Subnational Analysis of Economic Fitness and Income Dynamic: The Case of Mexican States

Abstract

In recent years, analytical tools of network theory have provided strong empirical support to the well-known hypothesis that regions develop through the local learning of capabilities (tacit productive knowledge). In this paper, we compare two indexes of competitiveness (or accumulated capabilities) for a subnational database of 32 Mexican states in the period 2004–2014. We find that Endogenous Fitness (i.e., region fitness and product complexity are derived jointly using only a Mexican exports database) has a better performance than Exogenous Fitness (i.e., product complexity comes from a world exports database and fitness is the sum of the complexity scores for the region’s competitive products). The performance criterion is established with the indicator’s capacity to meet a requirement of growth predictability: the existence of at least one laminar (ordered) regime in the fitness–income plane. In the Mexican data, Endogenous Fitness is a reliable predictor of per capita GDP in two distinct areas of the plane: one of continuous progress and opportunities, and another of stagnation and deteriorating fitness. The predictive capacity of this indicator becomes clear only when the metrics’ calculations are filtered by removing raw petroleum or oil-dependent states, while such capacity is robust to the inclusion of tourism—another important industry of the Mexican economy.

1. Introduction

Contrary to the propositions of conventional trade theory, the empirical evidence suggests that most countries are competitive in a variety of products. This evidence also indicates that the degree of diversification observed in the productive structure of countries is associated with their level of development [1,2,3]. In particular, richer countries tend to compete with many goods in international markets, some of them produced by very few countries and exhibiting a high added value, while the structure of poor countries is much less diversified and limited to unsophisticated goods facing many competitors [4].

Moreover, historical analyses of comparative economic systems assert that developing countries start a path of sustained growth after substantial modifications in their productive structure are undertaken, so that their industries are reconverted and their economies become more diversified [5,6,7,8,9,10]. Nonetheless, these structural transformations are not explained by neoclassical economists, nor are they thoroughly considered when formulating their growth theories (see Remark 1 in Appendix A1). However, these transformations and their implications on growth have been addressed by several scholars of alternative persuasions, as illustrated by pioneers of development economics [11,12,13], evolutionary economists [14,15], and post-Keynesian economists [16,17].

All in all, these studies argue that the productive diversity of a country (or region) is associated to its local capabilities; thus, economic development has to be conceived as a process where capabilities are created and adapted. In other words, growth is possible because the set of tacit productive knowledge widens through a dynamic of learning. These productive capabilities can be human (know-how), physical (infrastructure), and institutional (governance); whatever the case, they are a form of knowledge that is very difficult to transfer through patent acquisition, imitation, foreign direct investments, or imports. Accordingly, each region’s capabilities impinge critically on the nature of its productive structure and on the development path of its economy [18].

Recently, an innovative literature has emerged that endorses this point of view while providing a strong empirical support [19,20]. This line of research is a data-driven framework that uses network tools intensively. Likewise, it advocates a complexity vision that describes competitiveness as property emerging from a system with interactive productive units. Hence, economic development is seen as a form of exploration within a network, whose topology is described with a set of nodes that represent tradable products and links between nodes that are estimated through a measure of “proximity” [21,22] (see Remark 2). In this product space, any country’s productive structure (or export profile) can be characterized as the subset of nodes whose revealed comparative advantage (RCA) is relatively large (i.e., the country is competitive in producing such goods).

Although this methodology was initially elaborated for analyzing the fitness (competitiveness or economic complexity) of countries, it is also possible to carry out subnational studies to determine the competitiveness of the regional economies of a particular country. This is so, regardless of the fact that within a country there is labor mobility and a relatively homogeneous institutional setting. The approach is valid at this level of aggregation if those capabilities that make one region more competitive than others are related to the superiority of its tacit knowledge, which is not easily transferred. Among these, organizational (e.g., logistics) and technological (e.g., trained workers) capabilities might be critical. Likewise, studying productive knowledge at a relatively disaggregated level is very important since it allows the identification of the geographical location of potentially competitive industries inside the national territory. It is precisely at the state level that a large set of industrial policies is commonly designed and implemented in reality. Therefore, our paper is framed in the very recent, but growing, literature of the subnational analyses of complexity and economic development [23,24,25,26,27,28,29,30,31].

Here, we calculate several indexes of fitness for the 32 states that compose the Republic of the United States of Mexico (the main reason for selecting the Mexican case is data availability; see Appendix A2 for details). Our main objective is to compare two alternative measures of fitness and evaluate them according to their potential to predict income growth. The first one, Endogenous Fitness, is computed directly from the framework’s metrics when applied to a database of products exported by Mexican states. The algorithm for calculating these metrics produces jointly indicators of product complexity and region fitness. The second one, Exogenous Fitness, is estimated indirectly through the arithmetic sum of the complexity scores that correspond to the competitive products in the state; previously, we have obtained such scores by applying these metrics to an international database of exports.

