What is “long-term debt sustainability” or “kestävyysvaje” all about?


What’s at stake?

In Finland, when the media and various special interest groups debate about the current economic and fiscal policy stance of the government, one cannot avoid the term sustainability deficit or “kestävyysvaje”. In economic policy circles it is also known as the S2-indicator. Given the heated political discussion on fiscal stance, I thought it might be a good idea to try to explain it in ‘layman’s terms’ what the indicator is all about. So dear media and politicians, let’s have a go.

The idea of fiscal policy sustainability is mostly defined around the following abstraction: we say that a policy stance is sustainable if the present value (sum of discounted cash flows) of future primary balances (budgetary surplus/deficit without interest expenses) is equal to the current level of debt.  So sustainability is an intertemporal budgetary constraint for the government. Then we can define S2 or “kestävyysvaje” in the following way: S2 is the immediate and permanent one off fiscal adjustment that would ensure that the intertemporal constraint is met.

Debt dynamics (accounting identity)

By definition, we can express the change in annual debt by


The equation tells us that the annual change in government debt is the sum of : interest expenses on the current debt stock and the negative primary balance. This is an accounting identity and true by definition.

..and S2 derived from it

After some lengthy calculations, assuming that the interest rate is constant, we get the following expression for the S2-indicator

S2=rD_0-PB_0 +r\sum_{i=1}^{\infty}\frac{\Delta A_i}{(1+r)^i}

where the third term represents the ageing related costs according to the decomposition

\Delta PB_i=PB_i-PB_0=S2-\Delta A_i

The previous equations tell us that the “kestävyysvaje” is sum of three terms : 1) the interest rate times the current debt 2) primary deficit 3) present value of age related costs times the interest rate.

This all tells us that that S2 depends crucially on the initial debt and initial deficit and projected age related costs. Of course the expected rate of interest matters a great deal as well.

Where are we now?

European Commission currently sees that the “kestävyysvaje” for Finland is some 3,2 % of GDP at market prices, so some 6-7 billion euros. This would mean drastic budgetary cuts, if implemented one off. However, currently it is perceived that at least to some extent structural reforms can bring down the figure a bit.

Structural reforms lower the present value of ageing costs

As can be seen from the formulas above, to bring down the kestävyysvaje, one could implement structural reforms in order to bring down the present value of ageing costs


In my mind, the S2 is an indicator on where we stand, it should not be a strict and rigid policy rule that should be followed religiously. Given that there is more or less a  consensus on the figures across research institutions , and  COM, BoF, MoF, we should see it as a strong indicator that the current level of spending and debt is unsustainable with respect to the projected ageing related costs. Of course there  is a lot of uncertainty and sensitivity analysis is important.

What about net debt and the definition of general government figures?

Put aside the previous figurative considerations, I think we should be more worried of the fact that “TyEL” is included in the general government deficit figures. In practice I find it difficult to imagine that the government would confiscate the private pension system assets and liabilities. So if there is too much pessimism and uncertainty in the determination of kestävyysvaje, I think there is too much optimism that the pension system would provide budgetary revenues to the annual government budget.

On net versus gross debt: one should also consider whether the government could shrink its balance sheet by selling financial assets. This would bring down the kestävyysvaje, as S2 is determined on a gross debt basis. One could bring down the debt from current 102 bn to some 75 billion or so by considering selling the liquid financial assets. On the other hand, leveraged government investment activity might be rational, iff the risk adjusted returns on financial assets are at least large enough to cover the interest expenses on government debt. This is risky business however, and its therefore difficult to say what is the optimal anount of leverage.

Why all the fuss?

“According to the system of national liberty, the sovereign
has only three things to attend to… first, the duty of
protecting the society from the violence and invasion of
other independent societies… secondly, the duty of
protecting … every member of the society from the
injustice or oppression of every other member… and
thirdly, the duty of erecting and maintaining certain public
works and certain public institutions, which it can never be
in the interest of any individual to erect and maintain”
-Adam Smith 1776

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