Does India Smooth Consumption? The Permanent-Income Volatility Ratio for India and 108 Other Economies, 1961–2024

The permanent income hypothesis makes a sharp prediction about volatility. If the growth of income per head follows a first-order autoregression with coefficient ρ, consumption growth should have a standard deviation √(1−ρ²)/(1−βρ) times that of income growth. I prove this and show that the ratio exceeds one exactly when 0 < ρ < 2β/(1+β²). Using World Bank data on real private consumption and GDP per head for 109 economies with at least 30 years of data in 1961–2024, the observed ratio has a median of 1.177, and 76.1% of economies have consumption growth more volatile than GDP growth. The formula has no predictive power across countries: the correlation between predicted and observed ratios is −0.058. India is among the smoothest, with a ratio of 0.898 (14th of 109), below the 1.105 the formula predicts from its income persistence of 0.104. But Indian consumption tracks current income closely: the correlation of the two growth rates is 0.891 and the least-squares sensitivity of consumption growth to income growth is 0.789. The instrumental-variables estimate of the Campbell-Mankiw share of current-income consumers is 1.153, but the first-stage F statistic is 1.56, so it carries no information. The ratio rose from 0.765 in 1961–1990 to 0.968 in 1991–2024, and in 2020 consumption per head fell by 6.41% against 6.92% for GDP per head, far more than in the 1979 drought.