Once the rankings of these two indexes are computed and compared, we analyze the dynamic between per capita Gross Domestic Product (GDP_p) and each of these two fitness indicators for the 32 states along the sampled period. This is done through a variant of a procedure known as “Selective Predictability Scheme” which does not impose ex-ante linearity between variables. The proposed variant is very helpful when the analyst has a very limited number of observations [28]. According to this method, a variable (fitness) has predictive capacity over another (GDP_p) when there is a laminar (ordered) regime in a system defined in the fitness–income plane. That is, for any pair of coordinates in the area associated to the ordered regime, there is a high degree of predictability with respect to the direction that these variables will follow in the proximate future (around 10 years).

With these tools, we find empirical support to the hypothesis that Endogenous Fitness is more suitable for predicting purposes since the longitudinal data for the period 2004–2014 generates laminar regimes across the plane. Another interesting result is that there are two clear prospects for the Mexican regions. One for states with scant productive capabilities (either poor or heavily concentrated in few economic activities), where a daunting scenario prevails: a pattern of stagnation in GDP and regressive fitness. Another for states with a good backing of capabilities, where there is a virtuous circle: a pattern of continuous improvements in fitness along with positive growth in per capita income.

We divide the rest of the paper into six more sections and several appendixes. Section 2 explains how capabilities (an unobservable variable) can be inferred from a bipartite network established with the different states’ exported products (an observable variable). Section 3 specifies the mathematical formulas for the two metrics of fitness considered here and presents the associated rankings for the Mexican states. Section 4 describes the method of selective predictability and shows the empirical results for the dynamic of income and Exogenous Fitness. Section 5 explores the dynamics of income and Endogenous Fitness, once the sample is filtered by removing the most important export commodity in the country: raw petroleum. Section 6 evaluates the system predictability with an alternative indicator of competitiveness, which is frequently used in the literature: Economic Complexity. Section 7 conducts a sensibility analysis of the fitness index when a key service sector of the Mexican economy is included: tourism. Finally, the paper ends with a summary of the results and some additional considerations.

2. Productive Capabilities and Regional Development

The growth of an economy is an evolutionary process where new products keep appearing in the region’s productive structure as new capabilities emerge [32]. According to empirical evidence, the new products tend to be more sophisticated than the established ones; likewise, some of the latter are displaced in a process of creative destruction, as suggested by Schumpeter [33] and estimated by [34] based on the complexity framework. Therefore, if we associate the level of economic development with the available productive knowledge, then it is imperative to measure the nature and quantity of these capabilities. If we could determine the existing capabilities in a region, it would be possible to specify with some degree of confidence the path of its economy in the near future.

Unfortunately, the capabilities located in different regions (or countries) are not easy to quantify directly, and it is even more difficult to make regional comparisons. This is the case because (1) we are dealing with a multidimensional concept whose elements are not clearly delineated and (2) there are no accepted standards to create comparable indicators nation-wise (or world-wise). The number of existing capabilities around the world is very large, especially if we realize that some of them are close substitutes (i.e., a social norm can provide the same functions as a formal rule). Even if the analysis only considers complementary forms of productive knowledge, it is impossible to establish a mapping from these capabilities to different outputs—as in a neoclassical production function.

Consequently, for a better understanding of how the productive structure of a region evolves, we need a methodology that estimates these capabilities indirectly from a set of observable and measurable variables. Because the goods sold through markets are the output of a process that articulates these capabilities, the production pattern of a region can be formally associated to its underlying capabilities. Thus, instead of working with a tripartite network (products, capabilities, and regions) that includes a non-observable variable (nodes of capabilities), it is preferable to work with a bipartite network (products and regions) based only on observable variables.

The export profile of a region determines the location of its competitive nodes in the product space, and this, in turn, impinges upon the region’s development perspective (see Remark 3). Although all regions have the opportunity of gaining competitive advantages in new products while developing the required capabilities, the number and nature of such products are to a large extent conditioned by their current productive structures. In other words, each region’s subspace embodies its tacit productive knowledge and, hence, sets its growth potential. Thus, in order to infer the trajectory of income that a particular economy will follow in a time frame of 5–10 years, a first step is to establish a metric for evaluating the region’s degree of fitness (or sophistication) from the set of products that composes its export profile.

With this aim, two groups of researchers [4,20] have built indexes of competitiveness that combine two features: how diversified an economy is and how ubiquitous their competitive products are. While the Latin American authors talk about the Economic Complexity Index (ECI), the Italian researchers make reference to the Fitness Index (Fit). These two features are related to the links of the bipartite network and reveal non-monetary information with regard to the abundance and sophistication of the economies’ embodied capabilities. That is, these researchers use alternative metrics of the nodes’ centrality in the network for measuring the complexity of regions and products.

