77498 Spatial Dimensions of Trade Liberalization and Economic Convergence: Mexico 1985–2002 Patricio Aroca, Mariano Bosch, and William F. Maloney This article employs established techniques from the spatial economics literature to identify regional patterns of income and growth in Mexico and to examine how they have changed over the period spanned by trade liberalization and how they may be linked to the income divergence observed following liberalization. The article first shows that divergence has emerged in the form of several income clusters that only partially correspond to traditional geographic regions. Next, when regions are defined by spatial correlation in incomes, a ‘‘south’’ clearly exists, but the ‘‘north’’ seems to be restricted to the states directly on the U.S. border and there is no ‘‘center’’ region. Overall, the principal dynamic of both the increased spatial dependency and the increased divergence lies not on the border but in the sustained underperformance of the southern states, starting before the North American Free-Trade Agreement, and to a lesser extent in the superior performance of an emerging convergence club in the north-center of the country. Over the decades since Mexico’s dramatic unilateral trade liberalization in 1985 and its membership in the North American Free-Trade Agreement (NAFTA), per capita incomes have increasingly diverged across Mexican states. Measures of sigma convergence show a decrease in dispersion from 1970 to 1985 and then a sharp reversion to levels of inequality thereafter. A growing number of studies using traditional beta convergence analysis (Barro and Sala-i-Martin 1995) also find divergence or, at least, a slowdown of convergence (Juan Ramon and Rivera-Batiz 1996; Esquivel 1999; Messmacher 2000; Cermen ˜ o 2001; Esquivel and Messmacher 2002; Chiquiar 2005). Patricio Aroca is a professor and director of the Institute for Applied Regional Economy (IDEAR) at the Universidad Cato ´lica del Norte, Antofagasta, Chile; his email address is paroca@ucn.cl. Mariano Bosch is a PhD student in economics at the London School of Economics and Political Science; his email address is m.bosch@lse.ac.uk. William F. Maloney is a lead economist in the Office of the Chief Economist for Latin America at the World Bank; his email address is wmaloney@worldbank.org. The research for this article was financed by the Regional Studies Program of the Office of the Chief Economist for Latin America at the World Bank. The authors thank Gerardo Esquivel, Jaime de Melo, Gordon Hanson, Daniel Lederman, Miguel Messmacher, Raymond Robertson, and Lucas Siga for helpful discussions. They also thank Gabriel Victorio Montes Rojas for inspired research assistance. THE WORLD BANK ECONOMIC REVIEW, VOL. 19, NO. 3, pp. 345–378 doi:10.1093/wber/lhi018 Advance Access publication December 23, 2005 Ó The Author 2005. Published by Oxford University Press on behalf of the International Bank for Reconstruction and Development / THE WORLD BANK. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org. 345 346 THE WORLD BANK ECONOMIC REVIEW, VOL. 19, NO. 3 Concern is growing that this divergence is occurring in geographic patterns that will compound traditional inequalities: the northern states will reap most of the benefits of free trade and rapidly converge toward U.S. income levels, while the southern states will continue to lag, polarizing the country. However, the links from trade liberalization to the spatial location of economic activity and to economic convergence are not well understood, either theoretically or in the actual case of Mexico. This article employs established techniques from the spatial economics literature to identify regional patterns of income and growth and to show how they have changed over the period spanned by trade liberal- ization and how they may be linked to the observed divergence in income. I. BACKGROUND In 1985, Mexico began a process of unilateral liberalization that transformed it from an inward-looking economy based on import substitution to an open, liberal- ized economy. Trade-related reforms included a dramatic reduction of import licensing coverage from 90 percent of domestic production to 23 percent by 1988, a phased reduction of average levels of tariffs from 24 to 11 percent, and admittance to the General Agreement on Tariffs and Trade (GATT) in 1986. The pursuit of NAFTA, signed in 1994, would lead to a further reduction of average tariffs to 1.3 percent by 2001, the progressive liberalization of sensitive sectors, increased access to the U.S. market, and a greater attractiveness to foreign direct investment (Lustig, Bosworth, and Lawrence 1992; Lederman, Maloney, and Serven 2005). Early analyses of the impacts of reform and of the predicted impact of NAFTA looked at output and exports of specific industries but were silent about how their location might be affected.1 The emergence of the new economic geography (Krugman 1991) during the 1990s offered new tools for examining that question. It built on the interplay of agglomeration externalities of industry arising from the availability of specialized labor and intermediate inputs and technology spillovers on the one hand and transportation costs between markets on the other. Hanson (1997) suggested that Mexico’s traditional inward-looking policies led industry to locate near concentrations of industry and population in central Mexico City and to serve the peripheral regions—the south and the north—from this base. How- ever, the progressive liberalization of trade with the United States arguably made locating nearer the U.S. market more profitable, shifting the center of gravity of the Mexican economy to the north, potentially in a dramatic fashion. The benefits would likely dissipate with distance from the border, and, as some have argued, would increase the dispersion of welfare between north and south (Nicita 2004). However, these outcomes are not a foregone conclusion. To begin with, theory remains ambiguous. For example, Behrens and Gaigne (2003) suggest that a 1. See, for example, Maloney and Azevedo (1995) and Lustig, Bosworth, and Lawrence (1992). Lustig, Bosworth, and Lawrence specifically acknowledge the lack of reference to spatial considerations (p. 65). Aroca, Bosch, and Maloney 347 finding of increased polarization with trade liberalization depends critically on how transport costs are modeled.2 Second, historically, Krugman (1991) and others (see Head and Mayer 2004 for a review) have noted the remarkable persistence of patterns of industry distribution over very long periods of time, despite large changes in economic environment. Such persistence may reflect the power of accumulated agglomeration externalities, often initially sparked by trivial historical accident or the importance of natural advantages that anchor industries to their initial locales. Davis and others (1997) argue that Heckscher- Ohlin-Vanek performs surprisingly well in explaining the location of production in Japan and that Krugman-style geography models add little. Ellison and Glaeser (1999) find that only 21 percent of the U.S. industries exhibit degrees of geographic concentration significantly higher than those predicted by natural advantages, such as weather and natural resources. Redding and Vera Martin (2003) show that both theoretically and in 45 regions in Europe factor endow- ments are important determinants of the location of production.3 In neither the new economic geography nor the Heckscher-Ohlin-Vanek view is it clear whether the sudden increase in demand from abroad, and an increase in the supply of cheaper and