When Does Tax Buoyancy Above One Raise the Tax Ratio? Two Identities and Evidence from India and 107 Economies

Tax buoyancy, the percentage change in tax revenue per percentage change in nominal GDP, is widely read as a sign of whether the tax ratio will rise. I prove two exact least-squares identities that limit that reading. First, the buoyancy slope equals one plus the slope of the change in the log tax ratio on nominal growth. Second, the mean change in the log tax ratio equals the intercept plus buoyancy minus one times mean growth, so a buoyancy above one is neither necessary nor sufficient for a rising ratio. Using World Bank data on central government tax revenue and GDP in current local currency, I estimate buoyancy for India (44 consecutive-year pairs, 1975 to 2018) and for the 107 economies with at least 20 pairs. India's short-run buoyancy is 0.638 (standard error 0.273), 21st lowest of 107, yet revenue grew faster than GDP on average (13.3% against 12.4% a year in logs), because the intercept is positive. India's buoyancy rose from 0.06 in 1975 to 1991 to 1.21 in 1992 to 2007. Across economies the mean-group buoyancy is 1.001 (standard error 0.041), the pooled estimate 0.936 and the within estimate 0.914. Of 107 economies, 10 have buoyancy above one with a falling ratio and 28 have buoyancy below one with a rising ratio, so 38 contradict the usual reading. Buoyancy is 0.227 (standard error 0.060) higher in years of below-median nominal growth than in faster years.