Thursday, 27 March 2014

The Demand and Supply of Money and Other Financial Assets

I've read a few bits recently about the demand and supply of money, in particular over the question of whether the quantity of money is determined by supply and demand. puts the monetarist case very well and I'm going to try and paraphrase him here.

It's helpful to look at a simplified balance sheet, like that shown below.  Here we have lenders holding bank-issued money, borrowers with loans, and banks.  Banks have nil net worth, so money equals loans.

 Savers Borrowers Banks Money M -M Loans -L L

We can then hypothesise a money demand function that says that the demand for money balances is in some fixed proportion to nominal income.  Maybe this applies only in the long run, so that there is a gradual adjustment towards it, but in long run equilibrium the demand and supply of money will be equal, so we can write M = kPY.

What is the causal interpretation here?  Well, the quantity of money in existence is being determined in the loan market.  An increased demand or supply of loans leads to a greater supply of money.  Borrowers spend the money they borrow.  If this leads to lenders holding excess money balances then they will tend to spend these until income and money holdings are in balance again, basically until the condition M = kPY is met.

So in this limited framework, we might say that the quantity of money is supply determined and that the supply of money then determines nominal GDP.  We have skipped over the question of the extent to which loan volumes themselves depend on nominal GDP, but otherwise I tend to agree that this is a useful way of looking at these dynamics.  So saying here that the quantity of money is supply determined seems to me to be reasonable.

What I am less happy with is the idea that this is necessarily a story about money.  It is a story of money here, but that is because we have severely limited the number of monetary assets that appear.  So let's expand our balance sheet so that banks are now funded with transaction accounts (which we'll call money) and  what we'll call savings bonds, which cannot be used for exchange.

 Savers Borrowers Banks Money M -M Savings Bonds B -B Loans -L L

Now, we find that an increase in lending adds to the total quantity of money and savings bonds.  But, in itself, it doesn't tell us the split between the two.  To determine that we need to know something about the relative demand for each.  So, once we allow for banks to have liabilities other than money, we can no longer really say that the quantity of money is essentially supply determined.  Of course, banks will have preferences as to their liability mix, so supply conditions will matter as well, but no more so than demand.

The further point here, is that once we allow for a financial sector with liabilities other than money, the same principal applies to lending by non-bank financial intermediaries (NBFIs).  So, we can imagine that what we have called banks in the balance sheet above instead includes all financial intermediaries.  We have banks that issue money and savings bonds and NBFIs that issue only savings bonds (but that might hold money or borrow through loans).  We now need to specify that what we have called money means instead just that money held outside the financial sector and loans means loans outside the financial sector.

Now there is no immediate difference between additional lending by banks as opposed to NBFIs.  Both will initially increase the amount of money held outside the financial sector, but how the balance between money and savings bonds develops then depends very much on the preferences of savers.

So I don't have much of a problem with an analysis that says that the quantity of financial assets is determined in the lending market and that that quantity then impacts on nominal GDP.  However, in a world with many different financial assets, which are often close substitutes, this does not imply that the quantity of any one particular asset (including money) is itself supply determined.

Wednesday, 12 March 2014

Simulation Model for Samuelson and Inside Money

I know some people like the simulation models that I sometimes put on my blog, so I thought I'd do one using the Samuelson / inside money model that I described last time.

The balance sheet and flow of funds for this are those set out last time.  The equation listing and parameter values are given at the end of the post.

Most of the model is actually governed by accounting identities.  The only assumptions are as follows:

1. Workers attempt to balance their consumption so that they spend the same amount when working as in retirement.

2. The price of goods is sticky.  Price adjustment responds to the rate of loan growth (as an indicator of long term inflation) and the output gap.

3. The utility of holding land is such that at some point the marginal utility is zero.  This presumes some level of disutility from holding land, perhaps from having to maintain it.  (This simply allows me to have a zero interest rate on loans and deposits).

4. The price of land adjusts to equate the expected return on land to that on deposits for retiring workers.  The expected return on land for newborns, exceeds their cost of loans, but they are assumed to be subject to credit constraints. (The expected return on land for newborns is not modelled here - it's not necessary because of the credit constraint assumption -but for other simulations, it might be necessary to include it.)

5. The simulations are run using adaptive expectations.

The graphs below show a simulation of a change in the nominal growth rate in loan volume from zero to 2%.

Price stickiness allows a temporary increase in production.  Rising prices start to increase the expected returns on land relative to deposits, which makes it more attractive to hold land in retirement.  The balance of housing ownership therefore moves towards retireds.  This requires that the real value of loans must fall, even though it was initiated by a rise in the nominal value.

Model Listing

Retireds consume the full value of their assets:

Cr = ( Art-1 . pa + Dt-1 ) / pc

Workers consume an amount equal to what they expect to consume in retirement

Cw = E[Cwt+1]

subject to an inter-temporal budget constraint.

Cw . pc + E[Cwt+1] . E[pct+1] = C . pc + Awt-1 . pa - Lt-1 + Ar . ( E[pat+1] - pa )

These last two equations are rearranged to eliminate E[Cwt+1], and give an expression for Cw.
Output is total consumption

C = Cw + Cr

Deposits equals loans

D = L

Workers' housing is total housing less retireds' housing

Aw = A* - Ar

Retireds' housing is given by their budget constraint.

Ar = ( C . pc + Awt-1 . pa - Lt-1 - Cw . pc - D ) / pa

The following equations then determine price setting.  The price of goods adjusts at the nominal growth rate of loans, adjusted for a measure of the output gap.

pc = pct-1 . g . ( C / Cn )σ

The price of land is determined by the following expression, which equates the marginal expected return on land with the expected return on deposits (zero).  The first part of the LHS is the assumed marginal utility of holding land, the second is the expected capital gain.

( α . Arβ - λ ) + ( E[pat+1] / pa - 1 ) = 0

This is rearranged as an expression for pa.
Finally, expectations are adaptive, factoring in the growth rate for nominal loans.

E[pct+1] = E[pct]t-1 . g . ( pc / E[pct]t-1 )ε
E[pat+1] = E[pat]t-1 . g . ( pa / E[pat]t-1 )ε

Variables and Parameters

 Variable Description Opening Value Ar Land held by retireds 100 Aw Land held by workers 100 A* Total land 200 C Total consumption 400 Cn Stable price level of consumption 400 Cr Retireds' consumption 200 Cw Workers' consumption 200 D Deposits 100 L Loans 100 g Growth parameter for nominal loans 1.00 Pa Price of land 1.00 Pc Price of consumer goods 1.00

The expression E[Xt+1] means the value that agents in period t expect X to be in period t+1.
In the simulation the value of g is increased to 1.02 from period 2 onwards.

 Parameter Description Value α Land utility parameter 10.0 β Land utility parameter -0.50 λ Land utility parameter 1.00 ε Adjustment rate of expectations 0.75 σ Adjustment rate of consumer prices 0.50

[Edit - amended for errors noticed by Terry H and Anton]