Inequality of Opportunity in Mexico and its Regions: A Data-Driven Approach

Abstract

This research proposes a first approximation of Inequality of Opportunity (IOp) in Mexico based on a concept of ex-post compensation, fully consistent with Roemer’s approach. This framework considers the advantage reached by an individual to be determined by the circumstances and by the effort exerted. Following Brunori and Neidhöfer, we construct a data-driven procedure using regression trees to identify types based on circumstances. To identify effort, an algorithm estimates the distribution of outcome in each type based on coefficients of Bernstein polynomials. We present IOp indicators for both an ex-ante and an ex-post approach. Our results underline the differences, in terms of opportunities, faced by individuals, based on the territory in which they grew up, the household context, and personal characteristics. The education and the wealth of parents, and the area of residence at age of 14 are the principal circumstances that shape the trajectories, besides the skin tone or the region. Importantly, territorial variables are significant among the individuals in relative poor households at age of 14, but they hold less importance for the others. IOp is higher in rural areas, in the South and in the Center compared to other regions.

Keywords:

• Inequality of opportunity
• decision trees
• Mexico

Acknowledgements

The authors would like to acknowledge the Center for Studies Espinosa Yglesias (CEEY For its acronym in Spanish: Centro de Estudios Espinosa Yglesias) for collecting the data used in this study. We thank the anonymous reviewers for the pertinence of all their comments that permit us to improve the quality of manuscript. We are also grateful for comments provided by Paolo Brunuori, Guido Neidhöfer, Luis Monroy-Gómez-Franco and the CEEY research team. All errors remain our own.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

The dataset used for this research is available at the following link: https://ceey.org.mx/contenido/que-hacemos/emovi/. The code used is available at https://figshare.com/s/2998772d5ff3295e044a.

Notes

1 In the ex-ante approach, the strong criteria states that the distribution of outcome should be the same across all types (Lefranc et al., 2009), whereas that the weak criterion requires the same conditional mean across types. To follow the strong criterion there is a need of a large number of observations in each type (Vélez-Grajales et al., 2018a).

2 For example, it is easy to show that in a society with two types and two tranches, a situation of EOp ex-ante (same mean in each row) but where the cells of a column have different values is incompatible with EOp ex-post which states that outcome must be equal within-tranche.

3 The liberal reward principle states to conserve the deviation of outcome due to personal responsibility. The utilitarian reward principal search to maximize the sum of outcomes of individuals with same circumstances.

4 A simple example is that a transfer to equalize outcome within-tranche (in order to reach EOp ex-post) can be different for individuals of a same type (Bossman & Öztürk, 2021; Ramos & Van de Gaer, 2016).

5 For example, the arithmetic average reward (Roemer & Trannoy, 2015), or the minimal reward (Fleurbaey & Peragine, 2013).

6 The splitting criteria is detailed in Appendix A.

7 We also find that Log-normal and Kernel tend to misestimate empirical distributions when they move away from the assumed distribution.

8 EA stands for ex-ante. BT stands for between types.

9 The Gini coefficient decomposes inequality of outcome into Within-Group, Between-Group and an interaction term. This interaction term represents the overlapping among subgroups of the ranges of values. If the relative position of individuals within their subgroup is the same relative position that for the whole distribution, then the interaction term is null.

10 The Regions are: North (Baja California, Coahuila, Chihuahua, Monterrey, Sonora, Tamaulipas), North-West (Baja California Sur, Sinaloa, Zacatecas, Nayarit, Durango), Center-West (Aguascalientes, Colima, Jalisco, Michoacán, San Luis Potosí), South (Campeche, Chiapas, Guerrero, Oaxaca, Quintana Roo, Tabasco, Veracruz, Yucatán), Center (Guanajuato, Hidalgo, Mexico, Morelos, Puebla, Queretaro, Tlaxcala), and Mexico City.

11 If the respondent was living with both parents at age of 14, then the parents’ education variable is the average number of years schooled by both parents, and in the event that he/she was living with only one parent, we focus on the years of schooling of this parent.

12 Localities of less than 2500 inhabitants. The other localities are considered as urban areas.

13 The range of colours can be found in the cards associated to the questionnaire of the EMOVI 2017. These documents are available on the website of the Espinosa Yglesias Center for Studies (CEEY).

14 The original sample contains 17,665 observations, from which 16,457 were living with one or both parents at age of 14.

15 Vélez-Grajales et al. (2018a) estimate that the lower-bound of this contribution is around 30%. Monroy-Gómez-Franco and Corak (2020) include variables about neighbourhood characteristics (in addition to personal and family characteristics and territorial circumstances), finding that around 48% of inequality in outcomes is related to IOp.