Issues with Representing the Welfare of Agents

U(x) is fundamentally Unobservable, proxies are needed, here we deal with

some of the issues.

There are many issues, suppose U(x) is monotonic increasing in x

why not just use the elements of x?

• Many dimensions or few dimensions for x?

• Current or Lifetime individual wellbeing?

• Individuals or households?

• What should x contain, goods, “functionings and capabilities”?

• Consumption or Income measures?

• Complete Orderings or Partial orderings?

Many Factors versus One Factor

• While we do not observe U(x) we frequently observe some or all of the x.

• Problems with multivariate analysis are mainly technical and practical rather than logical.

• Essentially we have to decide a form for Ui( ), what x should contain and who the “i’s” should be.

• The problem of defining a poverty cutoff in multivariate states.-Poverty Boundaries and multivariate distances

• The problem of defining inequality in multivariate states - the Multivariate Gini Multivariate versions of other inequality measures.

Current Versus Lifetime Happiness

• Depends upon the questions being asked, typically welfare measurement is “current” cross sectional using the income of an individual without regard to their position in the lifecycle.

• Child Poverty, Pensioner Poverty – the same “sort” of poverty?

• The Example of Africa – Looking at income and life expectancy.

• Life chances and Intergenerational Effects – mobility analysis and The Dynastic Poor.

What Inequality?

Agents current life length is measured by t (0 < t < 80) and all agents live until 80. An agents lifetime income profile is given by f(t) where: f(t) = 0 for (0 < t < 20), (Childhood) = t for (20<t<60) (Working Life) = 60 for t>60. (Retirement) All agents self clone and have one child at t*, (where 20 < t* < 40). Agents leave the household at age 20 so that during age t* to t*+20 agents are head of a family sharing their income with their cloned child. The society starts at T=0 and has a generation cycle of t*. All agents have identical life cycles and are equal in every sense of the word with identical opportunities except that they are observed at different points in their lifecycle, yet Gini ≠ 1 varying with the duration of the generation cycle. For example in the long run of the population cycle for t* = 20 Gini = 400/(960+16x) where x is the expired duration of the generation cycle. With respect to poverty suppose the household poverty cutoff is set at 20 - ε per capita where ε is an arbitrarily small number, all households with children will be in the poor group when t*=20, no households will be in the poor group when t*=40. (For t* = 30 all children in the poor group for first half of the 20 year cycle, no children in poor group for second half of the cycle).

Households or Individuals

• Usually data is obtained by household utility is experienced by individuals – really a reprise of the problem of aggregating utilities but a bit worse because we have no information on the sharing rules (i.e. who gets what share of the x).

• If some notion of a sharing rule is established the problem basically becomes an issue of how we weight the data at the household level.

• Equivalence scales - the identification problem in budget studies - essentially we cannot elicit who gets what from knowing prices household income and expenditures.

• Square Root and other rules.

Goods versus Functionings and Capabilities

• Sen (Inequality Reexamined) argues that what people actually consume is less relevant than what they are capable of consuming

• Similar sentiment to the equal opportunity imperative – inequality not bad if it is a matter of choice, but bad if it is a matter of circumstance.

• The wellbeing of a person seen in terms of the quality of his being, living is seen as consisting of a collection of beings and doings and his achievement in this respect viewed as a vector of functionings.

• Functionings: adequate nourishment, good health, avoiding premature mortality, being happy, gaining self respect, being “socialized”.

Consumption Versus Income

• PIH arguments, that consumption is less variable than income and more closely related to lifetime wealth argue for various consumption variates.

• Perhaps this ignores the notion of household risk and its relationship to the extent to which income smoothing takes place.

• Also related to the extent to which current versus lifetime wellbeing is the object of attention.

• Measurement considerations (income is usually more accurately measured than consumption data) militates in favour of income.

Complete Orderings of Indices versus Partial Orderings of Dominance Relationships.

• Complete orderings (based upon comparisons of indices) always yield an answer but they may well be ambiguous.

• Partial orderings (based upon comparisons of distributions) are never ambiguous but they do not always give us answers.

• Gini coefficient versus Lorenz Dominance.• Poverty Indices versus Poverty Dominance.