Spatial Analysis of the Empirical Behavior of Municipal Institutional Capacity for the Formulation of Sustainable Growth Management Strategies with a Regional Focus: State of Veracruz, Mexico

As a governmental function, development for progress and welfare is a highly complex process that involves updating various attributes (such as a paradigm, critical or alternative, depending on of the way in which they are articulated regarding social aspects, environmental, and economic growth, as well as the institutional capacity of public and private actors). Regarding this, we are interested in the municipal institutional capacity (MIC) as a skill to carry out the functions and appropriate tasks that municipalities must fulfill in an effective, efficient, and sustainable way, and it varies considerably, depending on each local context. In order to analyze the relevance of the current official regionalization as a state government strategy for the centralized construction of MIC, an exploratory approach to its spatial behavior in the State of Veracruz, Mexico, was carried out. Given the nature of the study, a purely mixed approach, sequential exploratory design, subnational analysis methodology, and exploratory spatial data analysis (ESDA) were employed. The variable to be analyzed is the 2016 Municipal Functional Capacities Index (Índice de Capacidades Funcionales Municipales (ICFM)), with the Geostatistics Framework cartographic base of the 2020 Population and Housing Census. The analysis units are 212 municipalities in the 2014–2017 government period. As a result, it was confirmed that the current regionalization was irrelevant, owing to the absence of global spatial autocorrelation, and it was concluded that targeted interventions are necessary according to regional modeling techniques, based on scientific evidence.


Introduction
Institutional capacity (IC) is a common public management issue [1] that has gained space in development studies (the form of development that we mean is the development for progress and welfare, as conceived in The United Nations Global Goals for Sustainable Development (SDGs)) as both a theoretical question and operational concern, as there is consensus that conditions the results of government action [2][3][4][5][6][7][8][9][10][11][12]. Therefore, the strengthening of government capacities to manage development stands out in the objectives of various national and international projects that constitute axes of politics and contemporary public administration in Mexico such as the Sustainable Development Goals (SDG), the plans of development of the state and national government levels, as well as their sectoral and specific programs (Appendix A, Table A1).
Different authors agreed that the ICs vary considerably depending on each local context [2,[13][14][15][16], which explains the increase in the number of studies on determining used with claims of triangulation or increased validity, complementation, contextualization, and discovery and confirmation [29].
The first qualitative stage comprised the exploration of the theoretical approaches on institutional capacity, a focus on evidence-based policy, subnational analysis, exploratory spatial data analysis (ESDA), and background review through the collection and analysis of scientific sources such as journals and books in the ScienceDirect, Elsevier, and Google Scholar repositories, as well as the review of official, normative, and technical documents in national and international electronic institutional repositories such as the United Nations Development Programme (UNDP), the Government of Mexico, and the Government of the State of Veracruz.
This stage was supported by methods of content analysis and structured observation through data record techniques and file review. The results served as a basis for generating hypotheses that were tested in the second phase.
In the second phase, subnational analysis (SNA) was used as a research strategy for its usefulness to observe variations in relevant processes within countries [26]. In the election of SNA, its affinity with mixed methods was also considered [26,27]. The SNA research strategy makes it possible to operationalize theoretical models in order to know the state of the MIC in subnational spheres, either by breaking down capacity into dimensions and analyzing one or more of these in a particular way or by analyzing IC from a perspective comprehensive, where we proposed the ICFM as an index that supports and integrates 5 dimensions. These dimensions of capacity are (1) involvement of relevant actors; (2) identification; (3) formulation of policies and strategies; (4) budget, management, and implementation; (5) evaluation. Thus, to consult the ICFM methodology in an extensive detail, it can be carried out in the Informe de Desarrollo Humano Municipal 2010-2015 Transformando México desde lo local [7]. Therefore, the gap in our research design is understanding the dimensions separately, since we study the MIC using an integral index.
At this second phase, as an obligatory step in the scientific study of politics and development, the spatial behavior of MIC was described, spatial data were transformed into information with the support of the GeoDa spatial analysis software, and hypotheses were tested through quantitative analysis of spatial data patterns and graphical and statistical techniques. Among the indices to analyze spatial autocorrelation, the Moran's Index was used, as it is one of the best known and most widespread for this type of analysis. A characteristic of this index is that only the values of the analysis units, determined from the neighborhood criterion, are taken into account.
Finally, the results were contrasted with the theoretical approaches on institutional capacities to determine relevant information for the selection of modeling techniques based on scientific evidence, as further research.
The ICFM was built from the National Census of Municipal and Delegational Governments of the National Institute of Statistics and Geography (Instituto Nacional de Estadística y Geografía ((INEGI), 2017). The census gathers information through questionnaires answered directly by the bureaucrats; therefore, it entails at least two types of bias: (1) the bureaucrats limited to rationality and (2) the bureaucrat's uncertainty regarding the penalty or compensation for the response.

