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Money, prices, assets and evasions of responsibility

By Lorenzo

Understanding the equation of exchange can help see what a massive evasion of institutional responsibility lies behind the Great Recession and the Eurozone crisis.

Economist Irving Fisher developed the original algebraic formulation of the equation of exchange, in his The Purchasing Power of Money (1911):


Money x Velocity = Prices x Transactions.

Fisher’s use of the term velocity was rather unfortunate, as what he meant was turnover (the number of times money passed through different transactions in a given time period). As Fisher wrote:

the velocity of circulation, or rapidity of turnover … this velocity of circulation for an entire community is a sort of average of the rates of turnover of money for different persons. Each person has his own rate of turnover which he can readily calculate by dividing the amount of money he expends per year by the average amount he carries (Chapter 2).

But his equation already had a ‘T’ in it, so velocity it was. Fisher was using the equation of exchange to state the quantity theory of money more precisely.

Milton Friedman restated the quantity theory of money in 1956 (pdf), leading to the updated equation of exchange:

MV = Py

Money x Velocity = Prices x output of goods and service.

y was originally rendered as Q for quantity (of goods and services), but y has become a common usage. This equation has no ‘T’, but the velocity usage was already well established (alas). Velocity has become the (output / goods and services / income) velocity of money.  Just as P has become the goods and services price level. (Fisher was an early developer of price indices.)

Aggregate demand

Taking the right side of the updated equation, Py = Prices x output = GDP in money terms, or NGDP. (‘N’ for nominal, or in money terms.)

Another name for this is aggregate demand (for goods and services). Just as with velocity, aggregate demand is not a clear usage, but it is the accepted one, so we are stuck using with it.

If there was some organisation–let’s call it a central bank–that could control M and V, then aggregate demand will be whatever said central bank decides it will be.

That central banks control M is subject to some dispute, but let’s take that as read. They are the monopoly providers of monetary base, after all. How could central banks also control V? The short answer is that, as they control M, they also control the future path of M. And expectations about the future path of M are very important in determining V. Hence aggregate demand is whatever the central bank decides it will be.

Which rather takes the bite out of fiscal policy. The central government can run as big a budget deficit as it likes, if the central bank decides to tighten monetary policy to maintain, say, its inflation target (i.e. the rate of change of P), then the effect on aggregate demand of said budget deficits will be effectively completely negated. How long can this keep going? Until public debt reaches whatever the debt-servicing limit of said country is. For an extremely reliable payer such as the government of Japan, this can go on for years until the gross public debt is over twice GDP.

Conversely, the central government can run a whole series of budget surpluses. If the central bank runs a compensating monetary policy, as the RBA did during the Howard Government surpluses, then aggregate demand will chug along just fine.

The impotence of fiscal policy in the face of a competent central bank is the Sumner critique:

the fiscal multiplier will always be zero if the central bank directly or indirectly targets aggregate demand.

An alternative formulation is:

under almost any conditions, fiscal policy cannot be effective if monetary policy is aiming at a policy objective that is inconsistent with that fiscal policy.

For fiscal policy to “work”–in the sense of affecting aggregate demand–the central bank has to either be not reacting to reach any inconsistent policy goals or be impotent–i.e. for some reason be unable to affect aggregate demand.

Enter the alleged liquidity trap, when nominal interest rates are at the zero lower bound (ZLB), so cannot be cut any further. This can be formulated as a problem either because a particular interest rate is the central bank’s usual policy instrument or, more correctly, as expectations about future income being so dire that no amount of extra money injections will improve them–the famous “pushing on a string“.

The former formulation of the liquidity trap assumes that interest rates are a central bank’s only reliably effective policy instrument, which is quite false (but can have a profound effect on policy and expectations if central bankers believe it). Regarding either formulation, economist and central banker Lars Svensson published his “foolproof way” of escaping from a liquidity trap in 2003; there is no excuse for treating the ZLB as a genuine constraint on monetary policy. Indeed, the US Federal Reserve’s use of Quantitative Easing (QE) shows there is no such constraint. The Fed’s use of such “unconventional” (i.e. not-interest-rate) monetary policy explains the superior economic trajectory of the US economy over that of the Eurozone.

Inconvenient responsibility

But notice the scary implication of aggregate demand being whatever the central bank decides it will be. If recessions are generally due to falls in aggregate demand, then central banks are responsible for the business cycle (or most of it). Even if there is a supply shock, the central bank can shift aggregate demand to compensate. Whenever the economy gets plucked off (pdf) its normal growth trend, it is due to central bank failure–either something they did, or something they failed to do.