Intuitively, a region that possesses a large variety of capabilities has a high probability of producing many goods (diversification), and if part of this knowledge is scantly shared with other regions, then some of its export will not have many competitors (ubiquity). Both features are essential for a good characterization of competitiveness. It is not enough to infer a high degree of complexity (fitness) for a region by observing that some of its exports have a reduced ubiquity, since this could only be a consequence of the availability of a very scarce natural resource worldwide (e.g., raw diamonds exported by Sierra Leona or Botswana). Additionally, one cannot infer the presence of a very sophisticated economy by noticing a relatively large amount of exported product (e.g., in manufacturing and agriculture), since this could only be the result of cheap labor and fertile conditions for arable land.

3. Two Forms of Measuring Economic Fitness

In this paper, we focus on the fitness index developed in [20,35]. These authors estimate jointly two types of indicators: one for the economic fitness of regions and another for the complexity of products. Their metrics are derived from the idea that products exported by developed regions provide relatively little information about the complexity of a product, because these regions tend to produce many things due to their vast productive knowledge. In contrast, developing regions compete in international markets with a short list of very simple products (e.g., commodities or low value-added goods). Therefore, although it make sense to measure the competitiveness of a region considering the summation of its competitive exports’ complexity, it is not convenient to measure product complexity as the average competitiveness of all the regions that export such a good (see Remark 4).

Instead, a theoretically better definition of product complexity should, first of all, take into account that the sophistication of a good is negatively related with the number of regions exporting it (see Remark 5). That is, the more regions produce the good (high ubiquity), the lower its complexity tends to be. Secondly, this summation should give different weights to the regions producing it, so that highly diversified economies contribute very little to the sum. Hence, the fitness scores of all the regions that export the good competitively are added inversely. Therefore, a good that is produced by many regions with reduced fitness leads to its identification as a low complexity product. As can be inferred from this explanation, the metrics for the fitness of regions and the complexity of products are not associated linearly. Accordingly, they can be mathematically described by means of two coupled systems of non-linear difference equations:

$${\tilde{F}}_s^{\left(n\right)}= {\displaystyle \sum }_P{M}_{sp}{Q}_p^{M\left(n-1\right)}$$

(1)

$${\tilde{Q}}_p^{M\left(n\right)}=\frac{1}{{{\displaystyle \sum }}_s{M}_{sp}\frac{1}{F_s^{\left(n-1\right)}}}$$

(2)

where $M_{sp}$ is a binary state-product matrix, so that $M_{sp}=1$ if the Mexican state “s” is competitive in exporting product “p” (i.e., if $RC{A}_{sp}\ge 1$) and $M_{sp}=0$ otherwise; $F_s$ is a vector that defines the fitness (competitiveness or sophistication) of each of the S states that integrate the dataset; $Q_P^M$ is a vector that indicates the complexity scores of the P products exported competitively by the Mexican states; n refers to the iteration number of a recursive process described by the difference equations (in the empirical analyses presented here, n = 100; see Remark 6); the tilde (~) on the endogenous variable specifies that the results obtained in each iteration are normalized by the mean value of the corresponding indicator; thus, ${\tilde{F}}_s$ y ${\tilde{Q}}_p^M$ are the indicators before normalization. The initial conditions for the algorithm are as follows: $F_s^{\left(0\right)}=1$ and $Q_p^{M\left(0\right)}=1$; however, after a large number of iterations, the coupled systems converge to the same values, independently of the initial conditions [35].

The coefficient of the revealed comparative advantage (RCA) for product “p” is then defined as the ratio between the share of exports of product “p” in the Mexican state “s” and the total exports of that state, divided by the share of exports of product “p” across states with respect to the sum of all Mexican exports. Mathematically,

$${\mathrm{RCA}}_{sp}=\raisebox{1ex}{$\frac{x\left(s,p\right)}{{{\displaystyle \sum }}_{p}x\left(s,p\right)}$}\!\left/ \!\raisebox{-1ex}{$\frac{{{\displaystyle \sum }}_{s}x\left(s,p\right)}{{{\displaystyle \sum }}_{s,p}x\left(s,p\right)}.$}\right.$$

(3)

Consequently, the lower the fitness of a particular Mexican state ($F_s$), the higher the weight of that state in the summation, and the lower the complexity of the product. Moreover, it is important to notice in Equation (1) that, if a state becomes more diversified, its fitness score always increases. This does not necessarily happen with the averaging procedure of ECI, since the economic complexity of a region goes down when the productive structure is enlarged with a product whose complexity is lower than the average.

