INTRODUCTION

After almost three decades of regional economic development in Mexico, in the face of the challenges brought about by the consolidation of trade integration with the Unites States and given the heterogeneity of results in terms of economic growth patterns (^{De León Arias, 2019}), researching on specific regions such as the northern border is a necessity for the better identification of its economic growth dynamics.

The present article retrieves and updates the current scientific output, presented by ^{De León Arias (2008)}, regarding the dynamics of the productivity of the Northern Border (NB) over the period from 1970 to 2004. In this article, the period from 2004 to 2018 is addressed, the study disaggregates at federated state level, which allows characterizing the regional economic growth pattern from a study on growth accounting, commonly known as Solow growth model, and the contributions from the NB region by means of Harberger’s sunrise/sunset diagrams (1998). Particularly, the goal of the present research is to outline the production performance of the economic activity at Mexico’s Northern Border from an analysis of the accounting of factors at manufacturing level over the 1993-2018 period, and several subperiods relevant for the analysis. Moreover, the degree of contribution from each state to the growth of regional productivity is identified resorting to sunrise/sunset diagrams.

The method utilizes Solow’s residue to calculate Total Factor Productivity (TFP) by means of a Cobb-Douglas type function with constant returns that establishes the magnitude of the aggregated revenue contained in capital and work to enable the breakdown of the products’ growth rate; moreover, it quantifies its growth over time. Adding to the above, ^{Harberger’s (1998)} sunrise/sunset diagrams indicate the contributions from each of the federated states considering their own growth and contribution to the regional added value. In this way, it is possible to express performance in terms of productivity by state and displaying their contribution to the region.

The document is composed of five sections. In the first, we present the literature, in which ^{De León Arias (2008)} refers to the relevance of border regions to better explain the relationship between trade integration and regional economic growth (in the context of the new economic geography), as well as the bases of the so-called growth accounting. In the second section, the sources of growth at the NB region are identified. In the third one, the methodology of growth accounting is presented. In the fourth section, sunrise/sunset diagrams for each of the states comprised in the region are displayed; they will enable us to identify the particular contribution from each state to global regional growth. Finally, the last section presents the conclusions.

LITERATURE REVIEW

The analysis of productivity by means of growth accounting has experienced comprehensive development after the pioneering works by ^{Abramovitz (1986)} and ^{Solow (1956)}, later expanded by ^{Kendrick (1961)}, and particularly ^{Denison (1962)}. One of the later development lines was the incorporation of changes in the quality of labor and capital by means of a dual approach, in which the residual attributed to total factor productivity (TFP) is identified in the growth rates of such factors’ prices.³

Another aspect analyzed in this method is the incorporation of investments and development expenditures as key determinants of TFP (^{Griliches, 1973}, ¹⁹⁸⁸). From this standpoint, recently, a link between capital accumulation and innovation has been put forward, following neo-Schumpeter’s growth models (^{Aghion & Howitt, 2008}). Due to the characteristic low innovation level of Mexican regions, this methodologic line will not be approached in the present article.

Total Factor Productivity in the Northern Mexican Regions with Emphasis on the Norther Border

As regards the identification of the regional productivity dynamics in Mexico, following, we describe works in the literature regarding TFP. In this sort of studies, a research by ^{Hernández Laos (1992)} stands out as an early contribution from one of the forerunners of this topic in Latin America.

Among the analyses of regional productivity, a region which has been object of particular interest is Mexico’s NB. Particularly, ^{De León Arias (2008)} ran an analysis of factor productivity at regional level for the 1970-2004 period. Resorting to Solow’s residual, the author studied the federated states identified as regions, large cities and NB, and obtained a TFP growth of only 0.08% for the entire analyzed period. In the face of this, a deceleration in terms of productivity is noticed, with the exception of the subperiod from 1985 to 1993, in which the increase of TFP was 6.72%. Such growth is related to the trade aperture of the Mexican economy in the 1980’s decade. Moreover, it indicates that the NB region registers a reduced growth of factor productivity, which is attributed to a limited capability to incorporate technical progress.

In more recent research works, ^{Padilla Hermida and Guzmán Plata (2010)} analyze TFP and manufacturing growth in Mexico for the period from 1993 to 2007 by means of a Cobb-Douglas production function with four cross sections, including all the country’s federated states. Among their findings, they point out that the growth of national manufacturing production has an effect of 0.36% points on GDP growth, which implies very limited impacts from manufactures on the growth of Mexican economy. The above is supported on low factor productivity growth at regional level as it kept the same conditions as in the initial period, and even show tendencies to diverge in the regions of the country.

