Measurement Error and Policy Evaluation in the Frequency Domain

This paper explores frequency-specific implications of measurement error for the design of stabilization policy rules. Policy evaluation in the frequency domain is interesting because the characterization of policy effects frequency by frequency gives the policymaker additional information about the effects of a given policy. Further, some important aspects of policy analysis can be better understood in the frequency domain than in the time domain. In this paper, I develop a rich set of design limits that describe fundamental restrictions on how a policymaker can alter variance at different frequencies. I also examine the interaction of measurement error and model uncertainty to understand the effects of different sources of informational limit on optimal policymaking. In a linear feedback model with noisy state observations, measurement error seriously distorts the performance of the policy rule that is optimal for the noise-free system. Adjusting the policy to appropriately account for measurement error means that the policymaker becomes less responsive to the raw data. For a parameterized example which corresponds to the choice of monetary policy rules in a simple AR (1) environment, I show that an additive white noise process of measurement error has little impact at low frequencies but induces less active control at high frequencies, and even may lead to more aggressive policy actions at medium frequencies. Local robustness analysis indicates that measurement error reduces the policymaker's reaction to model uncertainty, especially at medium and high frequencies.