Skip to content

Revised Fisher Equation that explains Recessions and Depressions

Smart Taxes holds that taxation reform is one side of the agenda for change; the other is money reform.  Land value taxes will address inflation / bubble in one set of assets classes, albeit a very important one.  But even with effective land value taxes under an unreformed debt-based money system, other asset classes (such as shares or commodities) will quickly step in to replace land as an asset bubble – such is the logic of the system.

This short precis (reprinted below but without diagrams) of the paper by New Zealander Lowell Manning (hat tip to James Robertson), explains in economic speak how the current money creation system is the fundamental cause of recessions and depressions.  In revising one of the fundamental equations of contemporary economics concerning money supply, Manning explains why public debt grows inexorably and gives the solution to reducing it without crippling taxation or socially destructive services cuts.

James Robertson says of Manning’s work…

I hope Manning’s work will come to be accepted as important for economists, as the need for monetary reform belatedly penetrates their professional minds.

One practical conclusion is that:

“the effect of unearned interest on deposits is to transfer claims on the real wealth of the nation from those who produce the economic output to those in the investment sector who produce nothing. Houses and other assets become more expensive in terms of the inflated prices in the investment sector but must be bought using the less inflated money of the productive sector.

Unless inflation in the investment sector and the productive sector are equalised, there must be an ever-widening gap between debt-bound wage and salary earners on the one hand and the participants in the investment sector with net deposits in the banking system on the other.”



Paper presented at the 50th Anniversary Conference New Zealand Association of Economists (NZAE) 2nd July, 2009

by Lowell Manning.


“The Ripple Starts Here” revises the Fisher Equation of Exchange first put forward by Irving Fisher in 1911.

The original Fisher equation said simply that the amount of money M in circulation times its speed of circulation V must equal the gross Domestic Product PQ where P is the overall price level and Q the total volume of goods and services produced.


In Irving Fisher’s time his equation could not be easily checked because much of the information needed to do so was unavailable.  He spent a good deal of his subsequent career developing indices and associated data bases to better measure the economy. In Fisher’s day most economic transactions contributing to the economy were still made in cash and his equation took no account of either Domestic or foreign debt. These days in “modern” developed economies almost all transactions are debt based and cash is all but irrelevant.


The debt model presented in the paper changes Irving Fisher’s equation to a debt-based equivalent;

MdVp = PQ + (Ms + Mv)Vp

Where Md is the total debt in the economy (each dollar of debt is a dollar of money somewhere), Vp is the speed of the productive debt giving rise to PQ, Ms is the accumulated unearned interest on all bank deposits, and Mv is debt borrowed for speculation.

In the debt model Vp must be 1, because debt can only be spent once. The model can be visualised as millions of separate transactions where the money to produce the goods and services is borrowed during the production phase and then repaid when the product is consumed. The revised debt version of the Fisher equation of exchange then reduces to:

Total debt Md = PQ + (Ms+Mv)

As a first approximation Md is very nearly the country’s Domestic Credit plus its accumulated Current Account Deficit (In the paper, the accumulated Current Account Deficit is the total of all the annual deficits since 1954). Ms is the accumulated interest paid by the productive sector to the investment sector as unearned income.

Ms is really the seigniorage of the modern debt economy that began with interest paid on unproductive debt by the English Crown to the directors of the Bank of England in 1694. That debt and the associated introduction of fiat currency (banknotes) allowed the Crown to avoid politically dangerous tax increases to pay for its war costs. Ms broadly represents the “gap” so often referred to in monetary reform literature.

In New Zealand, Ms has been increasing exponentially at the rate of about 11.2% per year for decades whereas Md has been increasing exponentially at 8.6% per year.

Ms is inherently inflationary because, leaving aside any productivity changes, it means more and more debt has to be used for the same amount of production. In practice the productive sector usually borrows the extra debt each year to fund the unearned income and, by and large, passes on in its prices to consumers any change in its resulting costs.

Mv is the infamous investment “bubble” that grows and decays during each business cycle. When times are “good” the banks lend extensively to investors directly on the assumption that next week’s investment sector prices will be higher than this week’s prices. The banks do this because they increase their profit if they lend more.

Mv bubbles are typically liquidated during recessions and the year or two after they end.

In the revised Fisher equation, Md, PQ and Ms are readily available from statistics, and that means the bubble Mv can for the first time, be accurately quantified.


