Preliminary: Please Cite with Authors’ Permission Only.
Is NAFTA Polarizing México?
or Existe También el Sur?
Spatial Dimensions of Mexico’s Post-Liberalization Growth*
Patricio Aroca
Universidad Católica Del Norte
Antofagasta, Chile
Mariano Bosch
World Bank
William F. Maloney
World Bank
January 2003
Abstract: Standard parametric tests of convergence cannot capture
whether the increased dispersion among state incomes is due to a
steepening gradient between north and south, a few hot states randomly
distributed, or as an intermediate position, the emergence of
convergence clubs. This paper tests for spatial dependency in income
levels and growth rates before and after the trade liberalization of 1985.
Looking at levels of income per capita, we clearly identify a “South,”
but there is no “North” or “Center.” Beyond the frontline states on the
US border, we immediately enter an area as poor as the South and
incomes in the central zone itself are almost randomly distributed
geographically. Growth shows little evidence of spatial dependency in
any period: There is only weak evidence of a South and none of a North.
A strong co-movement of Chiapas and Oaxaca emerged in the 1995-00
period, but it had little historical precedent and whether it will continue
cannot be foreseen.
*
Our thanks to Daniel Lederman, Miguel Messmacher, and Raymond Robertson for helpful discussions. We
also thank Gabriel Victorio Montes Rojas for extraordinarily patient research assistance.
el norte es el que ordena…pero..
con su esperanza dura,
el sur también existe1
Benedetti.
I. Introduction
The 15 years beginning with Mexico’s dramatic unilateral trade liberalization in 1985
and including the North American Free Trade Agreement (NAFTA) have seen increasing
divergence of per capita incomes among Mexican states. Measures of sigma convergence
show a decrease in dispersion from 1970 to 1985, and then a sharp reversion to above
previous levels of inequality after 1989. A growing number of studies using traditional beta
convergence analysis,2 find at minimum a slowdown of convergence, and most divergence
(Juan-Ramon and Rivera Batiz 1996, Esquivel 1999, Messmacher 2000, Cermeño 2001,
Esquivel and Messmacher 2002, Chiquiar 2002). These findings raise the concern that trade
liberalization will lead to the polarization of the Mexican economy: the northern states may
industrialize and become increasingly integrated with the US, while the southern states will
remain “south” in Benedetti’s sense of “backward,” dependent, and forgotten. As evidence
in this direction, Hanson (1997) finds that after liberalization wages, which once decreased
with the distance from the national capital in the center, now decrease with the distance from
the border.
But a steeper North-South gradient where growth dynamism at its greatest near the
border is only one possibility scenario consistent with observed income divergence. A few
relatively high flying states could drive up inequality with no geographical pattern or as an
intermediate position, we may find multiple “convergence clubs” of states sharing spillovers
and common income levels and growth rates with little obvious geographical relationship
with the US.
This paper employs recent advances in spatial analysis to ask whether it makes any
sense to talk about a “north” or “south” or whether in fact the patterns of dynamism in
Mexico are geographically independent. Sigma, and Beta convergence approaches offer
point estimates of the central tendency of the data toward convergence or divergence.
1
Roughly translated from Benedetti’s famous poem, “The north rules and orders, but with a resilient hardbitten
hope, the south also exists (endures)”
2
See Barro and Sala-i-Martin, 1995
1
However, as Quah (1993) notes, they obscure vast amounts of information on the dynamics
of relative income movements among states and do not shed light on the spatial dimensions
of growth. A substantial literature has followed his lead in constructing Markov transition
matrices which tabulate the probabilities of moving among a finite number of intervals of the
national income distribution and hence characterize the dynamic patterns of relative income
movements.3 Employing these techniques for Mexico, Garcia-Verdu (2002) again finds little
evidence of convergence in the post 1985 period.
One advantage of these transition matrices is that they can be conditioned on state
characteristics, including geographical location, to permit inference about spatial patterns of
income dynamics. However, as Bulli (2001) notes, there are problems associated with the
naïve discretization of the income distribution. Quah (1997) proposes letting the number go
to infinity and conducting inference from kernel density plots.4 We begin by constructing
these for Mexico before and after the period of trade liberalization. We then condition them
on spatial characteristics to offer a view of the geographical dimensions of Mexico’s growth
process and more particularly, the “shape” of the divergence process. We are interested in
knowing if there is evidence of “spatial correlation” or “dependence” where either income
levels or growth rates are correlated by geographical location.
To further investigate the patterns of spatial dependency and to assess whether, in
fact, the observed changes in the kernels are statistically significant,
we employ tests
introduced for analyzing finite Markov transition matrices, and introduce parametric
measures of spatial dependence common in the spatial statistics literature but only recently
applied to the study of economic growth.
II. Data
The Mexican National Institute of Statistics, Geography and Information (INEGI)
tabulates official income data for Mexican 32 states GDP for 1970,1975,1980,1985,1988,
and then annually for the period 1993-2000. We follow Esquivel (1999), in making several
corrections to this data. First, most oil is pumped from the states of Tabasco and Campeche,
but the attribution of oil revenues has changed without obvious cause over time. Though the
3
4
See, for example, Fingleton, 1999; Rey, 2001; Lopez-Bazo et al, 1999; Puga, 1999
For the methodology behind estimating these kernels, readers are referred to the original paper (Quah 1997).
2
revenues are in fact allocated to all states via a federal sharing formula, in some years they
were entirely attributed to Tabasco, and in others to Campeche. We tried to correct for this,
excluding the oil production as captured in the mineral production category of the state
accounts, but still found the resulting growth series to be too erratic and exaggerated to be