As an alternative to the metric of Endogenous Fitness (EndoFit), where the indicator is calculated using only information of Mexican exports, there is a variant that makes use of export data for a large set of countries. This variant is defined in [28] as Exogenous Fitness (ExoFit) since the scores for the products’ complexity are obtained through EndoFit applied to the world exports database. Then, these scores are used as weights in the summation of the states’ competitive products in order to establish the fitness indicator. Here, we define the RCA coefficient with the regional share of the product in the total of state exports divided by its international share in the total of world exports. The idea is that the complexity of a product is a notion related to the nature of the required capabilities (or tacit knowledge), independently of the region where it is produced. Hence, data from tradable goods at a world scale help to reduce the possibility of a bias in the indicator coming from the local conditions that prevail in a particular economy, such as trade barriers or subsidies. Consequently, the mathematical formulation for calculating this metric is as follows:

$$\begin{array}{c}{\tilde{F}}_s= {\displaystyle {\displaystyle \sum }_p}{M}_{sp}{Q}_p\\ F_s= \frac{{\tilde{F}}_s}{{\tilde{F}}_s{}_s}\end{array}$$

(4)

where ${\tilde{F}}_s{}_s$ is the mean value across states of the non-normalized fitness indicator; $Q_p= Q_p^M=Q_p^W$ is the product complexity for the Mexican states’ export goods. This, in turn, is defined in terms of the product complexity calculated from the metric of Endogenous Fitness (Expressions 1 and 2) that uses the world exports database.

A thorough analysis of the Mexican economic complexity at a subnational level is presented in [23,31]. In both papers, the ECI metrics are considered, but the former uses export data while the latter uses industrial employment data (i.e., agriculture is not included). In Figure 1, we show the rankings for the 32 Mexican states in 2014 calculated with the two alternative indexes of fitness. Despite the fact that EndoFit is measured using exclusively data of products exported by the Mexican states, these two rankings are extremely similar. Therefore, we may argue that both metrics produce similar classifications for the 32 states in terms of their economic fitness, and in this regard there is no “Mexican bias”. However, the reader should be aware that similar rankings do not imply that both indicators are equivalent in all respects and that they have the same predictive (or explicative) power. A high Spearman correlation does not necessarily mean that the magnitude of the differences across scores is preserved between indicators (see Remark 7 and Appendix A6).

Notice that in both rankings the State of Mexico is at the top followed by Mexico City; the former is a very industrious state surrounding the country’s capital. Many of the states with a high score of fitness are located on the Mexican border with United States (Nuevo Léon, Baja California, Tamaulipas, Chihuahua, Sonora, and Coahuila); some others in the north-central region of Mexico called “El Bajío” (Querétaro, San Luis Potosí, and Guanajuato), a dynamic and prosperous territory; plus Jalisco in the central-pacific region, whose capital is the second largest city in the country (Guadalajara). In the other extreme, some of the states with the lowest ranking in both metrics are located on the southern Mexican border or close to it (Guerrero, Chiapas, Oaxaca, Campeche, and Tabasco); the first three are relatively poor in terms of their per capita GDP, while the last two are oil-dependent economies. Two important exceptions with regard to the geographical position are Nayarit (central-pacific region) and Baja California Sur (northern-pacific region). Coincidentally, these two have relatively small economies with a heavy reliance on tourism, which is especially important in the latter state.

4. The Dynamic of Income and Exogenous Fitness

In this section, we are interested in analyzing the dynamic process that relates a monetary indicator of aggregate performance (GDP_p) with our intrinsic indicator of the productive knowledge available in the region (ExoFit). The purpose is to establish whether or not Economic Fitness can be a reliable measure to predict income growth in a span of 10 years. This can be done by means of a variant of a non-parametric prediction method called the Selective Predictability Scheme (SPS). This procedure was developed in [36] based on some features of the Method of Analogues, initially designed for weather forecasting [37]. The idea is that by discovering regularities in the pattern of time series, one can find situations in the past that are close to those currently observed and, from this, infer which will be the system trajectory in the near future. The SPS methodology was originally implemented for the analysis of the income dynamic at the country level (see Remark 8), but it was later modified for its application at a subnational level in [28], where the number of observations across states tends to be rather limited.

Before describing how this method operates, it is important to emphasize that it does not assume a linear relationship between GDP_p and Fitness or any other functional relationship. This is a crucial advantage since the traditional regression analyses used by economists assume parameter homogeneity across all observations. That is, econometric estimates describe the relationship between variables for a hypothetical unit that corresponds to the average observation value across regions and periods; hence, it is difficult to believe that the same estimated parameter holds for any unit (region-period) in the sample. Thus, in an attempt to circumvent this problem analysts estimate polynomial functions for specific independent variables (see Appendix A6). In contrast, in this non-parametric method, linear or non-linear relationships are possible, which means that the functional form has to be detected from the data and not imposed by the statistical model. Moreover, it takes into account that the non-linearity of a system not only has to do with the functional relationship between variables, but also with different dynamics that emerge depending on whether certain driving forces increase or decrease.

