Friday, 11 April 2014

Debt Sustainability: we don't need wrong arithmetic to make it unpleasant

 Figure 1

The Observatório sobre Crises e Alternativas (OSCA), affiliated with the University of Coimbra, published yesterday an interesting document on the sustainability of Portuguese debt. The authors conclude that debt restructuring is unavoidable, while suggesting a possible scale for this operation. This post questions some of the analysis in the document and its conclusions.
The document gauges debt sustainability from the common statement of the government dynamic budget constraint:

Δbt = -dt +(ig) bt-1

where bt stands for the debt/GDP stock in year t, dt the primary surplus in the same year, i the interest rate on government bonds and g the growth rate of nominal GDP.
Using this equation, the authors simulate three scenarios:
  • A debt sustainability scenario, i.e. the conditions under which Δ bt < 0
  • The scenario according to the Fiscal Compact whereby the debt/ GDP ratio has to fall every year by 5% of the difference between the current ratio and 60% i.e. Δ bt < 0.05(bt-1 - 0.6)
  • And a similar scenario but requiring the annual correction of 1/20th of the difference between today’s bt = 126.6% and 60%, which they refer to as the President’s interpretation of the Fiscal Compact: Δ bt < 0.05
The document defends the inevitability of debt restructuring essentially by reduction ad absurdum. In the summary graph of the document (Figure 1 here) the authors purport to show that “in the last ten years the conditions of debt sustainability or fulfillment of the Fiscal compact have never been verified” (p. 6).

With d = 1.8% and g = 2.6%, the debt/ GDP ratio would approximately stabilize at current levels, so the authors conclude that debt sustainability would only apply for higher levels of both variables (the red rectangle in the northeast). The dots represent the combinations of d and g over the last decade, and since these never overlap with the red area, the constraints for enforcing debt sustainability are unreasonable. The conditions to comply with the Fiscal Compact are even more stringent.

But wait, if we try solving the equation above we actually get a straight line, rather than a point. It is obvious that d and g are substitutes and that, for instance, debt sustainability may still be achievable with primary deficits if higher nominal growth compensates for that. Figure 2 represents the correct version of this exercise and highlights the areas of sustainability missed by the OSCA document.

Figure 2

 So, contrary to the OSCA document, debt sustainability was achieved during the past decade, namely before the crisis. In fact, there is a second mistake in the analysis, as the authors use the implicit interest rate on government debt (i.e. a measure of the past cost of credit) to make a judgment about future sustainability. It is idle to remember here the discussions about the mythical 7% threshold that would prevent us from rolling over our past debt stock.

Currently, the implicit rate hovers at about 4% and the authors used this value in their analysis. With 1% inflation this translates into a 3% real interest rate, which is perhaps an optimistic view of our future cost of credit. Indeed, from all the variables in the equation i must be the most volatile. It is well known that sovereign debt markets can have multiple equilibria, and that a change in sentiment can turn what used to be sustainable into a debt problem. Consequently, long-term projections of debt sustainability must be taken with many grains of salt – especially if assuming constant interest rates (i). Or, putting it another way, the Euro crisis reminded us of the need to consolidate during periods of growth and avoid pro-cyclical fiscal policies.
The authors of the OSCA document are right in pointing that under constant assumptions about growth (g) and interest rates (i), sustainability will require painful and long consolidation through primary surpluses. They are also probably correct in arguing that consolidation (d) may harm growth (g) and become counterproductive for sustainability, at least in a midst of a deep recession. And it is finally unclear how the country can climb down the current debt level without some sort of restructuring, in the absence of higher inflation.
But markets react both ways, as the recent decrease of the yields on Portuguese debt is there to show (10-year bonds were paying 6.3% 6 months ago and 3.8% now). This is not the occasion to discuss whether these yields are more driven by the consolidation effort of the Portuguese government or the liquidity policies of the ECB, but at a time when the government is able to rollover debt at quite low rates (and even pre-finance some of next year’s needs), it is questionable that restructuring is now more urgent than it was a year or two ago.

Finally, the OSCA document proposes a ‘possible scenario’ for restructuring – rather than renegotiating an extension of maturities, the authors suggest a writedown of close to half of the current debt stock and a halving of the interest rate on the remainder to 2% nominal. This would amount to more than 75% haircut of current debt claims (similar to the Argentinean 2002 default). Given that a large share of Portuguese debt is currently owned by the official sector, it would be interesting to hear how the OSCA proposes to achieve such figures while avoiding immediate political aggravation and the future costs from a default of this magnitude. I, for one, think the authors stopped where they should have started the document.


  1. I guess there is a mistake in the equation. Or in the definition of the variables.

    Either dt is the primary deficit on year t or it should enter the equation with a negative sign.

    1. Thanks for spotting the typo - now corrected in the formula.

  2. This comment has been removed by the author.

  3. Dear Rui Esteves,

    Thank you for the correction of our mistake. We will replace the graph and the reading of the graph. Unfortunately the conclusions are not much different. Only in 2007 GDP growth and primary surplus are in the sustainability area. In your graph the nominal GDP growth is at 1,8 (it should be 2,6%) and primary surplus is at 2,6 (it should be 1,8). If you correct this you will find that 2007 is the only of the last 10 years in the sustainability area. Of course if you travel further back in time, as you did, other dots are in the sustainability area.

    Best regards

    José Caldas

    1. Dear José Caldas,

      thanks, but it was only a labeling typo - the values in Figure 2 are still correct. The choice of horizon is always a tricky question - I am not sure why the last 10 years are a better benchmark than the last 20 (or since our joining the Euro in 1999), especially since 8 of the last 10 are influenced by the global financial crisis and subsequent 'great recession' and the Euro crisis. My two main points were 1. That you were overstating the case for debt unsustainability by focusing on a period when g and d were both influenced by the recession and 2. That debt sustainability must be estimated in a forward-looking manner rather than using past implicit interest rates. But this leads me to agree with you on doubting the feasibility of the assumptions that underlie some political statements about this issue.

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  5. Evaluating debt sustainability consists in, roughly put, analyzing whether fiscal policy brings the debt trajectory upwards or downwards. If it is downwards — and may indeed require a primary surplus, r < g, etc. —, it is sustainable. Now, one may argue whether achieving primary surpluses is politically doable, but from an economic perspective, it certainly is for Portugal.

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