So, if unemployment surges, if economic conditions stay flat (compared to trend), it is the central bank’s fault. That is a scarily responsible place to be. It is hardly surprising that the original public use of the “pushing on a string” metaphor was agreed to with such alacrity by the then Chairman of the US Federal Reserve. Or that the ECB is very happy for people to blame Greece, the PIIGS countries generally, or fiscal austerity, or anyone but them, for the Eurozone crisis.

Eccles: Fed Chairman 1934-1951

M.S.Eccles: Fed Chairman 1934-1951

Holding the central bank responsible for aggregate demand, and thus the business cycle, is however, also not very congenial for the proponents of activist government. It being politically much harder to cut public spending than increase it, activist fiscal policy is a great basis for ever-increasing government. (In theory, budgetary deficits could be run by simply cutting taxes; in practice, increased spending is a normal element in fiscal stimulus.)

In the case of the Eurozone, if the Euro is a political project to promote ever-greater-union (i.e. the creation of a European superstate), then proponents are really not going to want the ECB, and by implication the Euro, being held responsible for the Eurozone crisis. Or, even worse, the Great Recession generally. (That is assuming people even notice monetary policy at all.)

Which is all very well, but leaves some questions unanswered: why leave out previously produced goods from the reformulated equation of exchange?; how can the expected future path of M affect V? and why is an interest rate the normal policy instrument of central banks? It turns out, these are related questions. For they are much about time.

Assets and time

Fisher’s original formulation of the equation of exchange included all transactions, including for previously produced goods–i.e purchases of existing assets and second-hand goods. The restated version quarantines off anything not part of current output. (Though services involved in selling existing assets or second-hand goods are part of current output, as are services in maintaining or managing existing assets.)  It thus includes all output connected to income and permits the national accounts statistics to be used.

As for the relationship between the future path of M and V, that is about income and assets. An asset is an asset because it is expected to provide benefits in future time periods. (So, second-hand goods with scarcity value–such as antiques–are assets.) For our purposes, these can be treated as either a stream of income or as a store of wealth or (more commonly) both.  Bonds (a congealed stream of income) are at one end, since their only value is the stream of income, and gold (which provides no income) is at the other. The ultimate point in holding any of these assets being access to good and services, to (current and past) output.

Treating assets as things whose benefits can be expressed in monetary terms, the prices of assets will therefore tend to be interconnected, depending as they do on expectations about future value. When expectations about future income are high, then income-producing assets will be at a premium. When expectations about future income are low, then assets deemed as reliable stores of wealth will tend to be at a premium. And money itself is an asset.

But money is an asset whose current and future supply the central bank controls. Thus, if one expects that money will increase in value (i.e. M is on a low path compared to y), then people will tend to hold it rather than spend it. Which means V (the rate of turnover of money) will fall, so (for any given level of M) Py (i.e spending) will fall. If spending falls, income also falls as one person’s spending is another person’s income.  Expectations about the future path of M lead to changes in V, lead to changes in aggregate demand.

Another way to consider this is the reciprocal of V, or k:

k = 1/V

Substituting in (by dividing both sides of the adjusted equation of exchange by V) gives us the famous Cambridge equation:

M = kPy

k is the propensity to hold money.  So the more people hold money, the lower Py will be for any level of M. To put it another way, the more desirable money is as an asset, the lower the level of spending for any level of M. If any rise in M will just leads to a rise in k, then the central bank is “pushing on a string” and the liquidity trap is operating. But the value of money as an asset depends on the future path of M, so it will matter a great deal whether people expect the increases in M to be temporary or permanent. Thus, Lars Svensson’s “foolproof way” out of the liquidity trap uses currency depreciation to signal central bank commitment to a higher future price level. That is, the increases in M are permanent, ensuring a depreciation in the value of money as an asset relative to output, leading to people moving out of holding money and into buying goods and services (plus the higher price level improves income expectations).

Debt-deflation and safe assets

Japan-resident economist Richard Koo has advanced the notion of Japan (and later other major market economies) as being in a “balance sheet recession” (pdf) where the creation of safe assets (Japanese public debt bonds) is a necessary response to the massive rise in bad debts in the Japanese financial system due to the bursting of the “bubble economy“. Koo is adapting Fisher’s Debt-Deflation theory of the Great Depression. (Fisher’s original publication is here [pdf].)

The problem is that Koo gets the debt part but not the deflation part. Expectations about future income are crucial to the burden of debt. That was Fisher’s point. If consumer prices drop by about 25% in three years, as they did in the US in 1929-1932, then incomes and income expectations also drop. The ability to service debts collapses and the wave of bad debts surges, profoundly destabilising the financial system.