better-quality inputs, will lead to the displacement of existing nonborder growth poles or to their reinvigoration. Both scenarios are consistent with localized and isolated hot spots or with large multistate agglom- erations distributed with no particular relation to the border. In Mexico these types of considerations suggest that the emerging geographic patterns of economic performance may be subtle and hard to predict. Thus, for example, the increased costs of exporting from established central industrial locations such as Aguascalientes, Guadalajara, and Queretaro might be offset by their well-trained workforces and lower levels of congestion. Domestic and foreign firms interested in serving the Mexican market may be attracted by the increased access to cheaper and higher quality inputs from abroad and the lowered risk implied by NAFTA.4 Further, the location of some potential growth industries is clearly driven by immobile endowments that are not necessarily concentrated on the border. Esquivel (2000) finds that two-thirds of the differ- ences in Mexican state incomes are a result of differences in natural characteristics (climate and vegetation).5 The elimination under NAFTA of import restrictions to the United States on mangos (produced in Guerrero and Michoacan), pineapples (Veracruz, Oaxaca, and Tabasco), and grapes in 1994 and the phasing out of 2. Hanson (1997) argues that the emergence of a second pole would lead to compression of the wage distribution rather than divergence. 3. Redding and Vera Martin (2003) show this should be the case in theory regardless of the degree of factor mobility. Working in a similar tradition, Bernstein and Weinstein (2002) reintroduce the impor- tance of transport costs as a means of anchoring the indeterminacy intrinsic to HOV when the number of goods exceeds the number of factors. 4. See Lustig, Bosworth, and Lawrence (1992) for a discussion of NAFTA as a signal to foreign investors that Mexico was locking in the new liberalized rules of the game. 5. See Gallup, Gaviria, and Lora (2003) for an English summary of Esquivel’s findings. 348 THE WORLD BANK ECONOMIC REVIEW, VOL. 19, NO. 3 restrictions on tomatoes (Jalisco) and avocados (Michoacan) by 2008 should have a stimulative effect on nonborder areas with natural endowments.6 Both agricul- tural production and exports have made large gains in the post-NAFTA period.7 Further, nonborder regions may offer other low-cost means of transport to the United States than by road. Mexico’s second and third largest airports are in Jalisco (center-south) and Yucata ´n (south). Air transport capacity, along with the high level of human capital and good governance, was important to Intel’s locating a plant in south-of-Mexico Costa Rica.8 Yucata ´n benefits from the shallow-water port of Progreso, which offers easy access to U.S. ports in the Gulf of Mexico and to ports in Central and South America and the Caribbean. In 2003, Yucata ´n had the second highest concentration of maquila employment of a nonborder state—exceeded only by Jalisco. The port of Veracruz, the entry point to Mexico during its first period of globalization in the sixteenth century, remains Mexico’s most important, with extensive road and rail networks that connect the central and southern states to Gulf of Mexico ports. Given this ready access to water transport, all other endowments being equal, a southern pole or a southeastern corridor enjoying the same benefits of proximity would seem as plausible as would the region’s being left behind. In fact, there is little evidence to date that the 1985 trade liberalization or NAFTA has led to a correlation of growth with proximity to the border. Hanson (1997) found no steepening of the north–south wage gradient after 1985. Using state per capita income data, Rodriguez-Pose and Sanchez-Reaza (2005) find no relationship in any time period—a result confirmed by the background regres- sions for this article.9 Esquivel (2000) finds no relationship between distance and level of income or growth. Chiquiar (2005) finds a relationship between changes in growth and distance, but that result appears to be limited to the span between 1970 and 1985 and 1985 and 1999 and does not survive when the period is broken into post-GATT (1985–1993) and post-NAFTA (1993–2002).10 In sum, the geographic patterns of growth with liberalization are likely to be more complex than initially expected. 6. No attempt is made to be comprehensive here. The examples here are meant merely to show that these central and southern states cultivate these crops, some almost exclusively, and hence were likely to benefit from NAFTA. 7. See Lederman, Maloney, and Serven (2005) for a discussion of the resilience of Mexican agriculture. 8. Rodriguez-Clare (2001) notes that Costa Rica’s better infrastructure in air transport gave it the edge over Chile. 9. Distance is never even remotely significant in a simple convergence regression for 1970–2002, 1970–85, and 1985–2002. When regional dummy variables are added, the results show that the Chiapas- Oaxaca-Guerrero region did unusually poorly relative to other regions in both 1970–85 and 1985–2002. The results are available from the authors on request. 10. Nicita’s (2004) ex post simulations find gains in household welfare from trade liberalization to be distributed broadly along a gradient from the north. However, the core estimations driving the simula- tions, the pass-through of tariffs to prices, imposes a linear distance from the border interactive term that implies that the predicted values used in the simulations will show the same gradient pattern. To be convincing, the actual decline in prices in each state during liberalization should be used. Aroca, Bosch, and Maloney 349 II. EXPLORING SPACE Sigma and beta convergence approaches offer point estimates of the central tendency of the data toward convergence or divergence. However, as Quah (1993) notes, they obscure vast amounts of information on the dynamics of relative income movements across states and shed no light on the spatial dimensions of growth. As an example, simple plots of the distribution of income levels and growth rates (available on request) confirm Juan Ramon and Rivera- Batiz’s (1996) findings of a concentration of both measures during 1970–80, consistent with parametric convergence test findings. However, from 1985 onwards, a prominent right tail appears in both income levels and growth rates, suggesting that a group of states has detached itself from the others. Such snapshots of the distribution can be informative, but they hide impor- tant information—in particular, how to get from one snapshot to another. For example, are the outliers in the extreme right tails in plots of the growth distribution the same states that persistently show higher growth or is the distribution broadly symmetric over the longer term, with random states some- times experiencing extraordinary growth? The first case would be consistent with the emergence of a spatial growth pole, while the second case would not. A substantial literature has followed Quah’s lead in constructing Markov transition matrices that tabulate the probabilities of states moving among a finite number of intervals of the national income distribution and hence char- acterize the dynamic patterns of relative income movements (Fingleton 1999; Lopez-Bazo and others 1999; Puga 1999; Rey 2001).11 To avoid problems associated with creating arbitrary discrete divisions in the distribution of income (Bulli 2001), Quah (1997) proposes approximating a continuous distribution with the use of kernel density estimates. An advantage of both the transition matrices and the kernels is that they can be conditioned on state characteristics, including geographic location, to permit drawing inferences about the spatial dimensions of Mexico’s growth process. Of interest is whether there is any evidence of ‘‘spatial correlation’’ or ‘‘spatial dependence,’’ where either income levels or growth rates are correlated within geographic areas, and whether groups of states have emerged as either positive or negative growth poles. Two sets of parametric tools are used to complement the visual analysis and facilitate statistical inference. First, as an approximate test of whether two kernels differ between time periods, the presence of a structural break is tested for in their discrete time analogues, with transition matrices capturing the movement of states among five income quintiles. Each i,j entry in the matrix represents the probability of a state transitioning from income class i to income ´a-Verdu 11. Employing these techniques for Mexico, Garcı ´ (2005) again finds no evidence of con- vergence in the post-1985 period. 