Abstract
In many countries around the world, living in one subnational unit versus another can be just as important as race or class as a determinant of differential access to opportunities and wellbeing. Despite this fact, scholars still heavily emphasize interpersonal income inequality. This article develops and implements new tools to shift from interpersonal to subnational inequality and from economic to social inequality. It develops a novel concept and measurement of subnational social inequality that overcomes the inconsistencies between definitions and measurements found in existing research on the subject. Focusing on Latin America, the article applies the new measurement tools to reveal differences in the evolution and rankings of interpersonal and subnational forms of inequality. Such findings challenge our existing knowledge of both the levels and the sources of inequality in the region. To make sense of these discoveries, the article suggests that the usual drivers of interpersonal inequality—such as neoliberal reforms and authoritarianism—might drive down subnational inequality, while wellknown inequality fighters—such as democratization and left party rule—might not be as effective at combating its subnational variety.
Similar content being viewed by others
Notes
Stratification refers to “how valued resources are allocated according to class, gender, race/ethnicity, and other statuses” (Lobao et al. 2007).
For instance, the correlation between regional GDP per capita and regional literacy rates is 0.26 for Mexico, 0.22 for Ecuador, 0.32 for Colombia, 0.56 for Chile, 0.64 for Peru, 0.71 for Brazil, and 0.56 for Argentina, based on latest Census and official data.
Alternative labels are used to describe related phenomena: spatial inequality, territorial inequality, regional/interregional inequality, and regional disparities among others. I prefer subnational inequality for several reasons. First, the term subnational limits the attention to inequality between political and administrative entities, emphasizing the political mechanisms involved in its production. Second, in the context of decentralization where many social services are provided by municipalities, the term subnational inequality is more adequate when referring to inequality between these administrative units. Third, the term regional is often used to address political units comprising of several nation states.
Bounded refers to variables that have maximum and minimum levels. Illiteracy, for instance, is a bounded variable limited to a 0 to 100 range.
Based on Goertz’ (Goertz 2006) definitions of concepts, I suggest that both gap and dispersion are core components or dimensions of the concept of subnational inequality. Since both are “necessary” for the notion of subnational inequality, the aggregation rule should be multiplication (Munck and Verkuilen 2002; Goertz 2006)
I restrict this exercise to eight countries since they are the only ones for which I found reliable data at the subnational level for both infant mortality and illiteracy.
For this section, I use an “adjusted range” and a weighted coefficient of variation rather than regular range and coefficient of variation. Regarding the “adjusted range,” some of the countries taken into consideration here have a much smaller number of subnational units than others, going from 6 (Costa Rica) to 33 (Colombia). If we calculate the regular range, we would take into consideration 33% of Costa Rica’s and 6% of Colombia’s subnational units. To avoid this imbalance, I compute the range with the top 15% and the bottom 15% of subnational units. If, for example, a country has 20 provinces, I take the average of the top 3 provinces and subtract it from the average of the bottom 3 provinces. Likewise, I use a weighted coefficient of variation because most countries of my sample exhibit large differences in the population sizes of subnational units. The weighted C.V gives more weight to more populous subnational units than to less populous ones.
I ranked from highest level of inequality to lowest level of inequality for 1970, 1990, and 2010 and added all values for each country. For instance, Peru in illiteracy ranked first in 1970 (1 point), first in 1990 (1 point), and third in 2010 (3 points). Similarly, Peru in infant mortality ranked first in 1990 (1 point) and fourth in 2010 (4 points). Adding all points results in a value of 10. Doing the same exercise for all the periods in which there is data available for all countries gives the following points: Peru, 10; Brazil, 11; Colombia, 12; Mexico, 21; Ecuador, 22; Argentina, 31; Chile, 35; Costa Rica, 38. These results give pretty clear break points between levels. High subnational social inequality covers countries with values ranging from 10 to 12; medium subnational social inequality covers countries ranging from 21 to 24, and low subnational social inequality ranges from values 31 to 38.
Very briefly, the transfers principle states that any transfer of the attribute under consideration between a worse off unit or individual to a better off must be reflected in a reduction or increment in the measurement of inequality (Dalton 1920; Allison 1978) The scale invariance principle requires that multiplying every value by a constant leaves the degree of inequality unchanged. The translation invariance principle requires the inequality measurement to remain unchanged when a uniform addition or subtraction is applied to all values of the distribution. Lastly, the decomposability axiom is achieved when a measurement is able to distinguish between group inequality and individual inequality (Bellù and Liberati 2006)
References
Allison PD. Measures of inequality. Am Sociol Rev. 1978;43:865–80.
Banerjee A, Somanathan R. The political economy of public goods: some evidence from India. J Dev Econ. 2007;82(2):287–314.