For his part, ^{De León Arias (2013)} analyzes the TFP of manufactures in Mexican states over 1970-2008 from sunset/sunrise diagrams for the purpose of finding the contribution level from each to employment, capital and product factors. On the basis of his results, the author points at the existence of noticeable differences between Mexican states, being Mexico City⁵ one of the “losers” with a negative growth rate of 2.17%. For their part, the “winners” that locate in the north and center of the country, as a set, reach a growth of 2.18%.

In a research developed by ^{Becerril Torres, Díaz Carreno, and Del Moral Barrera (2013)}, the socioeconomic regions of Mexico are studied over the period 1970-2008, from the measurement of technical changes and efficiency change. To do so, nonparametric techniques are utilized by means of Data Envelopment Analysis (DEA) of Malmquist index, its components and linear programming. Among their main findings, there is a TFP increase in each of the seven analyzed regions, which came from technologic change. Furthermore, this change has produced a displacement of the technological border and an increase in fluctuating intertemporal productivity.

For its part, the study by ^{Atayde Villegas (2016)} for the states of Mexico in the period from 1998 to 2013, by means of a TFP breakdown, develops an empirical model that carries out econometric estimations of an aggregated production function by means of the data panel methodology by means of a fixed effects method. Among the results, it is mentioned that the growth of TFP is moderated, as its increase was 1.5% for the entire period, being Mexico City and the states of Nuevo León, Chihuahua, and Veracruz, those with the highest growth rate.

For its part, the Klems model, developed by Instituto Nacional de Estadística y Geografía (Inegi) [National Institute of Statistics and Geography], in which by means of the variables capital (K), labor (L), energy (M) and services (S), it is possible to measure TFP at subsector level of the 77 economic activity groups and the total of the Mexican economy on the basis of Sistema de Cuentas Nacionales [System of National Accounts] with a view to calculating technical progress. In a more recent study, ^{Inegi (2020b)} analyzed factor productivity for the 1999-2019 period recording a significant volatility in returns each year, therefore, a growth rate of -0.34% in TFP for the entire period.

According to the review of the performance of the Mexican economy TFP, the general findings ratify marked regional differences and limited TFP growth, that is to say, most of the afore cited works exhibits a TFP growth pace under 2% a year, with a clear deceleration over the last 20 years, and so, a reduced dynamism of Mexican manufacturing activities. This was supported by ^{Loría (2009)}, who states that the Mexican economy has not been able to restore the structure of accumulation, as the differences in terms of productivity have been widened due to poor capital performance and investment. Particularly, in this regard, this result is frequently shared by studies on the growth of productivity in Mexico’s economy.

ANALYSIS OF THE SOURCES OF GROWTH

METHODOLOGY OF GROWTH ACCOUNTING

As regards the growth accounting methodology utilized in this article, it is necessary to point out that TFP is expressed as the relationship between actual production and the weighed addition of all the factors utilized in the production process. Its goal is to break down changes in production from variations in the amount of inputs and in all the residual factors, as well as technology, in the number of people involved in production, in the use of installed capacity and in the quality of production factors.

To calculate factor productivity, a Cobb-Douglas type function was utilized to allow identifying the relationships generated between production distribution and the variations of labor and capital. The Cobb-Douglas function uses constant scale returns from the characteristics of capital returns (equation 1) and labor returns (equation 2):

where α is a constant between 0 and 1, whose purpose is to measure the contributions of capital in production. That is to say, α limits capital contributions, while 1-α, those of labor. Owing to this, the Cobb-Douglas production function is ascertained by means of the following equation:

in which A refers to a parameter greater than 0, which calculates the productivity of the existing “residual” technology in the economy. The Cobb-Douglas function provides a high substitution degree between capital and labor and allows identifying the magnitude of the aggregated income contained in the capital and labor factors.

In this way, equation 4 shows the coefficients of capital and labor participation. Such estimators weigh the contribution of the two production factors, which allows identifying the participation coefficient of employment (1-α) obtained by means of the equation below:

The coefficient is defined as the mean of the addition of the quotients of the initial income between the initial product and the final income between the final product. To analyze the evolution of the sources of growth of the manufacturing sector at the NB region over the 1993-2018 period, TFP estimations were used for the purpose of verifying the existence or not of variations in the region’s productive activity. Consequently, the calculation of TFP contemplates the breakdown of

the growth rate between the addition of the rates of capital and labor growth, by means of weighing each factor as a result of its contribution to Gross Added Value (GAV) and its factor productivity. The estimator of TFP is referred by means of the following equation:

where gTFP is the rate of the growth of TFP; gQ is the growth of product; gK is capital growth; gL is employment increase; while α is the contribution from capital to the product. TFP estimations were carried out for the NB states (Baja California, Chihuahua, Coahuila, Nuevo León, Sonora, and Tamaulipas) from 1993 to 2018, as for the subperiods 1993-1998, 1999-2003, 2004-2008, 2009-2013, and 2014-2018, for the purpose of observing the growth dynamic of each of the factors and the product of the region as a whole.