350 THE WORLD BANK ECONOMIC REVIEW, VOL. 19, NO. 3 class j over a five-year period.12 Following Bickenbach and Bode (2001), a Q-statistic is constructed to test for a structural break between the subperiods, both at the individual interval level and for the matrices as a whole: X ^ijð1970À85Þ À p ðp ^ijð1985À2002Þ Þ2 ð1Þ Qi ¼ ni $ w2 ðBi À 1Þ p^ijð1985À2002Þ j2Bi ^ijð1985À2002Þ > 0g Bi ¼ fj : p where p^ij is the probability of a state moving from income interval i to income interval j. For the whole matrix the test is simply X ð2Þ Q¼ Qi : i Second, two parametric measures of spatial dependence are introduced: the global Moran and the local Moran. These are common in the spatial statistics literature but have only recently been applied to the study of economic growth (Rey 2001). The global Moran, Moran’s I-statistic (Anselin 1988, 1995), is calculated for each period t as: n P P n wij zi zj n i¼1 j¼1 ð3Þ It ¼ ; 8 t ¼ 1; 2; . . . ; T S Pn 2 zi i¼1 where n is the number of states; the wij terms are the elements of a binary contiguity matrix13 W(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 normalized vectors of the log of per capita GDP of states i and j, respec- tively.14 Essentially, Moran’s I aggregates the correlations between individual states and their spatial lags. Broadly speaking, in the same way that in time series econometrics a Durbin Watson test captures the comovement of contem- poraneous residuals with those of neighboring (lagged) time periods, the Moran captures comovement with neighboring states (spatial lags). Statistical signifi- cance can be tested by comparing Moran’s I-statistic with its theoretical mean and using a normal approximation. 12. The asymptotically unbiased and normally distributed maximum likelihood estimator of pij is determined by p ^ij ¼ nij =Æj nij , where nij is the number of transitions from income class i to income class j over a period of time. 13. Distance-based matrices were also employed and gave similar results, available on request, to those presented here. 14. zi = ln(GDPit/GDPt) denotes the logarithm of 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). Aroca, Bosch, and Maloney 351 The global Moran may, however, conceal patterns of comovement in parti- cular growth poles or convergence clubs, and it can be decomposed into the ‘‘local’’ Moran: P zi wij zj j ð4Þ Ii ¼ P z2 i =n which indicates spatial clustering around a particular state i, either of positive or of negative correlation, when the statistic is significantly different from zero.15 In principle, the Moran will also identify the existence of comovements in states driven by the presence or intensification of a gradient, for instance, from the U.S. border. III. DATA The Mexican National Institute of Statistics, Geography, and Informatics (INEGI) tabulates official GDP data for Mexico’s 32 states. The data are available for 1970, 1975, 1980, 1985, 1988, and then annually for 1993–2002. As in Esquivel (1999), several corrections are made to this data. First, most oil is pumped in the states of Tabasco and Campeche, but the attribution of oil revenues has changed without obvious cause over time. Though the revenues are allocated to all states according to a federal sharing formula, in some years they were attributed entirely to Tabasco and in others to Campeche. To correct for this, oil production as captured in the mineral production category of the state accounts was excluded, but the resulting growth series was still too erratic and exaggerated to be credible.16 This behavior is attributed to unresolved petroleum accounting issues since growth series for the remaining 30 non-oil- producing states behave more reasonably. Though dropping these states clearly implies losing some of the spatial story, this seems preferable to contaminating the analysis with clearly unreliable series. Second, population figures for Chiapas and Oaxaca were corrected for 1975, 1980, 1985, and 1988, because the 1980 census appears to have understated the states’ population-induced distortions in GDP per capita.17 Population figures for 15. Since the distribution of the statistic is usually unknown, Anselin (1995) suggests a Monte Carlo style method to generate it, consisting of the conditional randomization of the vector zj. That is, Moran statistics are calculated between state i and a large number of hypothetical ‘‘neighborhoods’’ constructed as random permutations of states drawn from the entire sample. Then, the true neighborhood Moran is compared against this distribution. 16. Chiapas also produces modest amounts of oil, and this production was also subtracted from the state product series in 1975 and 1980. 17. According to official figures, mining production as a share of Chiapas’s GDP went from 7.5 percent in 1970 to 18 percent in 1975, to 45 percent in 1980, and back to 7 percent in 1985. Clearly, the 1975 and 1980 data reflect arbitrary assignments of oil production to Chiapas. These were corrected to bring the ratio of mining production to GDP to 7.5 percent for the outlier years. 352 THE WORLD BANK ECONOMIC REVIEW, VOL. 19, NO. 3 those years were extrapolated using annual population growth rates between 1970 and 1990. Finally, Mexico State was merged with the Federal District of Mexico City. The two have long been part of a common industrial aggregate, and there are strong labor market links between them.18 The analysis is run both with and without this aggregation, and while the fundamental story does not change, the more moderate growth behavior of the Federal District with the aggregated data appears more plausible, and hence those results are reported. In sum, the analysis covers 29 states measured at five-year intervals with three observations before the unilateral trade liberalization of 1985 and three after (table 1, figure 1, and figure S.1 in the supplemental appendix, available at http://wber.oxfordjournals.org).19 The data indicate that regional differences in income in Mexico were vast in 2002: the GDP per capita of the poorest state, Oaxaca in the south, was only 23 percent of that of the richest state, Nuevo Leo´n in the north. IV. IDENTIFYING REGIONS—COVARIANCE OF INCOME LEVELS The analysis looks first at whether there has been any major reordering of income levels over time and whether there is any correlation across groups of neighboring states that would constitute a region or that would suggest emer- ging gradients. To see this, the stochastic kernel and its contour are plotted for levels