Bank Lending and Non-Bank Lending - A Model

I wrote last week about endogenous monetarism, the idea that bank lending is expansionary because of its impact on the money supply, even when it is seen as endogenous.

Base on some questions I've had, I thought it be useful to explore that idea a bit further with a little model.  I particularly wanted to look at the impact of household portfolio choices between deposits and other assets.

This model is based upon a simple closed economy with no government.  The national balance sheet is set out in the matrix below.  There are three sectors: households, firms and banks.  Households hold bank deposits (money) and bonds issued directly by firms.  Firms fund with bank loans and bonds and are assumed to hold no financial assets.  The balance sheet of banks is just loans and deposits.

	Households	Firms	Banks	Net
Loans		-L	L	0
Deposits	D		-D	0
Bonds	B	-B		0

The flow of funds is set out in the next matrix.  Investment is shown as both income and expenditure for firms.

	Households	Firms	Banks	Net
Income	Y	-Y		0
Consumer Spending	-C	C		0
Investment		-I , I		0
Loans		ΔL	-ΔL	0
Deposits	-ΔD		ΔD	0
Bonds	-ΔB	ΔB		0
Net	0	0	0	0

The only expenditure items in this economy are household consumer spending and investment by firms, so income is given by:

Y = C + I

We have a couple of behavioural assumptions.  The first relates to investment.  What we are going to do initially is assume that firms are credit-constrained.  Consequently, what determines their investment is the amount of money they can borrow.  We are going to assume firms invest every cent they can raise.  This means the function for investment can be written as: 

I = ΔL + ΔB

Note that although we are using this as a behavioural equation, it is also an accounting identity.   I'll say more about this later.

We'll assume consumer spending is simply a fixed amount plus a fixed proportion of income.

C = α₀ + α₁ . Y

The important thing to note about this function is that we are assuming that spending does not depend specifically on the balance of deposits.  We could add into the function a term for overall financial wealth - deposits plus bonds - that would be fine.  But we do not want a function where spending depends on one asset class and not the other.
 
However, we still need to say something about how households allocate their saving between bonds and deposits.  What we are going to do is treat this as exogenous, in particular, we are going to take ΔB, the purchase of new bonds by households, as determined independently of all the other variables.

This still allows us one free variable, so we are going to also choose to treat ΔL as exogenous.  We can think of this as being based on the whim of banks as to how much they want to lend.  This means that we have two separate decisions which impact firms' ability to fund their investment: the decision by households on how many new bonds to buy and the decision by banks on how much to lend.

These decisions have very different mechanics.  If banks decide to lend more, they will do so by creating more deposits.  No decision is required on the part of households to invest more into deposits - they don't need to decide to cut spending or to sell bonds - they just find their deposit holdings going up as a result of greater income flows.

The decision to invest in more bonds, however, does not result in any increase in deposits.  Households must decide to take existing money from their deposit accounts and invest in new bonds.  Nevertheless, because we are assuming that firms spend all the money they raise, this deposit money is quickly returned to households who end up with the same deposit balances as before.  The acquisition of new bonds ends up being funded, not by running down deposits after all, but by greater income.

The behavioural assumptions for investment and consumer spending allow us to express income using a standard multiplier equation:

		ΔL + ΔB + α0
Y	=	------------------
		( 1 - α1 )

It can be seen that both bank lending and bond purchase have an equivalent impact on income.

It is important to examine our assumptions carefully to see how this result arises.  Firstly we need to note the importance of assuming that consumer spending does not depend exclusively on deposits and not bonds.  For example, if we believed that whenever households invested $100 in bonds that they then cut their spending by $100, then we would have to reflect that in our consumption function and that would cancel out the term ΔB in the above income equation.

Secondly, we need to appreciate that this equation for income arises from how we have assumed investment is determined.  As already noted the equation we have for investment is simply an accounting identity.  By assuming that firms are credit constrained and therefore spend every cent of borrowed money, we are effectively saying that the amount of investment is determined by the amount banks are prepared to lend and the amount of bonds households are prepared to buy.

Even if we change our assumption about firms and treat them as not credit constrained, this identity must still hold.  But the way it works will be different.  For example, we might assume that unconstrained firms invest an amount based on some factor of national income, a sort of accelerator mechanism.  We could use a function like this, for example.

