How Fat Are the Tails of National Growth Rates? Subbotin Fits to 9,861 Country-Years, 1961–2024, and an Exact Kurtosis Decomposition Separating Within-Country Tails from Differences in Volatility

Annual growth of real GDP per head in 166 economies with at least 40 years of data, 1961–2024 (9,861 country-years, World Bank), is far from Gaussian. Pooled deviations from country means have kurtosis 52.77; deviations beyond three standard deviations occur 5.8 times as often as a Gaussian law predicts. Part of this is an artefact of pooling countries with different volatilities. I prove an exact decomposition: pooled kurtosis equals the weighted mean within-country kurtosis times a scale-dispersion factor, plus a covariance term between within-country kurtosis and the fourth power of country volatility. The scale factor alone is 3.87 here, and the covariance term contributes more than half of the 52.77, because volatile economies also have fat-tailed growth. After standardising each country, kurtosis falls to 6.59 but remains well above 3: 94.0% of countries have kurtosis above 3 and the Jarque–Bera test rejects normality in 71.1% of them. Maximum likelihood fits of the Subbotin (generalised error) family give shape 1.052 for standardised data, with a country-cluster bootstrap interval [1.003, 1.104] that excludes the Gaussian value 2 and lies just above the Laplace value 1. The Laplace law reproduces the tail frequencies closely: beyond three standard deviations it predicts 1.44% against 1.67% observed and the Gaussian 0.27%. India's within-country kurtosis is 4.50, China's 13.17 and Indonesia's 15.43.