The economics of inequality

Data sources and definitions

Dr. Matthias Schnetzer

October 21, 2022

Has inequality been rising lately?

What inequality do you mean exactly?

How is income defined and how do we measure it?

Income concepts according to Canberra Group

ID	Concept	Aggregate
1	Income from employment	1a + 1b
1a	Employee income
1b	Income from self-employment
2	Property income
3	Income from household production
4	Current transfers received
5	Income from production	1 + 3
6	Primary income	1 + 2 + 3
7	Current transfers paid (taxes, fees, etc.)
8	Disposable income	6 + 4 - 7

System of National Accounts (SNA)

ID	Concept
D.1	Compensation of employees
D.11	Wages and salaries
D.12	Employers social contributions
B.2G	Operating surplus, gross
B.3G	Mixed income, gross
D.4	Property income
D.41	Interest
D.42	Distributed income of corporations
D.43	Reinvested earnings on foreign direct investment
D.44	Investment income disbursements (e.g. insurances)
D.45	Rent

Austrian tax law

ID	Concept	Description
1	Income from agriculture and forestry	Farmers, forest managers
2	Income from self-employment	E.g. Freelancers, Architects, Lawyer, Doctors, Consultants, CEO if she holds > 25%
3	Business income	All other self-employed activities
4	Employee income	Employees, retirees
5	Renting and lease of land	Particularly renting of real estate properties
6	Property income	Savings accounts, dividends (final taxation with capital income tax)
7	Other income	Income from speculation, income from selling private property, etc.

Income data sources in Austria

Income Type	Aggregate time series	Long-term distribution	Short-term distribution
Employee income	WTD SSD	WTD SSD	WTD SSD SES EU-SILC HFCS
Self-employed	ITD (IWITD)		ITD (IWITD) EU-SILC HFCS
Property income	CGT (ITD)		EU-SILC HFCS
Transfers	Various admin. sources		EU-SILC HFCS
Disposable household income	SNA		HBS EU-SILC HFCS

Administrative and survey data sources: Wage tax data (WTD), Income tax data (ITD), Integrated wage and income tax data (IWITD), Social security data (SSD), Capital gains tax data (CGT), System of National Accounts (SNA), European Survey of Income and Living Conditions (EU-SILC), Household Finance and Consumption Survey (HFCS), Household Budgetary Survey (HBS), Structure of Earnings Survey (SES)

What is EU-SILC?

European Union Statistics on Income and Living Conditions (by Eurostat)
Harmonized sample survey in private households
Replaced European Community Household Panel (1994-2001) in 2003
Conducted in all EU member states and Switzerland, Norway, Iceland, Turkey, Serbia and Macedonia
Sample:
- 🇦🇹 Stratified random sample from population register with approx. 6,000 households annually
- 🇪🇺 approx. 135,000 households (use weights!)
Interview mode: CAPI/CATI
Rotating 4 year panel; Ad-hoc modules
Standard documentation for Austria:

Income data in EU-SILC

Individual level:

employee cash or near cash income
cash benefits or losses from self-employment
pension from individual private plans
unemployment benefits
old-age benefits
survivor benefits
sickness benefits
disability benefits
education-related allowances

Household level:

income from rental of a property or land
family/children related allowances
social exclusion not elsewhere classified
housing allowances
regular inter-household cash transfers received
alimonies received
interest, dividends, profit from capital investments in incorporated business
income received by people aged under 16

Do income data from various sources fit together?

Administrative versus survey data

Impact on response behavior:

Social desirability
Sociodemographic characteristics
Survey design
Learning effect

Mean reverting errors

How do we explain the mismatch?

What about capital income?

How do you measure personal income inequality?

Common properties of inequality measures

Anonymity principle: it does not matter who earns the income
Population principle: the absolute population size does not matter, only proportions do
Relative income (or scale) principle: Relative incomes matter, not the absolute levels
Dalton (or transfer) principle: A regressive transfer within the distribution increases inequality

Anonymity principle: In an economy composed of two people, Mr. Smith and Mrs. Jones, where one of them has 60% of the income and the other 40%, the inequality metric should be the same whether it is Mr. Smith or Mrs. Jones who has the 40% share
Population independence: The income inequality metric should not depend on whether an economy has a large or small population. An economy with only a few people should not be automatically judged by the metric as being more equal than a large economy with lots of people.
Scale principle: If every person’s income in an economy is doubled (or multiplied by any positive constant) then the overall metric of inequality should not change.
Dalton principle: In its weak form it says that if some income is transferred from a rich person to a poor person, while still preserving the order of income ranks, then the measured inequality should not increase. In its strong form, the measured level of inequality should decrease.

Lorenz curve and Gini coefficient

Gini coefficient: \[\frac{A}{(A+B)} \in (0, 1)\]
Alternative: Half of the relative mean absolute difference \[G= \frac{\sum_{i=1}^{n}\sum_{j=1}^{n}|y_i - y_j|}{2n^2\bar{y}}\]

Alternative inequality measures

Shares
Ratios (point or share ratios, e.g. Palma ratio)
General Entropy (GE) measures:
- Decomposable
- Determine distance parameter \(\alpha\) (lower values put more weight on changes in lower tail; higher values at the top;)
- \(\alpha = 0\): Theil‘s L (mean log deviation)
- \(\alpha = 1\): Theil‘s T: \(\frac{1}{N} \sum_{i=1}^{N}\frac{y_i}{\bar{y}} ln\left(\frac{y_i}{\bar{y}}\right) \in (0; ln(N))\)
- \(\alpha = 2\): Half the squared Coefficient of Variation (ratio of std. deviation to mean)

Income distribution in the National Accounts

National Accounts

Institutional sectors in the SNA

Ownership	(S.11) Non-financial corporations	(S.12) Financial corporations	(S.13) General government	(S.14) Households	(S.15) NPIs serving households
Public sector	Public non-financial corporations	Public financial corporations	All government units and government NPIs
National private sector	National private non-financial corporations	National private financial corporations		All households	All NPIs serving households
Foreign-controlled sector	Foreign-controlled non-financial corporations	Foreign-controlled financial corporations

Note: The sectors presented in this table are domestic sectors (S.1). S.2 accounts for the rest of the world (RoW).

Income accounts in the SNA

Income accounts
Gross domestic product (GDP) at market prices (I)
- Consumption of fixed capital
= Net domestic product
(I)
+ Primary incomes receivable from the rest of world	Rest of world
- Primary incomes payable to the rest of world	Rest of world
= Gross national income (GNI) at market prices
- Consumption of fixed capital	Depreciation
= Net national income at market prices
- Taxes on products	Government
+ Subsidies on products	Government
= Net national income at factor cost	Production factors

Data for Austria (in billion Euro)

Wage share = Compensation of Employees / Net national income at factor cost

Bibliography

Angel, Stefan/Disslbacher, Franziska/Humer, Stefan/Schnetzer, Matthias (2019). What did you really earn last year?: Explaining measurement error in survey income data. Journal of the Royal Statistical Society: Series A (Statistics in Society). DOI: 10.1111/rssa.12463

Cowell, Frank (2011). Measuring inequality. Oxford University Press.

Ertl, Michael/Humer, Stefan/Moser, Mathias/Schnetzer, Matthias (2022). The micro-macro gap in property incomes: Consequences for household income inequality. Journal of Income Distribution.

United Nations (2011). Canberra group handbook on household income statistics (2nd ed.). Geneva: United Nations.