Abstract
We document the contribution of skin color toward quantifying inequality of opportunity over a proxy indicator of wealth. Our Ferreira–Gignoux estimates of inequality of opportunity as a share of total wealth inequality show that once parental wealth is included as a circumstance variable, the share of inequality of opportunity rises above 40%, overall and for every age cohort. By contrast, the contribution of skin tone to total inequality of opportunity remains minor throughout.
Introduction
Since the seminal work of Van de Gaer (1993) and Roemer (1993, 1998), the economics literature on inequality of opportunity has expanded substantially both in terms of theoretical and methodological developments and empirical applications. 1 And yet, one aspect pending to be fully addressed thoroughly is the role of skin color as a circumstance affecting the access to advantages. 2 So far, most of the empirical studies quantifying the level of inequality of opportunity in different countries and regions 3 focus on the effects of parental education attainment, parental occupation, region of birth (urban or rural) and whether the person speaks an indigenous language. 4 This gap in the literature stems from the unavailability of information on people's skin color in most countries, especially in developing ones.
A recent wave of studies focuses on identifying the effects of skin color-based discrimination on different aspects of life in Mexico. Arceo-Gómez and Campos-Vázquez (2014) show that women with darker skin tones face a lower probability of being called back while looking for employment vis-a-vis their lighter skin tone equivalents. Using experimental data, Campos-Vázquez and Medina-Cortina (2018) show that skin color stereotypes have a negative effect on life achievement expectations of female teenagers in middle school. Meanwhile, the literature reports that people with darker skin tones have systematically lower educational attainment and lower earnings than those with lighter skin tones (Campos-Vázquez and Medina-Cortina 2019; Flores & Telles, 2012; Telles, 2014; Villarreal, 2010). At the same time, they are more likely to report having been discriminated against than the other population groups (Aguilar, 2011).
All this evidence suggests that skin color is an important circumstance in determining an individual's access to advantages in life in societies where skin color is among the dimensions of social stratification. In this paper, we provide the first estimations of inequality of opportunity in a measure of wealth accounting for skin color in Mexico, a country with high levels of inequality (Bustos & Leyva, 2017; Castillo Negrete Rovira, 2017; Reyes et al., 2017), low social mobility rates for those located at the extremes of the wealth distribution 5 and for which increasing evidence points to skin color as an important factor of stratification. Relying on the Intergenerational Social Mobility Module (MMSI 2016) of the National Household Survey, we provide estimations of inequality of opportunity, which are nationally representative for the Mexican population between 25 and 64 years old.
The existing literature on inequality of opportunity in Mexico documents an unequal distribution of opportunities among the population (Vélez-Grajales et al., 2018; Wendelspiess-Chávez-Juárez, 2015). The estimates that are comparable with those of other Latin American countries suggest that Mexico is among the countries with higher levels of inequality of opportunity in the region. By including skin color into the set of circumstances analyzed, we expect to provide a more accurate estimation of inequality of opportunity in the country. In principle, an existing correlation between skin tone and the wellbeing advantage (whose inequality is being measured) should translate into a higher share of total inequality “explained” by observed circumstances.
We measure inequality of opportunity as a share of total inequality in a proxy measure of wealth, following the method proposed by Ferreira and Gignoux (2011). We find that once the wealth of origin is included as a circumstance variable, alongside both parents’ education and father's occupation, inequality of opportunity reaches over 40%, overall and for every age cohort. However, including skin tone barely adds to the overall proportion of inequality of opportunity in total inequality. That is, despite its statistically significant contribution to the level of inequality of opportunity, skin tone is nowhere nearly as important as other circumstance variables in practical terms. Moreover, this minor contribution of skin tone to inequality of opportunity in wealth remains largely unaffected by the inclusion or omission of parental wealth, education, and occupation in the estimations. Furthermore, it remains minor when the analysis is performed for each ten-year age cohort. Therefore, we are hard-pressed to find any indirect contributions of skin tone to current wealth variation via family background circumstances. These results pose open questions for future research on the mechanisms behind the relationship between variables such as current wealth, the wealth of origin and skin tone.
The rest of the paper proceeds as follows. The second section provides a methodological discussion. The third section describes the data set and the variables used. The fourth section presents and discusses our results. Finally, the paper concludes with some remarks.
Methodology
Following Roemer (1998), we partition the population into “types,” each of which is defined by a specific combination of circumstances.
