Reflections on Monetary Economics

There is an interesting issue that crops up again and again in discussions about the relationship between debt and GDP. This is the distinction between debt incurred for real expenditure and debt incurred for purchase of existing assets (whether physical or financial).

On the face of it, the immediate use of new borrowing should make a big difference since it's obvious that the former implies actual GDP spending and the latter does not. However, if we consider the full stock-flow dynamics, the distinction is less clear.

To look at this we can consider a consumption function, where household spending (C) is a function of disposable income (YD), new borrowing (ΔL) and lagged net wealth (V_-1).

C = α₁ . YD + α₂ . ΔL + α₃ . V_-1 0 ≤ α₂ ≤ 1

The proportion (α₂) of new borrowing used for current spending clearly has an immediate impact. However, a proper accounting framework will require that if any new debt is not spent currently, then net wealth will be correspondingly higher. In the next period, spending will be greater as a result and will continue to be greater until any difference in net wealth has been eroded. In its simplest form, the cumulative effect on income will be the same.

The chart below illustrates the impact for a simple model. (A specification of this model is given at the end of this post.). The chart shows the cumulative effect on income for a one-off permanent increase in the absolute level of loans.

Cumulative GDP (deviation from base-line)

The results in the graph above are based on the assumption that the asset allocation of borrowed funds matches that for net wealth. More precisely, it assumes that if households invest 30% of their net wealth in deposits, then they will also invest 30% of any money borrowed for investment purposes into deposits. (This is the assumption used in Godley and Lavoie*). However, in general, people do not borrow money to invest in bank deposits. The people who hold bank deposits are not borrowers, but people with net wealth. Where money is borrowed for financial investment, this is much more likely to be for the acquisition of housing or marketable securities. If we reflect this in our asset allocation assumptions, the results of our simple model show that, in the long-run, debt for asset purchase actually has a greater impact than debt for spending. This is shown below:

Cumulative GDP (deviation from base-line)

This result arises because the debt creates a permanent change in the structure of investors' portfolios. The greater concentration of demand into variable price assets inflates values giving a more sustained wealth effect.

One way to think about this counter-intuitive result is as follows. In the simple model, with government spending and tax rates fixed, any change in the level of government debt held by the private sector can only come about via differences in national income, since that is the only free variable to affect the new issuance of bonds. The long-run impact therefore ultimately depends, not on anything that happens currently, but rather on the willingness of the private sector to hold government debt. In the latter scenario, the decision of households to invest more into marketable securities (including government bonds) has the perverse effect of reducing overall private sector bondholdings, because of the impact of the accounting constraints on banks' balance sheets.

In the real world, there are plenty of factors which could lead to a reverse effect. For a start, once growth is factored in, the front-loaded impact of borrowing for spending means that it may permanently push income ahead of the curve of the static steady state. It is also worth noting that the incorporation of yields into the portfolio preference functions will affect the results.

The point I wish to make is simply that the impact of the purpose of debt is a much more complex issue than is at first apparent, and that careful consideration of the full stock-flow dynamics is necessary to really bring this out.

Model Specification

The model is based on three sectors: households, banks and government. There are four asset classes: Bank deposits, government bonds, household loans and real assets (say, housing). The last is represented by a quantity multiplied by a price index. This is shown in the balance sheet matrix below:

	Households	Banks	Government	Net
Deposits	D	-D		0
Bonds	Bh	Bb	-B	0
Loans	-L	L		0
Real Assets	k.p			k.p
Net	B + k.p	0	-B	k.p

Banks are assumed to have nil net worth. This implies that household net worth must equate to total private sector bondholdings plus the value of real capital.

Variable	Definition
B	Government bonds
Bb	Bonds held by banks
Bh	Bonds held by households
C	Consumer spending
G	Government spending
L	Household loans
D	Deposits
V	Household net wealth
Y	GDP
YD	Household disposable income
k	Physical assets
p	Price index of physical assets

Greek letters are parameters.

GDP is consumer spending plus government spending

Y = C + G

Household income is the after-tax share of GDP

YD = ( 1 - τ ) . Y

The household budget constraint determines the change in money.

ΔD = YD - C + ΔL - ΔBh

Household net wealth is assets less liabilities

V = D + Bh + p . k - L

Consumer spending is based on disposable income, new borrowing and lagged net wealth.

C = α₁ . YD + α₂ . ΔL + α₃ . V_-1

Households allocate their gross asset holdings between bonds, real capital and deposits in constant ratios.

Bh = θ_b . ( V + L )

p . k = θ_k . ( V + L )

As k is constant, this latter equation is used to determine p.

The assumption about portfolio allocation is modified in the alternative scenario. New spending loans are added back into net assets and allocated as before, but the non-spending loans are assumed to be fully invested in either bonds or real assets, but not deposits. The portfolio equations are replaced with the following:

Bh = θ_b . [ V + L₀ + α₂ . ( L - L₀ ) ] + θ_b / ( θ_k + θ_b ) . ( 1 - α₂ ) . ( L - L₀ )

p . k = θ_k . [ V + L₀ + α₂ . ( L - L₀ ) ] + θ_k / ( θ_k + θ_b ) . ( 1 - α₂ ) . ( L - L₀ )

where L₀ is the outstanding loan balance at the start of the simulation. This is treated as before (and assumed to be invested across all assets) to keep the simulations comparable and avoid having to change any parameters or opening stocks values.

Parameter values and opening stock values are given below: