Lorenz regression analysis of inequality of opportunity and explained inequality
October 2026
Abstract: Inequality of opportunity (IOp) is typically operationalized as explained inequality: inequality in the conditional expectation of an advantage given circumstances. Existing methods work in two stages, first estimating a model for the outcome, and then applying an inequality index to the fitted values. Any bias in the first stage can therefore propagate to the second stage. By contrast, this paper builds instead on Lorenz regressions which optimize the object of interest directly — explained inequality — under a flexible single-index model. We show that this provides a robust and unified framework adapted to both continuous and binary outcomes and illustrate the method for income- and education-based IOp, where it integrates naturally into existing work while improving estimation stability, interpretability, and robustness.
| Type: | Working paper |
| Theme(s): | Econometrics and survey statistics Intergenerational transmission and equality of opportunity |
| Keywords: | Explained inequality, Inequality of opportunity, Shapley value decomposition, Single-index model |
| JEL Classification: | C14, C52, D31, D63 |
| RePEc:inq:inqwps:ecineq2026-698 |
Jacquemin, A., Heuchenne, C. & Van Kerm, P. (2026), 'Lorenz regression analysis of inequality of opportunity and explained inequality', ECINEQ Working Papers 699, Society for the Study of Economic Inequality, Italy.
@TECHREPORT{pvk-2013,
Author = {Jacquemin, Alexandre and Heuchenne, C{\'e}dric and Van Kerm, Philippe},
Title = {Lorenz regression analysis of inequality of opportunity and explained inequality},
Type = {ECINEQ Working Papers},
Series = {ECINEQ Working Papers},
Number = {699},
Institution = {Society for the Study of Economic Inequality},
Address = {Italy},
Month = oct,
Year = {2026}
}D'Aguanno, M.C., Guio, A.-C. & Van Kerm, P. (2026), 'Working, yet poor: The dynamics behind Europe’s in-work poverty rate', LISER Policy Brief 2026-21, Luxembourg Institute of Socio-Economic Research.
D'Aguanno, M.C., Guio, A.-C. & Van Kerm, P. (2026), 'Cross-country evidence on the individual dynamics of in-work poverty in the EU', Economic Systems, 50(2), 101360.
Doorley, K., Gromadzki, J., Lewandowski, P., Tuda, D. & Van Kerm, P. (2026), 'Automation and income inequality in Europe', Industrial and Labour Relations Review.
Sohst, R.R., Fusco, A. & Van Kerm, P. (2024), 'Foreign-born households’ contribution to inequality and polarization in European income distributions', LISER Working Paper 2024-06, Luxembourg Institute of Socio-Economic Research, Esch/Alzette, Luxembourg.
Sologon, D.M., Van Kerm, P., Li, J. & O'Donoghue, C. (2021), 'Accounting for differences in income inequality across countries: tax-benefit policy, labour market structure, returns and demographics', Journal of Economic Inequality, 19, 13-43.
Fusco, A., Sohst, R.R. & Van Kerm, P. (2021), 'Foreign-born households in the income distribution and their contribution to social indicators in European countries', in A.-C. Guio, E. Marlier & B. Nolan, Improving the understanding of poverty and social exclusion in Europe, Publications Office of the European Union, Luxembourg, Ch.5, pp.87-102.
Fusco, A., Gallo, G. & Van Kerm, P. (2021), 'Rotation Group Bias in the Estimation of EU Social Indicators', in A.-C. Guio, E. Marlier & B. Nolan, Improving the understanding of poverty and social exclusion in Europe, Publications Office of the European Union, Luxembourg, Ch.17, pp.295-312.
Sologon, D.M., Almeida, V. & Van Kerm, P. (2019), 'Accounting for the distributional effects of the 2007-2008 crisis and the Economic Adjustment Program in Portugal', LISER Working Paper 2019-05, Luxembourg Institute of Socio-Economic Research, Esch/Alzette, Luxembourg.
Jenkins, S.P. & Van Kerm, P. (2017), 'How does attrition affect estimates of persistent poverty rates? The case of EU-SILC', in A.B. Atkinson, A.-C. Guio & E. Marlier, Monitoring Social Inclusion in Europe, Eurostat, European Commission, Luxembourg, Ch.22, pp.402-417.
Jenkins, S.P. & Van Kerm, P. (2014), 'The Relationship between EU Indicators of Persistent and Current Poverty', Social Indicators Research, 116(2), 611-638.
