Template-type: ReDIF-Paper 1.0
Author-Name: La Torre, Davide      
Author-Email: davide.latorre@skema.edu
Author-Name: Marsiglio,Simone   
Author-Email: simone.marsiglio@unipi.it 
Author-Name: Mendivil, Franklin   
Author-Email: franklin.mendivil@acadiau.ca
Author-Name: Privileggi, Fabio   
Author-Email: fabio.privileggi@unito.it
Author-Workplace-Name: University of Turin
Author-Workplace-Homepage: http://www.est.unito.it/
Title: Stochastic Optimal Growth through State-Dependent Probabilities.
Abstract: We extend the classical discrete time stochastic one-sector optimal growth model with
logarithmic utility and Cobb-Douglas production ´a-la Brock and Mirman (1972) to allow
probabilities to be state-dependent. In this setting the probability of occurrence of a given
shock depends on the capital stock, thus, as the economy accumulates more capital, the
probability of occurrence of different shocks changes over time. We explicitly determine
the optimal policy and its relation with state-dependent probabilities both in the cen-
tralized and decentralized frameworks, focusing on two alternative scenarios in which the
probability function, assumed to take a logarithmic form, is either decreasing or increasing
with capital. We show that state-dependent probabilities introduce a wedge between the
centralized and decentralized solutions, as individual agents do not internalize the effects
of capital accumulation on the probability of shocks realization. In particular, when-
ever the probability is decreasing (increasing) in the capital stock the probability of the
most (least) favorable shock increases, leading the decentralized economy to underinvest
(overinvest) in capital accumulation, resulting in the long run into a steady state capital
distribution characterized by a leftward (rightward) shifted support. We also show how
the features of state-dependent probabilities affect the spread and shape of such a steady
state distribution, which tends to be more skewed (more evenly spread) whenever the
probability decreases (increases) with capital.
Length: pages 33
Creation-Date: 2023-09
File-URL: https://www.est.unito.it/do/home.pl/Download?doc=/allegati/wp2023dip/wp_12_2023.pdf
File-Format: Application/PDF
Handle: RePEc:uto:dipeco:202312