Koo’s problem is that he does not understand the Great Depression. A crucial feature of the 1929-1932 story is that all the major market economies were operating on the gold standard. Since gold set the value of money, rises in the value of gold caused the value of money to rise and the price level to fall. But that just means we can put the equation of exchange in gold terms (adapted from here):

G = kPy

Where G = gold stock and k = gold hoarding.

Since G is essentially fixed (as new production of gold is persistently a small ratio to existing supply, so G is relatively stable in its ratio to total output, to y) then shifts in k can have a major effect on the price level. Which is precisely what happened in 1929-32. The Bank of France enormously increased its gold holdings, the US Federal Reserve (the major holder of gold) failed to compensate; so P collapsed in all the goldzone countries, leading to massive falls in income, spending (Py) and production (y).


FDR took the US out of the Great Depression by massively depreciating the US$ against gold, creating strong expectations of rising prices (and thus incomes) leading to the sharpest economic recovery in US economic history.* He then brought economic recovery to a screeching halt by a high wage policy and other disastrous supply-side policies. Pushing up aggregate demand is not much good if you then push down aggregate supply.

So, expectations about the future path of M affect V (k) which drives Py, so central banks set the level of aggregate demand.

At which point, it is clear that no simple story about M is a satisfactory explanation for asset prices. They depend crucially on expectations about future income, Py. If expectations about Py are poor, then no amount of extra M that fails to shift those expectations is going to increase asset prices. The job of a central bank is all about expectations, because it is not simply the level of M that counts, but expectations about the future path of M. Money itself is an asset, and if people are confident that money will retain its value–because, for example, the central bank is persistently undershooting its low inflation target–but have poor expectations about income, then k can get very high indeed while the value of other assets remains flat. Both the Great Depression and Great Recession have been marked by huge increases in M with flat or falling asset prices.

Income expectations

The difference between the RBA and the BoJ, the Fed or ECB is that while all four central banks have inflation targets, the RBA also has an implicit income target. That is, the expectations are that the RBA will keep Py relatively stable (i.e. tolerate a higher rise in P if y is flat and vice versa) since its inflation target is an average over the business cycle.

Another way to look at that is to say the RBA is effectively operating an export price norm. (Which leads us back to Lars Svensson’s “fool proof” way out of a liquidity trap.) If income expectations do not collapse, there is not a flight to safe assets (such as money in a low inflation environment) and so spending does not collapse.

The huge failure of inflation targeting is the failure to realise the importance of managing income expectations when strong central bank credibility on inflation means money can be a safe asset. (And if you suspect that is something like the failure of the gold standard central banks to realise the importance of managing income expectations when fixed gold convertibility means money can be a safe asset, you would be correct.) Both inflation targeting and the gold standard permitted central banks to evade responsibility for aggregate demand while they were, nevertheless, driving aggregate demand.

Now or later

So far, I have talked about monetary policy without mentioning interest rates very much. A difficulty with interest rates and monetary policy is the importance of the difference between level and direction of movement of interest rates.

Interest rates are about choices between time periods. Interest rates consist of three basic components:

  1. “the risk free cost of capital“.
  2. the risks specific to the asset in question. (Rated at 0 for government bonds for which there is no expected default risk.)
  3. expected inflation.

If expected inflation (rate of change of P) is high, interest rates will be high. If expected inflation is low, interest rates will be low. (If weird things are happening with the other two components, that would not necessarily be true, but we can ignore that.) High inflation is loose money (lots of money being spent for a given level of output; the future path of M is expected to be high compared to output) and low inflation is tight money (not so much money being spent for a given level of output; the future path of M is expected to be low compared to output). Hence Milton Friedman’s comment that:

Low interest rates are generally a sign that money has been tight, as in Japan; high interest rates, that money has been easy. … After the U.S. experience during the Great Depression, and after inflation and rising interest rates in the 1970s and disinflation and falling interest rates in the 1980s, I thought the fallacy of identifying tight money with high interest rates and easy money with low interest rates was dead. Apparently, old fallacies never die.

But interest rates are the cost of credit. If people borrow more, they spend more (in particular, they invest more); hence lowering interest rates is deemed to be stimulatory (encouraging more borrowing and investing) and raising interest rates is deemed to be restrictive (discouraging borrowing and investing). Moreover, if people have loans with floating interest rates, then lowering rates frees up some of their income (encouraging spending), raising rates absorbs more of their income (discouraging spending).

What, people are still buying that low interest rates = loose monetary policy nonsense?

What, people are still buying that low interest rates = loose monetary policy nonsense?

