Archive for the Category Monetary Theory

 
 

IS/LM and AD

Commenter Joseph sent me an excellent set of PP slides by a professor at Harvard named Chris Foote.  He has a very clear derivation of the AD curve from the IS-LM model.  This slide caught my attention.

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The “spending hypothesis” obviously cannot explain the Great Depression.  In 1987 we saw an equally big stock market crash, and GDP kept booming.  (And don’t bother trying to concoct excuses about how things were different in 1987—I’ve swatted them all down 100 times.)

An investment backlash? Does that mean people switch from investment goods to consumer goods? If so, why did consumption also fall?  

Hoover actually favored public works projects, so fiscal policy explains nothing until at least 1932, when he raised taxes.   Was there a Great Depression in 2013?  I don’t think so.  And yet we had “savage” austerity in 2013.

OK, so it was tight money.  We’ve known that for 50 years, ever since Friedman and Schwartz. What interests me is the suggestion that the “money hypothesis” is contradicted by various stylized facts. Interest rates fell.  The real quantity of money rose.  In fact, these two stylized facts are exactly what you’d expect from tight money.  The fact that they seem to contradict the tight money hypothesis does not reflect poorly on the tight money hypothesis, but rather the IS-LM model that says tight money leads to a smaller level of real cash balances and a higher level of interest rates.

To see the absurdity of IS-LM, just consider a monetary policy shock that no one could question—hyperinflation.  Wheelbarrows full of billion mark currency notes. Can we all agree that that would be “easy money?”  Good.  We also know that hyperinflation leads to extremely high interest rates and extremely low real cash balances, just the opposite of the prediction of the IS-LM model.  In contrast, Milton Friedman would tell you that really tight money leads to low interest rates and large real cash balances, exactly what we do see.

Note the very last comment on the slide, about the significance of deflation.  The rest of the PP slides develop this idea further, and correctly show that while tight money might raise real interest rates, it could lower nominal rates through the Fisher effect.  Thus it could shift the IS curve.  That helps, but it seems to suggest that the IS-LM model can be rescued by switching the argument from nominal to real interest rates. Alas, that won’t work.  The Fisher effect is only one of the ways that monetary shocks impact interest rates.  Tight money also reduces expected future real GDP, and this also shifts the IS curve.  So it isn’t just nominal interest rates that fall, real rates also fell during the 1930s, as expected future real GDP plunged.  The IS-LM model is useless, and should be discarded.  The fact that it is used to derive the AD curve probably explains why I can’t seem to understand how Keynesians use the concept of AD; they are basing it on ideas that make no sense to me.

Here’s a simpler model.  AD is a hyperbola (a given level of NGDP).  This model does not assume NGDP targeting, just as the current AD model does not assume money supply targeting.  Changes in NGDP are caused by monetary policy.  The P/Y split for changes in NGDP is determined by the slopes of the SRAS and LRAS curves.  The LRAS curve is vertical.  Interest rates?  Yeah, they fluctuate a lot.

BTW, the PP slides end up with an excellent Greg Mankiw post from December 2008.  Mankiw recommends the Fed commit to a price level 30% higher in 10 years time.  Had they done so the recession would certainly have been much milder.

On the other hand if Mankiw had been head of the Fed in December 2008 they would have done almost exactly what they did under Bernanke, not what Mankiw recommended in 2008.  Mankiw’s policy views are pretty similar to Bernanke’s views.  Unfortunately there is also the formidable “FedBorg.” Had Mankiw been in charge, it would have been Bernanke who wrote the blog post suggesting the Fed should commit to a 30% higher price level in 10 years.  We are all just puppets, filling out the roles determined for us by blind fate.

Off topic:  Ramesh Ponnuru is right, I see lots of interest in NGDPLT among conservatives.

I have a post on AD over at Econlog, for those not burned out on the issue.

Just to show you that MMs don’t agree on everything, David Beckworth has a excellent post arguing against the Great Stagnation hypothesis.  Marcus Nunes is also skeptical.  In contrast, I accept the Great Stagnation hypothesis.  Fortunately it doesn’t matter for our monetary policy views, as we all favor targeting NGDP and ignoring RGDP.

Tony Yates on market monetarism

Tony Yates has a fairly extensive discussion of his views on market monetarism.  Before dissecting on the specifics, a few general comments:

1.  It’s hard for an outsider to grasp the nuances of any macro framework.  God knows I’ve been criticized for misstating the views of Austrians, MMTers, Keynesians, and many other groups. Yates does better than most.