The new debt model for New Zealand 1979-2009 is shown in the following figure.

The first and most relevant feature of the model is that all the curves are exponential. To keep afloat, the debt economy is locked into exponential growth of debt and GDP.

The second most relevant feature is that the exponential for the investment sector Ms (11.2%) is much greater than that for the total debt Md (8.6%). That means present and past monetary policy necessarily produces a rapid transfer of wealth from the productive sector to the investment sector. Wage and salary earners are fundamentally disadvantaged relative to those with deposits in the banking system who receive a “free-lunch” in the form of unearned income merely because they have those deposits. Producers get ever less while non-producers get more and more. There is a large, structural and on-going transfer of wealth taking place from the poor to the rich in society. In the present system that transfer in wealth can only be offset through large-scale income redistribution.

The third most relevant feature is that the current financial “architecture” is quite unsustainable. Economic “crashes” become unavoidable as investment sector expectations literally drown the ability of the productive sector to satisfy them.

The model suggests the only way to remedy that fundamental contradiction (assuming we persist with the current system) is for the investment sector to expand at the same rate as the productive economy. That in turn means that both the price and quantity of new debt have to be managed by the government or the reserve bank . Centuries of evidence show that private issue of debt for profit is diametrically opposed to such price and quantity controls. Banks earn more by lending more.

The most recent and classic case is the “meltdown” in the US where a whole raft of derivatives was designed to allow unrestrained and irresponsible lending to patently uncreditworthy customers. Such “pass the parcel” transfers of toxic debt accentuated the underlying systemic risk instead of reducing it. On such grounds alone there is a powerful case for public control of the issue of new debt (and money in the form of electronic cash) and public control of deposit interest rates.


The debt model offers valuable insights into other areas of major interest to economists.

First, It provides a specific and rational definition of recessions and depressions.

A depression occurs when the change in the total debt over time is less than what is needed to service the unearned interest that has to be paid to the investment sector Ms plus any increase in speculative investment Mv; that is, when there is no provision for either inflation or growth.

A recession occurs when the change in total debt over time is less than what is needed to service the financial system costs, being the unearned interest that has to be paid to the investment sector Ms, plus speculative investment Mv, plus inflation.

Secondly, New Zealand has borrowed ALL of its nominal GDP growth for decades. The accumulated current account deficit is about NZ$100 billion higher than it otherwise would have been, and savings and wealth in the country about NZ$ 100 billion lower. The paper introduces the concept of system liquidity, Mcd, being the GDP less the accumulated current account deficit. Mcd represents transaction account balances plus earned savings. The paper shows Mcd is dangerously low in New Zealand and that there are few earned savings left in the system. Mcd, the debt actually used to produce domestic goods and services, times its speed of circulation Vcd equals the domestically produced GDP. Until quite recently Vcd was reasonably close to what V is thought to have been in the original Fisher equation. The level of earned savings is defined primarily by the debt system mechanics and the current account deficit rather than by individual savers.

Finally, in the absence of tax or other incentives to encourage traditional savings, there is an inherent conflict of interest between increasing productive GDP output and households still holding debt. Economic efficiency will usually induce households to retire expensive debt instead of saving. In the debt model debt retirement reduces economic output.


The debt model does not, of itself, distinguish between “good” and “bad” GDP but it recognises implicitly that new debt creation should focus on productive activity. To achieve this there is good reason to reserve to the government the issue of new debt, with that debt being spent into circulation in the form of investment in education, health, research, infrastructure and business development.

Following first use of new domestic debt by the government the corresponding deposits would appear in the banking system from where the banks would on-lend it according to monetary policy guidelines published from time to time.

In its 78th annual report (p137) the Bank for International Settlements (BIS) wrote of the current turmoil in the world’s financial centres “A powerful interaction between financial market innovation, lax internal and external governance and easy global monetary conditions over many years has led us to today’s predicament.”

Presently the financial system itself is structured to not only allow, but to encourage those human and institutional failings to which the BIS properly refers. Those failings are largely driven by self interest and greed that are part of human nature. Since human nature is unlikely to change, the world financial architecture needs to be remodelled to keep sticky human fingers out of the global money pot.

Lowell Manning 5/7/09  (Link to paper)

Posted in News.

Tagged with , , , , .