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Estimation of Opportunity Inequality in Brazil using Nonparametric Local Logistic Regression

2010; Taylor & Francis; Volume: 46; Issue: 9 Linguagem: Inglês

10.1080/00220388.2010.500661

1743-9140

Erik Alencar de Figueirêdo, Flávio Augusto Ziegelmann,

Intergenerational and Educational Inequality Studies

Abstract Abstract This article measured opportunity inequality in Brazil by combining a series of theoretical and empirical tools. The database was built using a two-sample instrumental variable (TSIV), developed by Angrist and Krueger. After that, the axiomatic approach put forward by O'Neill et al. was used, in which the estimation of children's income distribution function is conditional on their fathers' wages. The inference process was based on nonparametric local logistic regression. The results indicate that Brazil has a high level of opportunity inequality. In other words, in the context of intergenerational mobility, those whose fathers belong to lower income strata have to expend greater effort in order to attain a certain income level. Acknowledgements The authors thank professors Fernando A. Veloso and Sérgio Ferreira. We take full responsibility for any errors or omissions. The first author wishes to thank the financial support of CNPq, by the Project 475225/2009-0. Notes 1. See United Nations Development Program (2006 United Nations Development Program. 2006. Human Development Report, New York: United Nations Development Program. [Google Scholar]). 2. From the second half of the 1990s, federal governments have adopted a series of income redistribution policies, classified as 'affirmative policies'. Among them, one may cite the system for preferred admission for racial minorities (blacks and Indians) at public universities, food grants and school attendance programmes. 3. Bossert et al. (1999 Bossert, W., Fleurbaey, M. and Van de Gaer, D. 1999. Responsibility, talent and compensation: a second best analysis. Review of Economic Design, 4(1): 35–55. [Google Scholar]) demonstrate that this procedure is not an easy task. 4. Alternative approaches define opportunity equality using the set of opportunities to which individuals have access. For further details, see Pattanaik and Xu (1990 Pattanaik, P. and Xu, Y. 1990. On ranking opportunity sets in terms of freedom of choice. Recherches Economiques de Louvain, 56: 383–390. [Google Scholar]) and Kranich (1996 Kranich, L. 1996. Equitable opportunities: an axiomatic approach. Journal of Economic Theory, 71(1): 132–147. [Google Scholar]). 5. For a list of variables used in empirical studies, see Ramos and Van de Gaer (2009 Ramos, X. and Van de Gaer, D. Empirical evidence on inequality of opportunity. Working paper. Accessed at http://www.idep-fr.org/IMG/pdf/ramosVandeGaer-4.pdf [Google Scholar]). 6. Recently, Lefranc et al. (2008 Lefranc, A., Pistolesi, N. and Trannoy, A. 2008. Inequality of opportunities vs. inequality of outcomes: Are Western societies all alike?. Review of Income and Wealth, 54(4): 513–546. [Crossref] , [Google Scholar]) developed a model that assesses opportunity equality based on conditional distributions and on stochastic dominance tests. 7. It should be underscored that notation z = y[e,x] excludes random factors (for example luck). For further details, see Lefranc et al. (2009 Lefranc, A., Pistolesi, N. and Trannoy, A. 2009. Equality of opportunity: definitions and testable conditions with an application to income in France. Journal of Public Economics, 93(11): 1189–1207. [Google Scholar]). 8. Earnings from all jobs divided by the number of working hours. 9. The classification follows the level of intensity of human capital required by the occupation. For example, category 1 (lower) is made up of agricultural labourers, fishermen, wood cutters, and so forth. Category 6 includes top-level managers, magistrates, those with higher education, and so forth. 10. The regression has 83 covariates and is robustly estimated under autocorrelation and heteroskedasticity. The results were omitted due to space restrictions. 11. A list of applications is provided in Cameron and Trivedi (2005 Cameron, A. and Trivedi, P. 2005. Microeconometrics: Methods and Applications, New York: Cambridge University Press. [Crossref] , [Google Scholar]). 12. Note that the study conducted by Ferreira and Veloso (2006 Ferreira, S. and Veloso, F. 2006. Intergenerational mobility of wages in Brazil. Brazilian Review of Econometrics, 26(2): 181–211. [Google Scholar]) only investigates intergenerational mobility, overlooking opportunity inequality issues. 13. That is, the income normalised by the mean. 14. Fleurbaey (1998 Fleurbaey, M. 1998. "Equality among responsible individuals". In Freedom in Economics: New Perspectives in Normative Economics, Edited by: Laslier, J.-F., Laslier, M., Gravel, N. and Trannoy, A. 206–234. London: Routledge. [Google Scholar]) discusses the limitations of bivariate models. 15. Bolsa Família was created in October 2003. 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