2.  The views expressed here are my own, and as Nick Rowe indicated in the comment section to Yates’s post, market monetarism is a set of views that share a family resemblance (as is true of Keynesianism, Austrianism, etc.)  Nick’s comments are well worth reading.

So the following will sound more negative than I actually intended.  Let’s go over Yates’s points one at a time.  He starts by listing 10 tenets of market monetarism (these are not his views on policy, but rather his interpretation of our views):

1.  Monetary policy is never ineffective at stabilising inflation or the real economy, even at the zero bound.

Nope.  Monetary policy may be unable to stabilize the economy when there are real shocks. Monetary policy is pretty good at stabilizing the economy when the instability is due to a combination of sticky nominal wages and fluctuating nominal spending.

2.  Fiscal policy is ineffective [at, see above...] always.

Nope.  Fiscal policy can work in many different ways.  If the central bank is targeting inflation (including indirect taxes) then fiscal policy can boost employment if the government reduces VAT taxes, or employer-side payroll taxes.  Under a fixed exchange rate regime the government can boost output with more spending on goods and services.  The US in 1940-41.  My point was that if the central bank is targeting something like “aggregate demand” (as it should), then it’s silly for fiscal policymakers to attempt to influence “aggregate demand.”  That doesn’t mean that certain government projects might not become more desirable at low real interest rates, for standard classical cost/benefit reasons.

3.  Fiscal policy is effective [at...], but not desirable.

I mostly agree, with the caveat of the final sentence in my previous comment.  I do understand that fiscal and monetary policy are not identical, and hence one can construct models with a role for both.  But I don’t find those models persuasive.  To call fiscal policy a “blunt instrument” would be an understatement.

4.  Those New Keynesian models omit to model money, and so don’t capture why monetary policy is effective.

Yes and no.  I happen to think that omitting money makes it harder to see the importance of monetary policy.  However on purely theoretical grounds any story told with changes in the supply and demand for money can also be told with a description of the future path of interest rates relative to the future path of the Wicksellian equilibrium interest rate.  But I could also create models where the key variable was the difference between the actual price of zinc, and the Wicksellian equilibrium price of zinc (where the latter term is defined as the nominal zinc price consistent with 5% NGDP growth.) How do we know of the price of zinc is above the Wicksellian equilibrium price of zinc?  Simple, if NGDP growth is above target.

5.  If you look at New Keynesian models carefully, they show that monetary policy is effective, even at the ZLB, which demonstrates why it, and not fiscal policy, should be used for stabilisation purposes always.

I think it’s more accurate to say that those models allow for the effectiveness of monetary policy at the zero bound.  You can graft onto the NK models something like Krugman’s “promise to be irresponsible.”  Or Lars Svensson’s “foolproof plan” for escaping a liquidity trap.  Of course it’s also possible to construct NK models with expectations traps that do not allow for effective monetary policy.  I don’t accept the assumptions that underlie those pessimistic versions of the model.

6.  Unlike in NK models, monetary policy isn’t just about OMOs, or even buying long dated government securities.  Expansions of the money supply can be used to buy all sorts of assets.

Yes and no.  I certainly don’t believe that developed countries would need to buy non-government securities to hit a reasonable target, such as 4% or 5% NGDP growth, level targeting.  But my deeper objection is that NKs frame the ineffectiveness issue backwards.  They start by asking what the central bank can do at the zero bound, when they should start by asking why we are at the zero bound.  More specifically, imagine a “do whatever it takes” central bank that keeps buying assets until inflation or NGDP growth expectations are on target.  What then?  This reframes the debate in a way that focuses on the real “zero bound” problem, the zero bound on the availability of eligible assets for the central bank to buy.  When framed this way it becomes apparent that the zero bound on interest rates is not the real issue, as a central bank could theoretically run out of eligible assets even at positive rates.

For example, a few years ago the Australian national debt had fallen close to zero.  Nominal interest rates were positive.  Now let’s suppose that the RBA were only allowed to buy Australian government debt.  That constraint would make monetary policy ineffective.  And it would have nothing to do with the zero bound on interest rates, which were (and are) positive in Australia.

