Kaldor on Endogenous Money

I recently re-read Nicholas Kaldor's article "The New Monetarism" from 1970.  This contained an early statement of the principle that money should be seen as endogenous, in response to Friedman and his followers, who appealed to the idea of an exogenous money supply.  Kaldor writes "The explanation ... for all the empirical findings on the 'stable money function' is that the 'money supply' is 'endogenous' not 'exogenous'."

Two points strike me from this paper:

The first point is that, for Kaldor, the question over the exogeneity or endogeneity of money is all about the causal relationship between money and nominal GDP.  The new monetarists that were the subject of the article (we'd probably call them old monetarists now) argued that there was a strong causal direction from changes in the money supply to changes in nominal GDP, with the latter manifesting itself purely as changes in the price level in the long run.

Endogenous money in this context is a rejection of that causal direction.  Money being endogenous means that it is changes in nominal GDP that cause changes in money or, alternatively, that changes in both are caused by some other factor.  This is interesting because nowadays it seems to be quite common to use the term endogenous money to simply talk about the idea that 'loans create deposits', even in the context of models where the deposits so created have a strong casual link  to nominal GDP.  This appears to me to be almost the opposite of what endogenous money was originally about.

Secondly, Kaldor's analysis is based on seeing money for its function and what it does, rather than identifying a money supply with a particular asset class.  As long as policy works to accommodate the demand for money, we might expect to see a perpetuation in the use of a particular medium - bank deposits, say - as the primary way of conducting exchange.  But we would be wrong to conclude that bank deposits and money are one and the same.  That they appear the same is only because it is convenient for them to function that way and because it has been allowed to happen.  But any stress on that relationship will simply mean that bank deposits will no longer function as money in the same way[1].  The practice of settling accounts will adapt, so that we may need to revise our view of what money is.  Money cannot be captured in the concept of a "money supply".

UPDATE:  Since posting this I noticed that John Cochrane has just done a post on Greece, including a comment on the use there of the rolling of post-dated cheques to deal with business to business payments.  Cochrane writes "Money is created when needed, apparently."  I'm not sure whether the apparently is intended to be ironic.

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[1] There's an interesting comparison to be made here with the Lucas Critique.

Banks and Liquidity Preference

Consider a simple economy with three sectors: households, firms and government.  There are two assets: government bills and loans to firms.  Firms can hold bills, but we'll assume their holdings are generally zero.  All loans to firms are made by households.  The national balance sheet looks like this.

	Households	Firms	Government
Loans	L	- L
Bills	B		- B

(To avoid needing to include money as a separate asset class, we'll assume here that the bills are used as the medium of exchange.  This could be through direct physical exchange.  Alternatively, all bills could be held in individual accounts in a central registry with households and firms making payments by instructing the registry to transfer ownership interests.)

For simplicity, we will assume that firms wish to invest as much as they can and are limited only by the amount that households are prepared to lend.  Household behaviour can then be split into two decisions that are strictly independent. 

First, they make a decision that determines the total addition to their holdings of financial assets.  It is usual to think of this as being a decision about how much they spend on consumption, given their income expectation and other factors.  The accumulation of financial assets - saving - is the residual.

Secondly, they make a decision which determines the split between making additional loans and acquiring additional bills.  It will be useful to think of this as being a decision about the amount of additional loans they want to make.  We can imagine that bills are riskless and households have no limits on how many they hold, but that loans to firms carry default risk and households wish to manage their exposure.

It is crucial to recognise that these are two separate decisions.  Households can decide to spend less on consumption, without changing their decision about how much to lend to firms.  Likewise, they can decide to lend more to firms, without changing their decision about how much to consume.  Putting this latter point another way, a household decision to save more is not a pre-condition of an increase in loans to firms.

Each decision affects expenditure independently.  We have assumed that firms will spend all they can borrow, so the decision to lend affects expenditure directly.  As we have noted, this is not dependent on a decision by households to consume less.  So although, for the economy as a whole, investment must equal income less consumption, both investment and consumption are separately determined, making income the thing that needs to adjust.

