Revista del Centro de Investigación de la Universidad La Salle
Vol. 13, No. 52, julio-diciembre 2019, pp. 101-120
DOI: http://doi.org/10.26457/recein.v13i52.2459
Eduardo Raúl Diaz1, Terri R. Lituchy2
1CETYS Universidad, Tijuana (México)
2CETYS Universidad, Mexicali (México)
Correspondencia del autor: eduardo.diaz@cetys.mx
Recibido: 01 January 2020 | Aceptado: 11 May 2020 | Publicado: 03 Jun 2020 |
Copyright © 2019 "Eduardo Raúl Diaz & Terri R. Lituchy." This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The underrepresentation of women in leadership roles in Mexico is well documented. The goal of this research was to measure female and male participant expectations of effective leaders. Podsakoff et al.’s (1990) scale of transformational and transactional leader behaviors was translated and adapted for this purpose. Factor analyses and t-tests were conducted. The results suggest that female and male participants attribute similar levels of importance to the role of the leader in the inspiring a shared purpose dimension. The results also suggest that females in the sample attribute less importance to working across organizational boundaries and setting high performance expectations than males in the sample. Limitations include the cross-sectional nature of the study and focus on graduate students and alumni. Few studies on leader behavior expectations from a gender
Keywords: culture; underrepresentation; leadership; expectations; graduate students
La sub-representación de mujeres en roles de liderazgo en México está bien documentada. El objetivo de esta investigación cuantitativa fue medir expectativas que sostienen participantes de género femenino y masculino sobre líderes efectivos. La escala de liderazgo transformacional y transaccional de Podsakoff et al. (1990) fue utilizada. Se realizaron Análisis Factorial Exploratorio y pruebas t de muestras independientes. Los resultados sugieren que los participantes de género masculino y femenino asignan niveles similares de importancia al rol del líder en inspirar un propósito compartido. Además, participantes de género femenino atribuyen menor importancia que sus contrapartes al rol del líder en trabajar a través de divisiones organizacionales y en establecer altas expectativas de desempeño. Las limitantes incluyen la naturaleza transversal del estudio y el enfoque en estudiantes de posgrado y egresados. Han sido pocas las investigaciones sobre expectativas en las conductas de líderes desde una perspectiva de género en México, lo cual informa sobre la novedad de este estudio.
Palabras clave: cultura; sub-representación; liderazgo; expectativas; estudiantes de posgrado
The underrepresentation of women in leadership roles in Mexico has been well-documented (Muller & Rowell, 1997; Madero Gómez, 2010; Camarena Adame & Saavedra García, 2018a; Camarena Adame & Saavedra García, 2018b; Cruz, 2018; Zabludovsky-Kuper, 2015). Generally speaking, women are underrepresented in leadership roles because of cultural and organizational barriers that have little to do with performance and leader effectiveness (Lupano Perugini & Castro Solano, 2011; Diehl & Dzubinski, 2016; Villasana, Alcaraz-Rodríguez, & Alvarez, 2016; Carriles Álvarez, Beltrán-Godoy, & Mata-Mata, 2019). The cultural barriers that hold women back have been documented in previous research (Eagly & Chin, 2010). The influence of culture was explained by Schein and Schein (2017), when they noted that social validation occurs when enough members of the group hold a similar belief, and peer pressure discourages others from challenging the overall basic assumptions.
Unfairly, women have been portrayed as emotionally driven leaders whose lack of reasoning creates disadvantages for their organizations (Santiago García, 2011). The reality is that people have widely different sets of skills and competencies, regardless of gender (Dzubinski & Diehl, 2018). The point to note here is that the behaviors traditionally associate with leadership are stereotypically masculine (Schein, 2001). Latin American countries are specially interesting for the study of leadership and gender because of long-standing stereotypes that are outdated, but still influential. Dubinsky et al. (2014) commented on the lack of female representation across Latin American culture, and the distorted image of the “Macho” character used to depict Latin American masculinity. This type of representation is no longer viable in a changing world, where expectations of leader behavior have changed, and the influence of women and people from different ethnicities, nationalities, and sexual orientation has strengthened (Eagly & Chin, 2010).