Now consider a country at the zero bound like the US.  Suppose that the Fed committed to unlimited “QE” in order to raise NGDP growth expectations up to the old 5% trend line.  They committed to buy T-securities until there were no more, then agency securities until those were exhausted, then Germany, Japanese, Canadian, British, etc., government bonds until those were exhausted, then AAA corporate bonds until those were exhausted, etc., etc.  Is that monetary policy effective?  It’s effective if the Fed can create expectations of sufficiently fast NGDP growth before running out of eligible assets.  Thus the real zero bound problem is not zero interest rates, but the possibility that the Fed might be legally prevented from buying assets that it needed to buy in order to satisfy the public’s demand for base money when NGDP growth is on target.

NKs tend to assume that since the Fed’s balance sheet has ballooned from 6% of GDP to over 20%, a still higher number would be needed if they had adopted a 5% NGDPLT policy in 2008.  Actually just the opposite is true.  With that 5% NGDPLT policy, we never would have hit the zero bound, and hence our monetary base/GDP ratio would be much lower (as is the case in Australia–which never hit the zero bound.)  NKs are monetary policy pessimists because they see interest rates as the lever of policy, whereas it’s more useful to think of them as the outcome of the policy regime.  Yes, NKs are correct that there is a liquidity effect and that easy money today is likely to lead to lower short-term interest rates today.  But as Woodford points out easy money today is not at policy at all; a policy is a change in the expected future path of monetary policy from today to the end of time.  It’s a policy regime.  And an expansionary policy by that criterion may well raise nominal interest rates.

7.  Societies should adopt nominal GDP targeting.

8.  [And/or] It follows from some combination of 1-6 that societies should adopt some form of nominal GDP targeting.

That’s basically right, although I certainly don’t think NGDP targeting is precisely optimal, just a good, pragmatic, easy to understand target that is superior to IT.  I’d prefer something like a nominal total labor compensation target, especially for countries like Kuwait where NGDP can be distorted by commodity price shocks.

9.  The crisis was caused by inflation targeting.  Following a MM perspective, including a nominal GDP target, would have averted it.

Yes and no, there were many causes.  If the Fed had adopted a “target the forecast” approach in their meeting after Lehman failed, monetary policy would have become dramatically more expansionary and the recession would have been significantly milder.  Ditto for replacing an inflation target with a price level target.  But I believe NGDPLT would have been better yet.

10.  Fiscal policy is ineffective away from the ZLB because it prompts an offsetting monetary policy response.

See my response to points 2 and 3.  Note that Yates ignores the “market” part of market monetarism.

A few general remarks:

1.  I accept the fact that it will never be possible to write down a macro model with microfoundations where NGDP targeting is optimal.  However, I also believe that we don’t know enough about the relative importance of price and wage rigidity, or the relative importance of various types of price rigidity, to construct useful models of that sort.

2. It’s a fair criticism of MM to point out that we don’t have much in the way of either sophisticated theoretical models or empirical studies to support our claims.  Like Keynes (1936) we rely heavily on a combination of basic economic models (AS/AD for me, where AD is a hyperbola), stylized facts that are highly suggestive, criticism of alternative approaches, and logic.  If someone bothered to write down the MM model (at least my version of it), the model would be as simplistic as the Keynesian cross.

3.  The real innovation of MM is that we’ve suggested that mainstream economists are thinking about the issues in the wrong way, and we have done so using many concepts that have come from those very same mainstream economists.  I tend to endlessly bore my readers with quotes from famous respected economists who used to claim that low interest rates don’t mean easy money, or that monetary policy remains highly effective at the zero bound.  In late 2008 these mainstream views were abandoned by the profession (including the famous economists I quote), for all the wrong reasons. For example, many economists simply misread the events in Japan (1993-2012) and become pessimistic about monetary policy.  A great deal of MM is simply reminding the profession that if the BOJ does what it did in fact do in 2013, that policy will be effective.  Ditto for the Swiss policy adopted a couple years earlier.

4.  Speaking for myself, I view MM partly as a sort of Deirdre McCloskey-like critique of modern macro methodology.  Milton Friedman (my hero) was famous for not having a well-defined “model.” Or for thinking in partial equilibrium terms.  His best ideas were not his “monetarist” ideas such as the 4% rule, but rather his critique of Keynesianism (low rates aren’t easy money, permanent income hypothesis, natural rate hypothesis, etc.) In my view MM is most effective as a critique of mainstream macro since 2008, and least effective when promoting NGDP targeting.

