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...

We formulate an optimal estimation process in a stochastic growth model with an unknown true probability model. We consider a general reduced model of capital accumulation with an infinite horizon and introduce a learning process in the stochastic dynamic programming. When the only available...

We study a variation of the one-sector stochastic optimal growth model with independent and identically distributed shocks where agents acquire information that enables them to accurately predict the next period’s productivity shock (but not shocks in later periods). Optimal policy depends on...

This paper provides a review of some results on the stability of random dynamical systems and indicates a number of applications to stochastic growth models, linear and non-linear time series models, statistical estimation of invariant distributions, and random iterations of quadratic maps....

We discuss an analytically tractable discrete-time dynamic game in which a finite number of players extract a renewable resource. We characterize a symmetric Markov-perfect Nash equilibrium of this game and derive a necessary and sufficient condition under which the resource does not become...

The paper introduces some simplifying tools and methods for studying Rational Beliefs and for proving existence of Rational Belief Equilibria. We identify a set of stable non-stationary stochastic processes, named SIDS processes. Furthermore we introduce the concept of a Rational Belief...

Let <InlineEquation ID="Equ1"> <EquationSource Format="TEX"><![CDATA[$\{X_j\}^\infty_0$]]></EquationSource> </InlineEquation> be a Markov chain with a unique stationary distribution <InlineEquation ID="Equ2"> <EquationSource Format="TEX"><![CDATA[$\pi$]]></EquationSource> </InlineEquation>. Let h be a bounded measurable function. Write <InlineEquation ID="Equ3"> <EquationSource Format="TEX"><![CDATA[$\lambda_{h}=\int hd\pi$]]></EquationSource> </InlineEquation> and <InlineEquation ID="Equ4"> <EquationSource Format="TEX"><![CDATA[$\hat{\lambda}_{hn}=\frac{1}{(n+1)}\sum^n_0h(X_j)$]] ></EquationSource> </InlineEquation>. This paper explores conditions for the <InlineEquation ID="Equ5"> <EquationSource Format="TEX"><![CDATA[$\sqrt{n}$]]></EquationSource> </InlineEquation> consistency and asymptotic normality of the estimate of <InlineEquation ID="Equ6"> <EquationSource Format="TEX"><![CDATA[$\hat{\lambda}_{hn}$]]></EquationSource> </InlineEquation> of <InlineEquation ID="Equ7"> <EquationSource Format="TEX"><![CDATA[$\lambda_h$]]></EquationSource> </InlineEquation> assuming the existence of a solution to the Poisson equation <InlineEquation ID="Equ8"> <EquationSource Format="TEX"><![CDATA[$h - \lambda_h=g-Pg$]]></EquationSource> </InlineEquation>....</equationsource></inlineequation></equationsource></inlineequation></equationsource></inlineequation></equationsource></inlineequation></equationsource></inlineequation></equationsource></inlineequation></equationsource></inlineequation></equationsource></inlineequation>