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] = e^β . E[e_LT]^(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[e_LT] = ( 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_-1^α . ( 1 / e )^(1-α) . yr / yrn

Variables and Parameters

Variable	Definition	Opening Value
FA	Financial assets	150
Hd	Demand for base money balances	10
Hs	Supply of base money balances	10
Y	Nominal GDP	100
YD	Nominal disposable income	75
e	Exchange rate	1.00
eLT	The long term equilibrium exchange rate	1.00
gr	Real public expenditure	25
mr	Real imports	25
p	Domestic price level	1.00
pxr	Real private expenditure	75
rd	Domestic interest rate	3.00%
rf	Foreign interest rate	3.00%
xr	Real exports	25
xrn	Baseline exports	25
yr	Real GDP	100
yrn	Normal real GDP	100

E[z] denotes the expected value of z.

Parameter	Definition	Value
α	Price adjustment rate	0.75
β	Expected exchange rate weighting	0.75
ε	Adjustment rate of financial asset holdings	0.10
θ	Target ratio of financial asset holdings	2.00
λ0	Money demand parameter	0.25
λ1	Money demand interest rate elasticity	-5.00
µ	Basic propensity to import	0.33
σm	Price elasticity of imports	0.30
σx	Price elasticity of exports	-0.10
τ	Tax rate	0.25

[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.]

On The Use of Rational Expectations

Lars Syll has a couple of posts (here and here) on rational expectations.  Of the various assumptions underlying microfounded macro this one is, for many heterodox economists, the most preposterous.

In my view, though, it is wrong to dismiss rational expectations out of hand.  I would not suggest it is embraced whole-heartedly with other concepts pushed aside if they don't fit neatly with it.  However, I do think it is important that economists appreciate the way that expectations shape results and in this respect, I think paying proper attention to the implications of rational expectations is an important discipline.

When constructing models, it's often necessary to say something about expectations.  In saying how people act in aggregate, we need to make some assumption about what their average expectations are.  This is particularly so when modelling financial markets.  The results we get from our model will then depend on the assumptions we have made.

In a sense, we have two choices when deciding how to model expectations.  We can either assume that people get it right or that they get it wrong.  Now, it's quite reasonable to suppose that people will almost invariably get it wrong.  The problem, though, is that it's not enough simply to say that people will get it wrong.  Unfortunately, if we don't want to use rational expectations, we have to make a further assumption about the precise manner in which people will get it wrong.  How confident can we be that this further assumption is the right one?

I think it is legitimate to make assumptions that involve people making systematic expectations error.  More than that, I think we have to make such assumptions to understand certain behavioural patterns that occur in the real world.  It is quite clear that people do make expectations errors and consequences follow from this.  These are things we need to be able to explain as economists and they cannot be explained by appealing to rational expectations.

However, what I think is really important is that we understand the extent to which our results depend on our assumptions about expectations formation.  It may be appropriate to assume that people make systematic errors, but we should still have some idea of how the model would perform under rational expectations.   This will inform us on the extent to which our result depends on these assumptions.  This is important, as any assumption we make about expectations is unlikely to be reliable.

Of course incorporation of rational expectations into models is not straightforward.  In many cases, expectations can be self-fulfilling, so use of that assumption can lead to indeterminate solutions.  Furthermore, adapting the structure and other assumptions of the model simply so that it can solved whilst preserving the preferred expectations theory, is not really a helpful approach.  We might decide that rational expectations just doesn't work in our model.  But that's not a good reason to abandon the model.

So we should always ask ourselves how the model would perform under rational expectations.  If we conclude then that our result depends purely on an expectation error, that doesn't invalidate the result.  But it is something we need to know and understand.

UK Housing - A Look at Some Ratios

Steve Keen has an article in Business Spectator on housing bubbles, a topic he has written about extensively before.  Comparing various countries, he describes the UK as having the "Big Daddy" of all possible housing bubbles.  Certainly, his graph is impressive, showing a fourfold rise in real house prices in the UK since the 1960s.

The graph below is perhaps less impressive.  This shows the average house price in the UK divided by disposable income per head.  Also shown is the ratio of household debt to disposable income.

 

There are various interesting things here.  First, the ratio of house prices to income, whilst higher than average, is not greatly so.  The last figure in the graph is 112% of the average for the period.  It is clear though that this depends on the period being observed.  If we were to look at the figures only from the early 90s onwards, for example, current levels would look much higher.  Taking the data back to 1955 (the earliest figures I could find) wouldn't change the picture much.  The current level is 115% of the average over that longer period.

Another thing we can see in the graph is the massive rise in household secured debt over this period, from around 20% of disposable income to a peak of around 130%.  Although the rate of change of this ratio has varied over the period, it is only in the last few years that it has shown any material decline.  What is also interesting is that the three peaks in relative house prices all come after a period of relatively strong growth in the debt ratio (less marked in the first instance).

There are good theoretical reasons for expecting a relationship between the level of secured debt (most of which is mortgage debt) and house prices.  What is less clear is the causal nature of that relationship.  It could be argued that both the rise in house prices and the increase in debt are the result of an increased demand for housing, which is itself caused by other factors.  Those factors might be demographic, interest rate related, speculative or something else.

An alternative analysis would see the increase in debt as itself part of the explanation for the increase in house prices.  Under this approach, there would be some level of latent demand that is constrained by the lack of finance.  As more mortgage debt becomes available, perhaps as a result of developments in the finance industry, this demand becomes effective.  Certainly, the latter two periods of growth in debt ratios have coincided with significant financial deregulation and innovation.

As always, the true answer is probably a mix of both.  However, my own view is that the latter effect is probably the more important.  It might reasonably be questioned whether a demand for debt levels over 100% of income has really been lying latent since the 1960s.  However, I think it is quite possible that as higher debt to income levels become the norm, they set a new benchmark.  This generates a new layer of latent demand.  Thus, the standard debt ratio slowly grows over time (although of course it cannot grow forever).

As a further piece of analysis, I looked at the net equity in housing relative to income.  This is shown in the graph below.  This is based on the graph for house prices, but I have subtracted out the average level of secured debt per property. 

 

The shape of line is fairly similar to that for house prices but with less slope, reflecting the rising debt.  From this graph, the current level of this ratio is pretty much equal to its average value for the period.  Why might this measure be relevant?  Well, one possible factor is that people in the UK may regard the net equity investment in their home as part of their core lifetime savings.  They accumulate wealth during their lifetime and feel more secure investing that wealth in owning their own home rather than in financial investments.  Under this analysis, relative returns on different assets are less important.

On this basis, the ratio of net equity to income simply reflects a normal lifecycle of saving.  If additional debt funding is provided to the housing market, the net equity investment stays the same.  The total investment in the market therefore increases, which will result in increased house prices.

Again, whilst I don't think this is a complete description, I think there is an element of truth in this as a description of the UK housing market.

So, does this mean the UK has currently got a housing bubble?  I think the answer depends mainly on what happens with debt, which may depend a lot on what happens with interest rates.  If interest rates remain relatively low going forward, then it is quite possible that the debt to income ratio can remain at a high level for quite a long time.  If that can happen, the UK could quite easily avoid a significant fall in real house prices.

None of this however addresses the inequitable ownership of property in the UK, which is itself symptomatic of these trends.  This is something I want to look at in later posts.

Sources: ONS, Bank of England, Nationwide, DCLG, own calculations.