Monday, 4 November 2013

Some Peculiar Dynamics with Long Term Money Neutrality

Certain monetarists would assert that, given time, there is a fixed relationship between the quantity of base money and the price level.  For example, in this post Scott Sumner says the following:

"If the Fed wants to increase all nominal variables by 100 fold, it simply increases the base 100 fold."

The idea behind this is simple.  What matters to agents are real variables.  If the only policy variable fixed in nominal terms is the quantity of base money, then the nominal values of everything else must ultimately be pegged off that.  It may take a long time, but in the end that's where it will end up.

If you can step back from how policy is actually conducted and imagine that the quantity of base money is actually used a policy tool, then it is a persuasive argument.  Actually, I think it is wrong but I'm going to leave my reasons for thinking so until a later post.  For now, I just wanted to look at one particular interesting aspect about the claim which is that it says nothing about what happens as the economy moves from one set of nominal prices to another.

I want to consider a very simple scenario.  I'm going to assume an economy at an equilibrium level of output with stable prices.  I then want to imagine a one-off increase in the level of base money and see how the economy might adjust to a new equilibrium.

The first thing to note is that it's not just a question of adjusting all prices.  Aside from base money, there will be a variety of financial assets and liabilities denominated in nominal terms.  As a rise in prices will reduce the real value of these, additional flows will need to take place to restore all the real ratios.  

For example, if the private sector is holding a certain amount of government debt, then the erosion in the real value of this debt may require a period of budget deficit for the private sector to accumulate more nominal debt.  If government spending is fixed in real terms, then this may require a period of reduced real output in order to reduce real tax revenues.

To look at this I used a little model of an economy with three sectors: a private sector, government (including the central bank) and the rest of the world.  The model has only two financial assets: government bonds, held by the private sector and the rest of the world, and base money.  As usual, a full equation listing with parameter values is given at the end of the post.

I then ran a simulation for a 10% increase in base money (achieved by a repurchase of government bonds).  The resulting path of nominal GDP and real GDP are shown below:

What is happening here is as follows.  The increase in base money and repurchase of debt causes a depreciation of the exchange rate.  Most of the exchange rate movement reflects a revision in the expected future exchange rate.  The construction of the model requires a future equilibrium exchange rate 10% lower reflecting a 10% higher price level which in turn reflects a 10% higher base money stock.  In fact, the exchange rate overshoots slightly due to a reduced domestic interest rate resulting from the base money increase.

The exchange rate depreciation initially boosts GDP due to improved trade.  However, the increase in the relative price of foreign goods, coupled with the increase in demand, immediately starts to push up domestic prices.  The erosion of the real value of private sector holdings of financial assets causes the private sector to cut spending in an attempt to accumulate more assets and restore the real ratio of assets to income.  This causes GDP to fall and to persist at a reduced level for some time, slowly returning to its original value.

I would stress that I am not suggesting that this is the inevitable path of GDP in response to monetary easing.  The particular pattern depends very much on the relative elasticities and response rates.  All I am interested in looking at here is the point that the simple intuitive result hides the possibility of a complex response which may be, at least temporarily, the opposite of what might be expected.

Equation listing

Real GDP is made up of private spending, public spending and net exports.

yr = pxr + gr + xr - mr

Nominal GDP is real GDP multiplied by the price level.

Y = yr . p

Private disposable income is a fixed proportion of nominal GDP based on the tax rate.

YD = ( 1 - τ ) . Y

The private sector is assumed to want to hold financial assets in some proportion (θ)to disposable income.  The acquisition of financial assets is based on the difference between this target amount and the outstanding amount.

ΔFA = ε . ( θ . YD - FA-1 )

Private spending is equal to disposable income less acquisition of financial assets.

pxr = ( YD - ΔFA ) / p

Exports and imports are based on relative prices (the foreign price level is assumed to be unity).   Imports are also based on private expenditure.

xr = xrn . ( p . e )σx

mr = µ . pxr . ( p . e )σm

Demand for base money is based on nominal GDP and the domestic interest rate.  Demand for money is equal to supply.

Hd = ( λ0 + λ1 . rd ) . Y

Hd = Hs

The first of these equations is rearranged as an equation for the interest rate.