6
Then, following Ferreira and Gignoux (2011), we measure inequality of opportunity based on the so-called weak criterion for equality of opportunity, which requires the expected value of each type's conditional advantage distribution to be equalized across all types.
7
Let
In order to estimate the share of total inequality in household wealth accrued by inequality of opportunities, the first step of the parametric estimation method proposed by Ferreira and Gignoux (2011) consists of computing a smoothed distribution of the advantage variable in which each individual's value is substituted with the predicted mean for the individual's type. Formally, this implies estimating a regression of the advantage variable y on the set of circumstance variables considered, that is,
Using the estimated coefficients for each circumstance (the vector of
A restriction for the last step is that not all inequality measures fulfill all the properties desirable for a measure of inequality of opportunity. For continuous variables with arbitrary mean and dispersion, 9 Ferreira et al. (2011) show that the Ordinary Least Squares (OLS) regressions’ R2 fulfils all the desirable properties; thus, constituting an adequate index for the estimation of the share of total inequality explained by inequality of opportunity. 10 As the advantage variable employed is a wealth index (described below), these measures will be employed. 11
Data
We use the 2016 Intergenerational Social Mobility Module of the National Household Survey (MMSI, 2016) conducted by Mexico's National Institute of Statistics and Geography. The survey is representative of the Mexican population (all genders) between 25 and 64 years old. The survey has a large set of retrospective questions enabling it to capture information concerning the characteristics of the household of origin when the respondent was 14 years old, as well as the educational level and work characteristics of the respondent's parents. It also includes a color palette designed to allow the self-identification of the respondent's skin color. The palette corresponds to the tone categorization designed for the Project on Race and Ethnicity in Latin America (PERLA; Telles, 2014).
The survey sample consists of 800 observations from each of the 32 states of Mexico. However, the design of the survey is such that it is only representative at the national level with a disaggregation to urban and rural communities. This prevents a state level disaggregation exercise in our analysis. We restrict the sample to only the observations that have information for the full set of circumstances. This implies a reduction of the sample size from 25,634 observations to 18,927 in the most demanding specification.
Though we are interested in wealth inequality, our data lack information on the financial value of disposable assets. However, with information on the assets available both in the respondent's household of origin when she was 14 and her present household, we can construct wealth indices for both households. This type of indices has long been employed for the distributional analysis of economic resources in developing economies (Filmer & Pritchett, 2001; McKenzie, 2005; Poirier et al., 2020; Wittenberg & Leibbrandt, 2017), as well as for the analysis of social mobility (Torche, 2015; Vélez-Grajales et al., 2014). A key aspect in the construction of this type of indices is that the suitability of the different-dimension reduction techniques used to construct them depends on the type of data used. For binary variables, like those we employ in this paper, a suitable technique is multiple correspondence analysis (MCA), which uses relative frequencies across binary variables to identify an underlying structure, with which one can rank individuals according to resource availability (in this case). This is a departure from the literature reliant on principal component analysis (PCA) to produce the asset index. PCA is not suitable for our case as it requires the minimization of Euclidean distances to calculate the weights used in the computation of the index, which is an inappropriate process for binary data. A suitable alternative to MCA is to perform PCA on a matrix of tetrachoric correlations of binary variables. Although the results presented in the paper are obtained using MCA to construct the wealth indices, we also estimate them using asset indices constructed with tetrachoric correlations as a robustness check. The results are almost identical.
The variables that we employ in the construction of the origin and current household indices are shown in Table 1.
Binary Variables Employed in the Construction of Both Asset Indexes.
To take full advantage of the data set, we define a set of circumstances as large as possible. We consider the circumstances employed by Ferreira and Gignoux (2011) (parents’ education, father's occupational status, indigenous status, sex, and whether the respondent lived in an urban or rural community) to which we add the household of origin asset index and the skin color of the respondent.
We define parental education using six categories: no formal education, incomplete primary education, complete primary education, completed middle school, completed high school, and college or graduate education. Father's occupational status is defined in binary terms as agricultural workers and the rest of occupations. Indigenous status is defined as having at least one parent who speaks an indigenous language. The criterion to assign urban or rural status was defined in terms of the respondent's perceived population in the community where she was born. If the perceived population was below 2,500 inhabitants, it is deemed a rural community. Otherwise, the community is considered urban.
As we only present parametric estimations, we use the continuous range of the origin's asset as a circumstances, allowing for a finer partition of the population and a better account of the level of inequality of opportunity. In the case of skin tone, we include the full PERLA scale which classifies skin tones in 11 categories. 12 We include the circumstances in a sequential order, detailed in Table 2.
