Endogenous Growth and Government Debt

Abstract

The feasibility of the policy of perpetual debt financing, given a particular path for expenditures and taxation, has been questioned over the years. Sargent and Wallace [17] argue that such a policy is not feasible in the sense that the debt/GNP ratio will explode. McCallum [8] and Darby [2] argue that this policy will be feasible if and only if the long-run growth rate of GNP exceeds the after-tax real interest rate. This particular condition was derived under the assumption of Ricardian equivalence, where the growth rate of GNP and the interest rate are exogenously given, and are not affected by the path of debt. Miller and Sargent [9] and Weil [20] make the point that once the assumption of Ricardian equivalence is dropped, then simple comparisons of long-run growth rates and interest rates are not sufficient to determine stability. Tirole [19] and O'Connell and Zeldes [10] demonstrate in Diamond's [3] model, without Ricardian equivalence, that Ponzi games such as this are feasible if and only if the economy is dynamically inefficient without debt. All of these studies assume that the long-run growth rate of GNP is exogenously given. This assumption is particularly strong in the absence of Ricardian equivalence. In a separate literature, a new generation of equilibrium growth models has recently been developed with positive sustained growth in the long-run equilibrium. In these models, long-run growth is endogenously determined, rather than being imposed on the model as some exogenously given process [7; 11; 12; 14; 15].1 All of these models find some way of introducing increasing returns to scale into the neoclassical growth model and yet preserving the fact that it can be interpreted as a decentralized equilibrium. This paper considers the feasibility of perpetual debt financing in an economy where the growth rate of GNP is endogenously determined and is a function of debt levels. The model of endogenous growth presented here is a modified version of the one given in Prescott and Boyd [12]. This particular model is chosen for two reasons. First, agents live for finite lengths of time; so Ricardian equivalence will not hold, in general, in this model. Also, the production function is linear in the capital stock; as will become clear below, this implies that the equilibrium paths of the state variables can be characterized as first order linear difference equations.