HT:  Ben Southwood.

The one thing you cannot do with cash

There are many theories of why people are willing to hold fiat money without any explicit backing. One theory that I’ve never been very fond of is that the ability to pay taxes with cash is what gives fiat money value.  This caught my attention:

DENVER (AP) — A marijuana business in Colorado has filed a lawsuit against the Internal Revenue Service for assessing a penalty for paying taxes in cash.

The IRS charges a 10 percent penalty on cash payments for federal employee withholding taxes. But many marijuana businesses are forced to pay taxes in cash because of difficulty accessing banking services

Thus it seems like taxes are one of the very few things that you cannot pay for in cash, at least not without a sizable penalty.  

Interest rates and monetary policy

Commenter Fed up asked the following question:

Start at IOR = 0% and fed funds rate = 8%.

Next, move to IOR = 2% and fed funds rate = 6%.

What happens?

If you have an interest rate-oriented view of monetary policy then this must be a bit of a head scratcher.  Higher IOR is “raising interest rates” and a lower fed funds rate is “lowering interest rates.” So which is it?

Monetary policy is not about interest rates; it’s about the supply and demand for base money.  In the first case the opportunity cost of holding reserves is 8%, in the second case it’s 4%.  In both cases banks don’t want to hold significant excess reserves, so the impact of higher IOR on the demand for the medium of account (base money) is trivial.  It’s slightly “tighter money” but without much effect.

The fed funds change is different.  Whereas a change in IOR affected the demand for base money, a change in the few funds rate is an effect of a change in the supply of base money.  That’s tighter easier money in the short run, ceteris paribus.  But whether it is actually tighter easier money depends on how the action impacts the expected future path of monetary policy.  For that you look at the response of the NGDP futures market–just as soon as policymakers figure out that they need to create such a market.

PS.  Lots of people have been sending me articles.  Narayana Kocherlakota endorses level targeting.  San Francisco Fed President John Williams suggests we consider NGDP targeting.  Put them together and you get NGDP level targeting.  Williams also says that the Swedish case shows that the Fed needs to be careful about using monetary policy to address financial instability.

PPS.  Martin Feldstein says inflation has been running well below the Fed’s 2% target over the past 12 months:

The Federal Reserve’s preferred measure of inflation—the price of consumer spending excluding food and energy—rose 1.4% over the past 12 months but increased since February at a 2.1% seasonally adjusted annual rate.

I agree.  Here’s the title provided by the WSJ editors:

Warning: Inflation Is Running Above 2%

PPPS.  Surprisingly, I agree with this:

I like to say to my students “no matter how many good arguments you think you have against real business cycle theory, it explains an overwhelming preponderance of the business cycles in the history of the human race.”

PPPPS.  TallDave sent me an interview where Larry Kudlow asks Alan Greenspan about market monetarism.  The answer is completely unintelligible, but Jim Pethokoukis is kind enough to also provide a much more thoughtful comment by Greenspan on NGDP targeting back when he was . . . younger.

PPPPPS.  Transparency in the Ukraine.

PPPPPPS.  Dogs are Republicans.

Posting will get less frequent over the next few weeks due to some trips I’ll be taking.

 

Reply to Mike Sproul

Mike Sproul has a new post (at JP Koning) that compares his “backing” theory of the value of money with my “quantity theoretic” approach.  (Just to be clear, market monetarism does not assume V is fixed, like some simple textbook models of the QTM.)

I’ve argued that US base money was once backed by gold, but no longer has any meaningful backing.  It’s not really a liability of the Fed.  Mike responds:

Scott’s argument is based on gold convertibility. On June 5, 1933, the Fed stopped redeeming FRN’s for a fixed quantity of gold. On that day, FRN’s supposedly stopped being the Fed’s liability. But there are at least three other ways that FRN’s can still be redeemed: (i) for the Fed’s bonds, (ii) for loans made by the Fed, (iii) for taxes owed to the federal government. The Fed closed one channel of redemption (the gold channel), while the other redemption channels (loan, tax, and bond) were left open.