Increased spending will raise output or prices (depending on what supply-side [i.e. capacity] constraints are operating). But the central bank changing the base interest rate is movement from a given spot (i.e. it is a directional movement at a given level). It can only change the overall looseness or tightness of money if it changes inflationary expectations. And the impact of the interest rate change will vary depending on how inflationary expectations are running; so keeping interest rates unchanged as inflationary expectations drop is contractionary, as the non-inflationary cost of credit will rise.

If you are already in your target inflation range, the ideal outcome is you encourage output without significantly changing the general trend of money “tightness”. In other words, it is the movement of money into or out of spending, and the consequent effect on output, which matters. So, somewhat paradoxically, low interest rates are a sign of monetary tightness but lowering interest rates are a signal for monetary easing.

Hence, and this is where the two collide, the concern about the Zero Bound or liquidity trap; when you cannot cut interest rates any further (you are at 0%p.a.) but folk still aren’t spending. The infamous “pushing on a string”. Which is where the low-interest-rates-are-loose-money fallacy comes from, I suspect. People know that cutting interest rates is intended to be stimulatory, so it is “obvious” that low interest rates mean loose money. Yes, cutting interest rates is intended to be stimulatory but, no, low interest rates are not a sign of loose money but its opposite. Because interest rates are the price of credit, a price which incorporates inflationary expectations (the expected path of M compared to y), and the tightness or looseness of money depends on the level of spending for a given level of output.

Another way to think of this is interest rates as (in part) the difference between the value of money now and the value of money later. If the path of M is expected to be low compared to output, then money will retain its value as an asset over time and interest rates will tend to be low. If the path of M is expected to be high compared to output, then money will tend to lose its value as an asset over time, and interest rates will tend to be high.

Hence Quantitative Easing–a way to have a stimulatory effect without cutting interest rates. Of course, if you are the Fed and meanwhile making it clear that you are sticking to your inflation target, then the shift in the expected future value of money (and so the price level and so incomes) is going to be, shall we say, somewhat ameliorated.

Which is back to the problem with inflation targeting–like the gold standard, it permits central banks to evade responsibility for aggregate demand while setting it (disastrously low).

And if central banks determine aggregate demand, the only way to hold them genuinely responsible for what they actually do is for them to explicitly and directly target it: also known as NGDP targeting.


*See Lars Svensson’s “foolproof way” of exiting a liquidity trap.


  1. Rajat
    Posted December 3, 2013 at 5:29 am | Permalink

    Lorenzo, thanks for this excellent post. I found it very helpful for understanding some of the things that Scott Sumner often glosses over in his inimitable way! One thing though: you refer to a quote by Lars Christensen on the “Sumner critique”. But the rest of the quote from Lars says:

    “…the fiscal multiplier will always be zero if the central bank directly or indirectly targets aggregate demand either as a result of an inflation target, an NGDP level target or for that matter a Bernanke-Evans style monetary rule.”

    In other words, Lars (and I think Scott as well) regard fiscal policy as impotent if the central bank targets any nominal variable, including inflation. A NGDP target is better than an inflation target because it allows for the CB to avoid tightening if the economy is hit by negative supply shocks or indirect tax increases (eg the UK), but adherence to either target should have prevented the Great Recession. I think the difference between the RBA and the Fed/ECB/BoJ/BoE is not so much the subtle differences in nominal target, but the performance of the CB. That was probably assisted by Australia being well above the ZLB back in 2008; but of course as you point out, that needn’t have been a constraint on the others. Therefore, I wouldn’t put inflation targeting in the same ‘villain’ category as the gold standard or the Euro.

  2. Posted December 3, 2013 at 2:29 pm | Permalink

    R@1 Glad you found the post helpful :)

    … regard fiscal policy as impotent if the central bank targets any nominal variable, including inflation


    not so much the subtle differences in nominal target, but the performance of the CB

    But the difference is precisely that the RBA had an implicit income target and the other CB’s did not. All the CB’s acted (more or less) to (roughly) achieve their target. The RBA did better at achieving its target, but it also had a (much) better target.

    Therefore, I wouldn’t put inflation targeting in the same ‘villain’ category as the gold standard or the Euro.

    The Euro has two difficulties–the ECB being far too restrictive and the problems of not being an Optimal Currency Area (OCA).

    The 1873-1913 gold standard had some not-an-OCA problems but otherwise worked relatively well. The 1928-1936 gold standard worked diabolically badly because the BoF, with the congruence of the Fed, drove up the value of gold, thereby driving up the value of money and driving down the price level.

    An inflation target is much more stable in the short run than a misfunctioning gold standard c1929-193. So, in that sense, is not as bad. But it allows the same evasion of responsibility for aggregate income.

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