Monday, 11 April 2016

Why the Inter-temporal Government Budget Constraint Cuts Both Ways



There are some heterodox economists who get very worked up over the notion of the inter-temporal government budget constraint (IGBC).  In my opinion, this is unjustified.  For a couple of reasons.

In the first place, where the constraint does hold, it is in itself little more than an accounting identity and not a limit on policy as we normally understand it.  If there is any kind of non-accounting constraint, it arises for other reasons such as resource constraints or the imposition of other objectives.  Secondly (and I rarely see this mentioned) the IGBC sometimes imposes a strong imperative for the use of active fiscal policy.

The IGBC says that the real discounted value of future primary surpluses is equal to the real value of current outstanding debt (where discounting takes place at the real effective rate of interest on government debt).

With regard to the first point, we can easily see that this condition will hold in a typical SFC model[1].  Such models settle down into a steady state where the real value of debt remains constant, with a primary surplus exactly offsetting the interest charge on outstanding debt.  This is a position which meets the IGBC, so the IGBC must hold for each preceding period as well.

In the typical SFC model, the policy instruments are the level of real government expenditure, the rate of tax and the nominal rate of interest.  The IGBC does not itself limit the choice of these variables.  This is because the models allow for the level of real output and/or the rate of inflation to be determined, with the mix depending on what is assumed about Phillips curve relationships.  Given the policy variables, both of these are relevant for the IGBC.  The level of output determines the tax take and hence the level of primary surpluses.  The level of inflation impacts on the real discount rate.

The upshot of this is that all the IGBC does in this type of model is limit the possible sets of solutions for output and inflation.

The assumptions of different types of model may combine to place more of a constraint on policy.  For a start, if taxes are assumed to be lump sum, then there is no scope for primary surpluses to be determined endogenously.  Even without lump sum taxes, the assumption that real output is supply side determined in the long run (a common, if questionable, assumption) will limit the endogeneity of the tax take.   Additionally, if the model assumptions incorporate a unique natural rate of interest, then it may be that the discount rate used for the IGBC must also be tightly constrained (although this does depend on what is assumed about how monetary policy is conducted).  A typical DSGE model will tend to incorporate these sorts of assumptions and will therefore impose a greater constraint on fiscal policy.

However, this constraint cuts both ways.  The usual message is to say that, given the exogenous output level and natural rate of interest, there is no scope for increased government expenditure now without requiring correspondingly higher taxes later.  But this is not in fact true in all circumstances and, in some cases, expansionary fiscal policy is exactly what is required.

Specifically, we can consider what happens if there is a permanent fall in the natural rate of interest (or at least a fall that everyone expects to be permanent), something that in Keynesian terms we might interpret as an increased propensity to save.  The DSGE response required of the central bank is a reduction in actual interest rates in an attempt to bring these in line with the lower natural rate.

This has consequences within the IGBC.  As the current level of debt is given, then a reduction in the long-term discount rate requires a reduction in future real primary surpluses.  If we assume that long-term  surpluses are to remain the same, then what is required is a short-term period of expansionary fiscal policy.

The IGBC plus the other assumptions of DSGE dictate that something  like this is required.  Monetary policy alone is inadequate.  This raises the question of what happens if the government declines to respond and instead decides to pursue a policy of austerity.  In fact, the only solution in the model [2] involves a period of deflation with the nominal interest rate hitting the zero lower bound.  This gives a period of higher real interest rates which increase the real value of outstanding government debt until it is equal to the future surpluses discounted at the new lower rate.

New Keynesian economists will generally recognise the need for fiscal policy when monetary policy is constrained by the zero lower bound.  They are usually only thinking of scenarios where there are temporary drops in the natural rate of interest that appears in their models.  But there are other possibilities, such as a permanent fall in the natural rate, that monetary policy can never deal with alone even unconstrained by the lower bound.  These situations require a fiscal policy response and the IGBC shows us why.


[1] Not necessarily in growth models which may be dynamically inefficient.
[2] That I can see, at any rate, but I'd be interested if anyone knows differently.

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