-del-Rio, 2013; Sorucco2012).
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 theinterquartile 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 acrossregions. Consistent with this finding, Panel (b) indicates that once Tarija isremoved 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 terms with respect
to the national average. Moreover, the natural logarithm is taken to rescale thedistances from the national average . The dotted lines represent the national
21

average in each period. The solid (45-degree) line represents the notion of lack ofmobility relative to the level of income in the initial period.
Considering the 1998-2000 period, five regions (Tarija, Pando, Oruro,
Cochabamba, and Potosi) moved upward, relative to their initial position. From
21

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

11

this group, the most notable case is Oruro, which used to be below the national
average at the beginning of the period and ended up above the national averageat the end of the period. In contrast, four regions (Santa Cruz, La Paz, Chuquisaca,
and Beni) moved backward. From this group, the largest backward divergenceoccurred in Chuquisaca and Beni.

22

Figure 4. Regional Income Mobility

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

22

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.

12

Considering the 2000-2014 period, four regions moved forward and five
regions moved backward, relative to their initial position. A notable case is Pando,
which used to be above the national average at the beginning of the period andended up below the national average at the end of the period. An extreme outlier
is Tarija, which shows the largest upward mobility in the whole country.

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 thefirst kind of dynamic analysis that help us understand the evolution of theexternal shape of the income distribution. Second, the estimation 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 1988-2000.
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 a vanishing middle. As a result,the period 1988-2000 shows a clear pattern of divergence towards the bottom andthe top of the distribution.
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 convergencearising from the top of the distribution. On the other, there is a process ofdivergence at the bottom of the distribution. This latter pattern appears to berobust 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 these patterns of convergencefrom the top and divergence at the bottom. 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 when Tarija is13

excluded.

Figure 5. Initial, Final, and Ergodic Distributions

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

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 of convergence. 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 predominant convergence clubs, both
located near each tail of the distribution, and another less predominant––andvanishing––club located near the center.

14

Figure 6. Intra-distribution Dynamics: Stochastic Kernel (Surface plots)

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

As expected, given the differences in growth rates, the intra-distribution
dynamics of the 2000-2014 period are largely different when compared to thoseof 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
23of 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).

23

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).

15

Figure 7. Intra-distribution Dynamics: Stochastic Kernel (Contour plots)

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

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, the 2000-2014 periodshows faster growth and decreasing regional disparities.
Next, through the lens of a distribution dynamics framework, this paper
evaluates the long-run equilibrium and transitional dynamics of the crosssectional distribution of regional income. The (ergodic) long-run equilibrium of
the 1988-2000 period is characterized by a wider distribution with noticeable16

thick tails. Furthermore, the transitional dynamics (stochastic kernel) analysis
highlights the shift of the density mass from the middle to the tails of the
distribution. Overall, these dynamics suggest a pattern of distributional
divergence with the formation of two regional clubs at the extremes of the
distribution and a vanishing middle.
The period 2000-2014, on the other hand, is characterized by a complex
pattern of (di)convergence: convergence from the top and divergence at thebottom. Although the convergence process seems to be stronger, 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 justbelow 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 convergence clubs.
Second, the implementation of the new (panel-time series) convergence test andclustering algorithm of Phillips and Sul (2007, 2009) could prove to be 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, thosestudies still suffer from the informational (and statistical) limitations thatcharacterize the classical regression approach. Further studies that integrate
spatial dependence into the distribution dynamics approach could still provide
24

a different and richer perspective in the Bolivian context.

24

See Gerolimetto and Magrini (2015, 2016) as innovative references that integrate spatial dependence into
the distribution dynamics approach.

17

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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).

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