Balanced cycles in an OLG model with a continuum of finitely-lived individuals

For an overlapping generations economy with varying life-cycle productivity, non-stationary endowments, continuous time starting at −∞ (hence allowing for full anticipation), constant-returns-to-scale production and ces utility we fully characterise equilibria where output is higher than investment, which is strictly positive. Net assets (aggregate savings minus the value of the capital stock) are constant in any equilibrium, and, for balanced growth equilibria (bge, defined for an economy with stationary endowments), net assets are non-zero only in the golden rule equilibrium, in accord with [12]. The number of bge is finite. Their parity, however, depends on the life-cycle productivity, in particular, on the relation between the intertemporal elasticity of substitution, the minimal working age and the minimal tax age.

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“…18). This is then in accord with the non-existence of pure bge claimed in [5] for a similar economy without production.…”

Section: Introductionsupporting

confidence: 85%

“…This allows to think of either prices or quantities as measures. 5 Def. 1 and lemma 5.a imply p C is a.e.…”

Section: Introductionmentioning

confidence: 99%

Equilibria in an overlapping generations model with transfer policies and exogenous growth

Mertens

Rubinchik

2012

Econ Theory

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“…5 Two other closely related papers are d 'Albis andAugeraud-Véron (2004, 2007). d 'Albis and Augeraud-Véron (2004) has production and log utility but age-independent wages, i.e., every individual alive at t receives the same competitive wage (there is no heterogeneity in the quantity of efficiency units supplied over the life-cycle).…”

Section: Related Literaturementioning

confidence: 99%

An Integral Equation Representation for Overlapping Generations in Continuous Time

Edmond

2007

SSRN Journal

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This paper develops a method for solving for the dynamic general equilibrium of a deterministic continuous time overlapping generations model with a finite-horizon life-cycle. The model has isoelastic preferences and allows for general assumptions about individual endowments and demographics. Solving for an equilibrium reduces to solving a nonlinear integral equation. In the special case of log utility, the integral equation is linear and global approximations to a solution are easily computed with linear algebra.Keywords: overlapping generations, continuous time, life-cycle, intertemporal prices.The overlapping generations model is one of the workhorses of modern macroeconomics. This paper outlines a continuous time OLG model where agents live for a given finite interval of time so that genuine life-cycle behavior is possible. 1In applied macroeconomics, OLG models are set in discrete time and individuals have many decision periods per lifetime (Auerbach and Kotlikoff, 1987;Ríos-Rull, 1996). Long-lived models of this kind are attractive because they allow for realistic timing conventions and an intuitive calibration to annual or quarterly data. In practice, however, long-lived discrete time models are difficult to work with computationally. The main advantage of the continuous time model outlined below is that it simultaneously permits agents to have many decisions per lifetime but is computationally simple.The model is presented in Section 1 and allows for isoelastic utility and general assumptions about individual endowments (and demographics). The main result of this paper is given in Section 2 which shows how to represent the equilibrium fixed point problem as a specific, generally nonlinear, integral equation which needs to be solved for an unknown intertemporal price function.

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“…In particular, we mention the work of d'Albis and Augeraud-Véron [6][7][8], who have developed several models describing the dynamical features of an economy featuring only a single commodity, that exhibit oscillations which earlier models could only produce by including multiple commodities. This is accomplished by modelling the population as a continuum of individuals that each live for a finite time and act in such a way that their personal welfare is maximized.…”

Section: Introductionmentioning

confidence: 99%

Center projections for smooth difference equations of mixed type

Hupkes

Augeraud-Véron

Lunel

2008

Journal of Differential Equations

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We study a class of mixed type difference equations that enjoy a special smoothening property, in the sense that solutions automatically satisfy an associated functional differential equation of mixed type. Using this connection, a finite dimensional center manifold is constructed that captures all solutions that remain sufficiently close to an equilibrium. The results enable a rigorous analysis of a recently developed model in economic theory, that exhibits periodic oscillations in the interest rates of a simple economy of overlapping generations.

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Balanced cycles in an OLG model with a continuum of finitely-lived individuals

Cited by 18 publications

References 7 publications

Equilibria in an overlapping generations model with transfer policies and exogenous growth

Equilibria in an overlapping generations model with transfer policies and exogenous growth

An Integral Equation Representation for Overlapping Generations in Continuous Time

Center projections for smooth difference equations of mixed type

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