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 alpha. Production is affected 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 alpha and p change. We establish mutual singularity of the invariant distributions as p varies between 0 and 1 whenever alpha < 1/2. More delicate is the case alpha > 1/2. Singularity with respect to Lebesgue measure also appears for values alpha, p such that alpha < p[superscript p] (1 - p) [superscript (1 - p)]. For alpha > p[superscript p] (1 - p) [superscript (1 - p)] and 1/3 <= p <= 2/3, Peres and Solomyak (1998) have shown that the distribution is a.e. absolutely continuous. Characterization of the invariant distribution in the remaining cases is still an open question. The entire analysis is summarized through a bifurcation diagram, drawn in terms of pairs (alpha, p).
Download Info
To download:
If you experience problems downloading a file, check if you have the
proper application to
view it first. Information about this may be contained
in the File-Format links below. In case of further problems read
the IDEAS help
page. Note that these files are not on the IDEAS
site. Please be patient as the files may be large.
Publisher Info
Paper provided by Cornell University, Center for Analytic Economics in its series Working Papers with number
01-04.
Find related papers by JEL classification: C61 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Optimization Techniques; Programming Models; Dynamic Analysis O41 - Economic Development, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models
References listed on IDEAS Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
Cited by: (explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)