## Friday, 26 July 2013

### 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.