I = β₀ + β₁ . Y

However, we can now no longer treat both ΔB and ΔL as separately determined, as they may now be inconsistent.  This makes sense.  If we are assuming firms are unconstrained, that means they can borrow what they want.  We can't simultaneously assume that firms can borrow as much as they like and that banks and investors need only invest what they want.  The two are not compatible.

Our equation for national income has now become the following:

		α0 + β0
Y	=	------------------
		( 1 - α1 -β1 )

Interestingly, this equation contains neither ΔL nor ΔB.  So where firms are not constrained overall by credit considerations, it makes no difference if they happen to be constrained in one particular source of finance.  If, for example, banks decided to cut their lending, firms would simply borrow more through issuing bonds to households.  Households would simply switch funds from deposits to bonds, running down deposit balances at the same rate as loans are reduced.

Of course at some point, the appetite of households for more bonds might dry up, but then we're back to our credit constraint assumption.

One particular point of interest with this model is the asymmetry in the impact of household's portfolio choice.   Looking at the credit-constrained version, we saw that a decision by households to switch from deposits into bonds raises national income.  This implies that a decision to switch out of bonds into deposits will reduce national income.  And yet both bonds and deposits ultimately fund firms.  How can it be that switching from one to the other can have any effect?

The first point to note is that this has nothing to do with the role of deposits as the medium of exchange.  Rather, we need to look again at how bonds and deposits relate to firms ability to spend.  A decision by households to hold more bonds directly enables firms to engage in greater spending; a decision to hold more deposits does not.  The action that leads to bank-funded expenditure by firms is the decision by banks to lend more, not the decision by households to hold more deposits.  Furthermore, banks are able to increase loans without needing a decision by households to hold more deposits.  However, if households decide to hold more deposits, but banks do not wish to lend, all that happens is income falls (as firms are starved of bond finance) and it keeps falling until households are forced to stop trying to accumulate deposits.

There's probably a lot more I could say here.  This little model provides a very useful framework for looking at this sort of issue and I might use it again.  The important point to note here though is the following.  Whether bank lending matters more than non-bank lending comes down to what we believe about the behaviour of savers.  If we think that when savers shift money out of deposits into other assets, that they then cut their own spending, then the amount of deposits (and therefore the amount of bank loans) matters.  If we think that savers will continue to spend the same when they change their portfolios, then it does not matter whether new lending comes through banks or through other channels.

Endogenous Monetarism

When I studied economics in the 1980s, the concept of endogenous money was very much a post-Keynesian weapon in the war against the monetarist orthodoxy of the time (see for example N. Kaldor - The Scourge of Monetarism).  Reading some accounts of endogenous money today however, I wonder if the monetarists didn't win the argument without the post-Keynesians noticing.

We start off OK with a recognition of two important features of a monetary economy.   The first is the role of the demand for and supply of loans in determining the money supply.  The second is that this process is related to the level of aggregate demand.  When new loans and new money are being created, spending goes up; when the banks stop lending and the money supply contracts, spending falls.

This is all fairly straightforward, but the problem comes when trying to explain the link.  It is at this point that there appears to be a tendency to fall back onto the quantity theory of money as an explanation.   The story seems to go: 1) banks expand lending, increasing the money supply; 2) an increase in the money supply leads to higher nominal GDP.

I don't like this story.  I've called it Endogenous Monetarism, but really it's just monetarism.  It completely ignores the wider picture of what is going on with financial balances.  I'm not intending to get into the arguments for rejecting the idea that money determines spending.  If you think of yourself as a monetarist, this post will do nothing to convince you otherwise.  Instead, I just want to look at why we don't need to rely on the quantity theory of money to understand the importance of banks and lending. 

To get a better understanding we need to see that the creation of money is simply a by-product of a different process, and it is that process which is driving demand.  The process in question relates to the credit constraints of borrowers.

The budget constraint of all agents requires that their expenditure (including asset purchase) in any period is limited to their income plus their assets plus their available credit - the amount they can borrow.  In general, there are always agents that would like to borrow more, but who are unable to.  If a change in credit conditions now allows them to borrow, their spending or asset purchase will increase.  

This has nothing to do with the money created.  In fact, it doesn't even require money to be created, because the same applies for non-bank lending, which does not create money.  The reason bank lending is of particular importance is simply because it accounts for the majority of lending to credit-constrained borrowers.  Decisions on bank lending therefore critically affect the overall level of credit constraint and hence the net savings ratio of the private sector.

The fact that non-bank lending does not increase the supply of bank deposits, and therefore simply transfers it from one party to another is not important.  Non-bank lending still increases gross financial assets, just not in deposit form, and it is wealth measures that matter, not exclusively money (unless of course you are a monetarist.)

