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 multiparameter 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.

Robust Monetary Policy in a Model of the Polish Economy: Is the Uncertainty Responsible for the Interest Rate Smoothing Effect?

“…Whereas robust control theory tells us how to make good decisions in the worst case scenario i.e. decision makers minimize worst-case loss (see Hansen and Sargent 2008;Barlevy 2011;Hudgins and Na 2016). Robust policy rules are found assuming that the moments of parameter uncertainty are not available and by using min-max methods where the maximization is taken over the range of parameter values and then we minimize with respect to control variables (cf.…”

Euro Area Monetary and Fiscal Policy Tracking Design in the Time-Frequency Domain

“…Section 3 builds a macroeconomic time-frequency accelerator model that is used within an optimal control system to determine optimal control feedback rules for monetary and fiscal policy. We convert the LQ tracking design into an LQ regulator design using the method employed by Crowley and Hudgins (2014) and Hudgins and Na (2014), and develop a MATLAB software program to compute the optimal joint fiscal and monetary policy. This framework allows the policymaker to render deterministic, stochastic LQG (Linear-Quadratic Gaussian) and robust controller designs, but the research presented in this paper only presents simulations for the deterministic LQ tracking control design.…”

“…The accelerator model has proved to be a useful theoretical and empirical tool over many decades since Samuelson (1939). Chow (1967), Kendrick (1981), Kendrick and Amman (2010), Kendrick and Shoukry (2013), Hudgins and Na (2014), and Crowley and Hudgins (2014) have all modeled quarterly fiscal policy within an applied macroeconomic optimal control LQ (Linear-Quadratic) tracking framework. Using U.S. data, Kendrick and Shoukry (2013) simulate the tracking performance and debt structure of the quarterly and annual models within a closedeconomy macroeconomic model that allows for monetary policy through interest rate components, but restricts the interest rate so that monetary policy is extremely passive.…”

“…Using U.S. data, Kendrick and Shoukry (2013) simulate the tracking performance and debt structure of the quarterly and annual models within a closedeconomy macroeconomic model that allows for monetary policy through interest rate components, but restricts the interest rate so that monetary policy is extremely passive. Hudgins and Na (2014) examine optimal robust policies using a similar model for the U.S. economy, but without money and interest rates.…”

Robust Control Design for an Uncertain Macroeconomic Dynamical System with Unknown Characteristics and Inequality Control Constraint

“…Day viewed the economic development as an adaptive process and proposed the adaptive economic theory, modelling, and dynamical analysis [8]. Hudgins and Na explored robust designs for an applied macroeconomic discrete-time LQ tracking model with perfect state measurements [9]. Berardi and Galimberti provided a critical review on several methods previously proposed in the literature of learning and expectations in macroeconomics in order to initialize its learning algorithms [10].…”