INTRODUCTION

The most recent phase of global economic development has been defined by an economic sector that revolves around information technologies with a series of policies designed to compete in the international market. Over the past couple of decades, the process of technological change has prompted companies to move towards hiring individuals with better skills and capacities, in pursuit of higher profits and production efficiency.

It is useful to note that since the advent of the Industrial Revolution, labor has been gradually supplanted by machinery. More recently, the constant onslaught of international competition has driven companies to acquire new tools to make their productive processes more efficient. Because these technologies require employees to possess specific skills, this replacement process has become quite apparent.

An analysis of technology development and its effect on the labor market suggests that the greater productivity derived from using technological innovations spurs demand for workers with greater capacities (skilled individuals), which in turn leads to higher wages. Said technological progress has typically been analyzed based on worker skills. Pursuant to ^{Acemoglu and Autor (2011)}, one way to measure labor performance is by observing the relative wages of skilled and unskilled persons. Using this method, researchers have observed a bias whereby the use of technology favors skilled labor and is detrimental to less-skilled labor, which in turn entails wage inequality.

Recently, the newer literature has argued that the changes in the allocation of workplaces or "tasks" between capital and labor, or between national and foreign workers, have altered the structure of labor demand in industrialized countries, polarizing employment. As described in ^{Autor (2013)}, the "task approach" applied to labor markets could be a promising way to adjust the conceptual tools researchers use to study the forces involved in these markets.

It is within this analytical framework that this paper was developed, aiming to analyze the behavior of wage inequality among different groups of occupations in the region of the Northern Border of Mexico (NBM) in 2005-2012. To do so, this paper is structured as follows: first, a literature review of technology changes in the labor market and the wage inequalities derived therein, as well as a brief description of the issues facing the Mexican labor market. Second, the situation of the labor market along the NBM and wage inequality in this region as explained by technological change. Third, the methodology used for the precise decomposition of the Gini index to measure inequality, followed by the results obtained. Finally, relevant conclusions.

TECHNOLOGICAL CHANGE, THE LABOR MARKET, AND WAGE INEQUALITY

According to the Skill-Biased Technological Change Hypothesis (SBTCH), when a technology is introduced in the labor market, it gives rise to an increase in demand for employees with more skills, which leads to a bias in favor of skilled workers, to the detriment of unskilled workers, exacerbating wage inequality. This hypothesis approaches technological change through the use of computer equipment, mainly due to the expanding role of this tool in the workplace.

Pursuant to the SBTCH approach, one of the potential responses to the origin of wage inequality is changing demand, derived from technological change and biased to the benefit of more skilled workers.

This phenomenon has been proven in developed countries by various researchers over the past few decades (^{Autor, Katz, and Kearney, 2008}; ^{Acemoglu et al., 2011}), and multiple research studies have asserted that introducing technologies into labor generates demand for more skilled workers, or at least requires that the tasks that workers carry out complement these technologies, leading to wage raises. In this context, education is of vital importance, because level of schooling determines access to using new technologies.

In developing countries, like Mexico, it has been observed that after the North American Free Trade Agreement (NAFTA) was signed, foreign direct investment began to shift, and the maquiladora scheme implemented during the economic restructuring allowed transnational companies to take root in the country, incorporating new technologies into productive processes, and producing an impact on the demand for labor and wages (^{Hanson, 2003}).

These changes in the Mexican economy have motivated various researchers to analyze the changing wage structure and composition of employment. One of the most common ways of studying the impact of technological change on the labor market is to analyze changes in labor and wage implications facing workers depending on their skills. This is precisely how we set out to explain changing wage inequality in this research paper.

THE MEXICAN LABOR MARKET

As mentioned earlier, the productive structure of the Mexican economy has undergone changes, and even when the number of opportunities has risen as a result of greater trade flows, employment indicators, according to ^{Mendoza (2010)}, have revealed that the labor market is unable to absorb the labor demand generated. As such, employment, underemployment, and migration to the United States are all relevant aspects of the nature of the Mexican labor market.

The labor market in Mexico also displays recurring phenomena, such as the rise in informal employment, growing flows of Mexican workers emigrating to the United States, and a rise in the dynamics of industrial and manufacturing activities.