Composition of the Circumstance Sets Employed.
Table 3 shows the sample proportions in the survey by specific circumstance categories. Among some noteworthy features, nearly three quarters of respondents report mestizo skin tones, about half are born in urban areas, and more than half grew up with fathers or mothers without complete primary education.
Composition of Each Age Group According to Circumstances.
Notes. The PERLA skin tones correspond directly to the PERLA scale designed by Telles (2014). The grouped skin tone scale is defined as follows. Urban community of origin is defined as those communities perceived by the respondent to have 2500 inhabitants or more. Indigenous populations are those with at least one parent being a indigenous tongue speaking person. Sample weights are employed.
Results
The first subsection provides the inequality of opportunity analysis. In the second subsection we delve into the role played by skin color in determining inequality of opportunity, and its relationship with the other circumstance variables.
Inequality of Opportunity
Table 4 shows results for the share of total inequality in the household assets distribution explained by inequality of opportunity. 13 Estimations are performed with six different sets of circumstances (see details in Table 2), which sequentially expand the set of circumstances under consideration. Our sequential approach to the inclusion of circumstances allows us to obtain some evidence on the weight of each circumstance in determining the total level of inequality of opportunity. As it is clear, considering only circumstances such as skin tone and indigenous status leads to a small amount of total inequality being accrued to inequality of opportunity. 14 The inclusion of variables such as the type of community of origin, parental educational achievement and the origin-household wealth index raises the contribution of circumstances substantially. The contribution of these circumstances implies moving from a society where at least less than 10% of total inequality is produced by factors outside the individuals’ control, to a society in which at least 43% of total inequality is produced by circumstances.
Parametric Estimations of Inequality of Opportunity.
Source. Authors’ calculations using MMSI (2016).
Notes. IORVAR stands for the ratio of the variance explained by the circumstances to the total variance of the household asset distribution. That is, R2 of the regression of the household index on the circumstance variables. Bootstrap standard errors are shown in parentheses, calculated with 1,000 repetitions. The estimation tables for these results are in the Appendix.
Figure 1 shows the contribution of each circumstance to inequality of opportunity in all sets according to the Shapley decomposition method. 15 We knew from Table 4 that including wealth of origin increases the share of inequality of opportunity in total wealth inequality, but now comparing the columns of sets 6 against all the others, we note that wealth of origin features the largest contribution to inequality of opportunity among the observed circumstances in the set. By contrast, all sets point to a small, yet statistically significant contribution of skin tone to total inequality of opportunity, accruing to less than two percentage points in the final set 16 .

Shapley decomposition of inequality of opportunity by circumstance. Note: The contribution of each circumstance adds up to the share of total inequality explained by inequality of opportunity. Circumstances are defined as indicated in the data section of the paper. Source: Authors’ calculations using MMSI (2016).
We now check whether the inclusion of an additional circumstance variable leads to an upward bias of the lower bound of inequality of opportunity in Mexico. As discussed in previous sections, the impossibility of accounting for all the circumstances exerting an influence on a person's life generates a downward bias in the estimations, as the effect of the missing circumstances ends up being accrued by the individual variation instead of the between-types variation. However, as Brunori et al. (2016) point out, increasing the number of variables measuring circumstances may generate an upward bias in the estimations due to the positive effect of ensuing finer sample partitions on the variance. As a criterion to choose the best specification, they propose to perform a cross-validation test and select the model that minimizes the mean square error. Table 5 presents the mean square errors of each model. The minimum square error is minimized with the model that includes both skin color and the household of origin's wealth index. Thus, we can conclude that the estimations do not suffer from an upward bias.
Mean Square Error.
Source. Authors’ calculations using data from MMSI (2016).
It is possible, however, that the circumstance variables are not orthogonal to each other. This would bias both the coefficients associated to each circumstance (and as a consequence the Shapley decomposition) and the estimation of the share of total inequality explained by circumstances due to overfitting and imperfect collinearity. This concern is particularly plausible for the case of the skin tone and indigenous status variables, as it is possible that the indigenous population is concentrated among the darkest skin tones of the scale. Should that be the case, then the skin tone variable might be actually capturing part of the effect associated to indigenous status.
