The Problem with Monetary Policy

The prevalent view regarding demand management is that is best achieved through monetary  policy - typically interest rate manipulation - rather than fiscal policy (at least when rates are not at the zero lower bound).  There are a number of aspects to this question, but one of the main objections would have to be the conflict between short term and long term effects.  Monetary policy often works in the short term by raising debt levels and inflating asset prices, but this can store up problems for the future.

Those who have worked with SFC models may be familiar with these dynamics, but they tend to figure less in mainstream constructs.  What I have attempted to do here, therefore, is look at this issue in the context of a simple model with optimising agents and rational expectations.  In addition to illustrating the problems with an over-reliance on monetary policy, it also brings out certain dynamics which seem relevant to recent economic trends.

I have based this on a simple model I have used previously to look at the question of why money has value, which I have extended to include a government sector.  A technical specification of the model is given at the end of this post.

The economy consists of overlapping generations that live for two periods, providing a fixed amount of labour in the first and not working in the second.  Households own land and consume a single consumption good, which is produced by labour alone with constant returns to scale.  Asset transactions take place at the end of the period.  The new generation is born just prior to the end of the period preceding the one in which they work, enabling them to buy land from the households that are due to die.

Newborns acquire land by taking out loans.  These loans are repaid with interest at the end of the first period.  At this point households may also buy or sell amounts of land.  The balance of funds is held on deposit.  Retireds finance their consumption by selling their land (at the end of the period) and using their deposits.

There is a government that spends in acquiring the consumption good and that levies taxes on workers.  The fiscal rule sets the level of spending and the rate of tax, which is applied to labour income only.  The balance is financed by issuing bonds.  Government issued bonds are acquired by banks, which also make the loans to newborns, in each case by issuing deposits.  The same interest rate is applied to loans, bonds and deposits.  This rate is set by the monetary authority.

The balance sheet for this economy is shown below.  Balances are shown as at the start of each period.  Loans, deposits and bonds are shown in nominal terms.  Land is shown as a quantity multiplied by a price.

	Workers	Retireds	Banks	Government
Land	Aw. Pa	Ar. Pa
Loans	-L		L
Deposits		D	-D
Bonds			B	-B

The flow of funds in a single period is then shown in the table below.  Repayment of all financial assets is shown gross of interest.  R is equal to the nominal interest rate plus one.

	Newborns	Workers	Retireds	Banks	Government
Consumer spending		-Cw . P	-Cr . P
Government spending					-G . P
Earnings		( G + Cr + Cw ) . P
Taxes		-T			T
Land purchases	-Aw . Pa	(Awt-1 - Ar) . Pa	Art-1 . Pa
Loans	L			- L
Loan repayment		- Lt-1 . Rt-1		Lt-1 . Rt-1
Bond issuance				- B	B
Bond redemption				Bt-1 . Rt-1	- Bt-1 . Rt-1
Deposits		- D		D
Deposit repayment			Dt-1 . Rt-1	- Dt-1 . Rt-1
Total	0	0	0	0	0

Households choose how much to consume in each period and how much land to hold in each period, subject to their budget constraints. 

Starting form a steady state, the particular experiment here involves a temporary (single period) reduction in government expenditure.  It is assumed that this reduction is unexpected, but that the subsequent reversion to the normal level is expected.

Under perfect price flexibility, with the nominal interest rate held constant, the level of output can be maintained by a one-off drop in the price level.  This raises the real value of deposits holdings causing retireds to increase their spending.  The fall in the price level also increases the real debt burden of workers, who respond by reducing their spending but the effect is less.  There is some knock-on effect due to redistribution between generations, but the economy settles fairly quickly back to the same (real) steady state values.  This is illustrated in the charts below.

 

What we wish to consider is whether the monetary authority can use the nominal interest rate to avoid this deflation.  This is equivalent to asking whether they can maintain the level of output even when the price of goods is fixed (but the price of land is allowed to vary). 