The exchange rate is based on the expected exchange rate for the next period and uncovered interest parity.

e = E[e+1] . ( 1 + rd ) / ( 1 + rf )

The expected exchange rate for the next period is a weighted average of the current period level and the long term equilibrium level. 

E[e+1] = eβ . E[eLT](1-β)

In the long run, the domestic interest rate tends towards the foreign interest rate and purchasing power parity holds.  The equilibrium exchange rate can be determined from the money demand function as follows.

E[eLT] = ( λ0 + λ1 . rf ) . yrn / Hs

Within this simple model, this rule of thumb mechanism produces expected exchange rates fairly close to their actual outcomes if the value of β is chosen appropriately.

Finally, prices are based on lagged prices, foreign prices and domestic output.

p = p-1α . ( 1 / e )(1-α) . yr / yrn

Variables and Parameters

Opening Value
Financial assets
Demand for base money balances
Supply of base money balances
Nominal GDP
Nominal disposable income
Exchange rate
The long term equilibrium exchange rate
Real public expenditure
Real imports
Domestic price level
Real private expenditure
Domestic interest rate
Foreign interest rate
Real exports
Baseline exports
Real GDP
Normal real GDP

E[z] denotes the expected value of z.

Price adjustment rate
Expected exchange rate weighting
Adjustment rate of financial asset holdings
Target ratio of financial asset holdings
Money demand parameter
Money demand interest rate elasticity
Basic propensity to import
Price elasticity of imports
Price elasticity of exports
Tax rate

[Edit - thanks to Anton van de Haar for drawing my attention to one or two incorrect values in the parameter listing - now hopefully all correct.]


  1. I think you are not modeling here what Sumner said. You increased the amount of cash-like assets by 10% and left the number of bonds constant, right? That would be fiscal policy. Sumner claims that swapping bonds for reserves would change prices, but there is no mechanism for that in the modern economy where reserves have no causality powers over how much people borrow and spend.

    1. This simulation involves repurchase of bonds, so initially there is a reduction in bonds equal to the increase in base money. So, definitely monetary policy, not fiscal policy. Over time, the amount of bonds increases again (it has to to bring all the real quantities back to their staring levels), but this doesn't happen through any change in (real) government spending or tax rates. It happens because of falling (real) tax revenues due to depressed output.

      I would be inclined to agree with you on the causal mechanisms (or lack of) relating to an expansion in the monetary base. In fact, I think there are lot's of reasons for questioning this claim, but I'm giving the monetarists the benefit of the doubt here, so I can just look at this one point.

  2. Nick,

    Although your method seems okay, your graph values look like they move a lot than what intuition suggests because 10% rise in monetary base is basically not much.

    Do you have the exchange rate movement directly related to the monetary base? Because in general it moves on asset demands and supplies - where one considers all assets.

  3. Well, this is a world where a 10% increase in the monetary base causes a 10% increase in all nominal values. In the graph above NGDP increases by 10% eventually. The variation in RGDP is smaller.

    The exchange rate movement is crucial to what is going on here. What happens with the exchange is this: I have assumed a monetarist world, where the quantity of base is set in nominal terms, but everything else (including government spending) is fixed in real terms. Because the model is simple enough to avoid various complexities, this means that the price level and the exchange rate are determined in the long run by the monetary base. Increase the base by 10% and eventually the price level will be 10% higher and the exchange rate 10%, because there is only one real equilibrium here. This, I believe, is how people like Scott Sumner see things.

    Because the log-run expected exchange rate falls, so does the current rate, as it's driven here by UIP. The fall in the exchange rate then pushes up prices helping to restore purchasing power parity. So, to some extent, the expectation of the end result actually helps cause that end result. Again, I think this is very much in line with how some of the market monetarists see things (and - to some extent - I agree with that).

    In this model, I have assumed perfect competition in international capital flows. This has meant I can just refer to domestic and foreign interest rates and don't need to look at the demand and supply of domestic and foreign assets. I have actually looked at a version with imperfect capital flows and it does change the results slightly, but not in a way that is very important for what I'm saying here.