Instead of using a measure of concentration that helps to delimit the predictability regions in the fitness–income plane, as in the original SPS, this newer version makes use of a measure of direction. The latter allows us to determine whether the vectors located in the threshold area of a specific cell of a grid, dividing the plane, tend to be positioned in parallel during the established time window [t₁, t₂]. In other words, the method estimates a coefficient ${\tilde{D}}_k\in \left(-1, 1\right]$, which measures the dispersion of directions for all vectors that depart from the threshold area around the centroid of cell k in t₁ and arrive at any point of the fitness–income plane in t₂. We divide the plane with a grid of 100 × 100 cells whose extension is defined in terms of the data range, while the sides of the threshold areas are established with a specific bandwidth for each of the two axes. The smaller the value of ${\tilde{D}}_k$, the larger the dispersion of the vectors’ direction. This coefficient is calculated for a cell when at least three observations at t₁ lie within the corresponding threshold area. For expositional reasons, the cells are colored according to the dispersion of observed trajectories in their threshold areas. A dark green color is used for cells whose vectors evolve in parallel, and a red color for cells whose vectors are directed unevenly. The mathematical expression for this measure of dispersion in the directions of motion is defined as an average dot product:

$${\tilde{D}}_k=\frac{2}{N\left(N-1\right)}{\displaystyle \sum }_{i<j}^{1,N}{\widehat{v}}_i·{\widehat{v}}_j$$

(5)

$$\begin{array}{l}\mathrm{with} {\widehat{v}}_i= \raisebox{1ex}{${\overrightarrow{v}}_i$}\!\left/ \!\raisebox{-1ex}{$\left|v_i\right|$}\right.; {\overrightarrow{v}}_i=a_i\widehat{i}+b_i\widehat{j}; \left|v_i\right|=\sqrt{a_i^2+b_i^2}; a_i=\log \left(F_i\left(t_2\right)\right)-\log \left(F_i\left(t_1\right)\right)\\ b_i=\log \left(GDP{p}_i\left(t_2\right)\right)-\log \left(GDP{p}_i\left(t_1\right)\right); \widehat{i}=\left(1,0\right); \widehat{j}=\left(0,1\right).\end{array}$$

(6)

where F_i is the fitness index; $\widehat{i}$ and $\widehat{j}$ are the versors (unit vectors) in the fitness and GDP_p directions; N is the number of states whose starting coordinates lie inside the threshold area of cell k. Because the time range of the available data is limited, we select as a window [t₁ = 2004, t₂ = 2014].

Furthermore, we obtain estimates of the versors’ directions in regions of the plane where there is historic information by establishing another grid with wider cells (10 × 10). As performed in [28], we sum all vectors within each cell and then calculate its corresponding versor. In this fashion, we can detect empirically the type of regions that describe the evolution of Mexican states in the fitness–income plane. Theoretically, there can be a region with a “laminar (ordered) regime” where most versors (or arrows) present similar directions, but also a region with a “chaotic regime” where the arrows point toward different directions with no distinguishable pattern. When the initial coordinates of a state are located in a laminar regime, it can be argued that the fitness index has certain predictability with regard to the future evolution of GDP_p, in contrast with the scenario that prevails when the state’s coordinates are positioned in a chaotic regime (see Remark 9).

Although per capita income and fitness are only two variables of a multidimensional vector that can help to predict economic growth, the methodology described above reduces this system to a bi-dimensional relationship when the laminar regime emerges. On the contrary, the chaotic regime can be empirically observed for two different reasons: (i) the system is indeed chaotic and, hence, similar initial conditions might exhibit very different trajectories, which ensues a low predictability; (ii) the multidimensional relationship cannot be synthetized with just two variables, so more information is required to understand the income dynamic in those states. In any case, if the data analysis shows the existence of different regimes, or several laminar regimes with different trajectories, this implies that the presumed non-linearity is, indeed, an empirical fact.

In Figure 2, we show the fitness–GDP_p plane in a logarithmic scale with the starting and ending coordinates for all yearly observations during the period 2004–2014 across the 32 states. In this case, we use the ExoFit metric for the horizontal axis. The most salient feature is that the trajectories of two particular states (Campeche and Tabasco) can be considered as outliers. The low fitness scores of such states seem to be in contradiction with their high GDP_p. This paradoxical combination is the result of these economies being heavily dependent on crude oil production. This is a signal that, for Economic Fitness to be a good predictor of future income growth, it may be important to recalculate the indicator without oil production, or set aside those states that are very dependent on the exploitation of this natural resource.