First Stage: Review of Theoretical Bases and Antecedents
The perception regarding development presented in this study is congruent with the one proposed by Mujica and Rincón [30], as a deliberate, multidimensional process of social change and structure and equalization of opportunities to promote capacities. IC studies seek to identify the institutional capacity deficit (ICD) [31] which, according to Oszlak and Orellana [32], could prevent or affect the performance of certain functions or the conclusion of programs or projects in development management. These gaps correspond to what Aguilar Villanueva [3] calls the institutional underdevelopment of the state.
Of course, in addressing the ICD problem, we consider essential the application of the evidence-based policy (EBP) approach, which claims that political actions must be supported by scientific knowledge in order to improve [33]. In this sense, it is also worth highlighting the importance of the application of the subnational analysis (SNA) strategy, which leads to a better understanding of the spatially uneven nature of contemporary transformations [27] and of spatial analysis, which studies the relationships between variables whose data are georeferenced and allow identifying the different spatial distributions of the variables and the importance that the spatial component exerts in these distribution patterns. According to Giraudy et al. [26] and Harbers and Ingram [27], the explanation of the spatial behavior of phenomena is an obligatory step in the scientific study of politics and development when variables related to geographic information (georeferenced data) are involved given that, by means of this, we can explicitly keep the concept of territory present in the analyses. Acevedo Bohórquez and Velásquez Ceballos [28], Giraudy et al. [26], and Harbers and Ingram [27] coincide in pointing out that studying subnational politics in a disciplined and evidence-based way implies evaluating the spatial effects through ESDA to avoid the risk of treating subnational units of analysis as independently distributed observations without previously considering the effect of spatial structures on the results, relationships of interest, and design and evaluation of analytical models. Therefore, supported by these authors, we considered that the information obtained in this way represents a valuable input for the formulation of correction strategies based on evidence, as it allows us to select an approach in accordance with the behavior of the data, whether it is national or subnational, leading to the implementation of targeted policies.
According to Acevedo Bohórquez and Velásquez Ceballos [28], this georeferenced information can present two types of spatial effects: spatial dependence and spatial heterogeneity. Spatial heterogeneity is related to the absence of stability in the behavior of phenomena in space, that is, the spatial units under observation are far from being homogeneous. This implies that functional parameters and forms vary with location and are not homogeneous across data sets. While spatial dependence refers to the fact that the data observed at one point in space are dependent on values observed at other points.
As Nohlen and Sturm [15] suggest, the concept of structural heterogeneity (SH) as a descriptive category is incorporated into the theoretical debate on development to designate a characteristic referred to a state of affairs and is used to explain asymmetric relationships such as different levels of development and imbalances in key development factors. Thus, it is particularly important for this study. Taking Montañez Gómez and Delgado Mahecha [14] into account, we considered that these differences between spaces require different levels of protection and encouragement to achieve equal opportunities for development.
Spatial dependence and spatial heterogeneity were analyzed in terms of spatial autocorrelation or spatial correlation. The main difference between the two is the univariate nature of the autocorrelation and the multivariate nature of the correlation (for a more in-depth study, refer to Siabato and Guzmán-Manrique [34]).