Similarly, ^{Castro (2007)}, who conducted an analysis of the wage gap from 1992 to 2002, asserted that the Mexican labor market has not generated the jobs required for a labor supply that is constantly growing.

As such, the case of Mexico is contradictory to the theory that states that higher levels of schooling lead to greater wage returns. One example of this is the rise in the number of students enrolled in university, which in turn drives up the unemployment rates for groups with higher levels of education. The main fallout from this includes employment in jobs that require little specialization, informality, and low wages.

Another piece of evidence that contributes to this explanation is shown in Figure 1, which presents wages from 2005 to 2012 for skilled (more than 12 years of schooling) and unskilled workers (less than 12 years of schooling), where a drastic drop in average wage compensation is observable for people with higher levels of education.

Source: Created by the authors based on data from ENOE.

Figure 1. Average Wages by Skill Level in Mexico 2005-2012 

The evidence shown here reveals how over the past decades, imbalances in the Mexican labor market have made it impossible for workers to reach their full potential. Even with the advent of increasingly technological productive processes tied to the skills that these employees have, wages have not reflected these abilities.

THE CASE OF THE NORTHERN BORDER OF MEXICO

A specific study of the Northern Border of Mexico (NBM) is essential to understanding the advent of technological change and its implications when it comes to wages, because it is one of the regions in the country characterized by advanced economic development, as compared to the southern border and even to some cities in the center of Mexico. ^{Ayala, Chapa, and Hernández (2009)} explained that states in the north have an industrial vocation because the manufacturing industry determines regional economic activity in the region’s dynamics. Its momentum is a result of its proximity to the United States, which in turn produces multiplicative effects in the services sector. Table 1 shows how the employed population was distributed by branch of economic activity between 2005 and 2012, and also presents the average annual growth rate during this time. We can also observe how the highest growth areas are tied to the services sector, as well as the extractive and electricity industries. The only sector with negative growth is the construction industry, which, since the real estate crisis in 2008 and 2009 in the United States, has experienced serious problems. The most dynamic sectors are those tied to the transformation industry, as well as professional and financial services and the trade sector, the latter two of which are known for a good deal of informal employment.

In Mexico informal employment is one of the features of the labor market. This phenomenon has taken off in the past decade. As such, in this research paper this quality is considered to have an impact on estimating wage inequality.

As a general overview of the trends of informality in the NBM and in Mexico, Figure 2 shows the employment rates in the informal sector in the years 2005 and 2012. It appears that the values in both entities are higher in the year 2012. The highest rates of participation in this sector are found in the state of Tamaulipas, and the national average is higher than the NBM average.

Source: Created by the authors based on data from ENOE, respective years.

Figure 2. Employment Rate in the Informal Sector in the NBM and Mexico, 2005 and 2012 

METHODOLOGY FOR THE PRECISE DECOMPOSITION OF WAGES USING THE GINI INDEX

For the empirical portion of this study, we have used the Gini index,² thanks to its generous interpretation. This index enables us to easily understand inequality levels because it is restricted to values ranging between zero and one (zero meaning no inequality and one being the maximum value). Moreover, it’s decomposition is a novel estimate because it can be done with precision. To decompose the Gini index, we proceed with the methodology originally set forth in ^{Shorrocks (2013)}, which allows us to conduct an exact decomposition (in other words with no residuals or random components) of any inequality index using the ^{Shapley (1954)} theoretical approach. The particular nature of this technique is that the decomposition is always “exact,” and the subgroups considered can be treated symmetrically (^{Shorrocks, 2013: 20}; ^{Kolenikov and Shorrocks, 2005}). Some of the applications in which this technique has been used worldwide include analyzing poverty and inequality in Russia (^{Kolenikov and Shorrocks, 2005}), in China (^{Wan, Lu, and Chen, 2007}; ^{Wan, 2002}; ^{Wan and Zhou, 2005}), and in Cameroon (^{Abdelkrim, 2006}). In the case of Mexico, it has been applied in works by ^{Ochoa, Huesca, and Calderón (2015)} and ^{Rodríguez, Huesca, and Camberos (2011)} in different categories of labor.

