A. Salary decomposition by ^{Ñopo (2004)}

^{Ñopo (2004)}, proposes a methodology based on a non-parametric decomposition by matching. Mainly, the author takes the salary gap decomposition by the Oaxaca-Blinder method developed in the seventies as a basis to explain the differences in the observable and non-observable individual characteristics from the formation of linear equations of salary income.

The matching technique developed by ^{Ñopo (2004)} is a non-parametric. The method answers the same question but considers differences across the wage distribution and not just the average unlike Oaxaca-Blinder. Matching does not require assuming a functional form for the model. The relationship between the explanatory variables need not be linear as assumed by the Mincerian regressions used in the ^{Oaxaca-Blinder (1973)} model. Due to specification errors, parametric techniques could lead to inaccurate inferences and the matching does take into account differences in the supports between the comparison groups. In contrast, Oaxaca-Blinder must extend its linear estimators outside the brackets for which they have been calculated. ^{Ñopo (2004)} shows that this tends to overestimate the unexplained factor of the wage gap.

Due to the nature of this method, combinations of characteristics pertaining to only certain individuals could not be calculated as the Oaxaca- Blinder method only estimates the combination of traits shared between native and Mexican workers. Consequently, this lack of disparity leads to inaccurate calculations in the results. ^{Ñopo (2004)} proposes a non-parametric decomposition method. The method responds by measuring the wage differential and its decomposition, but considering differences across the wage distribution and not only in the average as Oaxaca-Blinder does.

The Ñopo methodology restricts the comparison of differences only between natives and immigrants with comparable characteristics. Thus, it creates a synthetic sample of individuals by matching natives and immigrants with identical observable characteristics, so it does not need to assume any functional form in the relationship between characteristics and wages.

The advantages of this methodology are threefold. Firstly, it generates common support based on” the differences in common characteristics obtained from the distributions of characteristics of the individuals of interest and those who do not have them” (^{Botello, 2015}, p.17). Thus, the common support equals all those distributions of paired or similar observations of both groups, while those that are not paired and whose distribution is not similar are outside of the common support. Secondly, it provides information on the distribution of the unobservable or unexplained components of the wage gap. And thirdly, since it is a non-parametric estimate, it does not require validation of assumptions (^{Franco, 2010}; ^{Ñopo, 2004}). However, among the biggest disadvantages is the so-called” dimensionality curse,” which means that, due to the presence of many explanatory variables, it generates dispersion among the data (^{Franco, 2010}).

Based on the non-parametric method and with the use of matching, ^{Ñopo (2004)} develops a wage decomposition, that is, for the distribution of observations of the treated variable and control in X characteristics, the explanation of the wage difference is separated into four components.

First, the methodology selects Individual A from the sample without replacement; this means that not every observation in the sample is repeated, but the original line of the distribution of observations of this individual is maintained. Secondly, it selects all Individuals B (with replacement) who have the X characteristics identical to the previously selected Individual A. Then, a synthetic Individual B is constructed, which has similar characteristics to the average of that whole population. Furthermore, B is matched with the original individual A. Thus, a sample of the observations of both matched individuals is obtained (synthetic Individual B and original Individual A). This is done until the observations of the original Individual A are exhausted (^{Ñopo, 2004}).

Based on this, our objective was to generate the decomposition of the salary into the four components from the integration of these steps. This would result in a distribution of matched or similar characteristics (common support; for example, matched Mexican and matched native) and another distribution of unmatched characteristics (outside the common support; unmatched Mexican and unmatched native) of both populations.

The equation is broken down into the following four elements based on the description in the study of ^{Ñopo (2004)}:

∆ represents the total sum of the four components that would explain the average wage difference between the native and the Mexican based on the control variables.

∆ _M represents the part of the wage difference explained by the differences between two groups of Mexicans: those where the distribution of compatible observations of Mexicans is combined with the characteristics of the natives and those where the distribution of non-compatible observations of Mexicans is combined with the characteristics they do not share with the natives. This component is calculated as the difference of the expected wage [Y ] of Mexicans [MX] who are within the common support with the native (the distribution of matched characteristics), minus the expected wage of Mexicans who are outside the common support with the native, weighted with the probability measure where only Mexicans possess certain characteristics that natives do not.

∆ _X represents part of the wage difference explained by the difference in the expected salary [Y ] for having the same combination of observable characteristics between the native and the Mexican. It can refer to the combination of compatible characteristics or to the combination of characteristics that are within the common support.

∆ _N represents the part of the wage difference explained by the differences between two groups of natives: those where the distribution of non- compatible native observations is combined with those characteristics that the Mexican does not possess and those where the distribution of compatible native observation characteristics is combined with the characteristics of the Mexican.