credible. We attribute this behavior to unresolved petroleum accounting issues since the
remaining 30 non oil producing states behave more reasonably.5 Though dropping these
states clearly implies losing some of the spatial story, we find it preferable than
contaminating the analysis with clearly unreliable series.
Following Esquivel (1999) we also corrected populations figures for Chiapas and
Oaxaca for years 1975, 1980, 1985, 1988 as the 1980 census, when compared to other
household census appears to have understated the state’s population induced distortions in
the GDP per capita.6.
Finally we have merged the state of Mexico with Mexico DF (Federal District), the
capital. The rationale for this aggregation stems from the fact that there exist strong labor
market linkages between these two states which may lead to an overstatement of the capital
city’s per capita growth rates. Due to the exorbitant housing prices in DF, it has become
common to live in the state of Mexico and commute to the District.7 This has led to reported
population in the Mexico DF has remaining stable over the last 20 years while the population
in the state of Mexico doubled. We run the analysis both with and without this aggregation
(results available on request) and, while the fundamental story does not change, the more
moderate growth behavior of the aggregated capital city we find more plausible and we
report those results.
In sum, we have 29 states measured at 5 year intervals with 3 observations before the
unilateral trade liberalization of 1985 and 3 after8. Table 1 and figures 1,2a and 2b present
5
In fact, the state of Chiapas also produces some very modest amounts of oil and we subtracted this off from
the state product series in 1975 and 1980.
6
Population figures for years 1975, 1980, 1985, 1988 for Chiapas and Oaxaca were extrapolated using yearly
population growth rates between 1970 and 1990. According to official figures, the mining production over GDP
for Chiapas went from 7.5% in 1970 to 18% in 1975 up to 45% in 1980 and back to 7% in 1985. Clearly, years
1975 and 1980 saw arbitrary assignments of oil production to Chiapas. We have corrected for this as to allow
the ratio mining production over GDP to be 7.5% for the outlier years .
7
We would like to thank Miguel Messmacher for this suggestion.
8
When estimating the stochastic kernels and the transition matrices the years 1970, 1975, 1980, 1985, 1988,
1993 and 1998 were used. We tried to keep the 5 year period interval and at the same time avoid the 1995 crisis
which would have distorted our results.
3
that data and suggest that in the year 2000 regional differences in Mexico were vast. The
GDP per capita of the poorest state, Oaxaca in the South was only 23% of the richest, Nuevo
Leon in the North. The southern states overall enjoy less than half of the GDP per capita than
their northern counterparts.
III. Non-Parametric Measures: Transition Matrices Kernel Density Plots
Simple plots of the distribution of income levels and growth rates (available on
request) confirm Juan Ramon and Rivera-Batiz (1996) findings of a concentration in the
period 1970-80 consistent with parametric convergence tests findings. However, from 1985
onwards a prominent right tail appears in both levels and growth rates suggesting that a
group of states have detached from the others. Such snap shots of the distribution can be
informative, but they hide important information, and in particular, how we get from one
snapshot to another. We can ask, for example, whether the outliers in the extreme right tails
in plots of the growth distribution are the same states who persistently show higher growth,
or whether over the longer term, the distribution is broadly symmetric with random states
sometimes experiencing extraordinary growth.
Figures 3a and 3b plot the stochastic kernel as well as its contour plots for levels of
per capita income for the 1970-85 and 1985-1998 periods respectively. Both plot present
state income relative to the country (“country-relative”) in time t on the Y axis and in time
t+5 on the X axis. The exact scale is used in both the pre and post-liberalization periods to
facilitate inference about changes in the variance of the kernels. The cross-hairs depict the
country average in period t and in t+5. A couple points merit highlighting.
First, if there were no movement at all among states, figures 3a and 3b would consist
of a plane along the 45 degrees line shown. The fact that states do shift relative position
gives the kernel its volume. Slicing the volume parallel to the X axis reveals the distribution
of states at each initial income five years later. Again, the advantage over the simple
distribution plots is precisely that we can see changes of position that might be hidden by
identical “snap shot” distributions. Slicing parallel to the XY plane generates contour plots
that show the relative probabilities of finding combinations of initial and final incomes.
4
Second, significant convergence would result in a rotation of the kernel toward the Y
axis. States with lower incomes in t would have higher relative incomes in t+5 and vice
versa. Divergence would lead to the reverse. For broad illustrative purposes, we introduce a
state label at the position corresponding to the average value for each state. This reference is
only approximate since the kernel is estimated three time points for the each state, but given
the revealed persistence in relative income levels, they are informative.
In fact, the most salient feature of both figures is the high persistence in the
distribution. The probability mass is mainly concentrated in the diagonal of the plot showing
that states did not significantly change their relative position. States located above the 45
degree line saw a worsening of its relative position over time and those below, an
improvement.
Though the persistency is clear, striking differences emerge between the pre and post
85 kernels. First, the single peaked kernel in figure 3a has become a double or even triple
peaked kernel suggesting the formation of convergence clubs over the post 85 period. Several
forces are at play driving this evolution. First, the bottom end of the distribution has become
more compressed around 0.70 of the NAI (National Average Income) suggesting
convergence toward the mean of the very poorest states. Second, above average states
converged towards 1.3 of the NAI depopulating the center of the distribution. Finally, the