If we were instead to assume that there was just one decision and the amount to be loaned to firms had to be exactly equal to the amount saved, then we would have the sort of situation conjured up by loanable funds imagery.  We could imagine that the amount to be loaned was determined by the amount households decided to save.  This might be the case in a simple barter model where saving could only be undertaken by retaining real goods

How do banks fit into this picture?  The answer is all to do with the lending decision and not the saving decision.  If the amount to be loaned to firms is still decided entirely by households, then banks are mere conduits - what people often mean when they question whether banks are just intermediaries.  On the other hand, if part or all of that decision falls to banks, then they immediately become an active part of the process.

We can illustrate this by adding banks into our balance sheet in two different ways.  In the first (shown below), banks hold the loans and households hold deposits at the bank instead. 

	Households	Firms	Banks	Government
Deposits	D		- D
Loans		- L	L
Bills	B			-  B

We need to make two further assumptions here.

a) that households decide between bills and deposits in the same way that they did between bills and loans; and

b) that banks accept any amounts deposited, which they then automatically lend out.

In this case, we can see that the lending decision still rests entirely with households, notwithstanding that banks are making the actual loans.  This is a true banks-as-simple-intermediaries model.

Alternatively, we might add in banks as shown below:

	Households	Firms	Banks	Government
Deposits	D		- D
Loans		- L	L
Bills			B	- B

In this scenario, a decision by households to increase holdings of deposits is the same as a decision to save.  There is no way for households to do one and not the other.  Rather than making two separate decisions, households now only get to make one.  The split between loans and bills - essentially the decision to lend - is in the hands of banks.  So, now, bank behaviour is crucial.

In reality, we are somewhere between these  two situations.  Bank decisions on lending are important, but household decisions matter too.  A major factor in the financial crisis was non-banks (households, here) trying to switch from bank debt (deposits) to government securities (bills).

Once we start to consider separate objectives for households and banks, we need to start bringing interest rates into the picture (or rather interest rate differentials).

We can see here the critical importance of portfolio decisions and how they are made.  This basic idea is really what liquidity preference is about in Keynesian and post-Keynesian economics.  Liquidity preference is perhaps an unfortunate term because, although liquidity is an important element, we need to look at aspects of portfolio preference that go beyond that.

SFC / DSGE Hybrid

I did a little exercise recently trying to blend DSGE models with stock-flow consistent (SFC) models.  The basic idea was to take the accounting framework and policy set-up of an SFC model but use the behavioural assumptions of a DSGE model.  This is not because I think the behavioural assumptions of DSGE are better (I certainly don't); I'm just interested in seeing how it affects the results.

This post describes a simple hybrid model based on the SFC model called Model PC in Chapter 4 of Godley & Lavoie.  This consists of three sectors: households, the government and the central bank, and two assets: interest-bearing bonds and non-interest bearing money.  The flow of funds matrix for this model is shown below (for nominal amounts, with production shown as a separate column).  All rows and columns sum to zero.

	Households	Government	Central Bank	Production
Consumption	-C			C
Government spending		-G		G
Income	Y			-Y
Taxes	-T	T
Bond interest	R.Bh	-R.B	R.Bc
CB profit		CP	-CP
Change in bonds	-ΔBh	ΔB	-ΔBc
Change in money	-ΔH		ΔH

As with G&L, fiscal policy consists of setting the level of real government expenditure and the tax rate applied to GDP.  Monetary policy consists of setting the interest rate which applies to bonds.  The change in household wealth depends on household saving (which must be equal to the government deficit).

Household behavioural assumptions are needed to determine two things: a) how much households save; and b) how much of their savings they want to hold as money rather than bonds.  All of the other flows then follow, given the policy assumptions and the accounting constraints.

This is where I depart from G&L.  Rather than using the usual SFC behavioural assumptions, what we want to do here is use functions  that are consistent with what appears in a typical New Keynesian DSGE model.  So the starting point will be to assume that households maximise expected utility over time where utility for period t is given by:

                β^t  [ ln (c_t) + ψ ln ( H_t / p_t ) ]

That is utility depends on real consumption in the period and money holdings in the period.  from this we can derive functions for household expenditure and portfolio allocation.