We begin by considering the ^{Morduch and Sicular (2002)} Gini index equation, which is used to order the incomes of workers as y ₁ ≤ y ₂ ≤ ‧‧‧ ≤ y _i , and is written as follows:

(1)

The decomposition is calculated as the value of inequality for each subgroup k of workers as follows:

(2)

Where S represents the subgroup limited to size S∈ {0, 1, …,n – 1}. Each subgroup of workers contributes a ranking to wage i for , over the total in the distribution for y _i . Then, the term MV(𝜎 ⁱ (w), k) is obtained, which refers to the marginal value of adding a worker k to its group.³

In this way, the workers are randomly ordered by their income dispersion (y) using the symbol 𝜎 ⁱ (y), as follows:

(3)

As such, it is feasible to write the general formula for ^{Shapley's (1954)} value as the i-th possible order of subgroups, as follows:

(4)

The term MV(𝜎 ⁱ , 𝑔) indicates the effect present in the estimation when group g is eliminated for order σ i in the contribution of the set of groups S. For the case of six groups (our exercise was conducted for six labor groups), the inequality is decomposed as follows:

(5a)

(5b)

(5c)

(5d)

(5e)

(5f)

The preceding equations comprise the population with wage medians [₁, K, 𝜇₆] that isolate the average effect of income ?? from the rest of the medians in each subgroup, assigning the corresponding weight. As such, the decomposition is represented with two components, between and within, and G _k , which is the equivalent to the calculation of the Gini index in the equations expressed in (5a) and (5f) with the following formula:

(6)

And its respective components as,

(7)

(8)

G(y(𝜇/𝜇_𝑔)) permits normalizing the inequality with the vector of the income averages belonging to each group, where the average of the wages in each subgroup shall be equal to its median; and G(𝜇_𝑔) is precisely equal to the average inequality of the group in question. Expression (7) is deduced from the inequality existing between groups and expression (8) is obtained to represent the portion of inequality within subgroups.

THE RESULTS OF THE WAGE INEQUALITY DECOMPOSITION

Below is the occupational structure of workers by task type, aiming to observe the effect of technological change in the region through the classification proposed by ^{Acemoglu et al. (2011)}. Table 2 displays the occupational change in workers by task type in NBM states and Mexico overall in 2005 and 2012. When it comes to the distribution abstract, routine, and manual tasks in the NBM states, manual labor predominates. In Mexico overall, employment by task type reveals a gradual increase in manual occupations (1.28%), followed by routine (1.04%), while abstract show barely perceptible growth.

ANALYSIS OF THE PRECISE GINI DECOMPOSITION: TASKS AND SKILLS IN THE FORMAL AND INFORMAL SECTOR

In order to calculate the decomposition, the entire sample of workers was taken pursuant to the task classification, but we added in the sector in which the jobs are carried out, whether formal or informal, in order to control for this feature of labor, which is a structural problem of the labor economy in Mexico.

First, Figure 3 shows the evolution of the Gini coefficient in the period of study, comparing values for overall Mexico and the Northern Border. The country displays higher inequalities than the NBM region, and in both cases the trend during the analysis period is downward. In other words, the graph provides evidence that wage inequality in Mexico and the Northern Border region has fallen throughout the analysis period.

Source: Estimated by the authors using data from ENOE.

Figure 3. Wage Inequality in the NBM and Mexico, 2005-2012 (Gini Index) 

The results of the analysis of the decomposition by task type are given in Tables 3 and 4 below. The overall inequality index went from 0.406 to 0.369 in 2012 for the Northern Border, and for Mexico, it was 0.4. In other words, there is a slight reduction in inequality. This finding is aligned with a recent study by ^{Campos et al. (2014)}, who assert that inequality in Mexico has fallen. In our decomposition, we can infer with statistical reliance of 95% that the component within the labor collectives explains the majority of the inequality, going from 74% to 71% between 2005 and 2012. In the within component analysis for the NBM, the greatest contribution to inequality (although declining) is seen in workers performing manual tasks in the informal sector, with a value of 18%, which rose to 19.3% in 2012.