states of Mexico, Nuevo Leon and Quintana Roo grew in income enough to have formed the
last peak of the distribution with incomes above 1.7 NAI.
Global Spatial Association and Spatial Clustering.
Quah identified a similar “twin peaks” phenomenon in the Kernel derived from a
international cross section of per capital incomes and found it to be geographically drivenregional clusters of poor countries were getting poorer, the agglomerations of rich countries
were getting richer. To use the kernel density plots to see if the same geographical patterns
are emerging in Mexico, instead of generating it as the probability distribution of income in
t, t+5, we replace t+5 with the income of the state relative to the average income of its
contiguous neighbors (“neighbor-relative”) in t. If the local and economy wide distributions
5
of income are similar, that is, there are no clusters of states with similar incomes, we would
find a concentration of probabilities along the main diagonal. If, on the other hand, poor
states are found with poor states and rich with rich, we should expect a rotation toward a
vertical line at unity- a country relative poor state will have the same income as its
neighborhood.
Figures 4a and 4b plot the spatially conditioned kernal density plots. Several points
merit attention. First, geography is not destiny in Mexico the way it appears to be globally.
Most of the probability mass is off the vertical line at 1 on the X axis and is in fact broadly
aligned along the 45 degree line. We do not find Quah’s dramatic convergence clubs of rich
and poor states. Prior to 1985 there is some rotation and compression of the upper mass that
suggests that, particularly among northern states of Baja California Norte, Baja California
Sur, Chihuahua and Tamaulipas there is a nascent convergence club in incomes. Poor
southern states are also found to be better off relative to their neighbors than they are relative
to the country. For example, Chiapas’ income is around 50% of the NAI but it is as rich as
its neighbors (neighbor relative income is roughly unity).
But there is also a group of states (for example Zacatecas, Tlaxacala, Michoacan,
Nuevo Leon) whose mass lies largely on the 45 degree line suggesting no spatial
dependency. This pattern is exacerbated after 1985 where we can observe some rotation
towards the 45 degree line indicating a reduced relationship between states and their
neighborhood incomes. Had the clusters been totally determined by space the three observed
peaks would have been aligned along the vertical line at unity on the X axis. However,
figure 4b is fairly similar to the multiple peaked unconditional kernel of figure 3b. A more
detailed inspection shows the lower end peak is formed by a mass of southern and central
states, only Veracruz, Chiapas and in lesser degree Oaxaca have neighborhood relative
incomes close to unity. The intermediate peak, mainly consists of the northern states of Baja
California Norte, Baja California Sur, Coahila and some successful central states such as
Queretaro. There is some evidence of convergence among the northwest US border states ,
due to the catching up of Chihuahua and the poor performance of Baja California Norte.
However, as the northern converge club strengthened, the second line of states did not follow
thereby reducing spatial correlation and driving the rotation of the kernel towards the 45
6
degree line. Finally the third peak could not be more spatially independent as it is formed by
Nuevo Leon, Mexico and Quintana Roo. One state from each extreme of the country.
Growth
Figures 5a-b present an exactly analogous set of exercises replacing levels of income
with growth (see annex for definitions)9. Here, alignment along the axis suggests persistence
in growth rates: a fast growing state today will be fast tomorrow. Two things emerge
strikingly from the pre and post 1985 kernels. The mass of probabilities seems to occupy the
four quadrants equally more or less equally: A state that grows fast today is as likely to grow
slow tomorrow as to grow fast again. This is not so surprising when we remember that in the
pre liberalization period many of the northern states had alternating high and low growth
rates due to the 1982 debt crisis which hit the most dynamic states hardest. The distribution
shows greater variance in the post liberalization period, but still does not show strong
persistence in growth rates. Where extreme values can be found in the northwest quadrant
the orientation of the central mass appears to have rotated more to be more parallel to the Y
axis than before.
Conditioning on neighborhood (figures 6a-b) suggests little in the way of growth
convergence clusters. The central mass is fairly tightly aligned along the 45 degree reference
in the pre 85 period. In the post- 85 period, the variance again seems to have tightened some,
but there is no sign of rotation.
IV. Parametric Measures of Spatial Dependence
This section builds on the previous kernel analysis in two ways. First, although there
are as yet no methods for testing whether two kernels differ between two time period, we
offer a first approximation by employing tools recently developed for analyzing their
underlying Markov process for the case of a finite number of intervals. Second, we go into
further detail on the few suggested patterns of spatial dependence by employing techniques
common in the spatial statistics literature but only recently applied to the study of economic
growth (references).
9
In this case we did not referenced the states generating the mass of probabilities as the growth rates did not
show any persistency over time so the period averages would me meaningless.
7
Testing for structural break in income dynamics
To test for whether the stochastic kernels for the pre and the post liberalization period
are, in fact, statistically significant, we generate standard double entry transition matrices.
The income distribution has been divided in 5 different intervals relative to the mean for the
entire time span and the pre and post liberalisation period. Each i,j entry of the matrix
represents the probability of transiting from income state i to income state j in a five year
period time10. Following Quah we discritize the income distribution in quintiles.
Similar to its graphical counterparts the transition matrices show a high degree of
persistence as suggested by the high probabilities of remaining in the same interval tabulated
along the main diagonal of the matrix. For instance, the probability of a state in interval 1
