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.
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The authors are grateful to David Kendrick, Alex Ufier, and three anonymous referees for comments on earlier drafts of the paper.
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Appendix
Appendix
Tables 1, 2, 3 present the data graphed in Figs. 1, 2, 3, respectively, so that all of the data points can be compared with more detailed resolution. These data are in billions of constant dollars, so that a 1-point difference between data points represents $1 billion annualized. Consumption and investment are fixed at their initial values in period 1. Government purchases is fixed in period 0, and the first optimal policy action for government spending occurs in period 1. Deviations from targeted changes in government spending are penalized.
Tables 4, 5, 6 present the data graphed in Figs. 6, 7, 8, 9, respectively. The trajectories for government purchases under the H\(^{\infty }\)-control and 2-parameter minimax designs appear close in Fig. 6, but the differences are easily seen in Table 4.
Tables 7, 8, 9 show the data graphed in Figs. 11, 12, 13, respectively, where the deviations from targeted changes in government spending are not penalized.
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Hudgins, D., Na, J. Entering H\(^{\infty }\)-Optimal Control Robustness into a Macroeconomic LQ-Tracking Model. Comput Econ 47, 121–155 (2016). https://doi.org/10.1007/s10614-014-9472-5
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DOI: https://doi.org/10.1007/s10614-014-9472-5