R-star targeting when monetary policy is constrained by fiscal sustainability
Bhattarai et al., in this paper, use a New Keynesian model in a full-information environment in which tracking, even the correct, r-star generates macroeconomic instability and lower welfare. They find that tracking r-star is undesirable when there exists a channel through which an accumulation of nominal public debt leads to inflation. In particular:
The lack of proper fiscal policy adjustments prevents monetary policy from actively pursuing inflation stabilization. Instead, the monetary authority, constrained by government debt sustainabillity concerns, responds insufficiently to changes in the rate of inflation. Such accommodation by monetary policy allows inflation to adjust to stabilize public debt dynamics and achieve fiscal sustainabillity. Under this policy regime, variations in interest rates triggered by movements in r-star will change the level of public debt and thus the rate of inflation fluctuations that would be avoided if the central bank did not track r-star. We then show that not tracking r-star leads to higher macroeconomic stability and welfare. This leads to perils of tracking r-star.
The Perils of Tracking r-Star
Authors: Saroj Bhattarai, Jae Won Lee, Woong Yong Park
From: University of Texas – Austin, University of Virginia, Seoul National University
R-star targeting at the effective lower bound
Ajello and al. use a small-scale New Keynesian DSGE model to construct different scenarios in order to measure the effects of policymakers’ perceptions regarding the natural rate. They use US data from 1987 through the second quarter of 2019 for core personal consumption expenditures price inflation; real GDP growth; the unemployment rate; the effective Federal Funds Rate (FFR); the long-run unemployment rate; and FFR expectations. They look at potential policy responses, one in which the central bank correctly perceives the drop in r-star as well as two possible misperceptions, in which policymakers either miss the drop, believing the rate is higher than it is, or overstate the drop to be twice as large, believing the rate is lower than it actually is. Their conclusion:
[W]hen the FFR is close to the ELB, the costs are higher if policymakers mistakenly assume that r-star is greater than its true value. This happens because the ELB limits the ability of policymakers to counter a weaker economic outlook and correct course when they realize that monetary policy is not as accommodative as was previously thought. Therefore, when the policy rate is close to the lower bound, policymakers may prefer to act under the assumption of a lower r-star.

The Asymmetric Costs of Misperceiving R-star
Authors: Andrea Ajello, Isabel Cairó, Vasco Cúrdia, and Albert Queralto
From: Federal Reserve Board, Federal Reserve Bank of San Francisco