If monetarists have a rigorous definition of money that picks out one unique time series, I do not know of it. Suppose they find some correlation between, say, M2 and a price level. And suppose that correlation subsequently breaks down. They need not take this as evidence against their theory. For they can always search for another time series for the quantity of money and a different price deflator.
Likewise, economists building on Marxism, as I understand it, have not settled upon a rigorous theoretical definition of the distinction between productive and non-productive labor. For example, I don't think Marx - especially in the first volume of Theories of Surplus Value - argues that all services are unproductive of surplus value. Rather, his distinction is between labor that produces surplus value and other labor. Duncan Foley finds a tighter correlation between real national income, excluding services, and non-farm employment than he does between all national income and non-farm employment. By my argument, I do not take this as dispositive evidence for Marx's distinction. I worry that which correlation works best can vary by time period and time series.
Nevertheless, I find Foley's analysis of interest. Finance, Insurance, and Real Estate (FIRE) certainly seems to need more analysis by economists in these days.
- Duncan K. Foley (2011) "The Political Economy of Output and Employment 2001-2010"
- James K. Galbraith, Olivier G. Giovannoni, and Ann J. Russo (2007) "The Fed's Real Reaction Function: Monetary Policy, Inflation, Unemployment, Inequality - and Presidential Politics"