being found in that same interval in five years was 80% prior to 1985 and 93% after 1985.
This is preliminary evidence that, in fact, the transition matrices do differ between the two
periods in ways supportive of the beta convergence findings of increased dispersion after
1985. States in quintile one and two were able to move upwards in the distribution with
probability 7% and 5% respectively in the post 1985 period against 20% and 29% in the
previous time span suggesting that the increased dispersion was caused by a stagnation of the
poorer states. Following Bickenback and Boden (2001), we construct chi square statistics
tests for structural break in the matrix, both at the individual interval level and for the
matrices as a whole.
The test for our two sub-samples is based on a Q statistic
Qi =
∑n
j∈Bi
( pˆ i j (1970−85) − pˆ ij (1985−98) ) 2
i
pˆ ij (1985−98)
~ χ 2 ( Bi − 1)
Bi = { j : pˆ ij (1985−98) > 0}
10
The asymtotically imbiased and normally distributed Maximun likelihood estimator of
pij is determined by
pˆ ij = nij / ∑ j nij , where nij is the number of transitions from income class i to income class j over a period
of time.
8
Where p̂i j is the probability for a state to transit from income interval i to income interval j
For the whole matrix, the test is simply
Q = ∑ Qi
i
The Q statistics, suggest that the matrices are statistically different from each other, at the 1%
level and the main source of dissimilarity as noted before can be found in the poor income
intervals states (table 2). Prior to 1985, poor states had greater chances to move upwards in
the income distribution generating the usual finding of convergence over this period of time.
This is hinted in the kernels by the fact that the poor states are clearly below the 45 degree in
the pre-liberalization period (2a) and on or above it in the post liberalization period (2b).
Parametric measures of spatial association
The spatial econometrics literature offers several techniques heretofore little used in
the growth literature to more closely examine the dynamics suggested in the kernel density
plots.
The first measure of spatial dependence is Moran’s I statistic (the Global Moran)
which is the spatial analogue to the Durbin Watson statistic in time series (see Anselin 1988
and 1995). This is calculated for each period t as
n
It =
n
∑∑ w z z
n
S
i =1 j =1
n
ij i
∑z
i =1
j
, ∀ all t = 1,2,..., T
2
i
where n is the number of states; wij are the elements of a binary contiguity matrix W11(nxn),
taking the value 1 if states i and j share a common border and 0 if they do not; S is the sum of
all the elements of W; and zi and zj are normalized12 vectors of the log of per capita GDP of
states i and j respectively. Positive (clustering of similar values) spatial dependence, whereas
negative spatial correlation (clustering of different values). Statistical significance can be
11
Distance based matrices have been also employed giving similar results to the above presented.
The zi = ln(GDPit /GDPt) denotes the logarithm of the Gross Domestic Product per capita of region i in period
t, (GDPit), normalized by the sample mean of the same variable, GDPt (De la Fuente, 1997).
12
9
tested comparing the Moran’s I statistic with its theoretical mean and using a normal
approximation.
Figures 7a and b plot Moran’s I normal standardized values for the period 1970-2000
for both levels and growth rates, as well as the standard deviation of the GDP per capita for
the same period as a measure of sigma convergence. What is immediately clear is that,
viewing Mexico as a whole, spatial dependence in income levels has increased along with the
sigma divergence after a period when both had fallen. The correlation between both variables
is 0.85. By the year 2000 the global measure of spatial concentration is similar to the 70’s
levels. In levels, the relatively subtle indications of spatial dependence suggested in the
Kernels emerge as statistically significant in the Moran test.
However, in growth rates, only the period 1970-80 saw any traces of spatial
association. It is no longer the case that fast growing states are found next to fast, and slow
next to slow. In growth terms, there has been a despatialization of Mexico, far predating the
mid-1980s reforms that arguably has not been significantly reversed. The insignificance of
the Moran in growth rates is consistent with the very diffuse patterns observed in the kernels
for both periods.
The global Moran may, however, conceal patterns of comovement in particular
growth poles or convergence clubs. These can be more easily detected by the “Local” Moran
which calculates the Moran between an individual state and its spatial lag- the states which
share a common border:
Ii =
z i ∑ wij z j
j
∑z
2
i
/n
The local Moran can be interpreted as an indicator of spatial clustering, either of positive
correlation or negative where the null hypothesis is no spatial dependence. Local clusters are
identified where the statistic is significantly different from zero. Since the distribution of the
statistic is usually unknown, Anselin (1995) suggests a Montecarlo-style method to generate
it, consisting of the conditional randomization of the vector zj.13 That is, Moran statistics are
calculated between state i and a large number of hypothetical “neighborhoods” constructed as
13
It is conditional in the sense that zi remains fixed. The reasoning behind the randomization procedure lies in
the need to assess the statistical significance of the linkage of one region to its neighbors.
10
random permutations of states drawn from the entire sample. Then, the true neighborhood
Moran is compared against this distribution.
We present the local Moran statistics in several different ways. First, the maps in
figures 8a and 8b show the geographical distribution of significant local Moran’s for both the
10% and 5% levels for the years 1970 and 2000, the endpoints of our sample. Second, the
Moran scatterplots accompanying the maps graph the level of income of the state against that
of its spatial lag for the same period as a way of showing global spatial correlation. Clearly,
a significant positive slope suggests that rich states are found among rich (quadrant 1) and
poor among poor (quadrant 3). Quadrants 2 and 4 represent cases where rich states are found
among poor, or poor among rich respectively.
In fact this is a less efficient and
comprehensive way of presenting the information in the kernels but one which allows a
clearer view of the relative position of the states. Finally, table 3 shows significance levels