It is imperative that the gender imbalance in leadership roles be addressed. The fact is that modern organizations need to tap into diverse groups of talented workers to help them succeed in the highly competitive environments that they face today (Schein, 2001; Kellerman, 2012; Lewis, 2018). Part of the problem is that research on leadership and leader development tends to be scarce in developing countries, which means that academics and practitioners have access to a limited amount of literature that can help them understand effective management practices in some of the most dynamic markets in the world (Behrens, 2013). Research on leadership across cultures can be helpful to better understand the gender gap in leadership because females and males adjust their style of leadership in accordance with cultural norms (Eagly & Johannesen-Schmidt, 2001).
Based on the need to develop more research on leadership at the local level, academics created the Leadership Effectiveness in African and the African Diaspora (LEAD) project in 2007 (Bagire & Punnett, 2017). Over the years, the LEAD project has produced several studies on leader effectiveness in Africa and the African Diaspora, which includes North America, the Caribbean, and Mexico (Punnett et al., 2017; Galperin et al., 2014; Lituchy, Metwally, & Henderson, 2017; Michaud et al., 2019; Lituchy, Díaz, & Velez-Torres, 2017). The LEAD studies are starting to break-ground on the subject of leadership and Latin America. Specifically, in Mexico, the LEAD studies suggest an inclination for transformational leadership (TL) behaviors on the part of managers, while emphasizing relationship-oriented behaviors (Michaud et al., 2019; Lituchy et al., 2017).
In the present study, Podsakoff et al.’s (1990) leadership model was used, which is part of the measurement instrument used in the LEAD studies. The model is consistent with the Full Range Leadership model, which uses the Multifactor Leadership Questionnaire (MLQ) as its instrument (Avolio & Bass, 1999). Podsakoff et al.’s (1990) and Avolio & Bass’s (1999) theoretical approaches are cornerstones to the study of transformational leadership theory, and the LEAD studies. Research developed under these approaches usually assess transformational and transactional leader behavior. The hypotheses stated for this research are the following:
In both cases, the null hypothesis (H₀) holds that there are no statistically significant differences between females and males in the sample for the two types of leader behavior expectations.
This quantitative study measures expectations in leader behavior held by female and male graduate students and alumni. The reasoning behind the research design is that it is important to understand whether educated females and males in Mexico follow the same pattern of leader behavior expectations. This will be inferred by the importance they attribute to transformational and transactional behaviors in leaders. Differences in expectations on leader behavior could help explain the gender imbalance in leadership roles, and paths toward addressing the problem.
The sample consisted of 364 (151 female and 213 male) graduate students and alumni from one university located in northwestern Mexico (in the state of Baja California). They were part of the Master’s in Business Administration program. The majority, 92.6% were employed at the time of the survey and 7.4% were not working. The average age for females was 36 and 38 for males. On average, females had 13.36 years of work experience while males had 16.43. Their native language was Spanish. The selection criteria included their status as highly trained individuals with similar levels of education and experience. Zabludovsky-Kuper (2015) argued that women were underrepresented in leadership roles despite achieving educational parity and a large share of the labor force. In this research, it was important that the sample consisted of individuals who were in a position to share their expectations of leader behavior from personal experience.
This quantitative research was designed to measure female and male participant expectations of effective leaders by identifying potential differences in the importance attributed to specific leader behaviors. Respondents were asked to complete a questionnaire that listed leader behaviors by assigning value to each item in terms of importance. The measure of TL developed by Podsakoff et al. (1990) was used. Consistent with Fowler (2014), the survey research design was implemented because of its simplicity and application in the social sciences.
The participants were randomly selected from the graduate school and alumni records of one university in northwestern Mexico. Access to the database of alumni and current graduate students was provided by the appropriate authorities. The participants were approached via e-mail. Each participant received a link to the questionnaire on Qualtrics that contained the LEAD project (Michaud et al., 2019) scales translated to Spanish. Before they completed the survey, they were provided with a written description of the research, and the use of the data and anonymity were explained. Participation was voluntary.
