ricardomayerb edited Three Social Planner's problems.tex  almost 10 years ago

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In this paper, under full information the agent, in addition to knowing all parameters in his model, also observes current transitory and persistent components of productivity's evolution. Partial information means that she only knows the combined values of transitory and persistent components and knows the stochastic system that governs productivity evolution, implying the use of a different predictive conditional distribution for productivity compared to full information. Robustness, here, means that in addition to not been able to observe the transitory and persistent components behind productivity growth, she regards the stochastic system for productivity evolution as a mere approximation, searching for policies that work well under unspecified departures of the approximating model. This amounts to solving a penalized version of the partial information problem, where the penalization parameter is inversely related to how big of a departure from her approximating model she is willing to entertain when assessing potential realizations of the future.  \begin{equation} \label{eq:toy_bellman_full_info}  V(K_t,s_t, V^{FI}(K_t,s_t,  z_{t-1}) = \max_{v_t} u(C_t,L_t) + \beta E^{FI}_t V(K_{t+1}, V^{FI}(K_{t+1},  s_{t+1}, z_t | z_{t-1} ) \end{equation}