More on the Inter-Generational Implications of National Debt

There's been some more stuff recently on the role of public debt in inter-generational transfer, including from Nick Rowe, Roger Farmer and Simon Wren-Lewis.  It is remarkable that this topic causes so much disagreement, but in my view it is a good issue to discuss because it highlights the important role of asset balances.

I think one of the things that causes so much confusion here is that this inter-generational transfer cannot happen without the willing participation of the private sector.  Some people object to the notion on the basis that they cannot see how those alive today can be bound by what happened in the past.  But actually what is happening here is to a very great extent driven by the choices made by private individuals.

For a start, government debt can only arise in the first place if people wish to save.  It is quite correct that we cannot take resources from the future.  Some people can have more today, but only if others are willing to go without today, in the anticipation of more tomorrow.

Secondly, there is only ever a question of a burden on future generations if and when people wish to dissave, i.e. to spend out of their savings.  If people are prepared to hold on to public debt forever, then there is no great consequence.  (This is what happens in the Ricardian equivalence world, where planning over the infinite horizon means spending only income and not principal, from investments).

What gives rise to the potential burden is the possibility that at some point people will wish to reduce their bondholdings, by spending out of their savings.  If they do so in some future period, then real resources will have to be found for them in that period.  Maybe this can come from persuading others to save, but maybe it has to come by taxing them.  This is when the inter-generational transfer bites.

So the transfer arises from private decisions to save and dissave.  These are being made the whole time.  There is a continual turnover of some people accumulating financial assets and others running theirs down.  In general people do not want to spend in any period the exact amount they earn in that period.  All these plans ultimately have to tie up, which means that in some periods there will be increased competition for available resources and in others there will be less.  If you are unlucky enough to be living at a time when there is increased competition for resources then you will be squeezed and they may have to be through higher taxation.

Recognising the key role of private decisions in this process is important, because it helps us see that, whilst public debt is part of the mechanism through which the inter-generational transfer happens, it is more of a symptom than a cause.

(This idea of public debt as a symptom is one of the things I hoped to bring out in my previous two posts on the Diamond model here and  here.)

National Debt in a SFC Version of a Neoclassical Growth Model

In my last post, I set out the details of a Stock-Flow Consistent (SFC) model designed to capture the structure of the neo-classical model used by Diamond in his paper National Debit in a Neoclassical Growth Model.  Despite having an apparently very different format, this model produces identical results to those of Diamond, given suitable parameter values.

Part of the purpose of doing this was to examine some of the conclusions in Diamond, in particular those relating to the relevance of national debt.  One of Diamond's key results is that a higher level of national debt implies a lower level of output.  The intuition behind this is fairly simple.  For a given level of income, it is assumed households wish to hold a certain value of savings.  Savings are invested in either real capital or public debt.  So the higher the level of the public debt to GDP ratio, the lower the level of funds invested in real capital (relative to GDP).  This implies lower labour productivity and therefore a lower level of overall output.

In as far as it goes, I think there is some kind of reasonable basis to this argument.  However, the issue I want to look at is whether it makes sense to think about the level of debt as a policy variable.  In fact, governments do not set the level of public debt.  They set levels of spending and tax rates.  It may be that they do so hoping to achieve a particular level of debt, but the relationship between these things is not straightforward.  To illustrate this, I have used this model to run the following experiment:

I have started from a position of steady state growth, with an existing level of public debt and no government expenditure.  As in Diamond, interest on the debt is serviced by lump sum taxes and issuing new debt, to keep the debt / GDP ratio constant.  In addition to the tax rate, the nominal interest rate is a policy instrument.  I then shock with an unexpected increase in the real value of taxes by 10%, keeping the nominal interest rate constant[1].  The results are shown below.

 

 

 

As already mentioned, although these results are derived from an SFC model, they are completely consistent with Diamond's neoclassical model.  Amongst other things they are based on forward looking expectations and full wage and price flexibility.  The only period for which expectations are not realised is the period in which the tax rate changes.

The first thing to notice is that the tax increase results in both a fall in GDP and a fall in inflation.  Both expected and unexpected inflation are shown (actual inflation being the sum of the two).  In addition to the permanent reduction in expected inflation, there is a unexpected one-off drop in the price level in the period of change. 

This drop in the price level (which is necessary to clear the market in that period) is key to what is happening.  Because the existing stock of government bonds is given in nominal terms, this deflation sharply increases the real value of public debt.  We can therefore see how this fits with Diamond's result.  The fall in GDP comes about because productive capital is crowded out by higher public debt, reducing labour productivity.  But this resulted from an increase in taxes.  So a policy measure which might appear to be required to cut public debt actually has the reverse effect.

To conform to Diamond, I have had to make various assumptions, including full price flexibility.  But introducing price stickiness does not improve the situation.  We just get a fall in employment whilst prices are adjusting.  I should also point out that I have limited the analysis to the closed economy version.  Considering an open economy with external debt raises some additional issues.

However, I think the general point here is this.  The national debt is not a policy tool, nor does it make for a very good target variable.  Attempts to reduce it are prone to backfire.  This point may be clear to those familiar with SFC modelling, but it is not dependent on the characteristic assumptions of those models.  It is also implicit in neoclassical models such as Diamond's.

Parameter Values

The equation listing and description of variables is given in the previous post.  The parameter values used for the simulations were as set out below.  Some of these were chosen specifically to ensure consistency with Diamond.

α1	0.60	β1	-1.39	ψ1	-0.92	φ1	0.66
α2	1.00	β2	1.00	ψ2	1.33	φ2	5.00
α3	1.00	β3	-1.00	ψ3	-0.33	ε1	1.00
λ	1.33					ε2	1.00

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[1] Because all the debt is single period, this model actually behaves in neo-Fisherite manner, in that any change to the nominal interest rate simply changes the inflation rate, with no real effects.