Does spatial inequality rise then fall with development?
Kuznets (1955) and Williamson (1965) proposed an inverted-U: as a country industrialises, a few leading regions surge ahead and regional gaps widen; later, as the modern economy spreads out, the gaps close again. Lessmann (2014) tested this across 56 countries. This lab lets you rebuild the core pieces yourself — on the same synthetic data used in the post.
From a straight line to an N-shape
The same scatter supports three stories depending on the functional form. Press play to watch a straight line bend into an inverted-U, then into the cubic N-shape with a high-income upturn — the shape the cross-section data actually prefer.
What you'll do
- Build the WCV — drag region incomes and populations and watch the inequality index update.
- Curve Explorer — turn the polynomial dials and read off the turning points in dollars.
- OLS vs FE — see how country fixed effects sharpen the within-country inverted-U.
Build the weighted coefficient of variation
The WCV is the population-weighted spread of regional GDP per capita, divided by the country mean: a large poor region counts more than a tiny rich enclave. Drag the sliders for a three-region country and watch WCV respond.
Three regions
WCV = (1/ȳ) · [ Σ pⱼ (ȳ − yⱼ)² ]½
Result
Curve Explorer — find the turning points
The cross-section model is WCV = β₁Y + β₂Y² + β₃Y³ + … with Y = ln(GDP p.c.). An inverted-U needs β₁ > 0 and β₂ < 0; a positive β₃ adds the high-income upturn. Turning points solve β₁ + 2β₂Y + 3β₃Y² = 0. Drag the dials; the dashed lines mark where the curve turns.
Coefficients
Fitted curve & turning points
Cross-section OLS vs two-way fixed effects
Both estimators recover the inverted-U (β₁ > 0, β₂ < 0), but they answer different questions: OLS compares different countries; fixed effects compare each country with itself over time. The forest plot shows the income coefficients with 95% intervals.
The key contrast
The quadratic inverted-U is significant under both estimators. But the cubic high-income upturn is significant only in the cross-section — within countries it is statistically zero. The upturn is a between-country phenomenon (rich service economies differ from rich manufacturing ones), not something a single country lives through.