Entering H $$^{\infty }$$ ∞ -Optimal Control Robustness into a Macroeconomic LQ-Tracking Model

Abstract

This analysis explores robust designs for an applied macroeconomic discrete-time LQ tracking model with perfect state measurements. We develop a procedure that reframes the tracking problem as a regulator problem that is then used to simulate the deterministic, stochastic LQG, H-infinity, multiple-parameter minimax, and mixed stochastic/H-infinity control, for quarterly fiscal policy. We compare the results of the five different design structures within a closed-economy accelerator model using data for the United States for the period 1947---2012. When the consumption and investment tracking errors are more heavily emphasized, the H-infinity design renders the most aggressive fiscal policy, followed by the multiple-parameter minimax, mixed, LQG, and deterministic versions. When the control tracking errors are heavily weighted, the resulting fiscal policy is initially more aggressive under the multi-parameter specification than under the H-infinity and mixed designs. The results from both weighting schemes show that fiscal policy remains more aggressive under the robust designs than the deterministic model. The simulations show that the multi-parameter minimax and mixed designs provide a balancing compromise between the stochastic and robust methods when the worst-case concerns can be primarily limited to a subset of the state-space.