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.

We introduce a portfolio friction in a two-country DSGE model where investors face a constant probability to make new portfolio decisions. The friction leads to a more gradual portfolio adjustment to shocks and a weaker portfolio response to changes in expected excess returns. We apply the model to monthly data for the US and the rest of the world for equity portfolios. We show that the model is consistent with a broad set of evidence related to portfolios, equity prices, and excess returns for an intermediate level of friction. The evidence includes portfolio inertia, limited sensitivity to expected excess returns, a significant impact of financial shocks, excess return predictability, and asset price momentum and reversal.