Overlapping Generations

Overlapping Generations

The consumption-loan model was introduced by Paul Samuelson. The first general-equilibrium analysis was my 1971 JPE paper, in which it is shown that the failure of perfect-foresight equilibrium to be Pareto optimal is solely due to the unbounded horizon. I introduced the nomenclature “overlapping-generations model” in place of “consumption-loan model”, emphasizing the basic demographic structure of this model.

The first sunspots paper, my 1977 Malinvaud lecture, is based on the OG model. The open horizon is a source of bubbles and a source of non-optimality. The open horizon, restricted market participation, and incomplete markets are separate sources of sunspots, each of which in inherent to OG economies.

Neil Wallace argued strongly and successfully in the Kareken-Wallace 1980 Minneapolis Fed volume for the use of OG models in macroeconomics. My contribution with Dave Cass to that volume was also meant to be strongly supportive of OG as a basic model for macro. OG models are important because of their realism (people are born and do die), their tractability (individual wealths are finite even if social wealth is not), and their flexibility for the analysis of money and public debt (neither of which need be retired in OG economies). OG models are likely to be even more relevant for 21st century applied macro, since the relative sizes of the different demographic cohorts are likely to play critical roles.

The three JET papers (1980-81) with Yves Balasko provide the general analyses of existence and welfare in perfect-foresight OG economies. The economy is general, allowing for non-stationary preferences, endowments, and fiscal policies. Existence of competitive equilibrium follows from a basic limit and trucation argument that uses either Tychonoff’s Theorem or, equivalently, Cantor diagonalization. All proofs of existence of competitive equilibria in OG economies are based on this truncation and limit argument. We established that every perfect-foresight competitive equilibrium is weakly (or equivalently, short-run) Pareto optimal and every weakly Pareto optimal allocation can be supported as a competitive equilibrium. Weakly Pareto optimal allocations can only be improved upon (if at all) by allocations that differ in only a finite number of components, ruling out “chain letters blocking” in the optimality concept. Yves and I introduced “bonafide fiscal policies”, those money tax systems consistent with proper monetary equilibrium. We completely characterize bonafide fiscal policies for the OG economy with a single individual per generation. In our 1986 chapter in the Arrow Festschrift, Yves and I analyzed bonafidelity and the retirement of the public debt. All fiscal policies in which the public debt is retired in finite time are bonafide. Not all fiscal policies in which the public debt is asymptotically retired are bonafide.

Christian Ghiglino and I (2000) and (2003) analyzed the economic effects of restriction on government budget deficits. If the government can select among equilibria and the number of tax instruments is sufficiently large, then deficit restrictions are weakly irrelevant: “small” changes in the restrictions do not matter. If the government does not have these powers, deficit restrictions can very well matter.

The OG model is crucial to 21st century applied macro analysis, in which real world demographic facts are essential.

References