By means of spatial autocorrelation, the variability of a phenomenon through geographic space was analyzed in order to determine spatial patterns and describe their behavior [34], measuring the degree to which a variable correlates with itself in geographic space. Based on Siabato and Guzmán-Manrique [34], in practical terms, we can state that when the phenomenon tends to form conglomerates or clusters, autocorrelation is positive; if the phenomenon tends to be dispersed, the spatial autocorrelation is negative. However, when the phenomenon behaves randomly, without defined or structured behavior, there is no spatial autocorrelation.
In the literature, it was found that interest in studies that seek to evaluate the results of development in local governments based on their institutional capacities is recent in Latin America. In Cuba, prominent research includes a study by González Pérez et al. [35], which was carried out on the Bayamo municipality, and a case study of intervention, carried out on the Urbano Noris municipality by the Municipal Technical Group [36]. In Peru, the literature is more extensive, and the studies that stand out include those carried out on the district of Chavín de Huantar [37], the municipal government of the Province of Jaén [38], the Province of Chupaca [39], the District Municipality of Matapalo [40], and the district of Supe [41]. These studies have empirically verified the relationship between functional capacities and developmental outcomes.
In the case of Mexico, at the subnational level, there is a study of management capacities for development that analyzes the management components and their deficiencies in the Metropolitan Area of Toluca [42]. Furthermore, there are two MIC diagnostic studies that included the total number of municipalities with national coverage: the ICFM carried out by the UNDP, with data from 2016 [7], and the IDIM carried out by the Superior Audit of the Federation (Auditoría Superior de la Federación (ASF)), with data from 2013 [4]. Additionally, noteworthy, at the national level, are the programs that the National Institute for Federalism and Municipal Development (Instituto Nacional para el Federalismo y el Desarrollo Municipal (INAFED)) has implemented since 2004 (Table 1 to identify and develop the management capacities of municipalities throughout the country, based on their voluntary incorporation-a condition that has caused participation to be presented as an unstructured pattern among states (Appendix B, Figure A2). At an international level, these programs include the ISO 18091:2019 Quality management systems-Guidelines for the application of ISO 9001 in the local government and the same ISO 9001: 2015, Quality management systems-Requirements [43]. Hence, although references were found in the study of municipal government capacities, none were found from the perspective of the SNA using the spatial approach as a tool to support the construction of institutional capacity. Thus, the address of the problem from the proposed approach is innovative.
On the other hand, it was found that the State of Veracruz has undergone regionalization for various purposes: geomorphological purposes, considering 37 units belonging to 6 geomorphological provinces with 9 subprovinces [45]; cartographic landscape maps [46]; administrative purposes in terms of development planning, considering 10 regions [47], and recently, for the purposes of economic reactivation and return to the new normality, considering 5 regions [48].
The administrative regionalization based on 10 regions determined by criteria of geographic neighborhoods (as well as that based on 5 regions), was used for general purposes by different entities belonging to the Government of the State of Veracruz since 2005, promoted by the Statistical Information Center and Geographical of the State of Veracruz (CEIEG) [49], with some exceptions such as electoral, economic reactivation, and return to the new normality.

