Abstract
We give a set of sufficient conditions for uniqueness of a time-consistent stationary Markov consumption policy for a quasi-hyperbolic household under uncertainty. To the best of our knowledge, this uniqueness result is the first presented in the literature for general settings, i.e. under standard assumptions on preferences, as well as some new condition on a transition probability. This paper advocates a “generalized Bellman equation” method to overcome some predicaments of the known methods and also extends our recent existence result. Our method also works for returns unbounded from above. We provide a few natural extensions of optimal policy uniqueness: convergent and accurate computational algorithm, monotone comparative statics result and generalized Euler equation.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 293-310 |
| Number of pages | 18 |
| Journal | Journal of Economic Theory |
| Volume | 176 |
| DOIs | |
| State | Published - Jul 1 2018 |
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Keywords
- Generalized Bellman equation
- Markov equilibrium
- Time consistency
- Uniqueness
ASJC Scopus subject areas
- Economics and Econometrics
Cite this
On uniqueness of time-consistent Markov policies for quasi-hyperbolic consumers under uncertainty. / Balbus, Łukasz; Reffett, Kevin; Woźny, Łukasz.
In: Journal of Economic Theory, Vol. 176, 01.07.2018, p. 293-310.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - On uniqueness of time-consistent Markov policies for quasi-hyperbolic consumers under uncertainty
AU - Balbus, Łukasz
AU - Reffett, Kevin
AU - Woźny, Łukasz
PY - 2018/7/1
Y1 - 2018/7/1
N2 - We give a set of sufficient conditions for uniqueness of a time-consistent stationary Markov consumption policy for a quasi-hyperbolic household under uncertainty. To the best of our knowledge, this uniqueness result is the first presented in the literature for general settings, i.e. under standard assumptions on preferences, as well as some new condition on a transition probability. This paper advocates a “generalized Bellman equation” method to overcome some predicaments of the known methods and also extends our recent existence result. Our method also works for returns unbounded from above. We provide a few natural extensions of optimal policy uniqueness: convergent and accurate computational algorithm, monotone comparative statics result and generalized Euler equation.
AB - We give a set of sufficient conditions for uniqueness of a time-consistent stationary Markov consumption policy for a quasi-hyperbolic household under uncertainty. To the best of our knowledge, this uniqueness result is the first presented in the literature for general settings, i.e. under standard assumptions on preferences, as well as some new condition on a transition probability. This paper advocates a “generalized Bellman equation” method to overcome some predicaments of the known methods and also extends our recent existence result. Our method also works for returns unbounded from above. We provide a few natural extensions of optimal policy uniqueness: convergent and accurate computational algorithm, monotone comparative statics result and generalized Euler equation.
KW - Generalized Bellman equation
KW - Markov equilibrium
KW - Time consistency
KW - Uniqueness
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UR - http://www.scopus.com/inward/citedby.url?scp=85045210317&partnerID=8YFLogxK
U2 - 10.1016/j.jet.2018.04.003
DO - 10.1016/j.jet.2018.04.003
M3 - Article
AN - SCOPUS:85045210317
VL - 176
SP - 293
EP - 310
JO - Journal of Economic Theory
JF - Journal of Economic Theory
SN - 0022-0531
ER -