Barro RJ, SalaiMartin X. Convergence. J Political Econ. 1992;100(2):223–51.
Bellù L, Liberati P. Policy impacts on inequality. Inequality and axioms for its measurement. Food and Agriculture Organization FAO; 2006. http://www.fao.org/docs/up/easypol/447/inqulty_axms_msrmnt_054en.pdf.
Beramendi P. The political geography of inequality: regions and redistribution. Cambridge: Cambridge University Press; 2012.
Berdegué JA, Escobal J, Bebbington A. Explaining spatial diversity in Latin American rural development: structures, institutions, and coalitions. World Dev. 2015;73:129–37.
Birdsall N, Lustig N, McLeod D. Declining inequality in Latin America: some economics, some politics. In: Kingstone P, Yashar DJ, editors. Routledge handbook of Latin American politics. New York: Routledge; 2013. p. 158–80.
Bogliaccini JA. Trade liberalization, deindustrialization, and inequality: evidence from middleincome Latin American countries. Lat Am Res Rev. 2013;48(2):79–105.
Boix C. Origins and persistence of economic inequality. Annu Rev Political Sci. 2010;13(1):489–516.
Cederman L, Weidmann NB, Gleditsch KS. Horizontal inequalities and ethnonationalist civil war: a global comparison. Am Political Sci Rev. 2011;105(3):478–95.
Cornia GA. Income inequality in Latin America: Recent decline and prospects for its further reduction. Series Macroeconomics of Development 149. Chile: ECLAC; 2014. https://repositorio.cepal.org/handle/11362/36852.
Dalton H. The measurement of the inequality of incomes. Econ J. 1920:348–61.
De Ferranti D, Perry GE, Ferreira FHG, Walton M. Inequality in Latin America: breaking with history? Washington: World Bank Latin American and Caribbean Studies; 2004.
Elbers C, Lanjouw P, Mistiaen JA, Özler B. Reinterpreting betweengroup inequality. J Econ Inequal. 2008;6(3):231–45.
Etchemendy S. La economía política del neoliberalismo: Empresarios y trabajadores en América Latina, España y Portugal. Ciudad Autónoma de Buenos Aires: EUDEBA; 2016.
Falleti TG. Decentralization and subnational politics in Latin America. New York: Cambridge University Press; 2010.
Garay C. Social policy expansion in Latin America. New York: Cambridge University Press; 2017.
Gibson EL. Boundary control: subnational authoritarianism in federal democracies. New York: Cambridge University Press; 2013.
Gibson EL, Calvo E. Federalism and lowmaintenance constituencies: territorial dimensions of economic reform in Argentina. Stud Comp Int Dev. 2000;35(3):32–55.
Giraudy A, Moncada E, Snyder R. Subnational research in comparative politics. New York: Cambridge University Press; forthcoming.
Goertz G. Social science concepts: a user’s guide. Princeton: Princeton University Press; 2006.
Gyuris F. The political discourse of spatial disparities: geographical inequalities between science and propaganda. Cham: Springer International Publishing AG; 2014.
Harbers I, Steele A. The subnational state in Latin America: a typology of uneven presence and performance. APSA Annual Meeting & Exhibition. San Francisco; 2017.
Hoffman K, Centeno MA. The lopsided continent: inequality in Latin America. Annu Rev Sociol. 2003;29(1):363–90.
Huber E, Stephens JD. Democracy and the left: social policy and inequality in Latin America. Chicago: University of Chicago Press; 2012.
Huber E, Nielsen F, Pribble J, Stephens JD. Politics and inequality in Latin America and the Caribbean. Am Sociol Rev. 2006;71(6):943–63.
Jana M, Nathan JK. Market Inequality and Redistribution in Latin America and the Caribbean. J Polit 2013;75(3):672–685.
Kanbur SMR, Venables A. Spatial inequality and development. Oxford. New York: Oxford University Press; 2005.
Kaufman RR. The political effects of inequality in Latin America: some inconvenient facts. Comp Polit. 2009;41(3):359–79.
Lee MM, Zhang N. Legibility and the informational foundations of state capacity. J Politics. 2017;79(1):118–32.
Lobao LM, Hooks G, Tickamyer AR. The sociology of spatial inequality. New York: SUNY Press; 2007.
LópezCalva LF, Lustig NC. Declining inequality in Latin America: a decade of progress?. New York: Brookings Institution Press; 2010.
Marchante AJ, Ortega B. Quality of life and economic convergence across Spanish regions, 1980–2001. Reg Stud. 2006;40(5):471–83.
Munck GL, Verkuilen J. Conceptualizing and measuring democracy. Evaluating alternative indices. Comp Political Stud. 2002;35(1):5–34.