It is worth pointing out that data on manufacture were recorded in Inegi’s Economic Censuses in the years 1994, 1999, 2004, 2009, 2014, and 2020. The utilized variables were: people employed by the end of year; Gross Census Added Value; wages and net fixed assets. Data on the last three variables were deflated with the National Consumer Price Index (base 2018), as there is no such index at state or regional level. Total observations in NB states reach 360 cases.

Even if at present, methodologies such as the Klems model (^{Inegi, 2020b}) have been implemented, it is important to point out that by considering the space and time of the present research, on occasion there are comparability problems between censuses by period. Owing to this, in the article, Solow’s residue is utilized with a Cobb-Douglas type function as in other national and international studies (^{Tello, 2012}; ^{Padilla & Guzmán, 2010}).

Comparison of the TFP of National and NB Manufacturing Firms

Once factor production analysis was developed, Graph 1 shows the performance of factor productivity at NB and the national total over the study period, 1993-2018, divided into five subperiods. TFP shows similar growth tendencies for national and NB manufactures, making its importance for the development of the country in this sector clear. A good performance of the NB is noticed as, with the exception of the period from 2009-2013, positive TFP growth rates are registered.

Source: Own elaboration based on ^{Inegi’s Economic Censuses (1994},¹⁹⁹⁹, ²⁰⁰⁴, ²⁰⁰⁹, ²⁰¹⁴, ^2020a). * Growth rates.

Graph 1. Total factor productivity at the northern border region and national level (1993-2018)*  

Adding to the above, by observing the evolution over the entire period, it is noticed that the NB region registered an annual mean TFP growth of 2.15%, while the national annual mean had a growth rate of 1.23%. This might be explained by the dynamism of the NB region in terms of employment and production, while the national performance of manufactures was lower and unstable; mainly in central and southern States over the study period.

Once the statistical-descriptive analysis was carried out from the production dynamics of manufactures and with the results in terms of employment and production, by means of the TFP tool, it is attributed that the regional adjustment in the country due to the relocation of industrial activities, particularly the geographic restructuring of manufacturing firms, has promoted a change in the supremacy of activities and made the NB region turn into a significant employment hub for Mexican manufacturing firms.

SUNRISE/SUNSET DIAGRAMS APPLIED TO NORTHERN BORDER’S TFP

A number of studies on economic growth focus on demonstrating the existence of disparities or not in the growth of economies over time. In this regard, Harberger (1998) approaches an asymmetric process that takes place in the economic growth of the countries and involves several factors, among which noticeable are: i) contributions from the sectors that increase factor productivity concentrate in a handful of industries; ii) in an economy with TFP growth, there are winners and losers, the latter usually largely reflect TFP performance; and iii) it is not possible to point out a prevalence of one economy or state over the various periods.

In this sense, ^{Howitt (2015)} states that the growth of TFP, in addition to being unequal, is unpredictable, as it depends on the distribution of technologic change, which is even harder to forecast. In the face of this scenario, it is obvious to point that differences in the growth paces of activity propitiate winning and losing states, because resources change and because firms may be located in areas far from places where production generates higher revenues.

The study carried out by Harberger (1998) referring to sunset/sunrise diagrams is considered the starting point to ascertain the growth of production factors between sectors in an economy because it allows representing the TFP distribution in a graph by organizing the contributions from each of the region’s states. That is, there is a sunrise diagram when the rate of the accumulated factor productivity is positive. While a sunset diagram represents a negative TFP growth rate. In this way, the methodology of sunrise/sunset diagrams is as follows:

Graph 2 presents the sunrise/sunset diagrams at the NB region in five-year periods from 1993 to 2018. As regards the subperiod 1993-1998, there was a TFP growth rate of 0.72%. The states with positive rates were Sonora, Chihuahua, Baja California, and Coahuila, while the losing states were Tamaulipas and Nuevo León.

Source: Own elaboration based on ^{Inegi’s Economic Censuses (1994}, ¹⁹⁹⁹, ²⁰⁰⁴, ²⁰⁰⁹, ²⁰¹⁴, ^2020a).

