Existence of steady-state equilibrium in an overlapping-generations model with production

Konishi, Hideo; Perera‐Tallo, Fernando

doi:10.1007/bf01213853

Cited by 7 publications

(17 citation statements)

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“…The concavity of f implies that s 2 (0; 1) and " > 0 for all k > 0. Our existence condition (20) is close to the condition proposed by Bommier and Lee [5] who extend to a continuous-time framework the …ndings of Konishi and Perera-Tallo [23] for the Diamond model [13]. Their condition, named the "non-vanishing labor share", has the advantage of relying only on the production function.…”

Section: Aggregation and Competitive Equilibriumsupporting

confidence: 80%

Demographic structure and capital accumulation

d’Albis¹

2007

Journal of Economic Theory

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This paper develops an overlapping generations model to analyze the consequences of demographic structure changes induced by an exogenous shift in the birth rate. We …rst show that a …nite growth rate of the population that maximizes long-run capital per capita exists. Then, we examine the theoretical properties of this growth rate by showing that: (i) it corresponds to the demographic structure such that the average ages of capital holders and workers are equal; (ii) it is associated to an e¢ cient steady state; (iii) it increases with compulsory transfers from younger to older generations. Finally, we explain why standard overlapping generations models do not exhibit such a growth rate. JEL Classi…cation: D91; E13; J10Key words: Continuous-time overlapping-generations models; Population aging IntroductionOverlapping generations (OLG) models are the neoclassical literature's common tool for analyzing the economic consequences of demographic structure changes. In this paper, we focus on the impact of exogenous shifts in the birth rate on long-run capital accumulation. This relationship is crucial for analyzing the consequences of population aging on most macro-variables 1 , such as growth, assets prices and unemployment. An increase in the population growth rate simultaneously induces a reduction in capital per worker and an increase in savings; the problem is to …nd out which one has the strongest e¤ect. Standard OLG models with production in discrete or continuous time developed by Diamond [13] show that a birth-rate increase reduces long-run capital per capita. The economic intuition given to this result relies on the absence of intergenerational altruism: the size of future generations does not directly in ‡uence the saving choices of current generations. The reduction in aggregate consumption that follows a birth rate increase is therefore insu¢ cient for compensating the capital dilution e¤ect. Following Weil [36], the birth rate measures the degree of disconnection between generations, and newborn individuals are interpreted as "unloved children"or immigrants.Empirical studies, however, do not show that demographic structure changes have a signi…cant impact of on capital accumulation or, more precisely, on its marginal productivity. In a recent paper, Poterba [30] analyzes the historical relationship between population structure and assets return, including the interest rate. Using time series from the United States, Canada and the United Kingdom for the last seventy years. Poterba …nds no robust evidence of any impact of demographic variables on assets prices.At a …rst glance, these empirical …ndings seem to invalidate the OLG models while validating the Ramsey framework. In this framework 2 , where the population is composed of one unique, altruistic family, the demographic variables have no impact at the balanced equilibrium. That is because the optimal response to a birth-rate increase is to reduce consumption in order to keep capital per capita constant. However, in this paper, we argue tha...

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Section: Aggregation and Competitive Equilibriumsupporting

confidence: 80%

Demographic structure and capital accumulation

d’Albis¹

2007

Journal of Economic Theory

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“…Consider Figure 1. The curve ABCD depicts the set of intertemporally feasible steady state consumption plans, as given by (4). 2 This "intertemporal consumption possibility curve" was introduced by Ihori [3].…”

Section: Remarkmentioning

confidence: 99%

“…In a related article, Konishi and Perera-Tallo [4] discuss sufficient existence conditions for overlapping generations economies with productive capital. Their existence conditions are based on the concept of Ihori's [3] intertemporal consumption possibilities curve.…”

Section: Introductionmentioning

confidence: 99%

“…In this sense, checking for existence is easier than checking for the alternative existence conditions of Galor and Ryder [2, p. 371]. However, Konishi and Perera-Tallo [4] neither discuss stability nor do they consider uniqueness of equilibrium.…”

Section: Introductionmentioning

confidence: 99%

“…The paper uses the existence theorem provided by Konishi and Perera-Tallo [4, p. 533]. By strengthening of Konishi and Perera-Tallo's [4] existence conditions, the paper identifies those equilibria that are locally asymptotically stable. The paper then proceeds by showing that the condition for local asymptotic stability is sufficient for uniqueness of equilibrium.…”

Section: Introductionmentioning

confidence: 99%

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Existence, uniqueness, and stability of equilibrium in an OLG economy

Wendner

2003

Economic Theory

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This paper presents sufficient conditions for the existence of a unique and globally stable steady state equilibrium for OLG economies with production. The conditions impose separate requirements on the utility and production functions. Moreover, the conditions do not require assumptions concerning the third order derivatives of the production and utility functions. Copyright Springer-Verlag Berlin/Heidelberg 2003Existence, Uniqueness, Stability, Overlapping generations.,

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Bubbly Markov equilibria

Barbie

Hillebrand

2017

Econ Theory

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Bubbly Markov Equilibria (BME) are recursive equilibria on the natural state space which admit a non-trivial bubble. The present paper studies the existence and properties of BME in a general class of overlapping generations (OLG) economies with capital accumulation and stochastic production shocks. Using monotone methods, we develop a general approach to construct Markov equilibria and provide necessary and sufficient conditions for these equilibria to be bubbly. Our main result shows that a BME exists whenever the bubbleless equilibrium is Pareto inefficient either due to overaccumulation of capital or inefficient risksharing between generations.

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Existence of steady-state equilibrium in an overlapping-generations model with production

Cited by 7 publications

References 3 publications

Demographic structure and capital accumulation

Demographic structure and capital accumulation

Existence, uniqueness, and stability of equilibrium in an OLG economy

Bubbly Markov equilibria

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