Nigeria
| Overall inequality | Ex-Ante IOp | Ex-Post IOp | ||
|---|---|---|---|---|
| Absolute | Relative | Absolute | Relative | |
| 0.29 | 0.12 | 41.7% | 0.13 | 45.7% |
|
Note: Inequality of opportunity and overall inequality estimates are computed on equivalized household consumption expenditure. Circumstances: Sex, Ethnicity, Mother Education, Father Education, Birth Area. |
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Trees
This ex-ante tree uses a Conditional Inference Tree (Ctree) to partition the population. Each split is based on a circumstance, while terminal nodes define mutually exclusive types. Terminal cards report expected outcome in levels, its ratio to the population mean (1.00 equals the population mean), and population share. A single tree is an interpretable summary of the fitted partition; small sample changes can sometimes produce different splits.
This ex-post tree uses a Transformation Tree (Trafotree) and is read from left to right. Terminal cards report expected outcome in levels, its ratio to the population mean, and population share. The density in each card shows the full log-outcome distribution for one of the identified types. The dashed red marker is the log of the population mean. A curve farther to the right indicates generally higher outcomes, while its spread describes within-type dispersion.
Alluvial
Density
The colored layers show the estimated distributions of log-outcome for the ex-post types in one stacked chart. Read the thickness of each layer as that type’s density, not the height of its upper boundary. Peaks indicate common values; broader layers indicate more within-type dispersion. The dashed vertical line marks the log of the population mean outcome. The density function for the whole population is the mixture of the density functions from all the different types.
ECDF
For each ex-post type, the empirical cumulative distribution function (ECDF) reports the share of observations with log-outcome at or below each horizontal-axis value. At a fixed value, a lower curve means a smaller share lies below the threshold. Crossing curves indicate that the types cannot be uniformly ordered across the distribution.
Shapley Decomposition
The Shapley value decomposition allocates estimated inequality of opportunity (IOp) across the observed circumstances by averaging their marginal contributions over every possible inclusion order. These are model-based descriptive contributions, not causal effects.
Partial Dependence Plots (PDPs)
A Partial Dependence Plot (PDP) shows how the model’s average predicted outcome changes as one circumstance variable varies, averaging over the observed values of the remaining variables. It describes the fitted model and should not be interpreted as a causal effect; strong correlation or sparse data can also limit interpretation.
Descriptives
The descriptive material summarizes the analytic sample and the distributions of the outcome and circumstances used to estimate the trees. Use it to check variable definitions, sample coverage, and the empirical support behind the model results.