How unequally is income distributed? (poverty and inequality)

In brief

How unequally is income distributed, and how many are below the poverty threshold? Statable gives the at-risk-of-poverty rate (60% of the weighted median is common), the ratio of the top to the bottom fifth (S80/S20) and the Gini coefficient.

How it works in Statable

1. "New analysis", then choose the card "How unequally is income distributed?".
2. Choose "Which column contains the income?" and "Which column contains the weight?" (required).
3. Was the sample drawn in clusters or strata? Then name the columns, otherwise "Continue without clusters" and "Continue without strata".
4. The standard errors (SE) in the result take into account how the sample was drawn.

What the table looks like

• One column with the income. It must already be in the form in which it is to be compared, for example per person and weighted by household size (equivalised). Statable does not calculate an equivalence scale.
• One column with the weight: how many people a case represents. The weight is required.
• Optionally a column that names the cluster (for example the household) and a column with the stratum (for example the region). Without both, the people count as drawn individually.
• Rows with a gap in income or weight are left out, rows with weight 0 are not included; the numbers are shown in the result.

Reading the result

• The median is the value below which half of the weighted cases lie. The poverty threshold is a share of it, 60% is usual. Under "More options" you can choose 40, 50, 60 and 70%; the choice changes only the rate.
• The at-risk-of-poverty rate is the weighted share of cases with an income below the threshold (strictly smaller).
• S80/S20: the income of the top fifth divided by the income of the bottom fifth. At 4 the top fifth has four times as much. There is no standard error for it.
• The Gini coefficient runs from 0 (everyone has the same) to 100 (one person has everything).
• The standard error (SE) shows how much the number can vary because of the selection of the sample. The standard error of the rate uses the fixed threshold: the uncertainty of the threshold itself is not included.

Requirements and limits

• The rate measures relative at-risk-of-poverty. It says nothing about the standard of living, and it stays the same when all incomes rise in the same proportion.
• The standard error depends on the design of the sample. In an example survey with strata and clusters the standard error of the Gini is 0.31; if you assume the people were drawn individually, it is only 0.20. A wrong design gives intervals that are too narrow. Statable always names the design in the result.
• Standard errors from different methods are not comparable, for example with those of a simple bootstrap.
• With fewer than 200 cases the rate and the Gini vary strongly; Statable says so.
• Zeros are reported and are included everywhere. Negative incomes are reported and are included in the median and the rate; they block the Gini and S80/S20, with the reason. S80/S20 is also dropped if the bottom fifth has no income.

Reporting the result

Rate = 14.4% (SE = 0.50, fixed threshold), S80/S20 = 3.97, Gini = 26.49 (SE = 0.31), n = 14,827

Typical examples

• How many households are below the poverty threshold?
• How far apart are the top and the bottom fifth of incomes, and how high is the Gini?

For specialists

R (survey) with the design from clusters, strata and weight. Weighted median: smallest value with a cumulative weight share of at least 0.5, at exactly 0.5 the mean of the two neighbours. Gini = 2 Σ w y C / (N T) - 1 with the cumulative weight C (middle of the step); the standard error follows from the linearized form (influence values, svytotal). The standard error of the rate is svymean of the indicator with a fixed threshold. Checked on an extract of the EU-SILC example data against the R packages laeken and convey. The command is shown below the result.