and signs of the Moran statistics at 5 year intervals across the sample to offer greater detail
across time than is possible with the graphs.
The data suggest that spatial dependency in levels is not new. Even in 1970, there
was a cluster of poor states around Oaxaca, Guerrero, Puebla, Chiapas and Guerrero
corresponding to the traditional “Southern States” that appears strongly in the maps and in
quadrant 3 of the scatter plots and table 3 suggests that this relationship has been getting
stronger across time.
Baja California Norte and Baja California Sur, and Sonora appear in the quadrant 1 as
well-off states in better-off neighborhoods, and hence might be seen as a well-off
convergence cluster located in the north of the country along the US border. However, these
correlations seem to slowly disappear by the beginning of the 1990’s and the North, as a
spatial construct, vanishes. This is partly due to the fact that, as the figures 2a and 2b
suggest, the frontline states are better off, but the next tier- Durango, Sinaloa, Zacatecas and
San Luis Potosi are poor and this gap has been getting larger thereby diluting the spatial
correlation. The higher income of the frontline states has not spilled over much to the next
line. This pattern we noted from the kernel in figure 4b where the rotation towards the 45
degree line indicates this widening gap between the north and the second line of states.
Nor in the center do we find much in the way of convergence clusters. Most of the
Central states are located in quadrants 2 and 4 almost suggesting a downward sloping line (if
11
we abstract from the outliers) suggesting a tendency that rich states are found among poor
and vice versa. The greater variance in income per capita of this region (see table 1) does not
translated into spatial dependency: poor states such as Zacatecas, Michoacan, Hidalgo,
Nayarit and rich states such as Mexico, Aguascalientes and Queretano share the same
neighborhood. Consequently, we do not find any significant Moran statistics in this area for
any of the periods, with the exception on the negative values associated with Jalisco and
Mexico/DF indicating that this two states are well-off states surrounded by poor neighbors.
At this point these results suggest that the Mexico/DF agglomeration has not pulled along its
neighbors. In sum, the South exists, but there is no longer a North and there never was a
Center.
Growth appears even less spatially dependent in figure 9a and b, consistent with our
previous findings in the kernels. When we study long periods of growth using the entire pre
and post liberalization samples, only two clusters emerge. In the early period, we find
positive co movements among Baja California Norte, Baja California Sur, and Sonora with
their neighbors in the quadrant 3 of low growth states among low growth states. Chiapas
Oaxaca and Veracruz replicate this behavior in the post trade liberalization period .
Additionally, the Mexico/DF aggregation significantly under performs in the early period in
a time when its neighborhood was doing much better. These findings are consistent with the
income convergence observed before liberalization and the divergence after.
Looking more finely with five year periods, no significant patterns seem to survive
over time. Hidalgo and San Luis de Potosi constitute a high growth cluster by the end of the
70’s and a similar pattern emerges with the two states in the Yucatan peninsula in the 70’s.
Morelos showed local spatial instability and early 90’s respectively. Finally, Puebla
outperforms its neighbors southern states in the late 90’s.
Table 3 also suggests that the low growth cluster found in the north for the overall
period 70-85 may be due to a common vulnerability of the more industrial states to the oil
crisis and the US recession. Analogously, the southern cluster of low growth result appears
to be driven by the strongly significant Moran statistics found in both Chiapas and Oaxaca in
95-00. In both cases the related states grew below average for the country. That said, there
is not a consistent pattern of association of Chiapas with its neighbors and it is probably
premature to assert that, in growth terms, there is a South and there is pretty clearly no North.
12
Its also notable that the Mexico/DF aggregation never positively commoves with its
neighbors, nor do such higher performance middle states such as Queretaro, Jalisco or
Guanajuato.
V. Conclusions.
This paper employs several recent techniques from the spatial statistics literature to
investigate the geographical dimensions state income divergence in Mexico. The Moran
statistics and the kernel density plots tell us a consistent story: there is no gentle growth
driving gradient sloping down from the US and losing steam just before Chiapas. In levels,
the South exists, but there is no longer a North and there never was a Center.
This
conclusion, again, must be tempered by the finding that if we define the northern
neighborhood to only include the border states, we do find stronger evidence of a
convergence cluster. But the discrete income cliff after the front line after which a virtually
random pattern emerges interrupted only by the group of 3 or 4 Southern states suggests that
proximity to the North is not the exclusive or even overriding determinant of high income
levels. This is also supported by the findings that growth appears to be essentially randomly
distributed with the exception of a potential (low) growth cluster among Chiapas, Veracruz
and Oaxaca that is not shared with other states far from the border. These states are being
left behind, but exclusion from the benefits of NAFTA due the lack of proximity to the US
does not seem to be the cause.
13
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Puga, D. 1999. “The Rise and Fall of Regional Inequalities.” European Economic Review 43
(2): 303-334
Quah, D. T. 1993, ''Empirical cross-section dynamics in economic growth.” European
Economic Review 37; 427-443.
Quah, D. T. 1997 ''Empirics for growth and distribution: Stratification, polarization and
convergence clubs''. Journal of Economic Growth 2(1): 27-59.
Rey, S. J. 2001. “Spatial Empirics for Economic Growth and Convergence”, Geographical
Analysis 33(3): 195-214.
14
Annex I: Conditioning of Kernels.
Definitions:
yit the income per capita of state i in year t,
yt the national average income per capita in year t,
ywt th average income per capita of the spatial lag in year t.
Figures 9 a:
Kernels generated using three growth spans of 5 years each before and after 1985:
 yit + s
y
 t+s y
it


