The name is absent

To make explicit the IBC and TC expressions we start out from the budget equation for
period t:

dt-1=(st+dt)βt                                                                         (2.1)

where d is the stock of debt at the end of the period, s is the primary surplus, both as a
percentage of GDP, and β is the discount factor. Forwarding equation (2.1) one period,
iterating forward T periods and taking expectations conditional on information at time t
(Et) gives:

Taking finally the iteration to the limit and given convergence of the discounted sum we
get:

dt ⁼Et∑(αtjst+j)⁺limT→∞ Et(αtTdt+T)
j=1

which shows that:

dt ⁼Et∑^∞ (αtjst+j)^⇔limT→∞ Et(αtTdt+T)⁼0
j=1

The right-hand side term in (2.4) is the TC that excludes Ponzi schemes, so that the
discounted value of debt issued infinitely far in the future is zero, and the left term is the
government IBC, which states that outstanding debt is backed by future primary
surpluses. Bohn (1995) has shown that conditions of type (2.4) apply to a wide range of
general equilibrium stochastic models, providing therefore a rather general test for fiscal
sustainability.

A key characteristic of (2.4) is that, in a general equilibrium stochastic setting, the
discount rate α depends on the risky rate of return, which in turn depends on the
intertemporal marginal rate of substitution of consumers (Bohn, 1995). This means that
we should expect, in general, a non-zero correlation¹ between α and fiscal variables s and
d, and implies therefore that the factorization of expression (2.4) as discounted values of
expected fiscal terms is generally incorrect. This complicates the empirical testing of
fiscal sustainability.

Testing Sustainability

The most common empirical approach in the literature to test fiscal policy sustainability
is based on the analysis of the time series properties of fiscal data. Influential papers in
this stream of the literature are Hamilton and Flavin (1986), Trehan and Walsh (1988,
1991) and Quintos (1995).

¹      In particular, all three may depend on aggregate output.

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