is given by yt = θt(l — Zt) and θt is a stochastic productivity shock. The resource constraint is
yt = ct + gt with gt 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 yt = θtkt-1(l — lt)i-a
(where a = 0.4) and yt = ct + gt + kt — (l — δ)kt-i where δ is the depreciation rate which we set
equal to 0.05. The stochastic process {gt,θt} is exogenous and Markov. We assume consumers get
paid a competitive wage (in equilibrium equal to θt) and pay labour taxes to the government which
are levied at a proportional rate τt 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 {gt,θt}. We denote by
bt(g^, θt) 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 pt(g, θ). The market value of
debt is therefore given by vbt ≡ ʃ bt+ι(g, θ) pt(g, θ) dgdθ. Under these assumptions the government
faces the budget constraint
bt(gt, θt) + gt
τ tθt(l — It) = I
bt+ι((g,^ pbt(g,θ')dgdθ
Under incomplete markets we consider the extreme case where the government can only issue
one period risk free bonds8 so that
bt + gt — τ tθt(l — lt) = ptbt+∖.
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 θt 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 gt-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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