Before the sample is filtered for a new calculation of the fitness scores, we show the coefficients ${\tilde{D}}_k$ in the top panel of Figure 3. As mentioned above, and for illustrative purposes, the cells whose estimated value indicates a high dispersion in the directions of motion are highlighted with the color red, while vectors that follow closely the same trajectory are distinguished with the color green. Notice that there are relatively few greenish cells in the grid and quite a few with a reddish tone; hence, the ExoFit indicator that includes the whole sample is a relatively poor predictor of growth, even for those states that are not oil-dependent (see Remark 10). This result is also evident in the bottom panel of Figure 3, where versors are estimated with wider cells. For states with a fitness value below −1 (in the logarithmic scale), there seems to be a laminar regime since most arrows tend to point toward a similar direction. However, this is a bizarre scenario since it indicates that states with a low Economic Fitness tend to grow slightly but at the expense of a narrowing productive structure. In contrast, for states with middle and high fitness, there seems to be a chaotic regime since arrows exhibit opposite directions.

5. The Dynamic of Income and Endogenous Fitness without Raw Petroleum

The odd trajectories that Tabasco and Campeche follow in the fitness–income plane indicate that one should be careful when applying the SPS methodology in countries where few regions export large amounts of a particular good. In fact, some analysts have pointed out that the fitness metric can be exceedingly sensitive to small variations in the network topology [38] (see Remark 11). This is particularly troublesome in the case of a sparse bipartite trade network when there are niche products exported by a small number of regions. Accordingly, it is convenient to filter the sample and recalculate our indicators of competitiveness either discarding raw petroleum or excluding these two oil-dependent states.

Firstly, we analyze the fitness–income dynamic by removing raw petroleum from the world exports database, and calculating Exogenous Fitness at the state level with the two-step procedure mentioned above. As can be seen in Appendix A3, the condition required for ExoFit-oil to be a good predictor does not hold since uneven directions seem to prevail in most cells across the plane. From these plots, it is not possible to infer that an improvement in a state’s productive structure leads necessarily to a sustained positive growth. Therefore, in this section, we evaluate the predictive capacity (reliability) of an endogenous index using only the Mexican exports database, where raw petroleum is also excluded from the metrics’ calculations (EndoFit-oil); likewise, we define income as per capita GDP without oil mining.

As shown in Figure 4, in this setting, there are no isolated trajectories in the fitness–income plane, even for the oil-dependent states of Campeche and Tabasco. Moreover, there is a clear dynamic where there are neither high income trajectories for low fitness states, nor high fitness states that move through low income trajectories. Then, the estimated coefficients ${\tilde{D}}_k$ produce only green cells in the top panel of Figure 5, which is a remarkable result since it indicates high predictability for all the initial coordinates derived from the observations. However, instead of describing a large area with a homogeneous laminar regime, the versor drawn in the bottom panel signals the existence of two different areas with ordered regimes.

For low fitness states, there is some sort of development trap since the trajectories for the six estimated arrows indicate a process of deterioration in productive capabilities as well as a stagnant economy. On the other hand, there is another laminar regime that predicts a promising future for states whose current x-axis coordinate in the plane corresponds to scores of middle and high fitness. In this regime, states will not only exhibit a positive growth but also a continuous sophistication of its productive structure. These two results combined suggest that unproductive states (poor or oil-dependent) require the building up of capabilities for some years in order for their economy to enter into a virtuous cycle of growth and opportunities (see Remark 12). From a technical point of view, the presence of different ordered regimes is an empirical corroboration that the linear analysis of growth regressions is faulty and can result in misguided advice, as in [18].

Once we correct for oil-dependency, the EndoFit index meets our requirement of predictability; hence, we can assert that this metric can be a reliable indicator for forecasting the evolution of income, at the subnational level, in the Mexican economy. We present some sensibility tests in Appendix A4, where we recalculate the competitiveness indexes by removing the oil-dependent states from the sample. These exercises indicate that Endogenous Fitness is a robust indicator, at least in providing proper conditions for the predictability of economic growth. Therefore, we proceed in Figure 6 to describe the ranking for the 32 states according to this index. Notice that there are no radical changes across the sampled years; inclusively, the ranking is rather stable for the top 8 states. Likewise, the bottom 9 states for 2014 are the same as those presented in the list of Figure 1, where petroleum is included in the analysis. However, there are some changes in positions, with the case of Tabasco being the most notorious. This state moves from the last position to 24th place in the alternative ranking, while the state of Campeche also moves up in the ladder. This result implies that the fitness index with the complete sample penalizes those states whose economy depends heavily on the exports of one product. Furthermore, when the aim is to infer the growth of aggregate income without oil, it seems that excluding such a product from the fitness calculation is an appropriate advice.