y
t



 − 1 conditioned to



 yit

 y

 t y  −1
it − s 



y
t −s 

 yit

 y

 t y  − 1 conditioned to
it − s 


yt − s 

 yit

 y

 wt y  − 1
it − s 


ywt − s 

Figures 9b:
15
Table 1. Mexican 2000 GDP per capita by state, constant pesos 1993
State
Baja California
BC
CO
Coahuila
CU
Chihuahua
Nuevo León
NL
SO
Sonora
Tamaulipas
TA
BCs Baja California Sur
DU
Durango
San Luis Potosí
SL
SI
Sinaloa
ZA
Zacatecas
AG
Aguascalientes
CL
Colima
GU
Guanajuato
Hidalgo
HI
JA
Jalisco
Mexico and DF
MX
MI
Michoacán
Morelos
MO
NA
Nayarit
Querétaro
QU
CH
Chiapas
GE
Guerrero
OA
Oaxaca
Puebla
PU
TL
Tlaxcala
Veracruz
VC
QI
YU
Quintana Roo
Yucatán
CA
DF
MX
TB
Campeche
Distrito Federal
México
Tabasco
Total Nacional
Region
North
Central-North
Central
South
Yucatan
Peninsula
Not in the
sample
Population GDP millions
(Thousands
of pesos
GDP per
capita
2,487
2,298
3,053
3,834
2,217
2,753
424
1,449
2,299
2,537
1,354
944
543
4,663
2,236
6,322
21,702
3,986
1,555
920
1,404
3,921
3,080
3,439
5,077
963
6,909
48,157
45,976
66,009
101,689
40,458
44,793
7,906
18,001
25,505
30,074
11,314
16,958
8,244
48,373
21,013
94,653
493,328
34,921
20,733
8,255
25,401
25,070
24,149
21,797
50,601
7,994
60,767
19,361
20,006
21,622
26,522
18,249
16,269
18,644
12,426
11,092
11,855
8,358
17,959
15,193
10,374
9,400
14,972
22,732
8,762
13,331
8,971
18,088
6,394
7,842
6,339
9,967
8,304
8,795
875
1,658
19,555
19,807
22,350
11,945
15,924
334,770
158,558
17,301
1,441,500
23,056
38,903
12,107
9,145
14,787
691
8,605
13,097
1,892
97,483
GDP per
Standard
capita by
Deviation/
region
Mean
20,855
0.17
11,510
0.30
17,434
0.34
8,140
0.18
15,539
0.43
14,787
0.40
16
Figure 1: Mexican Regional Map
Baja California Norte
Sonora
Chihuahua
Coahuila De Zaragoza
Nuevo Leon
Tamaulipas
Zacatecas
Aguascalientes
Durango
San Luis Potosi
Sinaloa
Baja California Sur
Guanajuato
Nayarit
Hidalgo
Jalisco
Tlaxcala
Colima
N
W
S
Puebla
Queretaro de Arteaga
Michoacan de Ocampo
Mexico
Distrito Federal
E
Morelos
Guerrero
700
Yucatan
Veracruz-Llave
Oaxaca
0
Quintana Roo
Chiapas
700
Figure 2a: Mexican states relative GDP per capita: 1970
1400 Miles
Figure 2b: Mexican states relative GDP per capita: 2000
N
W
E
S
N
W
E
S
Mx30b.shp
0.427
0.609
0.802
1.051
1.354
Mx30b.shp
0.352 - 0.584
0.584 - 0.715
0.715 - 0.856
0.856 - 1.201
1.201 - 1.924
600
600
0
600
- 0.609
- 0.802
- 1.051
- 1.354
- 2.494
0
600
1200 Mile s
1200 Miles
17
Figure 3a: Kernel Density Plots, Levels, Unconditioned:1970-1985
2.5
2
Country relative, period t
NL
MX
BC
BCs
1.5
SOCO
QI
T AJA
CU
CL
SI QU
MO
AG
VC
YU
NA
GU DU
PU
HI
MISL
GE T L
ZC
CH
1
0.5
0
OA
0
0.5
1
1.5
2
2.5
Country relative, period t+5