The participants completed the LEAD project questionnaire. The survey included the Leader Behavior Description Questionnaire (LBDQ) and Ubuntu leadership factor. In this study, however, only certain demographic data and the TL scale were used. The questionnaire was translated to Spanish by the researcher and back-translated by a second research team member. The TL scale consists of 23 Likert-scale items. Each item describes a leader behavior, which respondents rated in terms of appropriateness with their expectations of effective leaders. It was developed by Podsakoff et al. (1990) and measures transformational and transactional leader behaviors. The items are listed on Table 1. The transformational leadership constructs in the original version of the instrument originated from the integration of key TL behaviors: 1. Articulating a shared vision, 2. Providing an appropriate model, 3 Facilitating acceptance of shared goals, 4. Setting high performance expectations, 5. Providing individualized support, and 6. Intellectual stimulation (Podsakoff et al, 1990). In the same study, the authors validated the questionnaire.
Exploratory factor analysis (EFA) was used to adapt the leadership constructs in Podsakoff et al.’s (1990) instrument to this study. It was necessary to adapt the instrument because it was originally designed for a different context, and in a different language. Several recommendations provided by Beavers et al. (2013) proved useful in determining the criteria in conducting EFA. Maximum likelihood estimation with direct oblimin rotation was selected as the process took place. The cut-off point established to identify the factors was 1.0, communalities ≥ .30 were included in the final solution, as well as factor loadings of ≥ .50 without cross loadings ≥ .30. Kaiser-Meyer-Olkin (KMO) test of sampling adequacy required a value of .80 or above, with statistically significant X². Internal consistency was measured through Cronbach’s alpha ≥ .70. To compare TL scores between females and males in the sample, independent samples t tests were used along with Levine’s test of equality of variances, which follows best practices in hypothesis testing (Nordstokke et al., 2011). Alpha levels were set ≤ .05. Descriptive statistics served to establish mean scores for females and males in every factor. The analysis was facilitated by SPSS, version 25, software.
In order to compare female and male leadership scores, it was necessary to ensure validity and reliability of the instrument. EFA identified three factors, which explained 69.36 percent of the variance. KMO measure was .94, and Bartlett’s test of sphericity was significant ($X^{2}= 5886.24$, $df = 190$, $p< .01$). Three items were eliminated during the process (encourages employees, is considerate of needs, and considerers feelings). Table 1 summarizes average scores (μ) per item, standard deviation, communalities, and factor loadings.
Table 1
Three-Factor Solution of Transformational and Transactional Leadership.
Item | μ | SD | Communalities | Factor loadings | ||
---|---|---|---|---|---|---|
1 | 2 | 3 | ||||
Understand the direction | 4.62 | 0.67 | 0.51 | 0.75 | ||
Visualizes the future | 4.43 | 0.69 | 0.62 | 0.55 | ||
Searchers for innovation | 4.52 | 0.70 | 0.62 | 0.60 | ||
Inspirers others for the future | 4.53 | 0.70 | 0.68 | 0.77 | ||
Obtains commitment from others | 4.42 | 0.81 | 0.62 | 0.63 | ||
Leads by doing | 4.56 | 0.70 | 0.56 | 0.74 | ||
Serves as an example | 4.54 | 0.68 | 0.72 | 0.90 | ||
Leads by example | 4.60 | 0.68 | 0.73 | 0.89 | ||
Promotes team integration | 4.58 | 0.62 | 0.72 | 0.85 | ||
Develops a team attitude | 4.54 | 0.67 | 0.75 | 0.86 | ||
Develops team spirit | 4.55 | 0.67 | 0.79 | 0.85 | ||
Set high expectations | 4.30 | 0.84 | 0.60 | 0.70 | ||
Insists on best performance | 4.19 | 0.89 | 0.68 | 0.84 | ||
Does not settle for second place | 3.99 | 1.01 | 0.56 | 0.73 | ||
Takes feelings into account | 3.66 | 1.05 | 0.46 | 0.70 | ||
Shows respect | 4.22 | 0.84 | 0.46 | 0.50 | ||
Challenges to think in new ways | 3.95 | 0.98 | 0.41 | -0.62 | ||
Presents critical questions | 4.40 | 0.74 | 0.67 | -0.70 | ||
Stimulates reframing | 4.36 | 0.75 | 0.89 | -0.98 | ||
Reexamines assumptions | 4.25 | 0.80 | 0.64 | -0.78 |
Note: These items were eliminated as a result of EFA: 1. Encourages employees, 2. Is considerate of needs, and 3. Considerers feelings.
