Abstract
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 εt 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,...,XtMINUS SIGN p+1} only.
If the variable being tracked follows an ARMA(p,q) process, the optimal signal is about a linear combination of {Xt,...,XtMINUS SIGN p+1} and {εt,...,εtMINUS SIGN 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.