Van Kerm, P. & Pi Alperin, M.N. (2013), 'Inequality, growth and mobility: The intertemporal distribution of income in European countries 2003--2007', Economic Modelling, 35(C), 931-939.
Jenkins, S.P. & Van Kerm, P. (2011), 'Patterns of persistent poverty: evidence from EU-SILC', ISER Working Paper 2011-30, Institute for Social and Economic Research, University of Essex, Colchester, UK.
Van Kerm, P. (2007), 'Extreme incomes and the estimation of poverty and inequality indicators from EU-SILC', IRISS Working Paper 2007-01, CEPS/INSTEAD, Differdange, Luxembourg.
Van Kerm, P. (2007), 'Extreme incomes and the estimation of poverty and inequality indicators from EU-SILC', in Comparative EU Statistics on Income and Living Conditions: Issues and Challenges, Proceedings of the EU-SILC Conference, Helsinki, 6-8 November 2006, Eurostat, European Commission, Luxembourg, pp.83-94.
Morelli, S., Nolan, B., Palomino, J.C. & Van Kerm, P. (2025), 'The influence of inheritances on wealth inequality in rich countries', Journal of Public Economics, 247(C), 105398.
Montorsi, C., Fusco, A., Van Kerm, P. & Bordas, S.A. (2024), 'Predicting depression in old age: Combining life course data with machine learning', Economics and Human Biology, 52(C), 101331.
van Acker, V. & Van Kerm, P. (2021), 'Design and implementation of the Socio-Economic Impact Survey', in M. Dijst, Socio-Economic Impacts of COVID-19: Collecting the Data, Les Rapports du LISER, Luxembourg Institute of Socio-Economic Research, Esch/Alzette, Luxembourg, Ch.3, pp.17-30.
Fusco, A., Gallo, G. & Van Kerm, P. (2021), 'Rotation Group Bias in the Estimation of EU Social Indicators', in A.-C. Guio, E. Marlier & B. Nolan, Improving the understanding of poverty and social exclusion in Europe, Publications Office of the European Union, Luxembourg, Ch.17, pp.295-312.
Jenkins, S.P. & Van Kerm, P. (2017), 'How does attrition affect estimates of persistent poverty rates? The case of EU-SILC', in A.B. Atkinson, A.-C. Guio & E. Marlier, Monitoring Social Inclusion in Europe, Eurostat, European Commission, Luxembourg, Ch.22, pp.402-417.
Van Kerm, P., Choe, C. & Yu, S. (2016), 'Decomposing quantile wage gaps: a conditional likelihood approach', Journal of the Royal Statistical Society (Series C: Applied Statistics), 65(4), 507-527.
Bia, M. & Van Kerm, P. (2014), 'Space-filling location selection', Stata Journal, 14(3), 605-622.
Van Kerm, P. (2012), 'Kernel-smoothed cumulative distribution function estimation with akdensity', Stata Journal, 12(3), 543-548.
Van Kerm, P. (2007), 'Extreme incomes and the estimation of poverty and inequality indicators from EU-SILC', IRISS Working Paper 2007-01, CEPS/INSTEAD, Differdange, Luxembourg.
Van Kerm, P. (2007), 'Extreme incomes and the estimation of poverty and inequality indicators from EU-SILC', in Comparative EU Statistics on Income and Living Conditions: Issues and Challenges, Proceedings of the EU-SILC Conference, Helsinki, 6-8 November 2006, Eurostat, European Commission, Luxembourg, pp.83-94.
Jenkins, S.P. & Van Kerm, P. (2005), 'Accounting for income distribution trends: A density function decomposition approach', Journal of Economic Inequality, 3, 43-61.
Yu, K., Van Kerm, P. & Zhang, J. (2005), 'Bayesian quantile regression: An application to the wage distribution in 1990s Britain', Sankhya (The Indian Journal of Statistics), 67, 359-377.
Van Kerm, P. (2003), 'Adaptive kernel density estimation', Stata Journal, 3(2), 148-156.
Van Kerm, P. (2002), 'Inference on inequality measures: A Monte Carlo experiment', in P. Moyes, C. Seidl & A. Shorrocks, Inequalities: Theory, experiments and applications, Journal of Economics supplement issues9, Springer-Verlag, Vienna, Austria, pp.283-306.