The adapted questionnaire seemed simpler than the original version developed by Podsakoff et al. (1990) as it went from 23 to 20 items. The new factors merged transformational and transactional behaviors, which is consistent with other leadership models (Kouzes & Posner, 2012; Heifetz, 1994). Alpha Cronbach coefficients were calculated for each factor and were named based on comparable leadership dimensions found in the literature (Table 2). The factors in the adapted version of the instrument are (1) shared purpose; α=.95; (2) high performance expectations, α =.85; and (3) boundary-spanning behaviors, α =.86. The adapted, Spanish version of the instrument is included as an Appendix.
Table 2
New Leadership Constructs and Theoretical Similarity.
Factors | No. Items | α | Leadership factor | Theoretical model coincidence |
---|---|---|---|---|
Shared purpose | 11 | .95 | Transformational | Idealized influence (Bass, 1981; 1985), Shared vision (Kouzes & Posner, 2012). |
High performance expectations | 5 | .85 | Transactional | Contingent reward (Bass, 1981; 1985). |
Boundary-spanning behavior. | 4 | .86 | Transformational | Adaptive leadership (Heifetz, 1994); Challenge the process (Kouzes & Posner, 2012) Intellectual stimulation (Bass, 1981; 1985). |
The new constructs were then used to compare female and male average scores in order to address the purpose of the study. As shown in Table 3, females and males attributed the same value to TL constructs aimed at promoting a shared purpose among their followers ($t=0.35, ns$). However, female participants attributed less importance than males to behaviors associated with setting high expectations ($t=2.19$, $p< .05$) and cross-boundary behaviors ($t=4.21$, $p< .01$).
Table 3
Independent Samples t Tests for Female and Male Participants
Factors | Female | Male | |||||
---|---|---|---|---|---|---|---|
N | μ | SD | N | μ | SD | t | |
Shared purpose | 151 | 49.68 | 7.51 | 213 | 49.92 | 5.50 | 0.35 |
High performance expectations | 151 | 19.81 | 3.82 | 213 | 20.67 | 3.58 | 2.19* |
Boundary-spanning behavior | 151 | 16.21 | 3.17 | 213 | 17.44 | 2.38 | 4.21** |
Levine’s test of equality of variances < .05 *$p < .05$, **$p< .01$
These results indicate that H1 can be partially retained. As noted in Table 3, there are no statistically significant differences between female and male groups in the sample for the shared purpose transformational factor. However, differences were found in the other transformational dimension, boundary-spanning behavior. Regarding the transactional leadership factor, high performance expectations, statistically significant differences were identified (Table 3), which leads to retain H2.
The results of this study suggest that males attributed greater importance to one transformational, and one transactional leadership factor than their female counterparts. Also, there were no significant differences in importance attributed to one transformational factor. Specifically, gender did not influence expectations of leader behavior for the shared purpose factor, but it did affect the results for the setting high expectations, and boundary-spanning behaviors. A secondary contribution from this research is the adaptation of Podsakoff et al.’s (1990) leadership instrument with graduate students in Mexico. EFA yielded a relatively clean result in that only three items were eliminated after a rigorous process. This created a simpler instrument that other researchers in Mexico may use in their work on leadership in Mexico.
The first finding is that females and males attribute similar levels of importance to TL behaviors associated with developing a shared purpose among members of a group. This result is consistent with the leadership model explained by Velázquez-Valadez and Salgado-Jurado (2015) as they aimed to contextualize leadership from the Latin American perspective to avoid overreliance on North American approaches. The authors noted that Mexican leaders have the capacity to reconcile task and relationship behaviors that can help secure follower commitment, loyalty, and purpose. These types of behaviors can be found in other TL models. For example, Kouzes and Posner’s (2012) Five Practices of Exemplary Leadership model includes the shared vision dimension (along with model the way, challenge the process, enable others to act, and encourage the heart), which measures the leader’s role in building consensus and getting everyone in the group to agree on a particular course of action.
In one study conducted under Kouzes and Posner’s model with undergraduate Mexican and Spanish students, nation of origin resulted in significant differences in the shared vision dimension, but no differences were reported when the group was divided by gender (Díaz, Sánchez-Vélez, & Santana-Serrano, 2019). The fact that females and males attributed similar levels of importance to this factor suggest that gender does not moderate consensus building and establishing shared goals and supports the claim that gender does not moderate TL. To this end, it is relatively safe to state that both females and males understand the importance of building consensus and leveraging participation from the group to determine a desired course of action.