The ability to redeem dollars for government bonds, at the going market price of bonds, has very different implications from the ability to redeem cash for a real good like gold, at a fixed nominal price.  I’d prefer to say cash can be “spent” on bonds, just as cash can be spent on cars or TVs. Indeed even during the Zimbabwe hyperinflation, the Zimbabwe dollar could still be “redeemed” for gold at the going market price of gold in terms of Zimbabwe dollars.  But that fact has no implications for the value of the Zimbabwe dollar.  If you increase the quantity of Zimbabwe dollars their value will fall, as they will buy fewer ounces of gold.  In contrast, before 1933 an increase in the quantity of US base money did not impact the amount of gold that could be purchased with one dollar (it was 1/20.67 ounces).  That’s the sort of “redemption” that matters for the price level.

Once we understand that both convertible and inconvertible FRN’s are a true liability of the Fed, it is easy to see that the quantity of inconvertible FRN’s could also be increased by any amount, and as long as the Fed’s assets rose in step, there would be no effect on the value of the dollar. (There is a comparable result in Finance theory: that the value of a convertible call option is equal to the value of an inconvertible call option.)

I don’t agree.  If the Fed doubles the monetary base by purchasing an equal amount of government debt at going market prices, the price level will double in the long run.  This is why I don’t accept the backing theory–I believe it is rejected by the evidence.  Here’s just one example.  In the early 1960s “Phillips Curve” ideology took root in America.  It was (erroneously) decided that we could trade-off more inflation for less unemployment.  So the Fed exogenously increased the monetary base at a much faster rate after 1962.  At first RGDP growth rose, then both RGDP and inflation, but eventually all we got was the Great Inflation, with no extra output.

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We can also observe the inflationary impact of open market purchases of bonds by looking at the response of financial market indicators.  If OMOs didn’t matter because the new money was fully backed, then financial markets would shrug off any Fed money printing. Indeed we can ask how central banks were able to achieve roughly 2% inflation once they set their minds to it.  Keep in mind that 2% inflation is not “normal.”  There is no normal inflation rate. Inflation averaged zero percent under the gold standard, and 8% from 1972 to 1981.  Then about 4% from 1982 to 1991.  Much more in some other countries.  There is no normal rate of inflation. In a related note, here’s Nick Rowe criticizing John Cochrane’s fiscal theory of the price level:

The Bank of Canada has been paying interest on reserves for 20 years. And when it wants to increase the inflation rate, because it fears inflation will fall below the 2% target if it does nothing, the Bank of Canada lowers the interest rate on reserves. And the Bank of Canada seems to have gotten the sign right, because it has hit the 2% inflation target on average, which would be an amazing fluke it if had been turning the steering wheel the wrong way for the last 20 years without going off in totally the wrong direction.

The Great Inflation was certainly not caused by deficits, which became much larger after 1981, precisely when the Great Inflation ended.  It was caused by printing money and buying bonds with the newly-issued money.

Mike continues:

But if the Fed issued billions of new dollars in exchange for assets of equal value, then I’d say there would be no inflation as long as the new dollars were fully backed by the Fed’s newly acquired assets. I’d also add a few words about how those dollars would only be issued if people wanted them badly enough to hand over bonds or other assets equal in value to the FRN’s that they received from the Fed.

This is where things get sticky, because Scott would once again agree that under these conditions, there would be no inflation. Except that Scott would say that the billions of new dollars would only be issued in response to a corresponding increase in money demand.

No, that is not my view.  The Fed might well increase the money supply even if the real demand for money did not rise.  There is always some price of bonds at which the Fed can induce people to exchange bonds for cash, even if they do not want to hold larger real cash balances.  They’ll spend the new cash almost immediately after being paid for the bonds.  That’s the famous “hot potato effect” that underlies the quantity theory.  I’d point to the 1960s and 1970s as an example of the Fed injecting new money in the economy far beyond any increase in desired real cash balances.

Scott is clearly wrong when he says that the backing theory doesn’t have much predictive power. It obviously has just as much predictive power as Scott’s theory, since every episode that can be explained by Scott’s theory can also be explained by my theory.

This is a tough one, because the identification problem is obviously a big problem in macro.  Not everyone might accept my claim that the Great Inflation was caused by an exogenous increase in the base, or my interpretation of market reactions to money announcement shocks, or my claim that successful 2% inflation targeting supports the assumption that Fed OMOs influence the price level.  But I wouldn’t say the QTM has no extra predictive power, rather it has predictive power that might be contested.  Central bankers would be in the best position to test the theory, as they can engineer exogenous changes if they wish.  I suspect that fact explains why most central bankers don’t adhere to the backing theory.  They think they see signs of their power.