    1. It's worth noting as well that it's a matter of interpretation here as to whether fiscal policy in this simulation is neutral or expansionary. I am assuming that real government expenditure is fixed (as is the tax rate), which would suggest neutral fiscal policy. However, as prices start to rise, nominal government expenditure goes up. This is crucial. If I was to fix nominal government spending, the expansion of NGDP would soon fizzle out. It is essential to this scenario that only the base is fixed in nominal terms.

    2. Oh got it - so the assumed model true or not is a Monetarist model and you are saying this is what happens in your own Monetarist model to them.

    3. Yes, sort of. It's still a Post-Keynesian style model, but structured around certain monetarists concepts that I wouldn't tend to use myself.

  4. The main question I have is why we assume that bond purchases have any effects other than on assets? The CB buys bonds, creates deposits in doing so, and then the former holders of bonds have to do something with their assets, so they buy new assets, and prices move up until everyone is indifferent holding the new cash. So, yes people feel wealthier, but how much of that filters through to the bottom 90% of the economy that don't really own assets, and how much can the upper wealth bracket contribute to gdp growth solely via the wealth effect? Home price increases would be the other logical outlet, but how much has that contributed in the past 5 years?

    1. Well, in this model the exchange rate is the only transmission mechanism. The same process that raises asset prices also depreciates the exchange rate (effectively raises the domestic equivalent price of foreign currency denominated assets). In the model above, this is the only asset price that can change. The exchange rate movement then impacts on prices and volumes. In fact, the only wealth effect here is a negative one, where rising prices reduces the real value of savings.

      I do think this process would follow from bond purchases in the real world as well, but perhaps not to the extent shown here.

  5. "The erosion of the real value of private sector holdings of financial assets causes.........."

    I can not convince myself that an erosion of value of existing holdings occurs. In fact, I think existing assets become more valuable (in money terms) when government buys government bonds.

    Existing assets include Government Bonds and all other existing assets. If Government recalls interest paying bonds and replaces them with non-interest paying cash, the total pool of assets available for investment is reduced. Now, more cash chases fewer assets. Average asset-pool-price should increase.

    Yes, more assets will be built when the price increases, BUT, the cost of construction will increase. This would reinforce the increased value of existing inventory.

    Unappreciated effects from competition will appear. As you say, with the increased supply of money driving down the exchange rate, foreign money can buy more of everything, including assets.

    Cantillon Effects will be unequal between young people and older people. Older people holding assets will see the value of assets increase. Young people will face more competition from foreign money. Young people, not holding many assets, will need to work harder and longer, paying more tax in the process, to accumulate assets.

    Higher wages for young people will be accompanied with higher wages for older people. Older people who have failed to accumulate more-than-adequate assets, will be lured or forced back into the work place, further increasing work place competition for young people.

    My conclusion is that an increase of money supply is very bad for young people. My conclusion would reverse if I were convinced that average asset value actually FALLS.

  6. Hi Roger,

    You are right generally that looser monetary policy will tend to push up the price of assets, including bonds. I avoided that issue in this model by assuming bonds which pay a floating rate of interest, so I could let the rate change and keep the price constant. Changing that assumption would affect the results a bit, but not, I believe, my overall conclusion that a deflationary impact on real GDP is possible even with rising prices. I might modify the model and play around with that a bit.

    I'm very interested in your observation on inter-generational effects. I have been recently playing around with some overlapping generations models, precisely because I am interested in the impact on wealth distribution of changes in asset prices and how that might affect spending. I intend to do some posts on this in the future.

  7. Hi Nick,

    The money expansion/GDP issue is nuanced with the nominal/real description. I find it hard to avoid switching concepts in mid-argument!

    Like you show in the graph, I think the inflation-adjusted GDP shows a decrease if government buys interest bearing bonds. I think the GDP using the reported numbers (I think we call that "nominal GDP in the U.S.) would go up for the reasons you explain.

    In the U.S., in my opinion, QE is acting exactly as you portray. The money supply is increasing none-the-less, but by a different mechanism. The mechanism of money supply increase, in my opinion, is the Federal Government deficit. This on-going money supply increase is having a different effect, an effect that I have not yet analyzed to my satisfaction.