of per capita income for 1970–85 and 1985–2002 (figures 2 and 3). Both plots show state income relative to average national income (‘‘country relative’’) in time t on the Y-axis and in time t + 5 on the X-axis. The same scale is used in both the pre- and post-liberalization periods to facilitate drawing inferences about changes in the variance of the kernels. The crosshairs depict the country average in period t and in t + 5. A couple of points merit highlighting. First, if there were no change at all in the relative position of states, figures 2 and 3 would consist of a bisecting plane along the 45-degree line shown. The fact that states do shift their relative position gives the kernel its volume. Slicing the volume parallel to the X-axis reveals the distribution of states at each initial income level five years later. Again, the advantage over the simple distribution plots is the ability to see changes of position that might be hidden by identical snapshot distributions. Slicing parallel to the XY plane generates contour plots that show the relative probabilities of finding combinations of initial and final incomes. Second, significant income convergence would result in a rotation of 18. This may potentially lead to an overstatement of the capital city’s per capita income. This has led to reported population in the Mexico DF, remaining stable over the last twenty years, while the popula- tion in the state of Mexico doubled. Our thanks to Miguel Messmacher for this insight. 19. To keep to a five-year interval while also avoiding the 1995 crisis, which would have distorted the results, data for 1970, 1975, 1980, 1985, 1988, 1993, 1998, and 2002 were used in estimating the stochastic kernels and the transition matrices. Aroca, Bosch, and Maloney 353 T A B L E 1 . Mexican 2002 GDP per Capita by State (1993 pesos) Region and State Population GDP (Millions GDP per Standard (Abbreviation) (in Thousands) of Pesos) Capita Deviation/Mean North 19,730 0.20 Baja California Norte (BC) 2,706 47,091 17,405 Coahuila de Zaragoza (CO) 2,444 49,651 20,314 Chihuahua (CU) 3,252 64,461 19,823 Nuevo Leo ´n (NL) 4,046 105,270 26,019 Sonora (SO) 2,370 39,729 16,763 Tamaulipas (TA) 2,990 45,124 15,094 Central-north 11,333 0.28 Baja California Sur (BCs) 464 8,330 17,968 Durango (DU) 1,536 18,953 12,341 San Luis Potosı ´ (SL) 2,373 25,656 10,811 Sinaloa (SI) 2,697 30,628 11,356 Zacatecas (ZA) 1,410 12,534 8,887 Central 16,507 0.33 Aguascalientes (AG) 995 18,386 18,470 Colima (CL) 569 8,119 14,263 Guanajuato (GU) 4,942 55,583 11,246 Hidalgo (HI) 2,330 20,364 8,741 Jalisco (JA) 6,639 95,731 14,420 Mexico and Federal 22,796 482,133 21,150 District (MX) Michoaca ´n (MI) 4,181 33,871 8,101 Morelos (MO) 1,659 20,537 12,382 Nayarit (NA) 977 8,333 8,527 Quere ´taro (QU) 1,515 26,224 17,313 South 7,761 0.18 Chiapas (CH) 4,232 26,307 6,216 Guerrero (GE) 3,221 23,979 7,445 Oaxaca (OA) 3,642 21,812 5,989 Puebla (PU) 5,362 51,219 9,552 Tlaxcala (TL) 1,022 8,011 7,841 Veracruz (VC) 7,225 60,395 8,359 Yucata ´n Peninsula 15,117 0.42 Quintana Roo (QI) 976 20,874 21,383 Yucata ´n (YU) 1,737 20,142 11,596 Not in sample Campeche (CA) 737 16,789 22,785 Distrito Federal (DF) 8,813 327,009 37,107 Me ´xico (MX) 13,984 155,124 11,093 Tabasco (TB) 1,996 17,050 8,542 Total 103,040 1,483,284 14,395 0.40 Source: Authors’ calculations based on census data from the Mexican National Institute of Statistics, Geography, and Informatics. 354 THE WORLD BANK ECONOMIC REVIEW, VOL. 19, NO. 3 F I G U R E 1 . Map of Mexican States Source: Author’s elaboration using ArcView from ESRI. 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, a state label is placed at the position corre- sponding to the average value for each state. This reference is only approximate since the kernel is estimated at three time points for each state, but given the revealed persistence in relative income levels, these reference points are informative. Indeed, the high persistence in the distribution is the most salient feature of both figures. The probability mass is concentrated mainly in the diagonal of the plot, showing that states did not significantly change their relative position. Though the persistence is clear, striking differences emerge between the pre- and post-liberalization kernels. The single-peaked kernel in figure 2 has become a double- or even triple-peaked kernel, suggesting the formation of convergence clubs after 1985. Several forces drive this evolution. First, the bottom end of the distribution has become more compressed at around 0.70 of national average income, suggesting convergence toward the mean for the very poorest states. Second, above-average states converged towards 1.3 of the national average, depopulating the center of the distribution. Finally, income in the states of Mexico, Nuevo Leo ´n, and Quintana Roo grew enough for the states to have formed the last peak of the distribution, with incomes above 1.7 of the national average. Another evolution, important to the finding of reduced beta conver- gence, is that poor states moved from below the 45-degree line in the Aroca, Bosch, and Maloney 355 F I G U R E 2 . Unconditioned Kernel Density Plots, Levels, 1970–85 (State Income Relative to National Average Income) Note: See table 1 for state abbreviations. Source: Authors’ calculations based on census data from the Mexican National Institute of Statistics, Geography, and Informatics. 356 THE WORLD BANK ECONOMIC REVIEW, VOL. 19, NO. 3 F I G U R E 3 . Unconditioned Kernel Density Plots, Levels, 1985–2002 (State Income Relative to National Average Income) Note: See table 1 for state abbreviations. Source: Authors’ calculations based on census data from the Mexican National Institute of Statistics, Geography, and Informatics. Aroca, Bosch, and Maloney 357 pre-liberalization period to on or above it in the post-liberalization period. This suggests reduced upward mobility of the poorest states in the post-liberalization period. The discrete transition matrices confirm the continuous kernel story. The persistence of income rankings is suggested by the high probabilities of remaining in the same interval tabulated along the main diagonal of the matrix (table 2). The Q-statistics suggest that the pre- and post-liberalization matrices are statis- tically different from each other at the 1 percent level, and a large part of the reason appears to be the changes in the dynamics of the poorer states suggested above. For instance, the probability of a state in interval 1 being in that same T A B L E 2 . Transition Matrices, 1970–2002 1970–2002 Number 1 2 3 4 5 35 1 0.86 0.14 0.00 0.00 0.00 35 2 0.17 0.69 0.14 0.00 0.00 35 3 0.00 0.14 0.77 0.09 0.00 35 4 0.00 0.00 0.03 0.80 0.17 34 5 0.00 0.00 0.00 0.18 0.82 1970–85 Number 1 2 3 4 5 20 1 0.80 0.20 0.00 0.00 0.00 14 2 0.07 0.64 0.29 0.00 0.00 21 3 0.00 0.14 0.76 0.10 0.00 13 4 0.00 0.00 0.00 0.92 0.08 19 5 0.00 0.00 0.00 0.21 0.79 1985–2002 Number 1 2 3 4 5 15 1 0.93 0.07 0.00 0.00 0.00 21 2 0.28 0.66 0.05 0.00 0.00 14 3 0.00 0.14 0.79 0.07 0.00 22 4 0.00 0.00 0.09 0.63 0.27 15 5 0.00 0.00 0.00 0.07 0.93 Degrees of freedom Q-statistic p-value Ho: ^ijð1985À2002Þ p ^ijð1970À85Þ ji ¼ 1 ¼p 1 5.71 0.02 Ho: ^ijð1985À2002Þ p ^ijð1970À85Þ ji ¼ 2 ¼p 2 18.92 0.00 Ho: ^ijð1985À2002Þ p ^ijð1970À85Þ ji ¼ 3 ¼p 2 0.18 0.91 Ho: ^ijð1985À2002Þ p ^ijð1970À85Þ ji ¼ 4 ¼p 2 4.68 0.09 Ho: ^ijð1985À2002Þ p ^ijð1970À85Þ ji ¼ 5 ¼p 1 6.31 0.01 Ho: ^ijð1985À2002Þ p ^ijð1970À85Þ 8i ¼p 8 35.83 0.00 Source: Authors’ calculations based on census data from the Mexican National Institute of Statistics, Geography, and Informatics. 