Figure 3b: Kernel Density Plots, Levels, Unconditioned:1985-1998)
2.5
Country relative, period t
2
NL
MX QI
1.5
1
CH
OA
0.5
0
0
0.5
CLQU
JA
TA
MO AG
SI
DU
SL
YU
NA
VC
HI
GU
TLPU
ZC
GE
MI
1
BC
BCs
SO CO
CU
1.5
2
2.5
Country relative, period t+5
18
Figure 4a: Kernel Density Plots, Levels, Conditional on Spatial Lag (Neighbors):1970-1985
3
2.5
2
NL
Country relative
MX
BC
BCs
SO
1.5
TA
CU CL
QU
SI MOAG
NA
VC
YU DU
GU
SL HI PU
TL GE
MI
CH
ZC
OA
1
0.5
0
0
0.5
1
CO
QI
JA
1.5
Neighbor relative
2
2.5
3
Figure 4b: Kernel Density Plots, Levels, Conditional on Spatial Lag (Neighbors):1985-1998
3
Country relative
2.5
2
NL
QI
1.5
MX
BC CO
BCs
SOCU
QU
CL
TA
AG JA
MO
SI DU
NA
YU
SL
HI GU VC
ZC TL PU
MI GE
CH
OA
1
0.5
0
0
0.5
1
1.5
2
2.5
3
Neighbor relative
19
Figure 5a: Kernel Density Plots, Growth, Unconditioned: 1970-1985
0.1
0.08
Country relative, period t
0.06
0.04
0.02
0
-0.02
-0.04
-0.06
-0.08
-0.1
-0.1
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
0.1
Country relative, period t+5
Figure 5b: Kernel Density Plots, Growth, Unconditioned: 1985-1998
0.1
0.08
Country relative, period t
0.06
0.04
0.02
0
-0.02
-0.04
-0.06
-0.08
-0.1
-0.1
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
0.1
Country relative, period t+5
20
Figure 6a: Kernel Density Plots, Growth, Conditional on Spatial Lag (Neighbors):1970-1985
0.1
0.08
0.06
Country relative
0.04
0.02
0
-0.02
-0.04
-0.06
-0.08
-0.1
-0.1
-0.08
-0.06 -0.04 -0.02
0
0.02
Neighbor relative
0.04
0.06
0.08
0.1
Figure 6b: Kernel Density Plots, Growth, Conditional on Spatial Lag (Neighbors):1985-1998
0.1
0.08
0.06
Country relative
0.04
0.02
0
-0.02
-0.04
-0.06
-0.08
-0.1
-0.1
-0.08
-0.06 -0.04
-0.02
0
0.02
Neighbor relative
0.04
0.06
0.08
0.1
21
Table 2. Transition Matrices 1970-1998
Transition Matrix 1970-1998
Number
1
2
35
1 0.86
0.14
35
2 0.17
0.69
35
3 0.00
0.14
35
4 0.00
0.00
34
5 0.00
0.00
3
0.00
0.14
0.77
0.03
0.00
4
0.00
0.00
0.09
0.80
0.18
5
0.00
0.00
0.00
0.17
0.82
Transition Matrix 1970-1985
1
20
1 0.80
14
2 0.07
21
3 0.00
13
4 0.00
19
5 0.00
2
0.20
0.64
0.14
0.00
0.00
3
0.00
0.29
0.76
0.00
0.00
4
0.00
0.00
0.10
0.92
0.21
5
0.00
0.00
0.00
0.08
0.79
Transtion Matrix 1985-1998
1
15
1 0.93
21
2 0.24
14
3 0.00
22
4 0.00
15
5 0.00
2
0.07
0.71
0.14
0.00
0.00
3
0.00
0.05
0.79
0.05
0.00
4
0.00
0.00
0.07
0.73
0.13
5
0.00
0.00
0.00
0.23
0.87
d.f Q-statistic P-value
Ho:
pˆ i j (1985−98) = pˆ i j (1970−85) | i = 1
1
5.71
0.02
Ho:
pˆ i j (1985−98) = pˆ i j (1970−85) | i = 2
2
18.40
0.00
ˆ i j (1985−98) = pˆ i j (1970 −85) | i = 3
Ho: p
2
0.18
0.91
Ho:
pˆ i j (1985−98) = pˆ i j (1970−85) | i = 4
2
2.57
0.28
Ho:
pˆ i j (1985−98) = pˆ i j (1970 −85) | i = 5
1
0.98
0.32
Ho:
