Why India Is Cheap: The Penn Effect in 153 Economies, 1990–2024, With an Exact Link Between Two Common Regressions and a Division-Bias Bound

Richer countries have higher price levels. This regularity, the Penn effect, determines how far GDP at market exchange rates understates real income in poor countries. Using World Bank WDI data (vintage 8 October 2026) for 153 economies with at least one million people, I measure the price level as GDP per capita in US dollars divided by GDP per capita in PPP dollars. In 2024 a 1% higher PPP income goes with a 0.2135% higher price level (s.e. 0.0224). The slope has stayed between 0.198 and 0.272 at five-year intervals since 1990. It is driven by high-income economies (slope 0.408); among low- and middle-income economies it is zero or negative, and a spline with a kink at the median income gives 0.004 below and 0.518 above. India's price level is 0.2418 of the US level, 36.0% below the value predicted by its income and the ninth-lowest residual of 153. I derive the Balassa–Samuelson elasticity, prove an exact formula linking the regression on PPP income to the regression on dollar income (predicted 0.2117, observed 0.2117), and show that classical error in PPPs biases the slope towards −1, so the reported slope is a lower bound if PPP errors are classical. Within countries, the change in the price level over 2000–2024 is almost unrelated to growth (slope 0.0739, s.e. 0.0823).