6. The Dynamic of Economic Complexity and Income

In this section, we present an additional analysis to assess whether the competitiveness indicator based upon product complexity derived from the metrics of Economic Complexity (i.e., the Latin American variant) surpasses our predictability requirement. This is also an exogenous index since the ECI scores for the Mexican states come from a weighted sum of their competitive products in international markets, where the weights are defined in terms of the product’s complexity calculated with a panel of countries. The states’ scores for this indicator come from El Atlas de la Complejidad Económica de México (for a description of the Mexican exports database, see Appendix A2).

When we compute the average of the yearly Spearman correlations for the two exogenous indicators (ExoFit and ECI), we notice that the estimate is relatively high: ${\overline{\rho }}_{ExEci}=0.91089$. However, as mentioned above, this result does not mean that both indexes are identical in all dimensions or that similar implications will be produced with any of these indicators. It is important to have in mind that this correlation coefficient is only one possible measure of similitude; thus, this finding does not guarantee that both indexes offer equivalent conditions for predictability. In fact, when the average of the yearly Cosine Similarity coefficients is estimated, the degree of similitude falls by 0.14289 (${\overline{Cosine}}_{ExECI}= 0.7680)$.

Anew, our dynamic analysis is based on the coefficients ${\tilde{D}}_k$ and the estimated versors in the fitness–income plane. The measure that we use for aggregate income comes, again, from per capita GDP excluding oil mining. From both panels of Figure 7, it is more than evident that our predictability requirement is not met. As in Figure 3, there is a significant dispersion of directions in most of the cells that can be empirically analyzed with the data. Moreover, there seems to be a non-linear relationship between ECI-oil and income since for states with an indicator below a certain level of competitiveness, ECI-oil tends to go down, while the opposite occurs for states with a relatively high level of productive knowledge. However, the income–fitness dynamic is not as straightforward as the one observed in the previous section with the EndoFit-oil index. A similar outcome is shown in Appendix A4 when ECI is evaluated removing the two oil-dependent states.

7. How Sensitive is the Fitness Index to the Inclusion of Tourism?

The results presented in sections four and five indicate that a very important product for a country and, in particular, for some of their states might interfere with the potential of the Selective Predictability Scheme as a forecasting tool. Consequently, in this section we analyze the effects of another key industry for some of the Mexican states: tourism. Because this is a service sector and the methodology for quantifying regions’ competitiveness is based mainly on exported goods, we make some arrangements in our database to include the value of tourism for each state in the metrics’ calculations. Due to data limitations, this is done here by estimating the income spent by foreign nationals when visiting a Mexican state (see Appendix A2 for details).

We recalculate Endogenous Fitness excluding raw petroleum and including tourism as another item of the productive structure (EndoFit + tourism-oil). Then, we present in Figure 8 the evolution of states’ rankings using this metric. In general, the rankings are not very different from those shown in Figure 6 where the indicator of Endogenous Fitness is only corrected by excluding raw petroleum. The stability of the rankings is also clear-cut; the top 12 positions are identical; 12 out of the 13 bottom states are the same, although in different positions. However, the state of Quintana Roo—where the touristic resorts of Cancun and Riviera Maya are located—moves drastically in the ranking; from 16th position to last position. Baja California Sur—where the resort of Cabo San Lucas is located—also goes down in the ranking, but to a much lesser extent; from 28th position to 31st.

With this result, we can conclude, again, that including industries that are extremely important for a region has negative consequences for its competitiveness score. Theoretically, this feature can be deleterious for the economy’s growth, if the concentration of the economic activity generates a more volatile environment or deters the creation of new capabilities through some form of “Dutch disease’. Here, we only want to determine empirically, if our index of EndoFit corrected by tourism loses or improves its predictive capacity. As can be seen from both panels of Figure 9, the dynamic of the system is still predictable. Even more, we can say that the estimated coefficients ${\tilde{D}}_k$ have a more uniform color of dark green in the different cells, although not in an ostensibly manner. Likewise, the plot of estimated versors in the fitness–income plane still identifies two laminar regimes. This outcome reaffirms the finding that in the Mexican economy there are two dynamic settings: a development trap for unproductive and low fitness states and a virtuous cycle for relatively rich and high fitness states.

Finally, in Appendix A5, we modify the specification of RCA by dividing the export value of a product in a state and in Mexico by population instead of the total export value in the corresponding region. This approach produces coefficients that are neutral to price changes, and precludes that the measurement of the products’ competitiveness, in a particular region, can be overshadowed by an industry with an extremely high export value. However, we find with our database that the indicator of Endogenous Fitness does not qualitatively improve its performance with this adjustment.

