Target Saving In An Overlapping Generations Model

We examine a model in which the utility function has been engineered so that it is optimal for consumers to aim for a fixed target level of retirement resources. In this case consumption displays excess sensitivity to current income as well as perfect old age insurance. In an overlapping generations model, this leads naturally to multiple and unstable equilibria. Under static expectations, it also leads to a well-defined dynamics, including possible historical traps, implosions involving ever-diminishing capital stock and ever-increasing interest rates, and the feasibility of optimal one-time interventions.Targets, history, excess sensitivity, static expectations, rational expectations, uniqueness.

Overlapping Generations: the First Jubilee.

Paul Samuelson's (1958) overlapping generations model has turned 50. Seldom has so simple a model been so influential. The paper, in spite of its ripe age, still elicits wonder. Starting from the uncontroversial observation that “we live in a world where new generations are always coming along” Samuelson built a model that violates the credo of the first fundamental welfare theorem with which we still inculcate undergraduates 50 years later. According to Samuelson, all is not necessarily well in the best of market economies: with overlapping generations, even absent the usual suspects such as distortions and market failures, a competitive equilibrium need not be Pareto efficient. Worst of all, this failure of the first welfare theorem in an overlapping generations model occurs in a framework that is, in many ways, more plausible and realistic than the world of agents living synchronous and finite existences in which the theorem is usually proved. Like Mona Lisa's enigmatic smile, the mysterious welfare properties of the overlapping generations model are, to a significant extent, responsible for its popularity—along with the many economic issues it has illuminated in the last half-century. I take it as my brief in this celebratory paper to provide, after a short exposition of the main results of the overlapping generations model under certainty, an explanation of why the welfare properties of the overlapping generations model differ so much from the canonical Arrow–Debreu framework and to review, in a deliberately nonencyclopedic mode, a few striking applications and extensions of Samuelson's deceptively straightforward model.

Future Targets and Multiple Equilibria

Multiple Pareto-rankable equilibria may obtain in an overlapping generations model where consumers save to reach a fixed target. Existence and uniqueness conditions are discussed. The model displays excess consumption sensitivity to current income and perfect old-age insurance.Multiple equilibria, saving, overlapping generations, excess sensitivity.

Inflation Forecast Targeting in an Overlapping Generations Model

In the framework of a standard overlapping generations model, it is shown that active inflation forecast targeting reinforces mechanisms that lead to indeterminacy of the monetary steady state and to countercyclical behavior of young-age consumption. The inflation forecast targeting rule which minimizes the volatility of inflation can be active or passive, depending on the characteristics of shocks and the risk aversion of households. Inflation forecast errors are always greater under active inflation forecast targeting than under passive inflation forecast targeting or strict money growth targeting. The monetary steady state is more likely to be indeterminate under an active rule of inflation forecast targeting than under the corresponding backward-looking rule (inflation targeting), but backward-looking rules can render the monetary steady state unstable.Monetary policy, Inflation forecast targeting, Overlapping generations model

Dynamic Heckscher-Ohlin Results from a 2x2x2x2 Overlapping Generations Model with Unequal Population Growth Rates

This paper considers a two-country world where the population in one country grows faster than the other, and investigates the implications of the addition of non-stationary population dynamics to a simple 2- commodity, 2-factor model of international trade within an overlapping- generations framework. The two countries in the world considered are assumed to be identical in every respect except, for their population growth rates initially. The effects of differential speed of population growth on relative factor endowments and patterns of international trade are explored by comparing simulation results obtained from the overlapping-generations general equilibrium model under autarky and trade scenarios. Unequal population growth rates are shown to give rise to differentials in wage rates and rentals for capital under autarky conditions. This, in turn, causes costs of production and relative prices to differ, creating the grounds for trade in the sense of Heckscher-Ohlin (HO). Yet, the results from simulation exercises indicate that static welfare results from the standard 2x2x2 HO model can not be generalized to hold in a dynamic setting with overlapping generations of individuals.Unequal population growth rates, Heckscher-Ohlin model, international trade, overlapping-generations

An Overlapping Generations Model of Electoral Competition

This paper presents a dynamic model of political competition between two "parties" with different policy preferences. A "party" is explicitly modeled as a sequence of overlapping generations of candidates, all of whom face finite decision horizons. In general, there is a conflict between the interests of the individual policymakers and those of the "party" , which includes subsequent generations of candidates. We characterize this conflict and suggest a scheme of "intergenerational transfers" within the party which can resolve or mitigate this conflict. The paper shows how the "overlapping generations" model can be usefully applied to the political arena.

Trade dynamics and endogenous growth: An overlapping generations model

Growth Models;International Trade

Maximum Sustainable Government Debt in the Overlapping Generations Model.

The theoretical determinants of maximum sustainable government debt are investigated using Diamond's overlapping-generations model. A level of debt is defined to be 'sustainable' f a steady state with non-degenerate values of economic variables exists. We show that a maximum sustainable level of debt almost always exists. Most interestingly, it normally occurs at a 'catastrophe' ather than a 'degeneracy' , i.e. where variables such as capital and consumption are in the interiors, rather than at the limits, of their economically meaningful ranges. This means that if debt is increased step by step, the economy may suddenly collapse without obvious warning.GOVERNMENT DEBT ; OVERLAPPING GENERATIONS

TARGET SAVING IN AN OVERLAPPING GENERATIONS MODEL

We examine a model in which the utility function has been engineered so that it is optimal for consumers to aim for a fixed target level of retirement resources. In this case consumption displays excess sensitivity to current income as well as perfect old age insurance. In an overlapping generations model, this leads naturally to multiple and unstable equilibria. Under static expectations, it also leads to a well-defined dynamics, including possible historical traps, implosions involving ever-diminishing capital stock and ever-increasing interest rates, and the feasibility of optimal one-time interventions.Targets, history, excess sensitivity, static expectations, Rational Expectations, uniqueness

Adaptive Learning in Stochastic Nonlinear Models When Shocks Follow a Markov Chain.

Local convergence results for adaptive learning of stochastic steady states in nonlinear models are extended to the case where the exogenous observable variables follow a ?nite Markov chain. The stability conditions for the corresponding nonstochastic model and its steady states yield convergence for the stochastic model when shocks are suf?ciently small. The results are applied to asset pricing and to an overlapping generations model. Large shocks can destabilize learning even if the steady state is stable with small shocks.bounded rationality; recursive algorithms; steady state; linearization; asset pricing; overlapping generations