developed in Romer (1986, 1987, 1990) and in Lucas (1988). For simplicity
we assume an AK production structure that captures the basic idea of these
models. The microfoundation of individual consumption-saving decisions
is given in an overlapping generations model in the tradition of Diamond
(1965).
With regard to the budget deficit the government is in control of three
instruments; the government purchase ratio, the budget deficit ratio, and
the tax rate. Assume that the purchase ratio is given exogenously. Then, the
government can follow either of two strategies, it fixes the deficit ratio or the
tax rate. If the government fixes the deficit ratio, then according to the budget
constraint the tax rate will be endogenous. And if the government fixes the tax
rate, then the deficit ratio is endogenous. Carlberg (1995) compares these
two strategies in overlapping generation models with neoclassical growth.
Given a fixed deficit ratio there are, in general, two steady states. However,
there is a critical deficit ratio. If the deficit ratio exceeds the critical level,
then there is no steady state. Given a fixed tax rate there is, in general, no
steady state. As an exception, if the future consumption elasticity is very large
and if the primary deficit ratio is extremely small, there will be two steady
states. One of them is stable, the other is unstable. Hence, as a main result, a
fixed deficit ratio is feasible. In contrast, a fixed tax rate is not sustainable.
Saint-Paul (1992) and Josten (2000) analyze public debt in overlapping
generations models with endogenous growth. Both consider continuous-time
overlapping generations models in the tradition of Blanchard (1995). Saint-
Paul assumes an AK technology and Josten assumes endogenous growth
throughhumancapital formation. They concentrate on a steady state in which
the government has to adjust the tax to maintain a fixed debt-output ratio.
This paper considers a fixed deficit ratio in an endogenous growth model.
It is shown that for given deficit ratio there are indeed two steady states, in
which the debt-output ratio stays constant. One of these steady states is stable;
the other is unstable. However, if the deficit ratio exceeds a critical level then
there is no steady state. In addition, the model allows to study transitional
dynamics induced by a change in the deficit ratio.
The rest of the paper is organized in the following way: Section 2 presents
the model. Section 3 analyzes stability. Section 4 probes into the effects of an
increase in the deficit ratio. Section 5 compares the main results to some
basic results derived from a simple model with a fixed primary deficit ratio.
Finally, Section 6 summarizes the results.
2. The Model
First, we consider the structure of production. A large number of identical
firms denoted by i manufacture a single commodity Y i by means of capital
Ki and labor Ni . The production function is of the Cobb–Douglas type: Y i =
AKα
i (EN i)β , with A>0,α>0,β >0, α +β =1, and E as an exogenously given
index of