Second Stage: Spatial Analysis and Hypothesis Testing
The findings of the first stage of the study served as the basis for generating the following hypotheses: H0. There is no spatial autocorrelation in the IC of the 212 municipalities of the State of Veracruz, Mexico in the 2014-2017 government period.

H1.
There is a spatial autocorrelation in the IC of the 212 municipalities of the State of Veracruz, Mexico, in the 2014-2017 government period.
It is worth mentioning that in determining the territorial units of analysis, the theoretical considerations proposed by Giraudy et al. [26] were taken into account (Table 2). In the selection of the IC database with municipal subnational disaggregation level, compliance with the greater number of practical criteria proposed by Harbers and Ingram [27] ( Table 3) and the most up-to-date extracted information were considered (in this respect, it is important to consider that, although the INAFED programs are updated annually, they only contain data from the municipalities that join voluntarily, as the participation of the municipalities of Veracruz has fluctuated between 6% and 4% from 2016 to 2020; therefore, it was considered an insufficient sample to achieve representativeness of the data (Appendix B, Table A2).   Hence, the units of analysis are 212 municipalities of the State of Veracruz, Mexico, in the 2014-2017 government period (Appendix B). The variable to be analyzed is the ICFM 2016 [7] (available for download at https://www.mx.undp.org/content/mexico/es/home/l ibrary/poverty/informe-de-desarrollo-humano-municipal-2010-2015--transformando-.html, accessed on 29 January 2022), while the cartographic base is the Geostatistical Framework of the Population and Housing Census 2020 [50], coverage of the State of Veracruz (this cartographic base was used given that the municipal division remains unchanged since 2004, with the creation of the municipalities of San Rafael and Santiago Sochiapan).
The main results of the quantitative analysis of spatial patterns carried out using the free software GeoDa 1.18 (6/16/2021) for Mac OS X 11 (Big Sur) are presented below.

Global Autocorrelation
From the first law of geography proposed by Tobler ("Everything is related to everything else, but things that are close are more related than things that are far away", 1970, cited in by Siabato and Guzmán-Manrique [34]), a first-order queen-type contiguity matrix using the physical neighborhood criterion was considered, and a matrix (W) of 212 × 212 was defined, according to the number of analysis units (Table 4); that is, to quantify spatial autocorrelation and define it as non-existent, positive, or negative, the ICFM of each municipality was compared with those of their bordering neighbors, as can be seen in Figure 1.

Hypothesis Testing
The alternative hypothesis (H1) assumes that the spatial autocorrelation is different from 0, and the null hypothesis (H0) assumes that the spatial autocorrelation is equal to 0. Therefore, to carry out the hypothesis test, we proceeded to calculate the univariate Moran's Index, obtaining 0.039 as a result (Figure 2).

