Stress-Testing U.S. Macroeconomic Policy: A Computational Approach Using Stochastic and Robust Designs in a Wavelet-Based Optimal Control Framework

This paper analyzes fiscal and monetary policy in a wavelet-based model under stochastic and mixed minimax robust optimal control. A state-space model is constructed after applying the Maximal Overlap Discrete Wavelet Transform to U.S. quarterly real GDP data. We derive the theoretical framework for the linear–quadratic Gaussian (LQG) design and the mixed design where the disturbances in a subset of frequency ranges are stochastic, and the other disturbances are modeled by a multiple-parameter minimax worst-case robust design. We then use the model to jointly simulate optimal fiscal and monetary policy to “stress test” the policies under the worst-case design. The results show that, compared to a deterministic design, the LQG framework introduces considerable variability into aggregate investment. Under active fiscal stabilization with restricted monetary policy, the minimax structure induces more aggressive fiscal spending, slightly larger aggregate consumption, and substantially lower aggregate investment compared to the LQG design. Thus, pursuing a minimax worst-case model induces larger government deficits and stifles long-term capital accumulation. Under active monetary stabilization with restricted fiscal policy, the simulations predict that both consumption and investment will be far less in the minimax design than in the stochastic design. This research is the first to integrate robust control and dynamic game theory with wavelet decomposition.