358 THE WORLD BANK ECONOMIC REVIEW, VOL. 19, NO. 3 interval five years later was 80 percent before 1985 and 93 percent after 1985. States in quintile one and two were able to move upward in the distribution with probability 7 and 5 percent in the post-liberalization period compared with 20 and 29 percent in the pre-liberalization period, suggesting that the increased sigma dispersion was caused partially by stagnation in the poorer states. The Spatial Dimension The next question is whether these convergence clubs translate into geographic ‘‘regions’’ as well. Quah (1997) identified a similar ‘‘twin peaks’’ phenomenon in the kernel derived from an international cross-section of per capita incomes and found it to be geographically driven—regional clusters of poor countries were getting poorer, while rich country agglomerations were getting richer. To see whether similar geographic patterns are emerging in Mexico, the kernels were regenerated, replacing t + 5 with the income of the state relative to the average income of its contiguous neighbors (‘‘neighbor relative’’) in time t (figure 4). If the local and economy-wide distributions of income are similar—if there are no clusters of states with similar incomes—probabilities would be concentrated along the main diagonal. If, however, poor states are found with poor states and rich with rich, there should be a rotation toward a vertical line at unity—a country- relative poor state will have the same income as that of its neighborhood. Several points merit notice in the spatially conditioned kernel density plots. First, geography is not destiny in Mexico to the degree that it appears to be globally. Had the income clusters identified previously been totally determined by geography, the three observed peaks would have been vertically aligned at unity on the Y-axis. However, the post-liberalization spatially conditioned kernel density plot of figure 4 is fairly similar to the multiple-peaked uncondi- tional kernel of figure 3, and there is a large group of states (including Michoacan, Nuevo Leo ´n, Tlaxacala, and Zacatecas) whose mass lies largely on the 45-degree line. In the post-liberalization period, the intermediate peak consists mainly of the northern states of Baja California Norte, Baja California Sur, Coahila, and some successful central states such as Aguascalientes, Jalisco, and Queretaro (recently arrived) which show a negative spatial corre- lation with neighbors. Mexico and Quintana Roo, driven by Cancun-related tourism, similarly constitute unusually high-income areas, with Quintana Roo joining Nuevo Leo ´n and Mexico as especially rich states in the third cluster identified in figure 3. Even after liberalization, the richest states could not be more independent spatially, since they are in three different regions of the country. There is no sign of Quah’s (1997) dramatic convergence clubs of rich and poor states. There is evidence, however, of spatial dependence that would suggest regio- nal effects. Before 1985, there was some rotation and compression of the upper mass that suggests that, particularly among the northern states of Baja California Norte, Baja California Sur, Chihuahua, and Tamaulipas, there is a nascent convergence club in incomes. However, as the border convergence club Aroca, Bosch, and Maloney 359 F I G U R E 4 . Kernel Density Plots, Levels, Conditional on Spatial Lag, Neighbors, 1970–85 and 1985–2002 Note: See table 1 for state abbreviations. Source: Authors’ calculations based on census data from the Mexican National Institute of Statistics, Geography, and Informatics. 360 THE WORLD BANK ECONOMIC REVIEW, VOL. 19, NO. 3 T A B L E 3 . Classification of Mexican States by Geographic Bands and Distance from the U.S. Border Geographic Band Distance From U.S. Border (Kilometers) Border 0–350 Baja California Norte, Chihuahua, Coahuila de Baja California Norte, Chihuahua, Coahuila, Zaragoza Nuevo Leo ´n, Sonora, Tamaulipas Nuevo Leo ´n, Sonora, Tamaulipas North 351–870 ´, Baja California Sur, Durango, San Luis Potosı Aguascalientes, Durango, Guanajuato, Sinaloa, Zacatecas Quere ´, Zacatecas ´taro, San Luis Potosı Center 871–1,130 Aguascalientes, Colima, Guanajuato, Hidalgo, Hidalgo, Jalisco, Mexico/Federal District, ´n, Jalisco, Mexico/Federal District, Michoaca Michoaca ´n, Morelos, Sinaloa Morelos, Nayarit, Quere ´taro South 1,131–1,416 Chiapas, Guerrero, Oaxaca, Puebla, Colima, Guerrero, Nayarit, Puebla, Tlaxcala, Tlaxcala, Veracruz Veracruz ´ n Peninsula Yucata >1416 ´n Quintana Roo, Yucata Baja California Sur, Chiapas, Oaxaca, Quintana Roo, Yucata ´n Source: Authors’ compilation. strengthened, the second line of states did not follow, and hence there is no strong rotation of the northern part of the country broadly imagined toward the Y-axis. Durango, San Luis Potosi, Sinaloa, and Zacatecas, all contiguous to the border states, are relatively poor and lie largely on the 45-degree line. There is also a group of poor southern states—Chiapas, Guerrero, Oaxaca, Puebla, and Vercruz—that is found to be better-off relative to their neighbors than relative to the country. For example, Chiapas’s income is around 50 percent of the national average, but it is as rich as its neighbors (a neighbor’s relative income of roughly unity). These results suggest that there may be aggregations, which might be called ‘‘border’’ and ‘‘southern’’ regions, which can be tested for statistically. Also of interest is how proximity to the United States may affect states in a common way, even if they are not contiguous. Thus, two additional definitions of neighborhood are introduced to the kernel analysis. The first is based on traditional geographic bands and is similar to the categories used by Hanson (2004).20 The second definition establishes five categories based on distance by land to the United States, the specification most likely to turn up evidence of a gradient, as discussed by Hanson (1997). The states associated with each neighborhood for the two classifications are shown in table 3. 20. The categorization here differs from that of Hanson by the inclusion of Aguascalientes with the central states and Puebla, Tlaxcala, and Veracruz with the south. However, when the calculations are run using Hanson’s classification, the results are almost identical. Aroca, Bosch, and Maloney 361 The contour plots pre- and post-liberalization, spatially conditioned by dis- tance from the United States using the bands-defined neighborhood, reveal a strengthened border cluster (figure S.2). This arises because the new neighborhood of the border states does not include the relatively poorer second-line states the way the contiguity matrix does. This is especially clear in the post-liberalization plot, which shows Baja California Norte, Chihuahua, Coahuila de Zaragoza, and Sonora all piled on the vertical axis. Nuevo Leo ´n remains by itself. Second, there also seems to be a prominent clustering of the southern states of Chiapas, Guerrero, Oaxaca, Tlaxcala, and Veracruz, which becomes clearer in the second period as Chiapas, Guerrero, Oaxaca, and Veracruz all move closer to the vertical line at 1 on the X-axis. This causes an extension of the kernel toward the vertical that suggests convergence in income. The kernel using distance from the United States (data not shown) is similar to that using the bands, but the results are less clearly delineated. This arises mainly because the south is split into two, leaving the poor states of Chiapas and Oaxaca associated with the far richer states of Baja California Sur, Quintana Roo, and Yucata ´n. In sum, the convergence clubs suggested in figures 2 and 3 partially map