Hypothesis Testing
The alternative hypothesis (H1) assumes that the spatial autocorrelation is different from 0, and the null hypothesis (H0) assumes that the spatial autocorrelation is equal to 0. Therefore, to carry out the hypothesis test, we proceeded to calculate the univariate Moran's Index, obtaining 0.039 as a result ( Figure 2).   To interpret the value of the Moran's Index and give it statistical validity, based on Getis [51], Siabato and Guzmán-Manrique [34], and Huitrón Mendoza [52], a complete spatial randomness test (CSR) was carried out. Considering a confidence level of 99% and a significance level of 0.01, the Monte Carlo simulation [53,54] was carried out as a reference distribution with 999 permutations (which can be understood as scenarios), a z-value of 1.0480, and a p-value of 0.15 ( Figure 3) were obtained. According to Getis [51] and Celemín [54], if the z-value score or the p-value indicates statistical significance, the null hypothesis can be rejected. Given that the p-value did not update the assumption of being less than or equal to the level of significance [55], the statistical significance of the z-value was evaluated [56].  To interpret the value of the Moran's Index and give it statistical validity, based on Getis [51], Siabato and Guzmán-Manrique [34], and Huitrón Mendoza [52], a complete spatial randomness test (CSR) was carried out. Considering a confidence level of 99% and a significance level of 0.01, the Monte Carlo simulation [53,54] was carried out as a reference distribution with 999 permutations (which can be understood as scenarios), a z-value of 1.0480, and a p-value of 0.15 ( Figure 3) were obtained. According to Getis [51] and Celemín [54], if the z-value score or the p-value indicates statistical significance, the null hypothesis can be rejected. Given that the p-value did not update the assumption of being less than or equal to the level of significance [55], the statistical significance of the z-value was evaluated [56].
14, x FOR PEER REVIEW 10 of 23 According to the table listing critical values of standard normal distribution [51,[56][57][58] for two-tailed situations [34], given that the critical value of z-value necessary to construct a distribution with a confidence value of 99% and a significance of 0.01 is 2.57 and 1.0480 < 2.57, based on Getis [51], Anselin et al. [53], Celemín [54], Siabato y Guzmán-Manrique [34], and the statistical evidence, the null hypothesis (H0) of the absence of spatial autocorrelation was confirmed. The Critical Values of Standard Normal Distribution for Two-Tailed Situations can be found in Johnson and Kuby [59].
To corroborate that the result was not influenced by an inappropriate election of neighborhood matrix, the neighborhood criterion of first-order queen matrix was changed to first-order rook (Appendix D, Table A3, and Figures A3 and A4, and it was observed that there were no significant changes, as the absence of spatial autocorrelation was confirmed with both arrangements.
Consequently, and in accordance with the three basic spatial patterns by Siabato and Guzmán-Manrique [34], in general, we can conclude that the ICFM variable behaves in space following a random pattern, as no defined or structured behavior was identified. The result of the analysis is statistically significant, with a confidence level of 99%.
When analyzing the behavior by quadrant, it can be observed how this unstructured pattern manifests itself. Quadrant I shows the municipalities with a high ICFM whose neighboring municipalities have a high ICFM (Figure 4). Quadrant II shows the municipalities with a low ICFM surrounded by the municipalities with a high ICFM ( Figure 5). Quadrant III shows the municipalities with a low ICFM surrounded by the municipalities with a low ICFM ( Figure 6). Quadrant IV shows the municipalities with a high ICFM surrounded by the municipalities with a low ICFM (Figure 7). At this point, it is convenient to highlight that the ICFM classification as high or low obeys the level of the IC of each municipality of the research context in relation to those of the other municipalities of the State of Veracruz. Thus, it should not be assumed to be comparable to the classification of very high, high, medium, and low levels of the 2010-2015 Municipal Human Development Report Changing Mexico from the local by UNDP [7]. According to the table listing critical values of standard normal distribution [51,[56][57][58] for two-tailed situations [34], given that the critical value of z-value necessary to construct a distribution with a confidence value of 99% and a significance of 0.01 is 2.57 and 1.0480 < 2.57, based on Getis [51], Anselin et al. [53], Celemín [54], Siabato y Guzmán-Manrique [34], and the statistical evidence, the null hypothesis (H0) of the absence of spatial autocorrelation was confirmed. The Critical Values of Standard Normal Distribution for Two-Tailed Situations can be found in Johnson and Kuby [59].
To corroborate that the result was not influenced by an inappropriate election of neighborhood matrix, the neighborhood criterion of first-order queen matrix was changed to first-order rook (Appendix D, Table A3, Figures A4 and A5, and it was observed that there were no significant changes, as the absence of spatial autocorrelation was confirmed with both arrangements.
Consequently, and in accordance with the three basic spatial patterns by Siabato and Guzmán-Manrique [34], in general, we can conclude that the ICFM variable behaves in space following a random pattern, as no defined or structured behavior was identified. The result of the analysis is statistically significant, with a confidence level of 99%.
When analyzing the behavior by quadrant, it can be observed how this unstructured pattern manifests itself. Quadrant I shows the municipalities with a high ICFM whose neighboring municipalities have a high ICFM (Figure 4). Quadrant II shows the municipalities with a low ICFM surrounded by the municipalities with a high ICFM ( Figure 5). Quadrant III shows the municipalities with a low ICFM surrounded by the municipalities with a low ICFM ( Figure 6). Quadrant IV shows the municipalities with a high ICFM surrounded by the municipalities with a low ICFM (Figure 7). At this point, it is convenient to highlight that the ICFM classification as high or low obeys the level of the IC of each municipality of the research context in relation to those of the other municipalities of the State of Veracruz. Thus, it should not be assumed to be comparable to the classification of very high, high, medium, and low levels of the 2010-2015 Municipal Human Development Report Changing Mexico from the local by UNDP [7].

