Advance warning: This post will only be of interest to those who have read the DeLong and Summers paper.

As has been referenced on this blog a number of times, the recent paper by Brad DeLong and Larry Summers has had a significant impact on the debate over optimal fiscal adjustment in a depressed economy.    Although the authors themselves note that the balance of arguments may be quite different in a non-creditworthy economy, the paper is still important to our debate (see also here and here).   

The key innovation in the paper is to incorporate the fiscal implications of potential “hysteresis effects.”  Put simply, these effects refer to long-lasting effects on future output – and thus on the future fiscal position – of fiscal adjustment measures today that reduce today’s output.   For example, the loss of a job due to weaker growth this year could have long-lasting fiscal implications if it makes it harder for the person losing their job to gain employment in the future. 

A striking conclusion in the paper is that, under what appear to be a relatively undemanding set of conditions, an expansion of government spending (or alternatively not engaging in some planned expenditure cut) could be self-financing from a long-term fiscal perspective.    Put another way, fiscal expansion could bring about improvement rather than disimprovement in a country’s underlying creditworthiness.  Thus, fiscal adjustment could be self-defeating from a creditworthiness perspective.   Given the influence of their argument, it is important to look closely at the assumptions that underlie this result. 

A key equation in the paper is equation 2.7.  It gives the effect on the fiscal balance in any future year of a one unit increase in government spending today.   (See the paper for all notation and detailed explanations.)  The impact on the budget is:

-(r –g )(1 – ??) + ???.

The first term gives the cost in any future period of today’s increase in government spending.   The assumption is that the government can allow the debt to GDP ratio to rise as a result of the increased spending, but then must pay of enough debt each year to keep the debt to GDP ratio constant at its higher level.   The second term captures the increase in government revenue in the future as a result of the permanently higher output due to hysteresis effects.  The condition for the overall impact to be positive – and thus for the increase in government spending to be self financing is:

r < g + ???/(1 – ??).

For reasons that will become apparent below, it is useful to re-write this equation as:

g > r - ???/(1 – ??).

There are two strong assumptions built into this result.   First, it is assumed that the optimal fiscal policy involves allowing the debt to GDP ratio moving to a permanently higher level.   There is a large literature on this question, which I cannot get into here.   Simon Wren-Lewis has some useful posts (see here and especially here).   I just note here that there is an active debate on whether there the debt to GDP ratio needs to return to some optimal level (and also on the optimal speed of that adjustment to that level).   The answer to that question could have a significant impact on the future fiscal costs of today’s expansion. 

I want to focus here on a second issue.   An implicit assumption is that the hysteresis effects are permanent.   There is the same adverse effect on future output one hundred years from now as there is next year.   This is not plausible.  It seems important to allow for some realistic “decay” in the hysteresis effect over time.   Today’s fiscal actions do lead to a “shadow” on future output; but that shadow is likely to diminish with the passage of time. 

Suppose that this decay rate is a constant ?.   That is, ? percent of the hysteresis effect disappears each year.   If the decay rate is, say, 7 percent, the half-life of the hysteresis effect would be 10 years – still quite long.  

To obtain the future fiscal effects of today’s one unit increase in government spending we have to identify the present value of both the costs and benefits.    Assuming a fixed real interest rate, r, the present discounted value is:

[-(r – g)( 1 – ??)]/r   +  [???][1/(r+?)].

We can then rewrite the condition for the fiscal expansion to be self financing as:

g > r – [???/(1 – ??)][r/(r+?)].

Note that we would obtain the DeLong and Summers condition if ? is zero. 

Allowance for this decay can have a substantial effect on the self-financing condition.  For example, with a real interest rate of 3.5 percent and a decay rate of 7 percent, the second term on the right-hand side of the condition above is just one-third its level with a decay rate of zero.   This would have a significant impact on any self-financing calculation. 

My purpose here is certainly not to detract from the importance of the DeLong and Summers paper.    The paper provides an extremely useful framework for thinking about future fiscal implications of today’s fiscal adjustment efforts.   But the results in the paper on the ease of passing the self-financing condition are stark (if comforting).   But they are based on important implicit assumptions.    This brief note has attempted to highlight some of those assumptions.