Males in the sample attributed greater importance than their female counterparts to leader behaviors aimed at setting high expectations for their followers. Burns (2010) and Bass (1981) argued that leadership has a transactional component. This means that part of being an effective leader includes setting clear standards and expectations that everyone understands. Research conducted by Hamstra et al. (2014) suggests that followers will perform better under transactional leaders. By setting high expectations, leaders can motivate their followers to outperform others. The authors noted, however, that a transformational approach will serve learning organizations better.
Consistent with this result, Eagly, Johannesen-Schmidt, and van Engen’s (2003) meta-analysis of research published on leadership and gender concluded that men tend to be more transactional than women in terms of behaviors that involve supervision and intervention when followers do not perform according to standard. This could give some support to the idea that women are less agentic or less willing to be energetic with followers who fail to meet desired outcomes. Although Eagly et al. (2003) pointed out that their study supported claims that women are more transformational, it is worth taking into account that leaders are expected to be agentic at times. Therefore, behaviors involving setting high expectations and monitoring compliance should be part of female and male management styles.
Males in the sample attributed greater importance than the female participants to leader behaviors that promote working across organizational boundaries. This was a somewhat surprising result because of previous research that suggest that women are placed in boundary-spanning organizational roles more often than men (Araújo-Pinzón et al., 2017). Senge (2006) argued that today’s organizations need to promote learning organizations capable of innovating and changing more rapidly than companies in the past. This in response to global dynamics that favor innovation and adaptability over consistency. Therefore, it makes sense that organizations will look for leaders who understand the importance of working across boundaries as part of interdisciplinary teams that can manage short and long-term projects. In this regard, female managers need to make sure they develop the skills needed to work across organizational barriers, otherwise, it will be difficult to close the gender gap in leadership. Therefore, it is imperative that aspiring female leaders understand the importance of their role in this regard by developing a deeper appreciation for boundary-spanning leadership.
The results presented here would seem to challenge the findings in previous research involving leadership and gender conducted by Díaz (2018) and Díaz et al. (2019). In those studies, no significant differences were identified between females and males across leadership factors. A key difference, however, rests in the fact that those studies were designed to measure and compare leadership self-efficacy between two gender groups. In the present research, the intention was to compare attributed importance to transformational and transactional leader behavior. At no time were the participants asked to assess their own behaviors or perceptions of self. Therefore, the results presented here do not suggest that females believe themselves to be less capable than the males in the group in any of the factors. They simply believe two of the behavior sets to be of less consequence.
Generally speaking, the results presented here are aligned with the findings explained by Schein et al. (1996). These authors noted that research with female and male management students suggest that stereotypical male behaviors tend to be associated with effective management behavior across cultures. Schein (2001) would go on to argue that there is enough evidence to suggest that women in most parts of the world face unfair barriers for advancement. She argued that awareness of these barriers was a crucial part of addressing the problem. Hopefully, the present study served this purpose by pointing out specific behaviors in which women can work on to address and help narrow the gender gap in leadership.
The implication that derives from this research is that aspiring female leaders can engage in specific training programs to improve their chances of being considered to occupy leadership roles. Debebe (2009) argued that leadership training is effective when participants articulate a clear leadership challenge, attach meaning to it, achieve the desired change through training, and apply the new skills in a relevant context. This kind of training works best when the trainees are aware of the barriers they face (Ely, Ibarra & Kolb, 2011). Hopefully, the information presented here gives appropriate guidance and helps articulate a relevant training challenge.
The importance of this research rests in the need to develop and support talented individuals on a large scale in a manner consistent with the realities of modern organizations and industries. Lewis (2018) argued that narrowing the gender gap in the workplace serves the economy as a whole. This implies that gender equity is not only a matter of social justice, but it represents a proven strategy for economic development. The fact is that modern organizations need to tap into diverse groups of talented workers to help them succeed in the highly competitive environments that they face today (Kellerman, 2012). The three leadership factors examined in this study are consistent with behaviors observed in modern organizations concerned with innovation and adapting quickly to the dynamics of the global economy (Senge, 2006).
