Fiscal Insurance and Debt Management in OECD Economies

is given by y_t = θ_t(l — Z_t) and θ_t is a stochastic productivity shock. The resource constraint is
y_t = c_t + g_t with g_t denoting exogenous government expenditure. Model 1 is the case of no capital
accumulation and Model 2 allows for capital. In this latter case we have y_t = θ_tk_t-1(l — l_t)^i-a
(where a = 0.4) and y_t = c_t + g_t + k_t — (l — δ)k_t-i where δ is the depreciation rate which we set
equal to 0.05. The stochastic process {g_t,θ_t} is exogenous and Markov. We assume consumers get
paid a competitive wage (in equilibrium equal to θ_t) and pay labour taxes to the government which
are levied at a proportional rate τ_t on labor income.

Under complete markets there exists a full range of Arrow Debreu securities such that at time
t there exists a spot market for claims contingent on all possible values of {g_t,θ_t}. We denote by
b_t(g^, θ_t) the quantity of bonds issued at t — l and which pay out at time t contingent on the
simultaneous occurrence of g and θ and the price of such a bond is p_t(g, θ). The market value of
debt is therefore given by vb_t ≡ ʃ b_t+ι(g, θ) p_t(g, θ) dgdθ. Under these assumptions the government
faces the budget constraint

Under incomplete markets we consider the extreme case where the government can only issue
one period risk free bonds⁸ so that

^bt ^{+ g}t ^{— τ} t^θt(^{l —} lt⁾ = ^p_t^bt+∖.

To solve our models for the optimal policy we make the standard Ramsey assumptions that
governments have a Hxed initial level of bonds and choose tax rates and government bonds so as to
maximize consumer welfare. Both the consumer and the government observe all shocks up to the
current period.

For the stochastic shocks we assume g follows a truncated AR(1), and θ_t a log AR(1) process
e.g.

g                             if (l — p⁵)g* + p⁵ gt-i + εf > g

gt = g                          if (l — p⁵)g* + p⁵ gt-i + 4 <g

(l — p)g* + p⁵ g_t-i + εf    otherwise

⁸We therefore assume exogenously incomplete asset markets. See Sleet and Yeltekin (2004) for an endogenous
explanation founded on asymmetric information.

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