Local Autocorrelation
On the other hand, given the value of Moran's Index (0.039), it was considered convenient to analyze the local autocorrelation in order to investigate if there are any poles of attraction. Considering the same weight matrix with the physical neighborhood criterion in first-order queen contiguity (Table 4)

Discussion
Both empirically (−0.35 ≤ I ≤ 0.35) [34] and statistically (with 99% confidence level and 0.01 significance level), based on Getis [51], Anselin et al. [53], Celemín [54], Siabato y Guzmán-Manrique [34], the results confirmed that owing to the absence of global spatial autocorrelation, the institutional capacities of the municipalities of the State of Veracruz, Mexico, in the government period 2014-2017, presented a random spatial behavior pattern [34]. Thus, in agreement with Giraudy et al. [26], we argue that this result justifies a strategy of independent units in future work on modeling interventions for capacity building as "an empirical test that shows that the spatial dependence among the units is low or non-existent would constitute a solid basis for a strategy of the independent units." [26].
On the other hand, the assumption raised by Nohlen and Sturm [15] regarding structural heterogeneity owing to the presence of asymmetric relationships in MIC levels was also confirmed as a key factor in development-a situation that, according to Montañez Gómez and Delgado Mahecha [14], requires different levels of protection and encouragement to achieve equal opportunities for development. These asymmetries, according to John Rawls [60], are inequalities of the basic structure, where the principles of social justice must be applied at the first instance, and according to Amartya Sen [61], the most obvious inequalities are in distribution, which must be counterbalanced to approach equality of basic capabilities.
Findings will serve as bases for establishing priorities and identifying promissory concepts and variables to determine the regionalization model [62] with the best adjustment for the centralized promotion of IC in the municipalities in future scenarios.

Conclusions
Based on the findings and the proposals of the SNA and the EBP, we conclude that for the purposes of the study and management of the MIC, the current official regionalization of the State of Veracruz, Mexico, based on the criterion of geographic neighborhoods, results in an arbitrary delimitation of spatial units, given that it is not justified theoretically or empirically, as it is not consistent with the pattern of random spatial behavior observed.
In turn, we consider that the dispersion observed in the MIC levels and the fact that this is low on average confirms the presence of structural heterogeneity, and with it, spaces that, in order to achieve equal opportunities for development, deserve greater protection and encouragement than others. Thus, consistent with EBP, centralized promotion of MIC development requires data-supported regionalization. Hence, future research will consider regionalization modeling techniques for the centralized impulse of MIC suitable for differentiated attention, based on the grouping of municipalities according to their IC level. From the behavior of the data, we also deduced that the application of modeling according to independent units and based on a policy to promote equality, supported by scientific evidence, is of potential value to strengthen the results of capacity building actions of INVEDEM, as well as to seek greater protection and encouragement to the municipalities that most require it, in accordance with their particular conditions as sustainable growth management strategy with a regional focus. Hence, the main implication of this study of spatial analysis of the empirical behavior in the municipal institutional capacity is to reveal a promising line of research in order to formulate sustainable growth management strategies with a regional focus, based on evidence.
Finally, it is important to specify that although the State of Veracruz has MIC studies, they lack temporal stability. In this respect, it is important to emphasize the limitation that this condition represents for historical-comparative studies that allow finding determinant factors of MIC. Therefore, it is also essential to launch an appeal to INVEDEM, in order to address this issue and assume active participation and leadership within the projects established in the State Program of Statistics and Geography 2019-2024, whose aims are to evaluate and determine the demand for statistical and geographic information, analyze relevant and current information, and integrate the state catalog of indicators. Data Availability Statement: The publicly archived datasets analyzed during the study were consulted at: https://www.mx.undp.org/content/dam/mexico/docs/Publicaciones/PublicacionesRed uccionPobreza/InformesDesarrolloHumano/idhmunicipal20102015/IDHMunicipal%20Bases%20d e%20datos%20y%20programas%20de%20calculo.zip and https://www.inegi.org.mx/contenidos/pr oductos/prod_serv/contenidos/espanol/bvinegi/productos/geografia/marcogeo/889463807469/3 0_veracruzignaciodelallave.zip; in both cases, accessed on 31 January 2021.

Conflicts of Interest:
The authors declare no conflict of interest.

Appendix D
Spatial analysis using first-order rook-type contiguity matrix.

Appendix D
Spatial analysis using first-order rook-type contiguity matrix.   Spatial analysis using first-order rook-type contiguity matrix.