onto border and southern regions of Mexico. However, there are no other obvious patterns of spatial association or clustering in the rest of the country. For all three definitions of neighborhood, northern and central states align mostly along the 45-degree line, showing little spatial dependence. Parametric Measures of Spatial Dependence Moran statistics are used to establish whether the patterns suggested by the spatially conditioned kernels are statistically significant. Moran’s I normal stan- dardized values for 1970–2002 are plotted for the three definitions of neighbor- hood along with the standard deviation of GDP per capita for the same period as a measure of sigma convergence. It is immediately clear that for Mexico as a whole spatial dependence in income levels has increased along with the sigma divergence after a period when both had fallen (figure 5). The contiguity-based neighbor- hoods most closely track the standard deviation (with a correlation coefficient of 0.85), but the other neighborhoods also follow a similar pattern, albeit less clearly. The subtle indications of spatial dependence suggested in the kernels emerge as statistically significant in the Moran test, most notably, and consistent with the kernels above, in the band measure that most clearly captures the border and southern concentrations of wealth and poverty. The local Moran statistics largely confirm the observations from the ker- nels.21 The local Moran statistics are presented in several formats. First, maps show the geographic distribution of significant local Moran statistics based on 21. Local Moran coefficients have also been calculated for the bands and distance matrices at five- year intervals, showing high correlations with the ones obtained using the contiguity criteria. Although results are not reported for the sake of brevity, we note any difference arising from the three different neighborhood definitions. 362 THE WORLD BANK ECONOMIC REVIEW, VOL. 19, NO. 3 F I G U R E 5 . Global Moran I (Levels) and Standard Deviation, 1970–2002 0.5 GATT NAFTA 5.5 0.4 4.5 0.3 3.5 0.2 2.5 0.1 1.5 0.5 0 1970 1975 1980 1985 1990 1995 2000 Moran's I (contiguity matrix) Moran's I (geographic bands) Moran's I (distance from US border) Standard Deviation Source: Authors’ calculations based on census data from the Mexican National Institute of Statistics, Geography, and Informatics. contiguity for the 10 and 5 percent levels for 1970 and 2002, the endpoints of the sample (figures 6 and 7). 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 to illuminate the relations captured by the statistics. A significant positive slope suggests that rich states are found in convergence clusters with other rich states (quadrant 1) and poor states with other poor states (quadrant 3). Quadrants 2 and 4 represent cases where rich states are found among poor states, or poor states among rich states. More details are provided in table 4, which shows significance levels and signs of the Moran statistics at five-year intervals across the sample for all three definitions of neighborhood. Three main findings emerge. First, in the early period, the analysis confirms a cluster of poor states around Chiapas, Guerrero, Oaxaca, and Puebla, corresponding to the traditional south- ern states. This cluster appears strongly in the maps and in quadrant 3 of the scatter plots, and table 4 suggests that this relationship has been getting stronger across time for all definitions of neighborhood. Second, for geographic bands and distance, the border states considered as a block clearly stand as a pole of high-income levels that has become stronger with time. However, the lack of any significance when the connectivity measure is used confirms that the income levels of the second-line states are not corre- lated with those of the border states, and hence it may not be useful to talk about the ‘‘north’’ more generally. Baja California Norte, Baja California Sur, and Aroca, Bosch, and Maloney 363 F I G U R E 6 . Significance of Local Moran for 1970 GDP per Capita—Map and Moran Scatterplot Source: Authors’ calculations based on census data from the Mexican National Institute of Statistics, Geography, and Informatics. Sonora appear in quadrant 1 of the scatter plots as well-off states in better-off neighborhoods and so might be seen as a well-off convergence cluster located in the north of the country along the U.S. border. However, these correlations seem to slowly disappear by the beginning of the 1990s and the ‘‘north,’’ as a spatial unity encompassing more than just the border states, disappears. The higher income of the frontline states has not spilled over much to the second line. 364 THE WORLD BANK ECONOMIC REVIEW, VOL. 19, NO. 3 F I G U R E 7 . Significance of Local Moran for 2002 GDP per Capita—Map and Moran Scatterplot Source: Authors’ calculations based on census data from the Mexican National Institute of Statistics, Geography, and Informatics. In the center, there is little evidence of convergence clusters, consistent with the findings of the kernel plots. Most of the central states are located in quadrants 2 and 4, almost suggesting a downward sloping line (if the outliers are ignored) and a tendency for rich states to be found among poor and poor among rich. The greater variance in income per capita in this region (table 1) underlies the finding of a lack of spatial dependence: poor states such as Hidalgo, Michoacan, Nayarit, and Zacatecas and rich states such as Aguascalientes, Mexico/Federal District, and Queretao share the same neighborhood. Conse- quently, no significant Moran statistics are found in this area for any period, T A B L E 4 . Local Moran, Levels 1970 1975 1980 1985 1993 2002 State C B D C B D C B D C B D C B D C B D Border Baja California Norte ++ ++ ++ ++ ++ ++ ++ ++ ++ + ++ ++ ++ ++ ++ ++ Chihuahua + + + + + ++ ++ ++ ++ Coahuila de Zaragoza ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ Nuevo Leo ´n ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ Sonora ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ Tamaulipas ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ North Baja California Sur ++ À + Durango + ++ + San Luis Potosi 365 Sinaloa Zacatecas Center Aguascalientes Colima ÀÀ À Guanajuato Hidalgo Jalisco À À ÀÀ ÀÀ Mexico/Federal District ÀÀ ÀÀ ÀÀ ÀÀ À Michoacan de Ocampo Morelos Nayarit ++ Queretaro de Arteaga (Continued) TABLE 4. Continued 1970 1975 1980 1985 1993 2002 State C B D C B D C B D C B D C B D C B D South Chiapas ++ + ++ ++ + ++ ++ ++ ++ Guerrero ++ ++ ++ + ++ ++ ++ + Oaxaca ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ 366 Puebla ++ ++ ++ + ++ + ++ + + ++ + Tlaxcala ++ ++ ++ + ++ + ++ + Veracruz-Llave + ++ ++ + ++ ++ ++ Yucata´n Peninsula Yucata´n À À À À Quintana Roo Note: C, contiguity matrix; B, geographic band; D, distance from U.S. border. Source: Authors’ analysis based on census data from the Mexican National Institute of Statistics, Geography, and Informatics. Aroca, Bosch, and Maloney 367 with the exception of the negative values associated with Jalisco and Mexico/ Federal District, indicating that these two are well-off states surrounded by poor neighbors. At this point, these results suggest that the Mexico/Federal District agglomeration has not pulled its neighbors along with it in any consistent fashion. In sum, both the kernel plots and the parametric measures suggest that, as a region with some degree of commonality of levels of income, the south exists, the north seems to be restricted to states directly on the U.S. border, and there is little evidence of a center. The absence of a clearly