The intelligent management of the public finances

Background

Much discussion has surrounded the contention that high public debt levels are associated with low / no economic growth. Specifically,well-publicised research has suggested that if the public debt to GDP ratio exceeds 90% then economic growth will slow down markedly and perhaps come to a standstill. The British government  has eagerly accepted this finding and has used it to justify its debt reduction strategy, which is that cuts to public spending are necessary if the economy is to return to growth. The government has hence proceeded to cut public spending on the promise that the cuts will reduce borrowing and thereby generate economic growth. However, instead of economic growth, the government’s cuts to public spending have coincided with stagnation and recession.  I suspect this is because the spending reductions have been indiscriminate.

The following sets out my view on why indiscriminate cuts to public spending will often increase the public debt ratio.  I also set out my view on why increases in government borrowing can, paradoxically, reduce the public debt ratio. I have used the term “public debt ratio” as shorthand for “debt to GDP ratio”.

Fiscal multipliers

A fiscal multiplier is simply a number that indicates how much additional income the private sector receives when the government increases its spending. For example, if the government increases its spending by £1 B on a project which has a fiscal multiplier of 0.5 then the private sector’s income will increase by £0.5 B (0.5 x £1 B). If the government increases its expenditure by £10 B on a project which has a fiscal multiplier of 1.5 then the private sector’s income will increase by £15 B (1.5 x £10 B).

Public spending and public debt

It can be shown that reducing government borrowing will not always lead to a reduction in the public debt ratio. Whether a reduction in the public debt ratio occurs depends on the value of the fiscal multiplier and the size of the current public debt ratio.  A reduction in government borrowing may actually produce the opposite of what is intended, ie, it will  INCREASE the public debt ratio.

Similarly, an increase in government borrowing does not always lead to an increase in the public debt ratio. Whether an increase in the public debt ratio occurs, again, depends on the value of the fiscal multiplier and the size of the current public debt ratio. An increase in government borrowing may actually DECREASE the public debt ratio.

Relationship between multipliers and the public debt ratio

A government can increase its borrowing whilst simultaneously reducing the public debt ratio by spending the borrowed funds on  projects which have multipliers that exceed the reciprocal of its current public debt ratio. Symbolically,

M  >  Y/D

where M is the project’s multiplier value, Y is current GDP, and D is current debt.

A government that wants to reduce its borrowing and simultaneously reduce the public debt ratio should seek savings from spending projects which have multipliers whose values are below the reciprocal of the current public debt ratio.

M  <  Y/D

 where M is the project’s  multiplier value, Y is current GDP, and D is current public debt

Here is a graph that shows the multiplier cut-off value for a range of public debt ratios.

Image

For example, a country with a debt ratio of 20% will need to find projects to invest in which have fiscal multiplier values of more than 5 if it is to reduce its debt ratio. A country with a debt ratio of 90% need only find projects to invest in which have  fiscal multiplier values of more than 1.11 in order to reduce its debt ratio. Refer to the note below to see the algebraic derivation.

Is the 90% public debt ratio critical?

The following graph responds to the research mentioned at the start of this post. That research purports to show that a 90% public debt ratio is critical to a nation’s growth prospects, This graph shows the effects of different multiplier values on the public debt ratio of a country . The chart is based on a current public debt ratio of 90%, and shows what happens after public debt and public spending is increased by 2% of GDP for a range of multiplier values.

The area enclosed by the lines before they intersect corresponds to a debt ratio > 90%. The area enclosed by the lines after the intersection point corresponds to debt ratios below 90%

Commentary

The graph shows that at low multiplier values, borrowing and spending will indeed increase the public debt ratio.  So at a multiplier value of zero, the post-spend public debt ratio rises from the pre-spend ratio of 90% to a post-spend ratio of 92%.  As the multiplier value increases the public debt ratio falls below 92%. If projects with sufficiently high multiplier values can be found and invested in then the public debt ratio falls below the 90% starting ratio. This happens when the multiplier is higher that the reciprocal of the current (pre-spend) public debt ratio of 90%, The point when this is reached is illustrated in the chart where the two lines cross on the the graph.  In this case, the value of the multiplier can be read from the graph as 1.1 (a more exact value is 1.11).

Summary

At low public debt levels, investment projects with high fiscal multiplier values must be found if increases in the public debt ratio are to be avoided.  Such projects are likely to be harder to find than low multiplier projects.

At higher public debt levels, including the fabled 90% level, investment projects with lower multiplier values are required if the public debt ratio is to be reduced. It is easier to find lower multiplier spending projects than it is to find higher multiplier investment projects.  At a 90% public debt ratio, spending projects with a multiplier of 1.11 (1/0.9) and above are needed to reduce the public debt ratio. At a public debt ratio of 20%, investment projects which have multipliers of 5 or more (1/0.2) are required to reduce the public debt ratio.

Policy implications

Governments that subscribe to the 90% public debt threshold myth  thesis will want to reduce their country’s public debt ratio so that economic growth resumes. They may choose to cut public spending to achieve reductions in the public debt ratio. If they go down the spending cuts route then they should select spending areas and projects to cut which have fiscal multipliers below the critical values shown in the first graph. If they do not select such projects then the spending cuts are likely to increase the public debt ratio – entirely the wrong result.

Most importantly, such governments should also consider increasing expenditure in areas and projects that have multipliers above the critical values. Borrowing to finance such spending will achieve reductions in the public debt ratio and are likely to promote employment opportunities and the well-being of the population.

Conclusion

Even if a 90% public debt ratio threshold exists so that a nation’s economy stagnates, the conclusion is that the government must not reduce spending indiscriminately. Instead, the government should seek out projects with a multiplier value of more than 1.11 to invest in. Borrowing and spending on these projects will simultaneously stimulate economic growth and reduce the public debt ratio. At the same time, the government should be looking to reduce existing spending on projects with low multiplier values. Such cuts will help to reduce the public debt ratio unlike cuts to projects with high multiplier values.

Reducing the public debt ratio is not a simple matter of taking an axe to public spending / borrowing.  This is a primitive  approach which risks doing damage to the economy and the people who depend on it (all of us). Debt reduction is more subtle; it requires the estimation and use of fiscal multipliers to select appropriate areas for spending increases and reductions. Appropriate borrowing and spending decisions can then be made. Failure to use multipliers as hurdle rates for this purpose is likely to result in recession and / or stagnation. The UK  may well be a testament to this.

Note

Current debt ratio  = D / Y  , where D is the public debt and Y is GDP

Change in debt (increased borrowings) = ΔD

Change in GDP = ΔY

New debt ratio = (D + ΔD) / (Y + ΔY) = (D + ΔD) /(Y + MΔD), where M is the multiplier.

For additional borrowing to reduce the current debt ratio we require (D / Y)  >  [ (D+ΔD) / (Y + MΔD) ]

Solving for M yields M > (Y/D)

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5 comments

    • Hi Neil

      Thanks for your comment.

      I have used the fiscal multiplier and the spending multiplier as synonyms. I have had a quick look at your article on the multiplier which I shall digest more fully once time permits. I am always willing to learn!

      My substantive point, that spending cuts are not the only way to reduce the public debt ratio, stands though.

      Kind regards

  1. Reblogged this on To the left of centre and commented:
    This is a topic that I have very interesting. It did seem obvious that trying to simply slash public spending may end up being counterproductive. This post seems to confirm that general view, but I’ll need to read it a bit more carefully to make sure I understand what it is saying and to get a sense of where the number are coming from.


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