Global asymptotic stability results for multisector models of optimal growth under uncertainty when future utilities are discounted

Brock, William A.; Majumdar, Mukul

doi:10.1016/0022-0531(78)90080-7

Cited by 44 publications

(37 citation statements)

References 13 publications

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“…A stochastic steady state is identi…ed as an invariant distribution, and, since the seminal papers by Lucas-Prescott [41] and Brock-Mirman [11], a large part of the literature on the subject has focused on the existence, uniqueness and global stability of this invariant distribution. See, for example, [44], [45], [10], [16], [28] and, more recently, [34], [6] and [57].…”

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confidence: 99%

The nature of the steady state in models of optimal growth under uncertainty

Mitra

Montrucchio

Privileggi³

2003

Economic Theory

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Summary. We study a one-sector stochastic optimal growth model with a representative agent. Utility is logarithmic and the production function is of the Cobb-Douglas form with capital exponent . Production is a¤ected by a multiplicative shock taking one of two values with positive probabilities p and 1 p. It is well known that for this economy, optimal paths converge to a unique steady state, which is an invariant distribution. We are concerned with properties of this distribution. By using the theory of Iterated Function Systems, we are able to characterize such a distribution in terms of singularity versus absolute continuity as parameters and p change. We establish mutual singularity of the invariant distributions as p varies between 0 and 1 whenever < 1=2. More delicate is the case > 1=2. Singularity with respect to Lebesgue

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confidence: 99%

The nature of the steady state in models of optimal growth under uncertainty

Mitra

Montrucchio

Privileggi³

2003

Economic Theory

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“…Using standard Inada-type assumptions, they showed that there exists a unique and globally stable equilibrium whenever the shock that perturbs production is supported on a closed bounded interval of the positive real numbers. Subsequently, the asymptotic behavior of the concave one-sector model with bounded shock was studied by many authors [13,14,6,15,7,11,18,9,2]. More general proofs were established, and various complications were incorporated.…”

Section: Introductionmentioning

confidence: 99%

Stochastic growth: asymptotic distributions

Stachurski¹

2003

Economic Theory

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This note studies conditions under which sequences of state variables generated by discrete-time stochastic optimal accumulation models have law of large numbers and central limit properties. Productivity shocks with unbounded support are considered. Instead of restrictions on the support of the shock, an “average contraction” property is required on technology. Copyright Springer-Verlag Berlin Heidelberg 2003Keywords and Phrases: Stochastic growth, Law of large numbers, Central limit theorem., JEL Classification Numbers: C51, C62, O41.,

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“…In many economic problems optimality conditions for feasible plans are stated in terms of the stochastic version of Euler-Lagrange conditions (primarily in the optimal growth literature; see [6], [12], [17], [9], [2] and, more recently, [7], [16]); in all these papers such conditions are de…ned speci…cally to prove main results for the model to discuss. Only in [1] the problem is treated in a more general perspective, however under the standard and rather restrictive assumptions adopted in dynamic programming; that is, under di¤erentiability, monotonicity and concavity of the return function and assuming that the exogenous shocks are described by a …rst order Markov process with a dense stationary transition function.…”

Section: Introductionmentioning

confidence: 99%

A characterization for solutions of stochastic discrete time optimization models

Privileggi

1995

Rivista di Matematica per le Scienze Economiche e Sociali

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A notion of …nitely optimal plan for intertemporal optimization problems as a necessary condition for optimality is introduced. Under interiority of a feasible plan and di¤erentiability of the return function, such a plan satis…es the stochastic analogue of deterministic Euler-Lagrange conditions, which become also su¢ cient conditions under concavity of the return function. Then, under more general assumptions, a su¢ cient criterion of optimality based on competitive plans supported by price systems and transversality conditions is discussed. Di¤erently from the current literature, no restrictive hypotheses on the probability measure of the random shocks are assumed.

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Global asymptotic stability results for multisector models of optimal growth under uncertainty when future utilities are discounted

Cited by 44 publications

References 13 publications

The nature of the steady state in models of optimal growth under uncertainty

The nature of the steady state in models of optimal growth under uncertainty

Stochastic growth: asymptotic distributions

A characterization for solutions of stochastic discrete time optimization models

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