Has India's Growth Become Less Volatile? Variance Breaks in Annual GDP Growth, 1961–2025, by the Inclán–Tiao Test, a Kurtosis-Robust Correction and a Permutation Test

I test whether the variance of India's annual real GDP growth changed between 1961 and 2025, using World Bank data and the cumulative-sum-of-squares statistic of Inclán and Tiao. I prove that under independent errors with kurtosis kappa the statistic converges to the square root of (kappa minus 1)/2 times the supremum of a Brownian bridge, so the usual critical value 1.358 is valid only for Gaussian data; a simulation at the Indian sample size gives a rejection rate of 19.6% for t(5) errors instead of 5%. The kurtosis-robust version is used alongside an exact permutation test. Over the full sample the most likely break is after 1979 (standard deviation 3.79 points before, 2.59 after), but no test rejects constancy because the 2020–21 pandemic swing restores the old volatility. Excluding 2020 and 2021, the break after 1979 is significant on both statistics (Inclán–Tiao 1.961, p = 0.0009; robust 1.361, p = 0.049) and the standard deviation falls from 3.79 to 1.85 points. The result survives allowing a simultaneous shift in mean growth from 3.39% to 6.21%. India has had five years of negative growth since 1961: four before 1980 and 2020. China, Indonesia and Brazil show breaks too; for the United States the break after 1984 is significant only without the pandemic years.