defined center group of states is perhaps unexpected if their performance were heavily influenced by the existence of north–south and Mexico City gradients. Their interaction might give rise to more complex income relations than, for instance, are seen on the border, but it is not obvious why an almost random distribution of rich and poor states should appear.22 V. IS THERE ANY LINK BETWEEN GEOGRAPHIC EVOLUTION AND DIVERGENCE? The next question is whether thinking of these groups as regions helps to explain the pattern of economic divergence or whether the comovement of the global Moran and the standard deviation are unrelated. Clearly, the post- liberalization divergence is driven by many forces, and disentangling them is complex. For instance, both Aguascalientes and Quintana Roo pulled away strongly from their local neighborhood, which would lead to greater divergence, while Mexico appeared to become less of an outlier in its neighborhood, which would lead to greater convergence. Applying techniques developed for subgroup decomposition of inequality developed by Shorrocks and Wan (2005) provides a more systematic, although still imperfect way of seeing how much of the increased dispersion has a geographic component. This can be done using the mean logarithm deviation index given by: 1X  ð5Þ E0 ðyÞ ¼ ln n i yi where n is the number of states, yi the income per capita of state I, and  is the mean income of the country. This involves simply partitioning the sample into a set of geographic regions and calculating the two components of aggregate 22. These findings are somewhat at odds with Hanson’s previous work arguing for the existence of gradients descending from Mexico City and the border, and we can think of perhaps two reasons why. First, he worked with wages which may be more equilibrated by migration flows than aggregate per capita income may be over the medium term. That said, again it is worth reemphasizing that he also found no increasing north–south gradient after trade liberalization. Second, it may be that his imposition of a linear relationship with distance from the border or Mexico City obscures the heterogeneity in the state data that is more easily detected by the kinds of techniques employed here. 368 THE WORLD BANK ECONOMIC REVIEW, VOL. 19, NO. 3 inequality: a within-group component, which is a weighted average of regional inequality, and a between-group component, which captures the inequality due to variations in average incomes across regions. The states are grouped accord- ing to the geographic bands division. Several points merit attention when the evolution of overall inequality and of between-group and within-group components is plotted together with the ratio of between-group to total inequality (figure S.3). First, the mean loga- rithmic deviation basically retrieves the same pattern of evolution of inequal- ity as the standard deviation in figure 5. Second, most of the increase in inequality (94 percent) between 1985 and 2002 occurs during 1985–93, prior to NAFTA. Both the between-group and the within-group component grew in this period, suggesting that although 60 percent of the increase in dispersion was interregional, much of the increase occurred within regions. Third, the 1994–2002 period was relatively stable in terms of inequality. However, differences across regions increased at a time when within-group inequality was decreasing. Overall, between-group inequality can explain 72 percent of the increase in total inequality from 1985 to 2002, with much of this inequal- ity explained by regional level movements between border, south, and rest (table 5). If the sample is divided into three regions (border, south, and rest), between-group inequality explains 66 percent. Again, this suggests a dominant role for the poor performance of the south in explaining the divergence across the period. VI. GROWTH Additional information on what may be driving dispersion can be gleaned from the evolution of the spatial distribution of growth rates. An analogous, if somewhat simplified, set of exercises can identify regional patterns of comove- ment in growth (see appendix at the end of this article for definitions). When the kernels are rerun with all possible definitions of neighborhood, they fail to reveal any significant visual regularities. Unconditional kernels show that the mass of probabilities seems to occupy the four quadrants more or less equally (figure 8): a state that grows fast today is as likely to grow slowly tomorrow as to continue to grow fast. This is not so surprising when it is remembered that in the pre-liberalization period many of the northern states had alternating high- and low-growth rates as a result of the 1982 debt crisis, which hit the most dynamic states the hardest. Something similar seems to have occurred at the end of the 1990s. The distribution shows greater variance in the post-liberalization period but still does not show strong persistence in growth rates. Conditioning on the different neighborhoods suggests little in the way of growth convergence clusters (figure 9). In every case, the central mass is fairly tightly aligned along the 45-degree reference, which suggests that states growing fast relative to the country also tend to grow fast relative to their neighbors. Aroca, Bosch, and Maloney 369 T A B L E 5 . Between- and Within-Group Inequality Contribution to Change in Ratio of Inequality Between-Group (Percent) Total Between Within to Total Inequality Between Within Year Inequality Group Group (Percent) Group Group 1970 0.078 0.038 0.040 49 1985 0.045 0.021 0.024 47 1993 0.073 0.038 0.035 52 2002 0.075 0.043 0.032 57 All regions 1970–85 50 50 1985–2002 72 28 Border-south-rest classification 1970–85 50 50 1985–2002 66 34 The overall Moran’s I-statistic using connectivity and the geographic bands suggests a degree of spatial dependence in the pre-liberalization period, but over time this dependence has decayed: there has been a despatialization of growth rates in Mexico (figure 10). For the distance from the U.S. neighborhood measure, however, no spatial dependence is apparent until the 1994–2002 period, coinciding with NAFTA. The local Morans at first seem to suggest that spatial growth patterns are dominated by the north–south dichotomy (table 6). During 1970–85, all mea- sures suggest positive comovements among border states in the third quadrant of low-growth states among low-growth states, but no other clusters (figure S.4). This border cluster disappears in the post-liberalization period, but Chia- pas, Guerrero, Oaxaca, Tlaxcala, and Veracruz replicate its behavior in the post-liberalization period: low-growth states among low-growth states (figure S.5). Additionally, the connectivity-based Moran suggests that the Mexico/ Federal District aggregation significantly underperforms in the early period, a time when its neighborhood was doing much better. These findings are consis- tent with the income convergence observed before liberalization and the diver- gence observed after. What is striking, however, is that for none of the definitions of neighborhood do the local Morans suggest a northern pole of growth in the post-liberalization period as a whole (see table 6, column 2). Instead, the local Morans suggest that there is mild evidence of a central cluster of high growth in the states of Aguascalientes and Guanajuato. Dividing the post-liberalization period into post-GATT and post-NAFTA subper- iods yields consistent but stronger results (figures 11 and 12). Since the only evidence of spatial dependence in the post-liberalization period comes in