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Multivariate Rational Inattention
Author(s) -
Miao Jianjun,
Wu Jieran,
Young Eric R.
Publication year - 2022
Publication title -
econometrica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 16.7
H-Index - 199
eISSN - 1468-0262
pISSN - 0012-9682
DOI - 10.3982/ecta18086
Subject(s) - multivariate statistics , semidefinite programming , covariance , mathematical optimization , gaussian , positive definite matrix , covariance matrix , mathematics , matrix (chemical analysis) , quadratic equation , computer science , optimal control , algorithm , statistics , physics , eigenvalues and eigenvectors , materials science , quantum mechanics , composite material , geometry
We study optimal control problems in the multivariate linear‐quadratic‐Gaussian framework under rational inattention. We propose a three‐step procedure to solve this problem using semidefinite programming and derive the optimal signal structure without strong prior restrictions. We analyze both the transition dynamics of the optimal posterior covariance matrix and its steady state. We characterize the optimal information structure for some special cases and develop numerical algorithms for general cases. Applying our methods to solve three multivariate economic models, we obtain some results qualitatively different from the literature.