8. Conclusions

The conception of economic development as a decentralized process of exploration where productive capabilities change and accumulate through time has been stimulated in recent years. The tools of network theory and the complexity vision of economic systems offer explanations for the competitiveness of nations and provide tests for empirical validation. Furthermore, this perspective contributes in designing innovative frameworks for public policy and forecasting. In particular, several indicators have been built and implemented to measure a region’s ability to compete as a result of the productive knowledge embodied in its economy. According to the literature, these non-monetary indicators convey information that is very relevant for inferring the development potential of a region; thus, they are a valuable metric for forecasting economic growth.

In general, for these tools and frameworks to be considered methodologically robust, it is important to analyze their performance with different databases. Therefore, in this paper, we study whether or not the condition required for the predictability of growth holds when using an indicator of fitness (competitiveness) with a subnational database of the 32 Mexican states. This requirement consists in observing an extended area of the fitness–income plane characterized by a laminar regime; that is, by a set of initial coordinates where the analyst can infer the trajectories that per capita GDP can follow in a range of 10 years. Our results show that the endogenous variant of this fitness indicator has a better performance than the exogenous one; in the former indicator “state fitness” and “product complexity” are calculated jointly from the Mexican exports database, while in the latter “product complexity” is derived from a world exports database. Moreover, our empirical analysis points out that the condition for a reliable forecast is met once the indicator is corrected by removing raw petroleum from the sampled products—a very important export commodity for Mexico and, especially, for the states of Campeche and Tabasco (see Remark 13).

Likewise, the application of the SPS for the Mexican case suggests the presence of two Mexicos: a productive one in the north and central parts of the country and an unproductive one in the South. Hence, several states are situated in a development trap of stagnation and a deteriorating productive structure. This result is somehow robust since it is observed in most of the fitness indicators considered here. Consequently, for a poor state to observe a surge in its per capita GDP, it requires a deep structural transformation. Marginal increases in fitness, and the slow building up of capabilities, do not guarantee a rapid take off of the region. Hence, an industrial policy is required for a large jump in productive knowledge to be possible and for the economy to move into a path of sustained growth. In other words, for these states to enter into a virtuous circle of growth and productive opportunities, a comprehensive industrial policy needs to be implemented with the aim of creating an environment conducive to the development and articulation of new capabilities.

From the complexity perspective, these policies should not be entirely developed from the top-down. Instead, their conception and implementation should be part of an ecosystem that encourages public, social and private agents to provide ideas, funds, and the processing of information. An environment that fosters the interaction of different insights enables a boost in aggregate productivity and an inclusive process of economic development. The policy menu in this ecosystem can be very wide: (i) the establishment of autonomous and decentralized councils of industrial coordination at the state/municipal level, to be in charge of managing socially oriented venture capital funds (see Remark 14); (ii) ex-ante guarantees in industries that are new for the region, which do not have to be paid ex-post when these projects happen to be successful (see Remark 15); (iii) a system of contests where projects of small and medium firms are awarded with funding due to their inventiveness and the strategic value of the proposed investments in the community (see Remark 16); (iv) the creation of critical infrastructure conducive to the crowding-in of private investments, such as roads, environmentally friendly sources of energy, train terminals, and industrial parks with free trade benefits (i.e., with their own customs and the avoidance of revisions in the ports of entry); (v) the establishment of “special economic zones” in populated but very depressed regions that require strong fiscal incentives to encourage very large investments, especially those that are labor-intensive [39,40]; (vi) the creation of information agencies at the federal level with a mandate to provide historical and updated data on economic activity, exports–imports, employment, and occupations at municipal and state levels, so that consultants, local governments, academicians, and entrepreneurs can produce meaningful analyses of regional development (see Remark 17).

It is important to emphasize that the results presented in this paper highlight the fact that analysts and practitioners should not use these metrics mechanically. The type of indicator considered (exogenous versus endogenous) and the way the regions and products are filtered can produce contrasting implications. As our exercises of excluding (including) raw petroleum (tourism) in the fitness indicators show, there is no assurance that a specific set of procedures will work in any context. For the time being, the intrinsic instability of the fitness algorithm (i.e., the coupled systems of non-linear difference equations) has to be balanced with a variety of sensibility analyses. Hopefully, in the near future, more reliable metrics will be developed so that a set of network tools can be implemented following standard protocols, such as those currently used in econometric analyses.

Lastly, it is important to recall that a forecasting technique only indicates which outcomes are likely to be produced in the future when the environment remains unperturbed. Therefore, knowing that a region is positioned in a development trap is only a first step in recognizing that a new environment is required for the economy entering into a process of sustained development. New tools have to be elaborated to study how alternative settings can produce a substantial improvement in the economy’s medium-term performance. For instance, it is important to know the proper policy priorities for a region to attain the multiple targets specified by a particular development mode [41]. Moreover, it is clear that it will be impossible for a laggard region to start being competitive in industries with a large strategic value when certain socioeconomic indicators have not achieved the required level (e.g., some of these industries can be highly dependent on the existence of a well-functioning public governance) [42].