ØStby G, Nordås R, Rød JK. Regional inequalities and civil conflict in subSaharan Africa. Int Stud Q. 2009;53(2):301–24.
OteroBahamon S. When the state minds the gap. The politics of subnational inequality in Latin America [Ph.D]. Evanston: Northwestern University; 2016.
Roberts KM, Arce M. Neoliberalism and lowerclass voting behavior in Peru. Comp Political Stud. 1998;31(2):217–46.
RodríguezPose A, Ezcurra R. Does decentralization matter for regional disparities? A crosscountry analysis. J Econ Geogr. 2010;10(5):619–44.
Rogers MZ. The politics of place and the limits of redistribution. New York: Routledge; 2015.
Royuela V, García GA. Economic and social convergence in Colombia. Reg Stud. 2015;49(2):219–39.
Schady NR. The political economy of expenditures by the Peruvian social fund (FONCODES), 1991–95. Am Political Sci Rev. 2000;94(2):289–304.
Sen A. Development as Freedom. Oxford: Oxford University Press; 1999.
Singh P. How solidarity works for welfare: subnationalism and social development in India. New York: Cambridge University Press; 2016.
Snyder R. Scaling down: the subnational comparative method. Stud Comp Int Dev. 2001;36(1):93–110.
Soares S, Guerreiro Osório R, Veras Soares F, Medeiros M, Zepeda E. Conditional cash transfers in Brazil, Chile and Mexico: impacts upon inequality. Estudios Económicos. 2009:207–24.
Stepan A, Linz JJ. Comparative perspectives on inequality and the quality of democracy in the United States. Perspect Politics. 2011;9(4):841–56.
Stewart F. Horizontal inequalities: a neglected dimension of development. QEH working paper series 81. WIDER; 2002. https://www.researchgate.net/publication/24119604_Horizontal_Inequalities_A_Neglected_Dimension_of_Development.
Stewart F, Langer A. Horizontal inequalities: explaining persistence and change. In: Stewart F, editor. Horizontal inequalities and conflict. UK: Palgrave Macmillan; 2008.
Tarrow SG, Katzenstein PJ, Graziano L. Territorial politics in industrial nations. New York: Praeger Publishers; 1978.
Thomas V, Wang Y, Fan X. Measuring education inequality: Gini coefficients of education. Policy research working paper series 2525. Washington: World Bank Publications; 2001.
Thorp R, Paredes M. Ethnicity and the persistence of inequality: the case of Peru. Basingstoke: Palgrave Macmillan; 2010.
Tilly C. Durable inequality. Berkeley: University of California Press; 1999.
United NationsHabitat. State of Latin American and Caribbean Cities: Towards a new Urban Transition. Nairobi: UN Habitat; 2012.
Wong WSD. The modifiable areal unit problem (MAUP). In: Fotheringham S, Rogerson P, editors. The SAGE handbook of spatial analysis. United States: SAGE Publications Ltd; 2008.
Zhang X, Kanbur R. Spatial inequality in education and health care in China. China Econ Rev. 2005;16(2):189–204.
Acknowledgements
I would like to thank Isabel Castillo, Rodrigo Barrenechea, Mariana Borges, Laura Garcia, Ana Arjona, James Mahoney, Alisha Holland, Edward Gibson, Tulia Falleti, Diana Rodriguez, Sandra Botero, Santiago Alles, Juan Diego Prieto, participants and discussants at Repal 2014, Lasa 2014, and IQMR 2015, and anonymous reviewers and editors for their excellent comments and suggestions. I also thank EDGS and the Buffet Center at Northwestern University for the financial support.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Appendix
Appendix
Inequality Measurements of Gap and Dispersion
Gap Measurements

a)
Range
Definition: The range provides the difference between the highest and the lowest value on a variable. When used in subnational analysis, it provides the full extent of variation of an attribute across spatial units. If subnational illiteracy rates go from 5 to 25, the range would be 20.
Advantages: It captures the idea of the gap between the betteroff and the worseoff areas, it is easy to compute and simple to understand.
Disadvantages: The range is not commonly used as an inequality measurement because it does not comply with the inequality axioms, or a group of desirable properties that inequality measurements should respect. There are four axioms: the transfers principle, the scale invariance principle, the translation invariance principle, and decomposability.^{Footnote 10} As the range only takes into account two units and it depends on the scale, it does not fulfill any of the axioms. However, the axioms for inequality measurements were mainly developed for the study of individual income inequality, and they are not necessarily suited for subnational inequality in social development indicators. In fact, and as was shown in the text with the examples of countries A and B, complying with the scale invariance axiom obscures the existence of subnational inequality.

b)
Ratios
Definition: The ratio is computed by dividing the highest value by the lowest value, or values set at different percentiles.