In other words, it represents the difference of the expected wage [Y ] of the natives [N ] who are outside the common support with the Mexican, minus the expected wage of the natives who are within the common support with the Mexican (the distribution of matched characteristics), weighted with the probability measure where only the natives possess certain characteristics that Mexicans do not.

In summary, ∆ _N and ∆ _M are the components that the author developed within the salary decomposition with the previous justification that, within the matching methodologies, the introduction of elements with characteristics that were not shared by both samples was not considered. These elements create a better understanding of the wage difference (^{Ñopo, 2004}).

∆₀, which is the unobserved component, explains the part of the difference that is not attributed to the observed characteristics but is rather related to the combination of elements that are not observable in individuals with the same level of job qualifications.

By defining each component, we can account for all the differences in wages for the labor market, including the ones induced by observable characteristics (∆ _M + ∆ _X + ∆ _N ) and non-observable characteristics (∆₀).

The methodology allows the use of dichotomous and continuous variables of X characteristics of the individuals. Thus, within the control variables, sex, age in years, education, marital status, health insurance, occupation, economic sector, hours worked and “potential” work experience were used (Table 1). The individual characteristics (demographic variables) of the workers were added sequentially; however, the job characteristics (labor market variables) were added with replacement in the following order: occupation, economic sector, hours worked, and work experience. This was done by ^{Ñopo (2004)} and ^{Ñopo et al. (2011)}, since it is not possible to know which labor variables are more endogenous than others, and also in the estimation it allows to keepinga high percentage of individuals within the common support. Finally, the “all variables” line includes all demographic and labor sets.

In summary, the ^{Ñopo (2004)} methodology only considers observable particularities, without considering those that are not observable, such as effort, interest in participating in the labor market, workers’ innate skills and cultural issues, among others.

A. Descriptive statistics for both groups

By 2019, 16.8% of the employed Mexicans who have a citizenship had preschool and elementary schooling (Table 1). However, only 38% of Mexicans have a bachelor’s degree, while the rest, who participate less in the labor market, have higher education. Using data from the 2007 Census Bureau, ^{Tinley (2009)} found that in the Mexican population over the age of 25, Hispanics were concentrated in a secondary level-with no more than 9 years of education-while the natives had 12 years of education on average.

More than ten years later, the Mexican population with citizenship has increased its educational level to high school with a diploma, obtaining an average of approximately 12 years of education.

In the following part of Table 1, the different characteristics of the population are aggregated and divided by education qualifications. In terms of gender, for both population groups, men dominate in proportion with a greater difference in the percentage of low and semi-skilled Mexicans. However, as education increases, so does the participation of women, and specifically, native women have a greater participation in the labor market. In terms of age, for Mexicans, there is a greater concentration in the medium and high levels of qualification, mainly between the ages of 30-44 and 45-65. For the natives, the age distribution is different compared to the Mexicans since, in this case, the low-skilled natives are younger (mostly between 15-29 years old) and the rest is distributed among more adult ages. For the remaining levels, natives are concentrated in adult ages.

As for medical insurance, the American health system is based on private and public medical insurance that can be obtained through employment or family. Table 1 shows that from the total number of employed Mexicans, 74% participate in health insurance; and as education increases, participation increases by seven percentage points. In the case of the native population, there is greater variation among the results as unskilled and skilled individuals have a participation rate of 81 and 96 % respectively. Nevertheless, Mexican immigrants tend to have lower participation in health insurance because it depends on factors such as economic stability or work. This means that Mexican immigrants suffer from a greater lack of protection and are in vulnerable positions that do not allow them to access health care. (^{CONAPO, 2013}).

Concerning the variable of years since arrival, Table 1 shows that for all three groups there is a greater proportion of immigrants who entered the country more than 15 years ago, that is, the great majority entered the country at the end of the 20th century or the beginning of the 21st century. However, the largest proportion of the immigrant population that has entered the country in the last 15 years tends to be skilled.

As for the economic sector, obtained from the variable of the type of industry in which immigrants are employed, Mexicans are mostly employed in the secondary and tertiary sectors. However, in the primary sector, the proportion of Mexicans respect to natives is greater.

The last section of Table 1 shows the average annual wage income, the estimated hourly wage, and the average hours worked by both groups. In this section, it is noted that low-skilled immigrants earn a higher annual salary and average hourly wage than natives, while for the other levels of educational qualification, both the annual salary and the hourly wage are lower for immigrants than for natives. Natives earn higher wages than those with middle and higher education.

Based on the area of occupation, a division of eleven categories was created, guided by the manual of occupations obtained from the IPUMS CPS platform (ref). These include occupations with high levels of qualification which are professionals, executives, athletes, education workers, art workers, officials, specialized personnel, and managing directors. Service occupations are related to protection workers, domestic service, street vendors, health care support, cleaning, maintenance, and personal services; the category of sales and administrative workers includes everything related to agents, sales and office workers, etc.; the category of construction, production and transportation workers includes everything related to extraction occupations, use of machinery, installation, repair and movement of materials; and finally, the category related to workers is dedicated to agriculture, fishing and hunting.

