Money, Velocity and Inflation in India, 1961–2021, and in 140 Economies, 1995–2024: An Exact Decomposition of the Quantity Equation and Why the Money–Inflation Slope Falls Below One at Low Inflation

The quantity equation MV = PY is an identity, so in log growth rates inflation equals money growth minus real growth plus velocity growth, exactly. I use it as an accounting device on World Bank data. For India, 1961–2021, broad money grew 13.96% a year (log), real GDP 4.94% and the GDP deflator 6.86%; the gap was closed by a fall in the income velocity of money of 2.15% a year, from 4.65 in 1961 to 1.22 in 2021, as broad money rose from 21.5% to 82.1% of GDP. Year to year, money growth and inflation in India are only weakly correlated (0.30); on 5-year averages the correlation is 0.61. Across 140 economies, 1995–2024, the slope of average inflation on average money growth is 0.881 (R squared 0.861), but it is 0.418 when average inflation is below 10% and 0.208 below 5%. I prove that the cross-country slope equals exactly one minus Cov(m, y − v)/Var(m), so a slope below one is not evidence against the quantity theory: it is a measure of how strongly money growth co-moves with real growth and with falling velocity. Among low-inflation economies those correlations are 0.729 and −0.775, which accounts for the whole shortfall.