Limitations of this study include three aspects that could be addressed through future research. First, the focus on one particular segment of the population (graduate students and alumni) makes the results applicable only to a relatively small segment of the population. Second, the cross-sectional nature of the study can only explain what the participants believed in the specific moment in time in which they took the survey. Clearly, this may not hold in the future. Third, the focus on one leadership approach ignores other potentially relevant leadership factors (e.g. leader personality).
Future studies may address these limitations by examining gender and leadership roles in other segments of the population (e.g. female managers), conducting longitudinal studies perhaps using pre-post tests, and grounding new research on other leadership models (e.g. leader-member exchange or implicit leadership theory). Another important area for future research includes examining the long-term effect of graduate education on working professionals like the ones in the sample. As far as the LEAD studies are concerned, it is expected that researchers will continue to explore leader behavior across different cultures, and across demographic variables.
The underrepresentation of women in leadership roles in Mexico remains relatively unexplored from a cultural perspective, although the gender imbalance in leadership has been established. Although this study was conducted under one leadership approach developed for a Western, economically developed society, considerations were taken to adjust the research to the Mexican sample under study. Specifically, the TL instrument used in the study was translated and adapted. This study is novel because it focuses on one specific demographic: highly educated individuals in Mexico who are being trained to occupy leadership roles through graduate education. It also approaches the problem of underrepresentation of women in leadership roles by examining expectations of effective leader behavior. By identifying the behaviors that these individuals value in leaders, it is possible to better understand why females and males lead differently, and create appropriate training and development strategies to support them, hopefully creating a situation where organizations can focus less on gender, and more on behavior and performance when determining who is fit to lead.
The main finding in this study is that females and males attribute similar levels of importance to the leader’s role in inspiring a shared purpose among followers, and that males attribute greater importance than females to the role of leaders in setting high expectations, and working across organizational boundaries. By presenting the results from this study in terms of specific leader dimensions, it is possible for females in the sample to focus their training and development efforts. Participants in this study can focus their training on goal-setting to ensure that their expectations are consistent with the capabilities of their followers and organizational goals. Training may also include behaviors involved in working across organizational boundaries and meeting the needs of modern-day organizations. The point here is that individuals in the sample can be trained to better understand the relevance of effective leader behavior, which could lead to participants embracing them and acting accordingly, leading to narrowing the gender gap in leadership. Finally, educators involved with graduate programs in Mexico can include the findings from this study in their syllabus. For example, students could read and discuss the work of Kouzes and Posner (2012) with successful CEOs to discover how to exercise shared vision, establishing high expectations, and challenging organizational boundaries.
This study was funded by CETYS Universidad under Research Initiative 102. Conflict of interest: The authors declare no conflict of interest on conducting this research. Data availability: The database created for this study may be available upon request.
Transformational Leadership Questionnaire: Spanish Adaptation
Inspirar un propósito compartido | Establecer altas expectativas de desempeño | Cruzar barreras organizacionales | |
---|---|---|---|
Tiene una comprensión clara hacia dónde se dirige la organización. | X | ||
Muestra una imagen interesante sobre el futuro de nuestro grupo. | X | ||
Busca oportunidades creativas e innovadoras para la organización | X | ||
Inspira a otros con sus planes para el futuro. | X | ||
Es capaz de conseguir que otros se comprometan con sus sueños. | X | ||
Lidera “haciendo” en vez de “diciendo”. | X | ||
Me proporciona un buen modelo para seguir. | X | ||
Lidera con el ejemplo | X | ||
Alienta a los empleados a integrase al equipo. | X | ||
Desarrolla una actitud de equipo y espíritu entre los empleados. | X | ||
Desarrolla una actitud y espíritu de equipo entre los empleados. | X | ||
Nos demuestra que espera mucho de nosotros. | X | ||
Insiste en obtener únicamente el mejor desempeño. | X | ||
No se conforma con el segundo lugar. | X | ||
Actúa son consideración por mis sentimientos | X | ||
Muestra respeto por mis sentimientos personales. | X | ||
Me reta a pensar en problemas viejos, pero de nuevas formas. | X | ||
Plantea preguntas que me incitan a pensar. | X | ||
Me estimula a repensar la forma en que hago las cosas. | X | ||
Tiene ideas que me han llevado a reexaminar los supuestos que sostengo sobre mi trabajo. | X |
Fuente: Podsakoff et al. (1990). Translated to Spanish by the authors.