PEP-PMMA Training Session Introduction to Distributive Analysis Lima, Peru Abdelkrim Araar / Jean-Yves Duclos 9-10 June 2007

The interest of distributive analysis Studying the distribution is of interest to researchers and decision- makers. Several ethical criteria are involved: –The desire to have low poverty; –The desire to have high equity and low inequality; –The desire to have high levels of living standards.

Population vs surveys For this, we need information on the standards of living of households and individuals. It is also useful to have information on socio- demographic characteristics such as household composition. Ideally, this information would be available for an entire population. This is usually not possible given the costs of surveys. Because of this, we usually use a selection of households that can be considered representative of a population.

Cross-section vs panel data There are two main types of household surveys Cross-section data: one-period data on individuals, households, firms, or governments. Panel data: also called longitudinal data, i.e., data on units observed at two or more time periods.

Statistical unit of interest What should the unit of interest be? From an ethical viewpoint, the unit of interest is usually the individual; it is also the one who feels deprivation or satisfaction. But the information is usually available at the household level: difficult to inquire into intra-household distribution.

Intra-household We usually proceed with:

Income or consumption? Researchers tend to use total expenditure rather than income as standards of living: Income can undergo seasonal variations (economic volatility, weather). Incomes can be underreported, for instance, for fear of tax penalties.

Price differences Since prices vary across time and space, it is important to compute living standards in real terms. Examples : –Using regional price indices (spatial variation of prices). –Using CPI indices (temporal variation of prices).

Sampling weights The ultimate goal is to estimate indices that are unbiased estimators of population indices. For this, we must take into account sampling weights. When the statistical unit is the individual, it is also necessary to take into account household size.

Distributive indices and expansion factors For example, to estimate average income, we have :

Standard errors –A standard error helps capture the variability of the difference between estimated and true values of indices (the “sampling error”). –The standard error is itself an estimate of the true standard deviation of that variability. –The greater your sample size, the smaller usually is the standard error. –If you take a sample that consists of the entire population, you actually have no sampling error because you don't have a sample, you have the entire population.