pˆ i j (1985−98) = pˆ i j (1970−85) ∀i
8
27.85
0.00
22
Figure 7a: Global Moran’s I (levels) and Standard deviation 1970-2000
2.8
0.45
2.6
0.4
2.4
0.35
2.2
0.3
2
0.25
1.8
0.2
1.6
0.15
1.4
0.1
1.2
0.05
1
1970
0
1975
1980
Moran's I
1985
1988
1993
1998
2000
Standard Deviation
Figure 7b: Global Moran’s I (growth rates)
5
4.5
4
3.5
3
2.5
2
1.5
1
0.5
0
1970-1975 1975-1980 1980-1985 1985-1988 1988-1993 1993-1998
23
Figure 8a: Significance of Local Moran for GDP per capita 1970: Map and Moran Scatterplot
Significance level
5%
10%
2.5
2
BCs
BC
1.5
1
SO
Spatial Lag
0.5
N
MI
ZC
0
SL
TL
HI
GE
-0.5
W
YU
OA
E
CH
MO
DU
NA AG
CL
QU
PU
GU
VC
SI
CU
TA
CO
NL
QI
JA
MX
-1
S
60 0
0
6 00
-1.5
1 200 Mi le s
-2
-2.5
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
Relative Gross Domestic Product Per Capita:1970
Figure 8b: Significance of Local Moran for GDP per capita 2000: Map and Moran Scatterplot
Significance level
5%
2.5
10%
2
1.5
YU
BCs
Spatial Lag
1
N
W
SO
0.5
ZC
SL
NA
CO
TA
DU
MO
HI
GE
-0.5
SI
MI
TL
0
BC
JA
GU
PU
CL
-0.5
0
QU
CU
NL
QI
AG
MX
VC
E
OA
-1
CH
S
-1.5
60 0
0
6 00
1 200 Mi le s
-2
-2.5
-2.5
-2
-1.5
-1
0.5
1
1.5
2
2.5
Relative Gross Domestic Product Per Capita:2000
24
Figure 9a: Significance of Local Moran for Growth of GDP per capita 1970-1985: Map and Moran Scatterplot
Significance level
5%
10%
2.5
2
1.5
Spatial Lag
1
N
W
E
0
SI
-0.5
0
6 00
HI
CL
DU
CH
OA
QU
TL
BC
-1.5
12 00 Mi le s
GU
PU
CO
JA MI GE
NL
AG
SL
ZC
NA
TA MO
CU
QI
SO
BCs
-1
S
600
YU
VC
MX
0.5
-2
-2.5
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
Relative Gross Domestic Product Per Capita Growth:1970-1985
Figure 9b: Significance of Local Moran for Growth of GDP per capita 1985-2000: Map and Moran Scatterplot
Significance level
5%
10%
2.5
2
1.5
YU
1
Spatial Lag
QI
N
W
E
S
600
0
6 00
1200 Mi le s
SO
0.5
JA
0
TL
NA
VC
-0.5
-1
CO
NL
DU ZC BC
MI SL QU
CL GU
BCs
GE SI
MO
MX
HI
TA
CU
AG
PU
OA
CH
-1.5
-2
-2.5
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
Relative Gross Domestic Product Per Capita Growth:1985-2000
25
State
Baja California
Coahuila
Chihuahua
Nuevo León
Sonora
Tamaulipas
Baja California Sur
Durango
San Luis Potosí
Sinaloa
Zacatecas
Aguascalientes
Colima
Guanajuato
Hidalgo
Jalisco
México
Michoacán
Morelos
Nayarit
Querétaro
Chiapas
Guerrero
Oaxaca
Puebla
Tlaxcala
Veracruz
Quintana Roo
Yucatán
70
++
Table 3. Significance of Local Moran Statistics : Levels and Growth
Levels
Growth
75
80
85
88
93
98 2000 70-75 75-80 80-85 85-88 88-93 93-98 95-00 70-85 85-00
+
+
+
+
+
+
++
++
++
++
+
++
+
++
+
++
--
--
-
-
-
+
-
-++
+
++
++
++
+
++
++
++
+
++
+
++
+
++
+
++
+
++
+
+
++
++
++
-
++
++
++
-
++
+
--
+
+
+
+
++
++
+
26