Advantages: Ratios can be used in crosscountry and crossattribute comparisons.
Disadvantages: As the ratio complies with the scale invariance principle, it does not allow us to tap the gap dimension of subnational inequality that makes a difference between country A and country B, in the text’s example. For this reason, the range is better suited than the ratio for our concept of subnational inequality.

c)
Beta Convergence (B.C)
Definition: Economists study subnational inequality by using sigma and beta convergence. Sigma convergence is the coefficient of variation, while beta convergence refers to the relationship between the initial level of an attribute and its growth rate over a time period. B.C takes place when the worseoff regions improve faster than the betteroff regions, lessening the range. Theoretically, B.C refers to the idea that when the worseoff catch up there is reduction in inequality. B.C is measured by running a lineal regression in which the growth rate of an indicator in each subnational unit in a previously established period of time is the dependent variable, and the initial level acts as the independent variable. If the coefficient (b) is negative, there is beta convergence (Barro and SalaiMartin 1992).
Disadvantages: It is possible that the worseoff grows so fast that it overcomes the better off, producing more inequality instead of reducing it. The measurement of B.C would suggest a reduction in inequality when an increment in inequality is taking place (Gyuris 2014: 213). Additionally, beta convergence describes whether inequality is increasing or decreasing, but gives no information on the extent of such inequality. Lastly, the fact that the time frame for which B.C is calculated must be predetermined raises suspicions, since the criteria for selecting the time period are not clear and often different time frames give different results. To sum up, B.C, although commonly used by economists, does not fulfill a few desirable attributes of a subnational inequality measurement.
Dispersion Measurements

a)
Standard Deviation and Coefficient of Variation.
Definition: The standard deviation provides an idea of the dispersion of an attribute around the mean. If the values of a given variable are very spread out, the standard deviation is high. When applied to spatial analysis it would tell, on average, how distant from the mean are the values of the different spatial units. The standard deviation can be weighted by population size. The weighted standard deviation acknowledges that each spatial unit has a different population size, reducing the impact of depopulated and outlier provinces in the distribution.
Disadvantages: The standard deviation, however, says little if not placed in the context of the mean. For example, the dispersion of a variable in a dataset with standard deviation of 3 looks very different if the mean is 5 or 500. If the mean is 5, the data is very dispersed. If the mean is 500, the data is not dispersed at all.
The coefficient of variation—our selected measurement for dispersion—is the solution to this problem because it is computed by dividing the standard deviation by the mean. It can also be weighted by the population size of each subnational unit. Additionally, it is independent of the unit in which the variable is measured. In every case, the higher the C.V, the greater the dispersion of a given attribute. The (weighted) C.V is as apt for inequality measurement as the Gini coefficient.

b)
Spatial Gini
Definition: The Gini Coefficient is a measure of dispersion because it measures the extent to which the distribution of an attribute among individuals or groups deviates from a perfectly equal distribution. It is defined in two main ways: as the average difference in an attribute between all pairs of individuals or groups or as the area between the Lorenz curve and the egalitarian line by the area of the egalitarian triangle. The Gini can be used for groups and individuals. When applied to spatial analysis, each spatial unit is considered to be a group with a population weight. The Gini captures whether the amount of an attribute possessed by each group is proportional to its size. It ranges from 0 where all subnational units have the same access, to 1 where there is absolute concentration of an attribute in one subnational unit.
Advantages: The Gini is probably the most commonly used measurement of inequality. It is scale invariant and sensitive to transfers.
Disadvantages: However, the Gini is used for continuous variables that are cumulative in nature, such as income or years of schooling. It is not commonly used for categorical (e.g., race), discrete (e.g., educational attainment), or bounded variables (e.g. illiteracy or infant mortality rates (Thomas et al. 2001). This is reflected in the fact that a Gini of a rate—for instance, illiteracy—is completely different from the Gini of its opposite—literacy.

c)
Theil Index
Definition: The Theil Index is a measure of dispersion that allows decomposition in between group and within group inequality. If disaggregate data is available, the Theil index would tell how much inequality corresponds to the differences between groups and the differences between individuals.
Disadvantages: Despite being very appropriate for spatial analysis due to its decomposable nature, the Theil Index suffers from a major shortcoming: it is sensitive to population size, which means that it is not comparable across countries with different numbers of subnational units (Elbers et al. 2008). In addition, the Theil Index is difficult to understand and compute and is not intuitive.
Rights and permissions
About this article
Cite this article
OteroBahamon, S. Subnational Inequality in Latin America: Empirical and Theoretical Implications of Moving beyond Interpersonal Inequality. St Comp Int Dev 54, 185–209 (2019). https://doi.org/10.1007/s12116019092816
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12116019092816