The DSGE expenditure function depends critically on the expected real interest rate, which is derived from the nominal interest rate and expected inflation.  This is not a feature of Model PC in G&L, but if this exercise is to be at all meaningful, we need to have an inflation mechanism here.  So I've used the standard New Keynesian Phillips curve, which sets current inflation as a function of expected future inflation and current output.

A typical DSGE model will also include a central bank reaction function to set the nominal interest rate.  I can do this in the model (and might look at this a subsequent post) but here I want to take the nominal interest rate as fixed. 

With the interest rate fixed, I then wanted to look at the impact of a 5% permanent real increase in government spending.  The results are shown below (showing deviations from baseline values):

The first chart shows the increase in nominal GDP (relative to baseline).  This actually looks pretty similar to what you might expect from a regular SFC model, with a slow progression to a higher steady state.

Looking at what is going on behind this, however, we can see that the increase in real GDP is temporary, just as there is a temporary rise in inflation.  The fact that NGDP continues to rise after the first period therefore purely reflects the fact that the price level is rising.  As with a typical SFC model, the initial impact on real consumption is that it increases.  However, unlike in a typical SFC model, rather than then continuing to rise, real consumption here falls back to lower than its original level.

This is entirely a result of the assumption about consumer spending.  In particular, the DSGE assumption about infinite horizons means that the changing balance of household assets has no feedback effect on spending, something that is key to typical stock-flow dynamics.

Interestingly, the balance of household assets is doing the opposite here to what it would do in a SFC model.  Rather than a slow accumulation of assets, the real level of bonds falls to a new lower level.  This decline is mainly due to higher inflation eroding the real value of bonds (although the nominal level of bonds also falls slightly)

It is important to note that this fall in the real value of bonds must happen if the system is to arrive at a new steady state.  In steady state, the government budget must be balanced.  With a permanent increase in spending and taxes pegged by the natural level of output, this requires that the real interest service cost must fall.  As the real interest rate is dictated here by the natural rate, the thing that has to give is the real level of bonds.

Model Specification

I have consolidated the government and central bank here for simplicity.  It makes no difference to the results.

Output is the sum of consumption and government spending.

(1)          y_t = c_t + g_t

The behavioural equations for consumption expenditure and money holdings are derived from the household utility function and budget constraint.

(2)          c_t = E[c_t+1] / ( β ( 1 + E[r_t] ) )

(3)          H_t = ψ [ 1 + R_t ( 1 - τ_t ) ] / [R_t ( 1 - τ_t ) ] . c_t . p_t

The level of bonds held by households is given by the consolidated government budget constraint.

(4)          Bh_t = Bh_t-1 [ 1+ R_t ( 1 - τ_t ) ] + ( g_t - τ_t . y_t ) . p_t - ( H_t - H_t-1 )

Inflation is based on expected future inflation and a measure of the output gap.  The price level is derived from this.

(5)          π_t = ( E[π_t+1] )^β . ψ y_t^ε

(6)         p_t = p_t-1 . π_t

The real interest rate is based on the nominal interest rate and inflation.

(7)          r_t = [ 1 + R_t ( 1 - τ_t ) ] / π_t - 1

Expected values are set to be equal to actual outcomes, with the exception of the period when government spending is first changed.  The equations allow solutions where the real value of household assets tends to infinity (either positive or negative).   The solution with infinite negative household assets is excluded on a no Ponzi condition.  The solution within infinite household assets is excluded as it not consistent with the utility maximisation assumption.

Variables

Name	Description
c	Consumption expenditure
g	Government expenditure
p	Price level
r	Real interest rate
y	Real GDP
Bh	Household bond holdings
H	Household money holdings
R	Nominal interest rate on bonds
π	Inflation
τ	Tax rate

 

Solution Technique

The first stage of solution is finding the steady state real values.  Each period is then solved sequentially using the steady state values as expected values for everything except inflation.  Each period is then solved again using the previous results for expected values (apart from inflation).  In each case expected inflation is estimated using a version of the fiscal theory of the price level, where expected future surpluses are discounted at the expected future effective rate on government debt and compared with the nominal value outstanding.  The whole process is repeated until the expectation errors on all variables is sufficiently small.