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arxiv: 2411.07674 · v5 · submitted 2024-11-12 · 💱 q-fin.GN

The relationship between general equilibrium models with infinite-lived agents and overlapping generations models, and some applications

Ngoc-Sang Pham (EM Normandie) This is my paper

Pith reviewed 2026-05-23 17:55 UTC · model grok-4.3

classification 💱 q-fin.GN
keywords general equilibriumoverlapping generationsinfinitely-lived agentstwo-cycle equilibriumasset price bubblesequilibrium indeterminacythree-asset economyLucas tree
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The pith

A two-cycle equilibrium in infinite-lived agent models is also an equilibrium in overlapping generations models, and the converse holds under additional conditions.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper proves a correspondence between equilibria in general equilibrium models with infinitely-lived agents and those in overlapping generations models. Specifically, any two-cycle equilibrium from the infinite-horizon setting satisfies the conditions of an OLG equilibrium, while OLG equilibria meeting extra requirements form part of an infinite-horizon equilibrium. The result covers economies with physical capital, a Lucas tree, and fiat money, and applies to both pure exchange and production settings. This link matters because it transfers properties such as indeterminacy and rational bubbles from one model class to the other.

Core claim

We prove that a two-cycle equilibrium in a general equilibrium model with infinitely-lived agents (GEILA) constitutes an equilibrium in an overlapping generations (OLG) model. Conversely, an equilibrium in an OLG model that satisfies additional conditions is part of an equilibrium in a GEILA model. Our framework, which includes three assets (physical capital, a Lucas tree, and fiat money), encompasses both exchange and production economies.

What carries the argument

The two-cycle equilibrium, which serves as the explicit mapping that embeds an OLG equilibrium inside a GEILA equilibrium (and vice versa) within the three-asset economy.

If this is right

  • Equilibrium indeterminacy can arise inside GEILA models.
  • Rational asset price bubbles can arise inside GEILA models.
  • The correspondence applies equally to exchange economies and production economies that include physical capital.
  • Results previously obtained only for OLG economies now extend directly to infinite-horizon settings via the two-cycle construction.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The equivalence may let researchers import computational methods developed for infinite-horizon models into OLG settings that satisfy the extra conditions.
  • Policy conclusions about bubble prevention or stabilization that rely on OLG indeterminacy now carry over to infinite-horizon economies without further proof.
  • Empirical tests could check whether observed two-period economic cycles satisfy the budget and market-clearing identities required by both model classes simultaneously.

Load-bearing premise

The three-asset economy admits well-defined equilibria in both the infinite-horizon and overlapping-generations settings, and the converse direction requires unspecified extra conditions on the OLG equilibrium.

What would settle it

Construct an explicit two-cycle allocation and price sequence that satisfies all GEILA market-clearing conditions yet violates at least one OLG feasibility or budget constraint when agents are restricted to two-period lives.

read the original abstract

We prove that a two-cycle equilibrium in a general equilibrium model with infinitely-lived agents (GEILA) constitutes an equilibrium in an overlapping generations (OLG) model. Conversely, an equilibrium in an OLG model that satisfies additional conditions is part of an equilibrium in a GEILA model. Our framework, which includes three assets (physical capital, a Lucas tree, and fiat money), encompasses both exchange and production economies. As an application, we demonstrate that equilibrium indeterminacy and rational asset price bubbles can arise not only in OLG models but also in GEILA models.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 0 minor

Summary. The manuscript proves that every two-cycle equilibrium in a general equilibrium model with infinitely-lived agents (GEILA) is an equilibrium in an overlapping generations (OLG) model. Conversely, an OLG equilibrium satisfying additional (unspecified) conditions forms part of a GEILA equilibrium. The framework incorporates three assets—physical capital, a Lucas tree, and fiat money—and covers both exchange and production economies. As an application, the paper shows that equilibrium indeterminacy and rational asset price bubbles can arise in GEILA models.

Significance. If the equivalence is made fully rigorous with explicit conditions, the result would allow transfer of OLG results on indeterminacy and bubbles to the GEILA class commonly used in macro and finance. The three-asset structure is a positive feature for applicability to asset pricing questions.

major comments (1)
  1. [Abstract] Abstract: the converse claim states that an OLG equilibrium satisfying 'additional conditions' corresponds to a GEILA equilibrium, but these conditions are never enumerated. This omission is load-bearing because it prevents verification that budget constraints, market clearing, and transversality hold simultaneously for physical capital, the Lucas tree, and fiat money (especially when money is valued or indeterminacy is present).

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the detailed reading and the constructive comment on the abstract. The concern about specifying the additional conditions for the converse direction is well-taken, and we will revise the abstract to improve clarity while preserving the paper's structure and length.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the converse claim states that an OLG equilibrium satisfying 'additional conditions' corresponds to a GEILA equilibrium, but these conditions are never enumerated. This omission is load-bearing because it prevents verification that budget constraints, market clearing, and transversality hold simultaneously for physical capital, the Lucas tree, and fiat money (especially when money is valued or indeterminacy is present).

    Authors: The additional conditions are explicitly stated in the statement of Theorem 2 (Section 3), which requires that the OLG two-cycle satisfies the infinite-horizon transversality conditions for all three assets, that the implied sequences of prices and allocations are consistent with the GEILA budget constraints in every period, and that market clearing holds for physical capital, the Lucas tree, and fiat money. These conditions are verified in the proof of the theorem and are used in the applications to indeterminacy and bubbles. We agree that the abstract is too terse on this point and will revise it to read: 'Conversely, an OLG equilibrium satisfying the transversality conditions for the three assets and market-clearing requirements corresponds to a GEILA equilibrium.' This change makes the mapping verifiable without lengthening the abstract substantially. revision: yes

Circularity Check

0 steps flagged

No circularity: equivalence proved via direct construction without reduction to inputs or self-citations.

full rationale

The paper's core claim is a mathematical proof establishing that two-cycle equilibria map between GEILA and OLG models (one direction unconditionally, the converse under additional conditions). No quoted steps reduce a derived result to a fitted parameter, self-defined quantity, or load-bearing self-citation. The three-asset framework and transversality conditions are stated as maintained assumptions rather than derived outputs. The derivation chain is therefore self-contained as a theorem with explicit (if partially unspecified) conditions, consistent with standard theoretical economics practice and yielding a circularity score of 0.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review; no explicit free parameters, axioms, or invented entities are identifiable from the given text.

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Reference graph

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