On a Class of Stable Random Dynamical Systems: Theory and Applications

Bhattacharya, Rabi; Majumdar, Mukul

doi:10.1006/jeth.1999.2627

Cited by 30 publications

(41 citation statements)

References 7 publications

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“…Let us recall the formulation of the one-sector growth model with a Cobb-Douglas production function G(x) = x , 0 < < 1, with a representative decision maker's utility given by u(c) = ln c. Suppose that an exogenous perturbation may reduce 6 production by some parameter 0 < k < 1 with probability p > 0 (the same for all t = 0; 1; : : :). This independent and identically distributed random shock enters multiplicatively into the production process so that output is given by G r (x) = rx where r 2 fk; 1g.…”

Section: One Sector Log-cobb-douglas Optimal Growthmentioning

confidence: 99%

“…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%

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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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Section: One Sector Log-cobb-douglas Optimal Growthmentioning

confidence: 99%

mentioning

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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“…Also, it is easy to see that [c,d] is invariant under F. Hence, for the long run analysis of the evolution of X n , we can take [c,d] as the effective state space. The splitting condition (H) is verified by a careful consideration of the structure of the model (Bhattacharya and Majumdar (2001). It should be stressed that while G is not a monotone function, on the (common) invariant interval [c,d] both F and G are monotone (increasing and decreasing respectively).…”

Section: Models Of Growth and Cyclesmentioning

confidence: 75%

“…This turns out to be crucial to derive the -consistency of the estimates. We also sketch in this section some applications of the results to example of growth and cycles under uncertainty [see Stokey and Lucas (1989), Ljungqvist and Sargent (2000) and Bhattacharya and Majumdar (2001)]. All the proofs are relegated to the last section.…”

Section: Introductionmentioning

confidence: 99%

Estimating the stationary distribution of a Markov chain

Athreya

Majumdar

2004

Studies in Economic Theory

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“…(i) it is independent of the set K and is onto; 2 Note that the no overlap condition (21) in this context is equivalent to the strong separation condition defined on p. 35 in [4].…”

Section: Definition 1 We Shall Say That a Set C ⊂ R Is A Generalized mentioning

confidence: 99%

Cantor type attractors in stochastic growth models

Mitra

Privileggi²

2006

Chaos, Solitons & Fractals

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We study a one-sector stochastic optimal growth model where production is affected by a shock taking one of two values. Such exogenous shock may enter multiplicatively or additively. A result is presented which provides sufficient conditions to ensure that the attractor of the iterated function system (IFS) representing the optimal policy, is a generalized topological Cantor set. To indicate the role of the strict monotonicity condition on the IFS in this result, examples of attractors, which are not of the Cantor type, are constructed with iterated function systems, whose maps are contractions and satisfy a no overlap property.Journal of Economic Literature Classification Numbers: C61, O41.

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On a Class of Stable Random Dynamical Systems: Theory and Applications

Cited by 30 publications

References 7 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

Estimating the stationary distribution of a Markov chain

Cantor type attractors in stochastic growth models

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