Dynamic Efficiency, the Riskless Rate, and Debt Ponzi Games under Uncertainty

In a dynamically efficient economy, can a government roll its debt forever and avoid the need to raise taxes? In a series of examples of economies with zero growth, this paper shows that such Ponzi games may be infeasible even when the average rate of return on bonds is negative, and may be feasible even when the average rate of return on bonds is positive. The paper then reveals the structure which underlies these examples. The average realized real rate of return on government debt for major OECD countries over the last 30 years has been smaller than the growth rate. Does this imply that governments can play a Ponzi debt game, rolling over their debt without ever increasing taxes? If only economies were both nonstochastic and in steady state, the answer to this question would be a simple one. All interest rates would be the same, and if the interest rate were less than the growth rate, the economy would be dynamically inefficient. In this case, the government could issue debt and roll it over forever, never increasing taxes, and covering interest payments by new debt issues. Debt would grow at the interest rate, but the ratio of debt to GNP would eventually tend to zero. Such a policy would crowd out the excessive capital accumulation characteristic of dynamically inefficient economies and, as we also know, it would in general be Pareto improving. Actual economies however are stochastic. And in actual economies, there are many different interest rates, some which are on average above the growth rate, some which are below. It has been shown in particular that stochastic economies may be dynamically efficient while having an average riskless real rate below the growth rate. But this brings us back, with an additional twist, to our initial question. In dynamically efficient economies (i.e., in economies that are not plagued by capital overaccumulation), can governments issue and roll over riskless debt, and thus play a Ponzi debt game? This is the issue we take up in this paper. Our paper is constructed using the Socratic method. This means two things. First, that our objective in this paper is not to derive new theoretical results on dynamic efficiency and Ponzi games. Instead, we explicitly and unabashedly rely on existing theoretical results (most often developed in contexts quite different from ours) to study an issue— the feasibility of Ponzi debt games in dynamically efficient economies with low safe interest rates— that often leaves macroeconomists somewhat baffled. Second, that we use an unorthodox exposition style. Instead of proceeding from the general to the particular, we rely on a series of simple, but increasingly richer, examples to clear up common misconceptions on Ponzi games in stochastic economies. These results require various conditions, both technical and substantive, to be satisfied. One such substantive condition is that the interest rate be equal to the social marginal product of capital, an assumption which fails for example if there are external returns to capital. For an analysis of dynamic efficiency and Ponzi games in an endogenous growth model with external returns to capital, see Saint-Paul (1992). See Abel, Mankiw, Summers and Zeckhauser (1989). 1 Blanchard and Weil: Dynamic Efficiency, the Riskless Rate, and Debt Ponzi Games Produced by The Berkeley Electronic Press, 2002 We use these examples to move from the specific to the general, and to reveal the theoretical structure that we need to understand when and why Ponzi games can exist in dynamically efficient economies under uncertainty. Sections 1 to 4 of the paper present our four examples. All share the following features. First, all characterize economies which are subject to technological shocks and thus to uncertainty, so that assets with different risk characteristics have different rates of return. Second, all characterize overlapping generation economies with capital accumulation, thus economies for which capital overaccumulation—dynamic inefficiency— is not ruled out a priori. But, third, in each case, we choose, relying on the criterion derived by Zilcha (1991), underlying taste and technology parameters such the economy is actually dynamically efficient. In each of these economies, we then ask what would happen to the debt-to-GNP ratio if the government were to issue debt and roll it over time, issuing new debt to pay interest on the existing debt. And each of the four examples gives us a very different answer. In our first example, the average riskless rate is negative; nevertheless, the expected value of the debt-to-GNP ratio under a rollover strategy explodes, and thus the government cannot play a debt Ponzi game. In the second, the average riskless rate is again negative, and, furthermore, the expected value of the debt-to-GNP ratio under rollover goes to zero. But the fact that a Ponzi game appears viable in expected value does not imply that it is feasible. Indeed, in this example, with strictly positive probability, debt rollover leads to an arbitrarily large value of the debt-to-GNP ratio and is thus again infeasible. By then, the reader may suspect that dynamic efficiency rules out Ponzi games, no matter what the behavior of the average riskless rate may be. But the last two examples show this guess to be wrong. In our third example, the riskless rate is always negative and under a Ponzi debt game, the debt-to-GNP ratio goes to zero with certainty, so that rollover is indeed feasible. Our fourth example offers a nearly perfect counterpoint to the first. In that example the average riskless rate is positive; yet by issuing and rolling over two-period bonds, the government can still play a Ponzi debt game. . . We spend section 5 of the paper to reveal the structure behind the results, to explain why Ponzi games are feasible in the last two examples but not in the first two, and to acknowledge our many debts to the literature up to 1990, when this paper was first written. The literature on debt Ponzi games has made much progress since then (in the direction pointed out by this paper!): the last section of the paper reviews these contributions. We do not want to give the answers away in the introduction. For the 2 Advances in Macroeconomics Vol. 1 [2001], No. 2, Article 3