Inequality (2022/2023)

Course code
cod wi: DT000001
Name of lecturers
Francesco Andreoli, Claudio Zoli
Francesco Andreoli
Number of ECTS credits allocated
Academic sector
Language of instruction
Anno accademico 2022/2023 Dottorato di ricerca dal Oct 1, 2022 al Sep 30, 2023.

Lesson timetable

Go to lesson schedule

Learning outcomes

This 20 hours/5 lectures PhD module combines theoretical and empirical approaches to outline economic and statistics arguments for the analysis of economic inequality.

The objective of the module is to address two key questions, raised by two of the main contributors to modern inequality analysis, that systematically emerge in public economics and in the policy literature: the first question, addressed by Amartya Sen, is “Inequality of what?”; the second question, that stems from the lifelong research of Tony Atkinson, is “What can be done?”

The first part of the module focuses on the first question. We will define and document evidence about different notions of inequality that are intertwined with micro- and macroeconomic analysis: inequality of income, inequality across the life-cycle, inequality across and within groups (such as cohorts, generations, regions, families, genders, skills, human capital). The module will then survey and organize result son the normative underpinnings of measurement and analysis of inequality and related concepts, such as poverty, and social welfare. Empirical issues arising when implementing these models (data and inference) will be also discussed. The presentation will emphasize differences between unidimensional (such as in income or in health) and multidimensional inequality (based on the joint distribution of income and health, or inequality of income along the life course) and will investigate related phenomena, such as (ethnic and income) polarization, segregation, mobility, equality of opportunity.

The second part of the module will move from the analysis of distributions to that of redistribution of income or of endowments. The theory of (optimal) redistribution will be reviewed, drawing distinctions between implementation and expected effects on inequality of taxation and of targeted and universal (in kind and in cash) transfers. The module will focus on ex-post evaluation of the distributional impact of policies. We will review the identification of causal treatment effects along the whole distribution of an outcome, as well discuss implementation using distribution regression methods. Selected applications of these methods to the evaluation of the effects of early intervention (i.e. education and human capital reforms, the so-called “pre-distribution”) on inequality will be presented.


Lecturers: Francesco Andreoli (12hours), Claudio Zoli (8hours)


1) FA: Inequality of what? This lecture introduces evidence about inequalities related to income (cardinal variable), education (discrete variable) and skills (ordinal variable) across individuals and families, along the lifecycle, and across groups defined by the cohort, the region of residence, the family background, gender. It also surveys main data sources and empirical strategies adopted in analyzing inequalities.

2) CZ: Foundations of inequality measurement. The lecture will illustrate the basic principle behind the measurement of inequality and some of the more common criteria adopted in this framework, such as risk, social welfare, Lorenz curves, stochastic dominance.

3) CZ: From unidimensional to multidimensional inequality. Will be highlighted the main challenges related to the extension of the framework of analysis to multidimensional distribution. This is the case for instance when considering distributions of bundles of different goods or, as is the case for the Human Development Index, when combining evaluations based on the distribution of income, health and education across the population.

4) FA: Inequality and related concepts: This lecture deepens the analysis of alternative concepts of inequality, such as inequality of opportunity and will present presenting data sources and empirical results produced in the recent years, including a discussion about the relation between inequality, mobility and equality of opportunity (represented by the so-called Great Gatsby curve). The lecture will also analyze the relation between the distribution of income across individuals and in space (segregation).

5) FA: Causal analysis of intervention: from average to distributional impacts of intervention. This lecture will discuss the fundamental problem of causal identification and will outline the most interesting theoretical effects for policy evaluation (ATE, CATE, ATT, LATE, ITT and QTE). Identification results for these effects will be presented, with a specific focus on implementation using distributional regression methods (DiD, CiC, RIF, RIF-DiD, Quantile Regression). Reweighing methods for counterfactual analysis will be introduced.

Selected teaching material and references will be distributed during the lecures.

Students can have a broad overview of frontier research in inequality at the following links:

- (Lecture material from the Winter School on Inequality and Social Welfare Theory organized by the DSE)
- (Harvard-based lab on spatial inequality in US)
- (PSE-based database about trends in income inequality)
- (Stanford-based inequality lab)

Reference books

See the teaching bibliography

Assessment methods and criteria

Students presentation based on selected readings agreed upon with the teachers.