If there is less money in the economy than there should be, there will be less spending than there should be. If maximal, sustainable, long-term output growth is desired, ensuring that the rate of money growth required for it is extant is essential.

How do we know what should be the desired money growth?

Given that changes in broad money growth have real impacts on changes in nominal spending, how do we know what rate of production we should aim for? This is where we must deal with the notion of sustainable output. Sustainable output is that amount of goods and services produced when the economy is producing with no inflation over the long-term. If we acknowledge a long-term relationship between money growth and nominal spending, then it would follow that there exists a quantity of money in circulation required for sustainable output to be achieved.

The difference, then, between actual money growth and that money growth consistent with desired output growth is the money gap. How can we measure that desired rate of money growth, and hence, the money gap? By making use of a monetary rule.

A monetary rule makes use of some variant of the classic quantity theory of money. Retooling the equation allows us derive a rate of money growth compatible with the economy producing at equilibrium rate concurrent with long-term price stability:

The Monetary Rule ∆Md = ∆P + ∆RGDPd - ∆Ve Where, ∆Md = Money Growth Compatible with Sustainable Output Growth ∆Ve = Expected Change in Velocity of Circulation ∆P = Price Stability Rate of Inflation ∆RGDPd = Sustainable Real GDP Growth

How can we know the extent to which actual money growth departs from the desired rate?

By way of the monetary rule we may attain the prescribed rate of growth of money. The difference, then, between the actual rate growth of money, and that prescribed rate, will give the money gap.

The Money Gap Mg = ∆M - ∆Md Where, Mg = Money Gap ∆M = Actual Money Growth ∆Md = Prescribed Money Growth

We should also note the consequences of departing from our aim too severely, and for too great a length of time. If there occurs a sustained money gap with positive values above 0.5% to 1% (i.e. a sustained positive money gap, given ±0.5 - 1% as margin of error), this indicates excessive money growth that must inevitably manifest in unsustainable output growth and inflation with a time lag. If there occurs a sustained money gap with negative values below -0.5% to -1%, this indicates too little money growth that must manifest in a decrease in inflation and even deflation and output below trend. Examples of both forms of money gap are illustrated in the diagram below.

In summary, if we take as our aim the instantiation of a rate of output growth consistent with price stability, and we acknowledge the long-term relationship between money growth and nominal spending growth, then the sustained minimisation of the money gap is an essential means to this end. Both theoretical[1] and empirical analysis has established the long-term relationship between broad money growth and nominal spending growth, and while a general statement concerning the dangers of unsustainable excesses in money growth may be valid, there is still left the question - what counts as excessive? The money gap goes some ways to addressing this issue by way of providing a benchmark[2] with which to compare actual rates of money growth, and hence providing a more precise account of the difference between actual money growth and the prescribed rate.

Money Gap Map

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[1] See Tim Congdon’s Money and Prices in Boom and Bust. IEA, London. See https://iea.org.uk/publications/research/money-and-asset-prices-in-boom-and-bust

[2] See Pedro Schwartz and Juan Castaneda’s report to the European Parliament for an application of this concept. See http://www.europarl.europa.eu/document/activities/cont/200712/20071220ATT16955/20071220ATT16955EN.pdf