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Analytical Results for Dynamic Rational Inattention Problems

Author

Listed:
  • Mirko Wiederholt

    (Goethe University Frankfurt)

  • Filip Matejka

    (CERGE-EI)

  • Bartosz Mackowiak

    (European Central Bank)

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 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.

Suggested Citation

  • Mirko Wiederholt & Filip Matejka & Bartosz Mackowiak, 2015. "Analytical Results for Dynamic Rational Inattention Problems," 2015 Meeting Papers 1316, Society for Economic Dynamics.
  • Handle: RePEc:red:sed015:1316
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    File URL: https://economicdynamics.org/meetpapers/2015/paper_1316.pdf
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