Mike ends with 4 specific objections to the QTM:

(i) The rival money problem. When the Mexican central bank issues a paper peso, it will get 1 peso’s worth of assets in return. The quantity theory implies that those assets are a free lunch to the Mexican central bank, and that they could actually be thrown away without affecting the value of the peso. This free lunch would attract rival moneys.

We occasionally do observe rival monies taking hold during extreme hyperinflation. The mystery is why doesn’t it happen with other inflation episodes.  Fiat currencies have survived some pretty high rates of trend inflation, especially in Latin America.  My best guess is the answer is “network effects.”  There are huge efficiency gains from using a single currency in a given region.  It’s hard to dislodge the incumbent.

(ii) The counterfeiter problem. If the Fed increased the quantity of FRN’s by 10% through open-market operations, the quantity theory predicts about 10% inflation. If the same 10% increase in the money supply were caused by counterfeiters, the quantity theory predicts the same 10% inflation. In this topsy-turvy quantity theory world, the Fed is supposedly no better than a counterfeiter, even though the Fed puts its name on its FRN’s, recognizes those FRN’s as its liability, holds assets against those FRN’s, and stands ready to use its assets to buy back the FRN’s that it issued.

When I teach monetary economics I ask my students to think of the Fed as a counterfeiter.  I say that’s the best way to understand monetary economics.  And there is some ambiguity to the “stands ready” in the final line of the quotation. Was that true during the Great Inflation?

(iii) The currency buy-back problem. Quantity theorists often claim that central banks don’t need assets, since the value of the currency is supposedly maintained merely by the interaction of money supply and money demand. But suppose the demand for money falls by 20%. If the central bank does not buy back 20% of the money in circulation, then the quantity theory says that the money will fall in value. But then it becomes clear that the central bank does need assets, to buy back any refluxing currency. And since the demand for money could fall to zero, the central bank must hold enough assets to buy back 100% of the money it has issued. In other words, even the quantity theory implies that the central bank must back its money.

There are two ways to address this.  One possibility is that the central bank does not reduce the base when needed to hit a particular inflation target.  That describes the 1960s and 1970s. But what about when they are successfully targeting inflation at 2%?  In that case they’d need some assets to do open market sales, but they might well get by with far less than 100% backing.  The last point (about a 100% fall in money demand) feeds into his final objection:

(iv) The last period problem. I’ll leave this one to David Glasner:

“For a pure medium of exchange, a fiat money, to have value, there must be an expectation that it will be accepted in exchange by someone else. Without that expectation, a fiat money could not, by definition, have value. But at some point, before the world comes to its end, it will be clear that there will be no one who will accept the money because there will be no one left with whom to exchange it. But if it is clear that at some time in the future, no one will accept fiat money and it will then lose its value, a logical process of backward induction implies that it must lose its value now.”

There are two possibilities here.  One is that the public never believes the world will lend with certainty, rather that each year there is a 1/1000 chance of the world ending.  In that case people would still hold cash as long as the liquidity benefits exceeded 0.10% (10 basis points), which seems quite plausible given the fact that people still hold substantial quantities of cash when inflation reaches double digits.

Now let’s consider a case with a definite end of the road, say the German mark or French franc in 2001.  In that case the public would expect redemption for a alternative asset with a relatively similar real value (euros in the case.)  I’m actually not sure whether it matters if the central bank holds the assets used for redemption, rather than some other institution like the Treasury.  But yes, they would expect some sort of backing in that case.  But even so, OMPs will still be inflationary, which contradicts the claims made by backing proponents.

One final point.  We all agree that gold need not be “backed” to have value.  The QTM implicitly thinks of cash as a sort of paper gold.  It’s a real asset that has value because it provides liquidity services.  As an analogy, gasoline makes cars go.  Motor oil doesn’t propel a car forward.  But motor oil has value because it lubricates engine parts.  It’s harder to model the value of motor oil than gasoline, because the advantages are less obvious.  Similarly, it’s harder to model the value of cash than gold or houses or stocks.  But cash lubricates transactions, and hence a medium of exchange has value.  But once you have that monetary system in place, having twice as much cash adds no extra value.  Instead all prices double, and the value of cash falls in half.  It’s the monetary system that has real value.