Academic staff

Francesco Andreoli, Lidia Ceriani, Claudio Zoli

Referent

Francesco Andreoli

Credits

4

Language

English

Class attendance

Free Choice

Location

VERONA

Moodle Seminars 0

Learning objectives

This 16-hour PhD module combines theoretical and empirical approaches to the analysis of economic inequality. The objective is to address two key questions that systematically emerge in public economics and in the policy literature: the first, raised by Amartya Sen, is "Inequality of what?"; the second, stemming from the lifelong research of Tony Atkinson, is "What can be done?"
The first part focuses on Sen's question. It defines and documents evidence about different notions of inequality intertwined with micro- and macroeconomic analysis: inequality of income, inequality across the life cycle, inequality across and within groups (cohorts, generations, regions, families, genders, skill levels, human capital). It surveys the normative underpinnings of inequality measurement and related concepts --- including poverty and social welfare --- and discusses the empirical issues arising when implementing these models (data and inference). The presentation emphasises differences between unidimensional inequality (income, health) and multidimensional inequality (joint distributions of income and health, or inequality of income along the life course), and investigates related phenomena such as polarisation, segregation, mobility, and equality of opportunity. A dedicated module introduces the measurement of poverty and wellbeing at the individual and multidimensional levels, including international comparisons.
The second part moves from the analysis of distributions to the analysis of redistribution. The theory of optimal redistribution is reviewed, drawing distinctions between the implementation and expected distributional effects of taxation and of targeted and universal transfers (in kind and in cash). The module focuses on the ex-post evaluation of the distributional impact of policies, reviewing the identification of causal treatment effects along the whole distribution of an outcome and discussing implementation via distributional regression methods. Selected applications to the evaluation of early interventions (education and human capital reforms, the so-called "pre-distribution") are presented.

Prerequisites and basic notions

Econometrics, microeconomics

Program

Lecturers: Francesco Andreoli (6hours - FA), Lidia Ceriani (6hours - LC), Claudio Zoli (4hours - CZ)
Topics:
CZ-1 Foundations of Inequality Measurement.
This lecture illustrates the basic principles behind the measurement of inequality and the most common criteria adopted in this framework, including risk, social welfare functions, Lorenz curves, and stochastic dominance.
CZ-2 From Unidimensional to Multidimensional Inequality.
This lecture highlights the main challenges in extending the inequality framework to multidimensional distributions --- for instance, when considering distributions of bundles of different goods or, as in the Human Development Index, when combining income, health, and education. The connections between multidimensional inequality and concepts such as polarisation and segregation are discussed.
LC-1 Measuring Poverty and Wellbeing.
This lecture introduces the conceptual and empirical foundations of monetary poverty measurement via a three-step approach. Step 1 develops the welfare indicator, contrasting income (Haig-Simons) with consumption expenditure as the preferred measure in developing-country contexts, with adjustments for price variation (CPIs, PPP) and household composition (equivalence scales). Step 2 compares relative (Eurostat: 60% of median), absolute (Cost of Basic Needs), and subjective (Leyden) poverty lines, including the World Bank's June 2025 update to $3.00/day (2021 PPP). Step 3 presents the Foster--Greer--Thorbecke class P_{α}, covering P₀ (headcount), P₁ (poverty gap), and P₂ (squared gap), their axiomatic properties, additive subgroup decomposability, and application to global poverty trends.
LC-2 Measuring Inequality and Top Incomes.
This lecture covers inequality measurement, the critical reading of global Gini statistics, and top incomes --- bridging the lectures by FA and CZ. After introducing distributional representations (Pen's Parade, Lorenz curve and dominance), it surveys the Gini, Generalised Entropy (GE(0), GE(1)), and Atkinson indices and their subgroup decompositions. A section on reading Ginis critically (Ceriani & Verme, 2025) shows how welfare metric, sub-metric, equivalence scale, top-coding, DINA anchoring, and survey design choices generate divergences of 6--10 Gini points on average across databases, with a practical guide to WB PIP, WID.world, LIS, WIID, and Eurostat. The lecture closes with top income and wealth trends: the WID/DINA methodology combining surveys, tax records, and national accounts; the doubling of the US top-1% share since 1980; its concentration in Anglo-Saxon economies; and the role of institutions --- rather than technology alone --- in driving cross-country divergence.
Hands-On Sessions
Both LC lectures are accompanied by a guided computer session providing Stata (.do) and R (.R) code.
FA-1 Inequality and Related Concepts.
This lecture deepens the analysis of alternative concepts of inequality, notably related to mobility of incomes, both over time and across generations. A particular emphasis will be given to the role of inequalities experienced early in life on inequalities on outcomes, and the way fairness consideration are incorporated into the measurement of dynamic inequalities. We will in investigate these inequalities through the modern lenses of inequality of opportunity theory. During the lecture, we will present data sources and empirical results from recent research, including a discussion of the relation between inequality, mobility, and equality of opportunity (the "Great Gatsby curve").
FA-2 Causal Analysis of Interventions: From Average to Distributional Impacts.
This lecture discusses the fundamental problem of causal identification and outlines the most relevant theoretical objects for policy evaluation (ATE, CATE, ATT, LATE, ITT, and QTE). Identification results for these effects are presented, with a specific focus on implementation using distributional regression methods (DiD, CiC, RIF, RIF-DiD, Quantile Regression). We will discuss the importance of these methods for assessing reforms aiming at re- and pre-distribution of endowments and incomes.
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:
- http://dse.univr.it/it/index.php/past-events-mainmenu-43 (Lecture material from the Winter School on Inequality and Social Welfare Theory organized by the DSE)
- https://opportunityinsights.org/ (Harvard-based lab on spatial inequality in US)
- https://wid.world/ (PSE-based database about trends in income inequality)
- https://inequality.stanford.edu/ (Stanford-based inequality lab)

Bibliography

Didactic methods

Classroom treaching in person.

Learning assessment procedures

Students presentation based on a critical analysis of selected research readings on the subject agreed upon with the instructors.

Assessment

Quality of the presentation; critical reading and discussion of the research work presented; adoption of appropriate terminology and analytical tools.

Scheduled Lessons

Sustainable Development Goals - SDGs

This initiative contributes to the achievement of the Sustainable Development Goals of the UN Agenda 2030. More information on sustainability