To check if this is the situation, we plot the distribution of skin tones for both the population with parents that spoke an indigenous language and for the rest of the Mexican population. As Figure 2 shows, in both cases all skin tonalities are present, and the indigenous population is not concentrated around the darkest skin tones. However, it is worth noting that, as expected, the share of the population with the lightest tonalities is smaller within the indingeous population than in the rest of the population.

Skin tone distribution of indigenous and non indigenous populations. Note: Authors’ calculations using data from MMSI (2016).
Furthermore, Figure 3 shows that the share of each skin tone's population that is indigenous is relatively constant across tones, fluctuating between slightly less than 10% and slightly more than 20%, never constituting a majority in any of them. Although this serves to strengthen the case that skin tone and indigenous status are variables that codify different sets of information, it does not allow us to ascertain the presence of collinearity between any other variables. In order to attend this concern, we calculate the variance inflation factors (VIF) for each circumstance set.

Distributions of indigenous status in each skin tone. Source: Authors’ calculations based on data from MMSI (2016).
The variance inflation factor provides a measure of the increase in the variance of an estimated regression coefficient due to the collinearity between the associated variable and the rest of covariates in the model. The closer it is to one, the lower the influence of collinearity in the estimation of the parameters. As Table 6 shows, the VIF of all variables across the six models remains close to one. This result attenuates our concerns of imprecision in the estimation of each circumstance coefficient due to collinearity among the circumstances.
Variance Inflation Factor for Different Circumstance Sets.
In the specific cases of skin tone and indigenous status, the values are very close to one across all regressions. Together with Figures 2 and 3, this helps dispel any concerns of possible model overfitting in our estimations.
Layers of Inequality of Opportunity: Skin Color and Household Wealth
So far, our results indicate that once considered jointly with other circumstances, skin color plays a minor role in generating inequality of opportunity. This is true both for the net effect, identified in the sixth set of circumstances, and any indirect effect through other circumstances. This second type of effect, suggested by Navarrete (2016) would imply that in the sequential inclusion of circumstances, the addition of the skin tone scale should produce a level of inequality of opportunity similar to the one observed once the whole set of circumstances is included. As Figure 1 shows, this is not the case. As a result, the underestimation hypothesis is not supported by the data under the selected model specifications.
An alternative hypothesis is that skin color acts as a second-order stratifier in Mexican society. That is, skin color matters in terms of inequality of opportunity after disparities in education and wealth have stratified Mexican society (as shown in Figure 1). To provide some evidence on this matter, Figures 4 and 5 decompose the population with origins at both extremes of the wealth-index distribution by their skin color and their current quintile.

Distribution of the population at the bottom quintile of the origin wealth distribution by skin tone and current quintile of wealth. Source: Authors’ calculations using data from MMSI (2016).

Distribution of the population at the top quintile of the origin wealth distribution by skin tone and current quintile of wealth. Source: Authors’ calculations using data from MMSI (2016).
Figures 4 and 5 show two important features in support of the role of skin color as a second stratifier. First, the majority of those who start at the bottom and the top quintile remain in the same position when they reach adulthood. This suggests a prominent role of economic resources at origin in determining the current position of individuals. Second, light-skinned individuals represent a larger proportion of the population that starts at the top, than of the population that starts at the bottom. Third, individuals with lighter skin tones are less likely to fall through the distribution than their darker skinned peers, while they also experience a higher probability of moving upwards when starting at the bottom. However, notice that only a very small proportion of those who start at the bottom manage to climb the whole distribution. Likewise, only a small fraction of those who start at the top fall all the way down to the bottom.
Together with the results on the components of inequality of opportunity presented in the previous section, these results imply that the primary stratifier of wealth in Mexican society is the economic resources available. It is more than likely, given Mexico's colonial past, that the historical origins of this stratification by economic resources are linked to ethnicity and skin color. However, and as a direct consequence of the high levels of intergenerational persistence of wealth status, we can claim that the role of the available economic resources as an independent stratifier crystalized through time until it became the main stratifier of Mexican society in the present. 17
To observe how skin tone acts as a stratifier once the principal effect of household wealth is removed, we proceed to calculate the share of inequality inside each quintile of the origin asset index “explained” by circumstances. The results of this exercise are presented in Figure 6.

Share of intra-quintile inequality explained by circumstances. Source: Authors’ calculations using data from MMSI (2016).