The charts below illustrate the outcome where the monetary authority adjusts the interest rate for ten periods but then holds it stable (the chart for government spending is as above).  Compensating for the reduced government spending requires cutting the interest rate in the first period.  This boosts private spending through a wealth effect.  Lower interest rates increase the price of land, increasing the spending power of those holding it.

However, even when government spending returns to its baseline value, the interest rate needs to stay low.  In boosting private spending, the reduced interest rate has led to greater private debt and reduced financial savings.  This reduces the spending capacity of both workers and retireds.  In fact, in order to counter this and keep private spending at the original level, the interest rate has to be reduced again.

As soon as the interest rate is held stable, private spending drops and output settles at a permanently lower level (but land prices and debt levels stay at a higher level).  To keep private spending at the level needed to ensure no output gap, the monetary authority would need to keep cutting the interest rate and inflating land values indefinitely.  It is easy to see why this must be.  In a steady state, the values of all balances must be constant.  For the level of bonds to be constant, the government's budget must be balanced, i.e. we need the following equation to hold.

                                                          G . P - T + ( R - 1 ) B = 0

With a given level of output, T is fixed.  A fall in G therefore requires a higher level of ( R - 1 ) B.  Cutting the interest rate reduces R.  But it also reduces B, because B is equal to the net financial position of the private sector.  As R falls, households borrow more and also run down deposits, so B falls.  In order to achieve a steady state, R needs to rise, not fall.  But as soon as the monetary authority increases R, the immediate impact is a fall in output

There is therefore no way (within this model) that the interest rate can be used to achieve price stability in both goods and land and a zero output gap, unless fiscal policy adjusts accordingly.

Technical Specification

The number of household in each generation is constant.  Each household in the ith generation chooses c_i,1, c_i,2, a_i,1 and a_i,2 to maximise expected utility, where c is consumption and a is holding of land and the second subscripts indicate whether the value is for the first or second period of life.  Labour is assumed to be supplied in a fixed quantity in the first period of life only.  Utility is given by:

 (1)          U_i = ( ln c_i,1 + φ ln a_i,1 ) + β^-1 ( ln c_i,2 + φ ln a_i,2 )

The budget constraints can be derived from the flow of funds matrix.

(2)          q₀ a_i,1  ≤  l_i

(3)          c_i,1 + q₁ ( a_i,2 - a_i,1 ) + d_i  ≤  w_i - t_i - R₁ l_i p₀ / p₁

(4)          c_i,2  ≤  q₂ a_i,2 + R₂ d_i p₁ / p₂

where w, t, l and d are wages, taxes, loans and deposits respectively, all expressed in terms of the consumer good.  R is one plus the nominal interest rate, p is the price of the consumer good and q is the price of land expressed in terms of the consumer good.  The subscript for R indicates the period in which the interest is paid.

Production is by labour only and at constant returns to scale, so competition ensures that the total wages of each generation are equal to total spending.

(5)          w_i  =  c_i,1 + c_i-1,2 + g_i

where g_i is government spending in the period in which the ith generation is working, expressed in terms of the consumer good.  Taxes are a proportion (τ_i) of wages.

(6)          t_i  =  τ_i w_i

The total amount of available land is fixed.

(7)          a_i,1 + a_i-1,2  =  a*

Parameters for the simulations were: β = 1.50, φ = 0.10.  Baseline values were: g = 100, τ = 0.25, R = 1.30, a* = 125.  The shock was a one-period reduction in g to 95.  

Initial simulations were constructed over a long period using steady state solutions as proxy for expected future values.  Expected values were then adjusted and the process repeated until the expectation error was negligible.

[EDIT: After originally posting this, I noticed an error in the model used to generate the graphs. I have corrected this and replaced the graphs.  The narrative remains the same.]

Diamond-Dybvig and the Monetary Circuit

One of the main models of the role of banks is Diamond-Dybvig (DD).  This seeks to explain how banks might be able to provide valuable intermediation between:

a) savers who are uncertain when they might want their money back, and

b) entrepreneurs who need funds for a minimum period of time in order to generate returns.

