Consider the following graphs of the US data since 1960 on the price level3 (top left), money supply4 (top right), real output5 (bottom left) and the velocity of money6 (bottom right). Note that US recessions are shaded in grey.

When applying the quantity theory of money ???? = ????, or the rule-of-thumb version of it based on growth rates, we often treat velocity as constant in the long run. Is this a reasonable simplification? Are there times when the V-is-constant approximation would have been particularly unhelpful?

FRED - Consumer Price Index for All Urban Consumers: All Items FRED - M2 Money Stock 240 12,000 200 10,000 160 8,000 (Billions of Dollars) (Index 1982-84-100) 120 6,000 BO 4,000 2,000 0 1960 1970 1980 1990 2000 2010 1960 1970 1980 1990 2000 2010 Source: US. Bureau of Labor Statistics Source: Board of Governors of the Federal Reserve System (US) Shaded areas indicate US recessions - 2015 research. stlouisfed.org Shaded areas indicate US recessions - 2015 research. stlouisfed.org FRED - Real Gross Domestic Product FRED - Velocity of M2 Money Stock 18,000 2.3 16,000 2.2 14,000 2.1 12,000 2.0 (Ratio) (Billions of Chained 2009 Dollars 10,000 1.9 8,000 1.8 6,000 1.7 4,000 1.6 2,000 1.5 1960 1970 1980 1990 2000 2010 1960 1970 1960 1990 2000 2010 Source: US. Bureau of Economic Analysis Source: Federal Reserve Bank of St. Louis Shaded areas indicate US recessions - 2015 research.stlouisfed.org Shaded areas indicate US recessions - 2015 research.stlouisfed.org