    I think the inter-generational effects of the on-going-budget-deficit may not be the same as created by a Treasury Bond buyback.

  8. I'm wondering whether an impetus for higher asset values could come from the fact that bank deposits are less safe than treasuries. JKH says that most of the treasuries bought by QE were not held by banks but rather held by non-bank institutions that then asked banks to sell them on their behalf to the Fed. So the people who were previously holding the treasuries end up holding bank deposits rather than directly holding bank reserves. Those people left with bank deposits have a problem because unlike treasuries, bank deposits are at risk (if over the insured limit) if their bank were to collapse. So I suppose that risky nature of bank deposits gives a bit of a “hot potato” effect from QE?
    The other thing with QE is that it may make the currency weak in good times but in times of panic all the foreign assets may get sold and the money may see a rush back to safety at home. That happened to Japan didn't it in 2008? They got a spike in the value of the Yen just at the time when companies were already very stressed.

    1. I think what you describe in the first paragraph is right. I think this is all part of the portfolio preference approach to asset pricing, that goes beyond simply looking at discounted expected future rates. So, the different perceived risk on Treasuries and deposits is one of the factors that determines demand for each and when the supply changes, asset prices have to change to induce people to hold what is actually out there.

      I'm not convinced on the bit about the currency though. Is the effect you describe actually caused by the QE? If it's a result of a panic, surely the panic leads to the QE, not the other way round?

    2. I thought the Japan experience was that they had had lots of QE already well before 2008. That had helped induce Japanese holdings of lots of foreign assets in the lead up to 2008 (perhaps a significant contribution to the global asset bubble). When the panic hit those were sold off and there was a rush back to the Yen. Currency speculators got on board and the Yen surged.

    3. Well, I think I'd say that the QE was pushing funds abroad which would have put downwards pressure on the exchange rate, and that it was something else that caused the repatriation. But I think we could agree that the QE might create a position where the currency was prone to such effects.

  9. Your experiment reminds me a bit of the first two chapters of Gurley and Shaw, Money in a Theory of Finance, 1960. Were you at all thinking about that or primarily motivated by Scott's post?

    1. No, I'm not familiar with text. Maybe, I should look at it. This was purely prompted by Scott's post and similar claims I've seen.

  10. "If you can step back from how policy is actually conducted and imagine that the quantity of base money is actually used a policy tool, then it is a persuasive argument. Actually, I think it is wrong but I'm going to leave my reasons for thinking so until a later post" Looking forward to that post. I can see how nominal variables can be manipulated via the base quantity, but it's not clear to me how it can impact real variables. As a comment on JP Koning's blog I was trying to think how base quantity in the (interbank) payments system affects quantity in the real world payments system, i.e. "working capital" for the private sector (easiest to think of this as corporations); Anyways, no need to reply to this comment; will look forward to your post.

  11. Hi Nick, I programmed your model in Vensim in order to see how it behaves. Which variable(s) did you change in order to get the graphs you showed?

    A short remark: I believe that the basic propensity to import shouldn't be 0,33 but 1/33 (else the model is not stable).

    1. Hi,

      Variable changed is Hs, which is increased by 10%.

      You're right - the parameter there should be 1/3 (I think that's what you meant) - I'd just shown the rounded figure there.

  12. Yes, I meant 1/3. I furthermore noticed that the stable initial values of Hd and Hs are 40, is that correct?

    When running a simulation with Hs jumping from 40 to 44, I find the Nominal GDP curve that you show, but the real GDP curve looks different. It instantly falls from 100 tot about 99 and then slowly increases again to 100. But maybe something is wrong with my program, I have to check...

    1. I have a starting steady state value of 10 for Hs. It's always possible that I've transcribed something incorrectly, so do let me know if you find an error.

  13. In your equations, you state Hd = Hs, but that must be Hs=Hd, I assume.
    Furthermore, Hd = (L0 + L1*rD)*Y = ( 0.25+5*0.03)*100 = 40 initial value, I assume

    1. Ah! Lambda 1 should be -5, not 5. That is a transcription error. Sorry about that and thanks for spotting it. I'll edit the post.