First, note that the lower bound of within-quintile inequality of opportunity is relatively small even in the case of the top quintile, which has the highest value (slightly above 15%). This suggests that once the starker difference in terms of the household of origin's wealth is controlled for, individuals inside each quintile have relatively similar circumstances of origin. However, note that both at the bottom and at the top, household wealth remains the circumstance contributing the largest share of inequality of opportunity. Second, the effect of skin tone varies with the observed quintile, but in all cases remains small compared with other factors such as parental education and being originally from an urban community.
The persistent yet small contribution of skin tone to inequality of opportunity suggests that the hypothesis of skin color acting as a secondary element upon which Mexican society is stratified is not far from reality. This is in line with recent research by Monroy-Gómez-Franco and Vélez-Grajales (2020) who find that differences in social mobility by skin color are significant yet small once regional differences in economic development are considered.
It is worth noting that the vast majority of the Mexican population between 25 and 60 years old belongs in the intermediate skin tone group (nearly three quarters, Table 3), which translates into their ubiquitous presence in all quintiles. Thus, individuals from both the darkest and the lightest skin tones constitute a minority of the population. This is another possible driver of the small effect of skin tone color on inequality of opportunity.
Cohort Analysis
In order to investigate potential differences across cohorts in our sample, we calculate inequality of opportunity for five cohorts in our sample: 25–30, 30–40, 40–50, 50–60, and 60–65 years old. The results appear in Table 7.
Inequality of Opportunity by Cohort.
Note. The circumstance sets correspond to those defined in Table 2. Author's calculations using information from MMSI (2016).
Some key results are worth highlighting. First, the contribution of skin tone toward wealth inequality remains small and similar across all cohorts, yet statistically significant, ranging between 1.38% and 2.08% in the most complete set of circumstances. This confirms our finding that skin color is a stratifier in Mexican society yet not the main one. Second, the (lower bound) share of inequality of opportunity ranges between 40% (40–50 cohort) and 49% (youngest cohort), namely nine percentage points. That is, circumstances beyond people's control explain at least 40% of the variance in household assets, highlighting the persistent levels of inequality of opportunity in Mexico even among the relatively least unequal cohorts. Moreover, remarkably, inequality of opportunity remains fairly constant at 40% for all the cohorts with people older than 40 years. Finally, we must note that, due to the characteristics of the dataset, we cannot fully disentangle the effect of the life-cycle stage from the cohort effects.
Conclusion
We sought to analyze the role played by skin color as a circumstance variable (partially) explaining the share of inequality of opportunity in total wealth inequality in Mexico. Our results show that the contribution of skin tone to inequality of opportunity in wealth is statistically significant but small (particularly vis-a-vis other circumstance variables). Meanwhile, when added, origin-household wealth substantially increases the share of inequality of opportunity and becomes its most important contributor.
While only suggestive, our results do not point to a major role of skin tone as a source of inequality of opportunity in wealth in Mexico (even when the analysis is performed on age-cohort subsamples). Neither directly nor indirectly through its correlation with family background circumstances like wealth, parental education or occupation. Rather, we find indicative evidence that skin tone plays a secondary role in promoting further inequality of opportunity once family background variables, chiefly origin-household wealth but also parental education, have exerted their stratifying effects.
However, we should caution that our results just document the small (but statistically significant) conditional association between a specific “survey instrument” for skin tone, namely, the PERLA palette, and one specific measure of wealth. The association between alternative measures of skin tone and alternative measures of material wealth may or may not be similar in magnitude. Future research should test the robustness and concomitant empirical validity of our results to alternative methodological choices for the measurement of both skin tone and wealth. Furthermore, future research should prioritize data sets enabling a full disentanglement of life-cycle effects from birth-cohort effects. In the same vein, it is necessary to prioritize data sets with information at the level of the individual that allow for a full assessment of the contribution of sex to inequality of opportunity. This remains an area in need of urgent exploration by the literature on the subject.
Should further research ascertain the robustness of our results, then unlike the neighboring country north of the Rio Grande, suppressing color discrimination in Mexico could have at best a minor instrumental role in reducing inequality of opportunity in wealth (while being intrinsically warranted and necessary). Rather, directly tackling the socioeconomic inequalities in family circumstances (wealth, parental background, etc.) appears to be a more promising route.
Footnotes
Acknowledgments
We are thankful to the participants at the “Equal Chances: Equality of Opportunity and Social Mobility Around the World” Conference in Bari in 14th and 15th of December of 2018, the participants of the Eastern Economic Association Meeting of 2019 and the reviewers for their comments and observations.
Declaration of Conflicting Interests
The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.
Funding
The author(s) received no financial support for the research, authorship and/or publication of this article.