Graph 2. Sunrise/Sunset diagrams of TFP growth at NB region (1993-2018)  

Over the period from 1999 to 2003, the regions’ performance experienced an increase in TFP of 2.33% a year because four states—Chihuahua, Tamaulipas, Baja California, and Nuevo León— significantly increased their productivity, which entailed a reduction of actual costs, and so, a higher efficiency in production processes. Such states as a set contributed with 70% of the region’s total production. For their part, the states of Sonora and Coahuila had negative returns.

For the subperiod 2004-2008, there was a TFP growth of 3.49% in the region’s total. It is important to point out that five states in the region experienced increases in factor productivity, being Nuevo León and Coahuila the ones with the most contributions. Both states, as a set, produced 45% of the region’s production, which is a symptom of a good performance over the period.

For its part, in the 2004-2013 period, there is a noticeable decrease in the manufacturing firms in the region, as they have negative returns for TFP at a rate of -1.95%. From the financial crisis that started in the U.S. with effects on the global economy, the region experienced a fall in labor and also closing firms, mainly in maquiladoras, which reduced production and employment. In point of fact, with the exception of Sonora, the rest of the states had negative growth rates.

Over the 2014-2018 period, there was a noticeable recovery for the region as it had a TFP growth rate of 5.17%. All the states had increases in productivity, being noticeable Nuevo León with a contribution of 1.86 points and Coahuila, with 1.46 TFP points, reaching 64% of factor productivity as a set, which is an indication of their importance in the region’s development. Finally, for the entire period 1993-2018, the region registered a TFP growth rate of 2.1%. The state with the most contribution was Nuevo León, with 0.69 points, which is 33% of the region’s total. The rest of contributions were low: Sonora, 0.35 points; Chihuahua, 0.34; and, Coahuila, 0.33, in the regional total. Owing to this, the performance of factor productivity was barely above two units within the entire period.

It is evident that the process of trade aperture in the middle of the 1980’s and NAFTA’s coming into force in 1994 propitiated a spatial reorganization of industrial activities, as the main manufacturing firms moved toward the NB for the purpose of creating agglomeration economies and reducing transportation costs (^{Valdivia López, 2008}). This is supported by ^{Díaz-Bautista, Avilés and Rosas Chimal (2003)} by pointing out that the NB became an important area for the growth of the country due to the relevance of its industrial dynamic linked to foreign investment in the region.

In this regard, ^{Calderón Villareal and Martínez Morales (2005)} express that a set of processes have combined and allowed the restructuring of manufacturing activities: firstly, globalization favored trade aperture and with this the relocation of firms in cities at the border with the U.S.; second, the transformation of traditional manufacturing activities; and in the third place, the disaggregation of the activities of former industrial centers in Mexico, specifically the decentralization of manufacturing firms in Mexico City.

CONCLUSIONS

On the basis of the regional economy area, the present article analyzes and describes the dynamic of Mexican manufacturing firms through the study of the northern border region. Results are analyzed from two standpoints; performance in terms of factor productivity in the region from 1993 to 2018, and the particular performance of each of the border states according to their contribution to the NB region.

In this regard, the dynamism of border states is evident, as their performance allows verifying their relevance and transcendence for Mexican manufacturing firms. The results denote a great boost for the region’s manufacturing firms, as regards production and employment, accounting for 37.4% of the population employed, and slightly more than 37.5% of the national total censual gross added value. This means that the NB region has become a significant employment hub for Mexican manufacturing firms.

In like manner, with the trade aperture in the country and NAFTA coming into force, Mexican manufacturing activities reconfigured and brought about noticeable changes in the region’s growth. In this new stage, NB states have been benefited by the arrival of a large number of maquilas, becoming the region that holds supremacy in terms of employment and production of Mexican manufacturing enterprises.

The analysis applied from sunrise/sunset diagrams allowed describing the performance of each of the states distinguishing those that boosted the growth of TFP regarding those that reduced it, and understanding the spatial dynamics generated in the region. In this regard, the northern border had good results, as all its states registered positive growth rates and very similar contributions to TFP over the entire period, though the states of Nuevo León and Coahuila were considered “winners” for they presented the highest contributions to the increase of factor productivity. Owing to this, based on the information in the diagrams, the continuous progress displayed by the NB region was verified.

In terms of TFP, the obtained results allow making two major considerations. On one side, they verify that the northern border region has turned into the largest employment hub in the country, as it displays a noticeable growth in creation of job posts. And, on the other, such increase in the region has been insufficient to boost a larger growth of Mexican manufacturing firms, that is to say, the boost to the region has not become greater dynamism of factor productivity at national level. Owing to this, it is fundamental to develop regional policies that improve productivity and promote the strengthening and growth of Mexican manufacturing firms.