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Leverage cycles 35
economy j is denoted as Y p j,t
, then the net present value of future output in real
terms, or the discounted sum of all future income, NPV j,t
is given as:
NPV j,t
=
P
Y j, t+i
(1 + j
) i
i=0
where ρ is some constant discount rate to be specified later. 17 It is convenient to
express the future path of potential output as the product of the current level and
compounded future growth rates. If the growth rate is assumed to be constant at
σ j
, then we have:
i
1+
P
NPV j,t
= Y
j
j, t
i=0 1+ j
In turn, this simplifies to:
P 1
NPV j,t
= Y j, t
j
j
This framework suggests three opportunities to set off a leverage cycle as
debt capacity turns out to be less ample than anticipated when new debt was
accumulated. Because the calculation of debt capacity involves a ratio, the
mistake could be in the numerator (the right level of output at which to start the
path) or the denominator (expected growth or the appropriate discount rate).
Three types of expectation errors are illustrated by Greece, Ireland and Italy.
According to IMF estimates, Greek real GDP was 10% above its potential level by
2008. Since this was not sufficiently recognised at the time (contemporaneous
estimates of potential output were more optimistic), these dynamics opened up
the possibility that borrowers might misinterpret an overstretched economy as a
new standard of sustainable output, and take on excessive debt.
Revisions to the denominator have a more dramatic impact. Ireland is the
advanced economy for which the IMF’s estimate of potential output growth
moved within the widest range. In the mid-1980s, the Irish economy was
expected to expand at a sub 2% pace. By 1998, the estimate of secular growth
had breached 9%. Robust estimates followed for a time, but then the assessment
turned markedly lower, declining by about one percentage point every year
starting in 2000, and bottoming at net contractions in potential output from
2009 to 2011. These sharp swings in growth prospects followed through to even
sharper movements in the nation’s ability to take on debt in real terms through
the extrapolation of current potential output growth estimates in estimating the
present value of future income streams.
17 Assuming a constant discount rate may be giving the game away at the outset. Cochrane (2011) argues
that time variation in the discount rate is critical in understanding asset prices.