Within these occupations, Mexican workers with few qualifications are mainly found working in personal care services, cleaning, construction, transportation, and production, in addition to having large participation in agriculture. The same situation applies to the natives, only 4% of their population stands out in areas that require high qualification.

Mexicans have a high concentration of medium and semi-skilled workers in the same areas as low-skilled Mexicans except agriculture, where their participation has decreased. However, there is still a high concentration in the areas of services, installation and repair, technicians, and food preparation.

For the qualified Mexican population, there is a greater concentration of work in professional areas (teachers and related, engineers, mathematicians, athletes, scientists) in service areas, and in sales and food preparation. In the case of natives, they are more concentrated as professionals, and the remaining 38% are in sales and to a lesser extent in domestic services and personal care. The percentage of skilled Mexicans is much more distributed among professional categories. However, although their participation is mostly in low-skilled areas upon arrival to the United States, greater participation is observed in high-skilled areas as education increases.

The theory of the dual market/labor segmentation does not state a clear division between the low skilled and the semi-skilled. There is a polarization in the distribution of occupational participation of the qualified Mexican compared to the native since the latter is more concentrated in high qualification areas. Qualified Mexicans are less concentrated in these types of occupations and have a greater distribution in lower and medium specialization occupations compared to natives. This may suggest that qualified Mexicans are overqualified to perform some productive activities, and therefore, this situation affects their wages. Another factor that may be related to this decrease in participation in highly specialized areas is that employers are looking for individuals or natives who have studied and are familiar with the American educational system (^{Aydemir & Borjas, 2006}). Also, qualified Mexicans could work with a similar regulatory framework within occupations such as computer science, engineering, or administration; however, in occupations such as law, medicine, and architecture they need much more specific knowledge and human capital, making their entry much more difficult (^{Piñeiro & Ruiz, 2010}).

For both groups, it was found that as education increases, they have greater participation, especially when they have health insurance, work in occupations that require more specialization, work the same amount of hours in average and get a higher salary. However, native and low-skilled Mexicans showed greater differences in participation in age, marital status, work hours, and salary. Low-skilled Mexicans are mostly middle-aged and married, while the low-skilled native population is young and mostly single. Between the two, Mexicans earn a higher salary, which means that due to their age and marital status, they may have to work several jobs with a greater amount of overtime because of the need for a higher salary to cover family expenses and possibly to send remittances.

Also, within the same occupation, the natives have greater participation in technical and professional occupations, which is even greater when education increases. For the rest of the occupations, their participation decreases as education increases although this does not happen with Mexicans, which may even be overqualified.

B. Decomposition of worker’s wage difference by type of qualification

The methodology of Ñopo performs a salary decomposition to observe the differences that would be explained by observed and non-observed characteristics.

The analysis of the wage difference concerning low-skilled workers (Table 2) showed a total difference of -16.1%, between the Mexicans and the natives, indicating that the natives earn less than the low-skilled Mexicans. The percentage of the variations decreases or increases as the control characteristics are added.

Likewise, when adding occupation to the analysis, it is observed that the greatest differences are due to the observable characteristics and that these contribute 20% of said inequality, which means that there is a greater difference in the distribution of characteristics of natives vs. Mexicans due to the type of occupation where they work (they move away from the zero value where it would show the possibility that both distributions can be matched).

Another variable that was largely attributed to unobservable characteristics was “potential” work experience, that is, regardless of the individual’s experience, one percent of the difference would be explained by unobservable characteristics. However, the explanation of the difference by observed characteristics becomes greater for characteristics that natives possess and Mexicans do not share.

The fact that Mexicans are better paid can be attributed to the “self- selected” characteristics. ^{Tinley (2009)} suggested that Latinos could increase their salary due to the effort of having multiple jobs and the willingness to work overtime. As seen in Table 1, the average number of hours worked by the unskilled Mexicans reaches approximately 40 hours per week, while for the native it is only 30 hours. In addition, low-skilled immigrants are mostly married and send highest level of remittances to their country of origin, which justifies the need to increase their salaries for different jobs and the application of overtime.

These results are in line with the arguments of ^{Alarcón and Ramírez- García (2011)}, who argue that the concentration of Mexican immigrants in low-skilled jobs is expressed in a wage differential with respect to natives and European and Asian immigrants. While nearly half (46 percent) of the native-born population received incomes above $40 000 per year, 54 percent of Europeans were in the same income group, as were 48 percent of Asians. On the other hand, only 17 percent of Mexicans had that level of income. Among the latter, like the Central Americans, more than 60 percent receive earned income of less than US$30 000 per year. Clearly, in economic terms, the wage gap between Mexicans and U.S. natives is so wide that it obscures their prospects for successful economic integration.

