Analytical Results for Dynamic Rational Inattention Problems
Mirko Wiederholt, Filip Matějka, Bartosz Maćkowiak · RePEc: Research Papers in Economics · 2015
Dynamic rational inattention problems are notoriously difficult to solve. We consider a standard linear quadratic Gaussian tracking problem, as in Sims (2003), Section 4. Let Xt denote the variable being tracked and let t denote the time t innovation in the variable being tracked. We show that if the variable being tracked follows an AR(p) process, the optimal signal is about a linear combination of {Xt, ..., Xt-p+1} only. If the variable being tracked follows an ARMA(p, q) process, the optimal signal is about a linear combination of {Xt, ..., Xt-p+1} and {t, ..., t-q+1} only. Furthermore, the agent can attain the optimum with a single informative signal. These results make it much easier to solve dynamic rational inattention problems.