In this model, entrepreneurs can only pay an interest return if they can borrow for the time required.  If required, they can repay early, but with zero interest.  Savers can lend to entrepreneurs directly, but they face an uncertain return, because they don't know when they might want to realise their investment.

Instead, savers deposit with the bank, which lends to entrepreneurs.  The bank deposit contract pays interest, even on an early withdrawal.  The bank can do this because the deposit contract also provides that, in the event the deposit is held for the full term, it pays less than the saver would get from lending directly.  The bank subsidises early withdrawers at the expense of late withdrawers, and can do this because it knows that not everyone will be an early withdrawer.  In the model, savers prefer the deposit contract to direct lending, because they are risk averse and it offers less uncertainty in returns.

This is a model of banking where deposits seem to precede loans.  Savers place deposits with the bank, which lends them out.  In fact, there isn't even any money in the model, just goods.  Loans and deposits are loans of goods and deposits of goods.  So it is physically impossible for the bank to make a loan, before it has taken a deposit.

This is not necessarily a problem for the model, but it seems at odds with the story where "loans create deposits".  So I thought it would be interesting to construct a version of DD that looked a little like something a circuit theorist might identify with.  There's no great message here - I just like thinking about the connection between different ideas.

So, as with DD we imagine there is a single good that can be consumed or used in production.  Entrepreneurs have productive projects that take two periods to generate a non-zero return.

Both savers and entrepreneurs open accounts with the bank.  The account balances all start at zero.  The bank agrees to provide the entrepreneurs with overdraft credit.  Overdrafts must be repaid after two periods with interest at 6.25% per period (simple interest, so 12.5% in total).  The bank may require early repayment, but no interest is then payable.

The bank pays interest on positive balances at 4% per period (again simple interest, with no compounding).  All interest is paid simply by debiting and crediting the appropriate accounts.

There is no provision for positive balances to be "withdrawn".  They can only be used for payments.  However, the bank undertakes to try and maintain the real value of such deposit balances, by targeting the dollar price of goods.  (We might then think of this bank as a whole banking system, with the central bank trying to maintain price stability by influencing the volume of lending).

Having got their credit agreed, the entrepreneurs then buy goods from the savers for $100.  This involves the entrepreneurs instructing the bank to debit $100 from their accounts and credit it to the accounts of the savers.  The entrepreneurs, as a group, then has a negative balance of $100 on their accounts (they are in overdraft) and the savers, as a group, have positive balances of $100.

In period 1, the bank credits the accounts of all savers at 4%, so total deposit balances are $104.   

Now, savers want to realise half their savings ($52 in total).  They can only do this through buying goods from entrepreneurs.  To maintain the value of the dollar, the bank must create demand for dollars (and prompt supply of goods).  It does this by calling in $52 of the entrepreneurs' overdraft.  Entrepreneurs terminate 52% of their projects and sell the goods they were using to savers.  Appropriate debits and credits reduce both savers' and entrepreneurs' balances by $52.  Deposits are now $52 and loans (overdrafts) are $48.

In period 2, entrepreneurs' investments are realised.  The bank credits a further 4% interest to the remaining balance of savers accounts taking them to $54.  It debits 12.5% interest from the remaining overdraft balances of $48, taking these also to $54.

Entrepreneurs sell goods to savers for $54.  The bank makes the appropriate debits and credits, leaving all balances at zero.

By arranging things this way, the bank has provided savers with a certain return of 4%, regardless of when they want their money, rather than an uncertain return of either 0% or 6.25%.

DD use their model to consider bank runs.  We can do the same here.  The more savers try to realise their savings early, the more the bank has to call loans to maintain the value of the deposits.  This reduces returns to those who are saving for the full term, eventually to the point that they lose their entire investment.  There is therefore an incentive not to be the last one holding deposits.

However, in this model this run is more in the nature of a run on the currency, not quite what DD is concerned with.  To look at a run on an individual bank here, we would need to consider a model with more than one discrete banking entity.