the exercise using neighborhood defined as the distance from the United States, the 370 THE WORLD BANK ECONOMIC REVIEW, VOL. 19, NO. 3 F I G U R E 8 . Unconditioned Kernel Density Plots, Growth, 1970–85 and 1985–2002 Source: Authors’ calculations based on census data from the Mexican National Institute of Statistics, Geography, and Informatics. Moran scatterplots are calculated using this measure of neighborhood. During 1985–93, the only major development is the extremely poor performance of southern states, especially Chiapas, Tlaxacla, and Veracruz. Although some southern states such as Puebla were growing faster than average, other poor Aroca, Bosch, and Maloney 371 F I G U R E 9 . Kernel Density Plots, Growth, Conditional on Spatial Lag, Neighbors, 1970–85 and 1985–2002 Source: Authors’ calculations based on census data from the Mexican National Institute of Statistics, Geography, and Informatics. central and northern states like Hidalgo, Nayarit, and Zacatecas performed below average, while rich states such as Aguascalientes, Chihuahua, and Quin- tana Roo grew steadily. These tendencies are consistent with increased income dispersion over this period, but they make clear geographic generalization 372 THE WORLD BANK ECONOMIC REVIEW, VOL. 19, NO. 3 F I G U R E 1 0 . Global Moran I, Growth Rates 5 GATT NAFTA 4 3 2 1 0 1970-75 1975-80 1980-85 1985-93 1994-2002 -1 -2 Moran's I (contiguity matrix) Moran's I (geographic bands) Moran's I (distance from the U.S. border) Source: Authors’ calculations based on census data from the Mexican National Institute of Statistics, Geography, and Informatics. difficult. Neither the north as a whole nor the border area constitutes a pole of comoving states driving divergence. The 1994–2002 period is also characterized by increasing but less dramatic diver- gence. However, again the border states do not seem to constitute a growth pole. Chihuaha, Coahuila de Zaragoza, and Nuevo Leo ´n perform above average, and Coahuila and Nuevo Leo ´n commove significantly. But Baja California Norte grows at below-average rates and Sonora and Tamaulipas at average rates. Clearly, this above-average performance by rich states while poor states grow at below-average rates will contribute to divergence. But, it is not the case that the border states as a group grew in a common way or dramatically outperformed the rest of the country. A clear growth pole does emerge among the second-line and central states of Aguascalientes, Guanajuato, Queretaro, and Zacatecas (see table 6, figure 12). Since these states are roughly equidistant from the border, this, not the comovement of the border states, is what drives the significant distance-based Moran I in this period. Since most of these states are relatively rich, their success suggests a potentially important dynamic outside of the border-south dynamic discussed above. The south as a whole still underperforms, especially Guerrero, although the southern block seems less coordinated than when the entire post-liberalization period is considered. In sum, it seems difficult to argue that a special reaction to NAFTA of the states closest to the border was the driving force behind divergence. The consistently poor performance of the south, which does form a regional cluster, emerges as a central element in the story. Aroca, Bosch, and Maloney 373 T A B L E 6 . Local Moran, Growth Rates 1970–85 1985–2002 1985–93 1994–2002 State C B D C B D C B D C B D Border Baja California ++ ++ Norte Chihuahua Coahuila de + + + Zaragoza Nuevo Leo ´n ++ ++ + + + Sonora ++ ++ ++ Tamaulipas ++ ++ North Baja California Sur + À Durango ++ San Luis Potosi + Sinaloa Zacatecas ++ ++ Center Aguascalientes + ++ Colima Guanajuato + ++ ++ Hidalgo Jalisco Mexico/Federal ÀÀ District Michoacan de Ocampo Morelos À + Nayarit À ++ + Queretaro de ++ Arteaga South Chiapas ++ ++ ++ ÀÀ Guerrero ++ + ++ + + Oaxaca ++ + ++ Puebla + À Tlaxcala + ++ ++ ++ + Veracruz-Llave À ÀÀ ++ ++ ++ ++ ++ ++ Yucata´n Peninsula Yucata´n + Quintana Roo Note: C, contiguity matrix; B, geographic band; D, distance from U.S. border. Source: Authors’ analysis based on census data from the Mexican National Institute of Statistics, Geography, and Informatics. 374 THE WORLD BANK ECONOMIC REVIEW, VOL. 19, NO. 3 F I G U R E 1 1 . Significance of Local Moran for Growth of GDP per Capita, 1985–93: Map and Moran Scatterplot Note: See table 1 for state abbreviations. Source: Authors’ calculations based on census data from the Mexican National Institute of Statistics, Geography, and Informatics. VII. CONCLUSIONS This article employs established techniques from the spatial statistics literature to investigate how spatial patterns of economic activity evolved during the period of Aroca, Bosch, and Maloney 375 F I G U R E 1 2 . Significance of Local Moran for Growth of GDP per Capita, 1994–2002: Map and Moran Scatterplot Note: See table 1 for state abbreviations. Source: Authors’ calculations based on census data from the Mexican National Institute of Statistics, Geography, and Informatics. trade liberalization and how these patterns may be related to the finding of increased divergence among state incomes. Three main findings emerge. First, the post-liberalization period was characterized by a tremendous increase in dispersion, which materialized in the constitution of several income clusters. However, these income clusters only partially map to geographic regions. 376 THE WORLD BANK ECONOMIC REVIEW, VOL. 19, NO. 3 Second, when regions are defined by spatial correlation in incomes, a ‘‘south’’ clearly exists, but the ‘‘north’’ seems to be restricted to the states directly on the U.S. border. Income levels fall off sharply immediately below the border and are distributed with no geographic pattern throughout the remaining, mostly cen- tral areas of the country. These findings appear inconsistent with the idea of an income gradient radiating from Mexico City and, to a lesser extent, a powerful gradient radiating down from the U.S. border. Third, overall the central dynamic of both the increased spatial dependency and the increased divergence lies not on the border, but more in developments in the south and to some degree in an emerging growth cluster in the north-center. The majority of the increased divergence of state incomes in the post-liberal- ization period is due to the increasing gap between the south and the rest of the country, and only modest explanatory power is gained by breaking out the border region. Further, post-liberalization growth rates are not especially tied to closeness to the U.S. border and, consistent with the nonspatial parametric literature, do not offer strong support for an increasing gradient from north to south. The substantial divergence occurring in the 1985–93 period seems unre- lated to the consolidation of a faster growing northern block, not even one of just the border states—only the south shows covarying growth rates across this period. In sum, two more likely explanations for the divergence occurring after trade liberalization than the strengthening of the border states are the sustained underperformance of the southern states, beginning before NAFTA, the treaty most affecting local agricultural industries, and to a lesser extent the superior perfor- mance of an emerging convergence club in the north-center of the country. APPENDIX. CONDITIONING OF KERNELS Definitions yt is the national average income per yit is the income per capita of state i in year t, " capita in year t, and ywt is the average income per capita of the spatial lag in year t. 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