Understanding that it is not the money creation aspect that matters is important because it affects how we think about policy.  Although banks demand special attention, we cannot afford to lose sight of the wider aspects of debt levels (see Bank Lending Compared To Total Credit).  If we focus on money, we're missing the thing that really matters.

This post is not intended to convert those who believe in the quantity theory of money anyway.  This is an appeal to those who think of themselves as post-Keynesians to please try and avoid the trap of accepting the most important principle of monetarism without even realising it.

UK Trade Elasticities

Between 2007 and 2009, the UK saw a 20% fall in its real exchange rate.  Whilst this was not enough to put the trade balance into surplus, it does appear to have achieved some reduction in the large deficits which have persisted since 1998.

The graph below shows the trade balance as a percentage of GDP and the real effective exchange rate.



What I wanted to do was to break down the trade balance into price and quantity measures for both exports and imports, to see where the apparent effect was coming from.  No doubt, someone has down this before somewhere, but it's the sort of thing I find useful to explore myself.

Before having a look at this, it is worth considering the Marshal-Lerner condition.  The idea behind this condition is a fall in the exchange rate will cause export volumes to rise and import volumes to fall.  However, any such devaluation will also raise the domestic equivalent price of imported goods.  The Marshal Lerner condition therefore says that combined price elasticities of exports and imports needs to exceed one in order to overcome the rise in price of imports, if a devaluation is to improve the trade balance.

The purpose of this exercise is to look at what this means in practice.

We can write the percentage trade balance as:

B  =  ( X - M ) / Y

where B, X, M and Y are the balance of trade as a percentage of GDP, exports, imports and GDP, all in nominal terms.

We can rewrite this as:

B  =  x . w . px  -  m . pm

where:

x is real exports divided by the real volume of world trade

w is the real volume of world trade divided by real GDP

px is the export deflator divided by the GDP deflator

m is real imports divided by real GDP

pm is the import deflator divided by the GDP deflator

The first thing we want to do is to remove the effect of changes in w, because this is unlikely to be significantly dependent upon the exchange rate.  This is done by calculating a trend value for each of real world trade and real GDP and adjusting exports accordingly.  This gives an adjusted trade balance as shown below.

This is basically what the trade balance would have been if both world trade and GDP had been equal to their trend values (assuming the other parameters are independent).

We can now break down the impact on the trade balance by looking at how each of x, m, px and pm changed over the relevant period.  These are shown in the graphs below, firstly for px and pm, and secondly for x and m.

One of the most interesting things about these graphs is how closely the price deflators for imports and exports move together.  Both appear to adjust in response to the exchange rate movement, with the import deflator moving only slightly more.  This contrasts with the theory behind the Marshal Lerner condition, which assumes that only import prices will change and that they will change one for one.

In fact what we see is significant price adjustment in both exports and imports to take account of the revaluation.  Overseas vendors reduce their foreign currency prices to stay competitive within the UK market and UK exporters increase their prices to take advantage of the lower exchange rate.  This partly reflects an element of re-export within UK trade, but it also suggest a high degree of pricing flexibility for exporters and importers.

We can next look at the response of export and import volumes (ignore the spike in both exports and imports in 2006, which relates to MTIC fraud).  First of all, we notice that there is very little change in export volume.  There is perhaps a slight increase after the devaluation, but not much.  The effect on imports is more noticeable.  The sharp fall in sterling checks a steady upward trend and actually causes a significant, but temporary fall in the import ratio.  This dip in import propensity is the main cause of the spike we see in the adjusted trade balance graph.

One interesting point here is that the UK appears to fail the Marshal Lerner condition.  My own estimates for the long-term price elasticities of exports and imports are -0.1 and -0.6 respectively.  If prices changed as assumed by Marshal-Lerner, then a devaluation of sterling would lead to a worsening of the trade balance.  However, the close correlation of price movements in both imports and exports means that the volume improvements do in fact improve the balance of trade.

Nevertheless, the other notable thing about these graphs is the strong upward trend in the UK's import ratio.  The decline in the exchange rate halts this for a while, but we can see that it is then starting to resume its upward course.  The growing propensity to import remains one of the UK's greatest long-term constraints.

Data used
IKBH,IKBI,YBHA,IKBK,IKBL,ABMI - source ONS
World trade volume deflated by US HICP - source OECD
Real effective exchange rate - source BIS