Table 3. Exact Decomposition of the Gini Index for Wage Inequality by Groups of Formal (F) and Informal (I) Tasks, Northern Border and Mexico, 2005 

Contribution and Group	Frontera			Mexico
	Absolute	Relative	% within	Absolute	Relative	% within
Between	0.103	0.254		0.130	0.298
Within	0.303	0.746		0.103	0.254
Total Gini	0.406	1.000		0.435	1.000
Subgroups/Sk			% within			% within
Occupations
Abstract f	0.046	0.113	15.178	0.035	0.081	11.530
Abstract i	0.029	0.071	9.469	0.028	0.065	9.310
Routine f	0.062	0.152	20.408	0.037	0.085	12.036
Routine i	0.058	0.143	19.156	0.077	0.177	25.194
Manual f	0.032	0.080	10.719	0.022	0.050	7.183
Manual i	0.076	0.187	25.070	0.106	0.244	34.747
Sum within	0.303		100.000	0.306		100.00
G(𝜇𝑔)	0.165			0.212
G(y(𝜇 / 𝜇𝑔))	0.365			0.388

Source: Created by the authors based on ENOE 2005.

Table 4. Exact Decomposition of the Gini Index for Wage Inequality by Groups of Formal (F) and Informal (I) Tasks, Northern Border and Mexico, 2012 

Contribution and Group	Border			Mexico
	Absolute	Relative	% within	Absolute	Relative	% within
Between	0.104	0.281		0.120	0.301
Within	0.265	0.719		0.279	0.699
Total Gini	0.369	1.000		0.400	1.000
Subgroups/Sk			% intra			% intra
Occupations
Abstract f	0.036	0.098	13.611	0.027	0.068	9.767
Abstract i	0.025	0.068	9.475	0.026	0.065	9.330
Routine f	0.053	0.143	19.901	0.032	0.080	11.404
Routine i	0.054	0.147	20.433	0.074	0.186	26.585
Manual f	0.026	0.070	9.751	0.018	0.046	6.617
Manual i	0.071	0.193	26.829	0.101	0.254	36.297
Sum within	0.265		100.000	0.279		100.000
G(𝜇𝑔)	0.169			0.196
G(y(𝜇 / 𝜇𝑔))	0.331			0.355

Source: Created by the authors based on ENOE 2012.

Figures 4 and 5 present the between and within components respectively, for Mexico and the Northern Border region.⁶

Source: Created by the authors based on ENOE, respective years.

Figure 4. Between-Group Wage Inequality by Task, Mexico and NBM 

Source: Created by the authors based on ENOE, respective years.

Figure 5. Within-Group Wage Inequality by Task, Mexico and NBM 

In both components, the values for the country are higher than those presented in the NBM. Likewise, the within element throughout the period saw a reduction.

CONCLUSIONS

This research presents a novel empirical application in the realm of labor and wage analysis, which helps explain the inequality in Mexico and the Northern Border region in the years 2005-2012 by task type and the skills workers possess in the Mexican labor market. The Gini index is decomposed accurately and reveals changes in wage inequality with greater precision.

The results signal that it is the within-group effect that has reduced the wage gap with a share of 70% in total inequality; in other words, inequality is explained within groups of workers, and the reduction is observed in the Gini index for the NBM, which went from 0.406 to 0.369 in 2012, while going from 0.435 to 0.40 in the final year of analysis for the overall country.

Once we determined that the wage inequality is explained within groups, it was important to demonstrate the proportion by which each of these groups of workers contributes to the disparity. In that sense, the results show that workers who perform manual tasks in the informal sector contribute 18%, a value that by 2012 had risen to 19.2% in the Northern Border region, while for the country as a whole, the greatest contribution is in the same group, but with a percentage participation of 25.4%.

These findings allow us to conclude that wage inequality in Mexico is explained in large measure by informal manual activities, followed by routine, while abstract activities have the weakest tie to the informal sector and also contribute the least to the falling inequality seen in both the NBM and Mexico as a whole.

The findings of this research paper also show, in light of the aforementioned theory of the impact of technology on the labor market, that contrary to what has happened in countries such as the United States and Canada, and what happened in Mexico in the 1990s, where biased technological change spurred a rise in wage inequality, in recent times, in Mexico and its NBM, wage inequality has narrowed, and the principal cause behind this reduction is considered to be the falling wages of skilled workers or those with higher levels of schooling.

Likewise, another cause that may not make any difference to wages is the introduction of technology, which may be insufficient to generate a demand for higher skills or mean that these groups of workers may now be engaging in routine activities.