The total wage difference has a value of 15.9% among semi-skilled (Table 3) native workers compared to semi-skilled Mexican workers; that is, the total difference increases detrimentally for Mexicans as education increases. Semi-skilled native workers earn on average 16% more than Mexican workers. Occupation and demographic variables, in this case, have a positive effect on the unobservable component and a smaller positive effect on the observable component. The latter denotes that the component in the characteristics of the natives is smaller than in the previous case, which means that, by reducing this value for this qualification group, there is a greater possibility that the Mexicans will be matched with the natives. However, there are still differences in the distribution of native characteristics that Mexicans do not share. That is, even though the value is lower than in the previous section for DN (Characteristics that natives have), there are still differences in characteristics that Mexicans do not reach, and that can partly explain the wage difference. In DM (Characteristics that Mexicans have), if Mexicans achieve the same characteristics as the natives, their wages would be expected to increase. In other words, if the Mexican were to achieve the same distribution of characteristics as the native, in occupation plus demographic variables, he could have an increase in his remuneration of 2%.

These results can be explained by ^{Borjas (1990)}, who mentions that wage differences may be due to variables: 1) level of schooling, 2) English language proficiency, 3) adoption of U.S. citizenship, 4) participation in the labor market, and 5) home ownership, which would facilitate the integration of Mexican immigrants to the United States.

For the third and last model with the Ñopo method (Table 4), a total difference of 29.4% was obtained, which means that the most qualified Mexicans are less affected since the average salary difference is less in favor of the native compared to the situation with the semi-qualified workers. Occupation is a variable that minimally reduces the effect of the difference due to unobserved characteristics. For this group, DN is lower than in the previous case, which shows the greatest possibilities that the component will equal zero and that both distributions of characteristics of the two groups will be matched; this is also observed in the common support of the distributions of both populations, where the only control characteristic that shows a greater difference in the common support is years of experience. However, qualified natives are paid more than Mexicans, which implies that there is a wage differential against the latter. This can be explained by differences in human capital mainly due to differences in training, formation, and work experience in addition to non-observable factors. Even though the distribution of natives and Mexicans has greater possibilities of being matched when a Mexican obtains a negative difference, they would be at greater risk of over-qualification and unemployment. From the perspective of ^{Portes and Rumbaut (2001)}, schooling, as well as language skills in the receiving country, is considered one of the most important factors for the economic and social integration of immigrants.

According to ^{Franco (2010)}, education is the variable that best reduces the unobservable component, and the gap can be explained by differences in education and not by unobservable. However, since this work delimits the effect of the wage difference by qualification, thus generating a much more specific effect for each educational group, the differences for the semi- skilled and skilled workers in this case would be explained by unobservable components and would even be greater than the total difference. As the author mention, it is evident that immigrants’ salaries grow with increased education, but despite staying longer in the country or achieving citizenship, it is not enough to close the gap or, in this case, the salary difference. In this sense, for individuals with the same productive labor capacities, the unobservable component would be remunerated based on the group they belong to as foreigners, which, as ^{Muñoz-Comet (2014)} mentions, manages to deduct their level of productivity. At the same time, this explains how they could be displaced to lower-paid sectors such as the secondary sector and the existence of a greater risk of unemployment and over-qualification.

The methodology used by ^{Ñopo (2004)} allowed for the decomposition of the four components of the wage difference by control characteristics. In the resulting models, Mexican immigrants suffer a greater impact due to characteristics that are not observable as observable for all levels. However, the introduction of occupation and years of experience contributed greatly to the explanation of the differences because greater changes were observed within the components of these variables.

It is worth noting that low-skilled natives earn less than Mexican citizens, and the components help to affirm that the observed characteristics of the low-skilled Mexican are better rewarded than those of the natives themselves. As the estimation results show, there were positive wage differences for natives, but for Mexicans, the negative effect was found in the last two skill levels. Both models are repeated in the results mechanics since the Mexicans had a negative wage difference and both the unobservable and observable components contributed to the wage difference. For these levels of qualification, the characteristics of the natives are better rewarded. Even though both groups share characteristics, the Mexican citizens do not reach the required characteristics that make the natives obtain a better salary. However, this difference in characteristics that natives possess decreases as education increases, which suggests great possibilities that Mexicans will achieve the characteristics of natives.

Nonetheless, the results manifest that the assimilation that immigrants develop as a result of obtaining citizenship, among other things, and the effect of education on human capital are not sufficient to resolve a reduction in the differences between Mexicans and the native population.