Time will tell whether this turns out to be the case. No One Right Answer Let me conclude by sharing something I learned from Thomas and hold dear. It's actually hidden in the last line of the abstract from our first published paper. It says: "Estimates of the natural rate of interest, however, are very imprecise and subject to realtime measurement error. "14 To some, that may sound like a negative statement. But it's also what makes empirical research so exciting and challenging. There is no one right answer and no single way to view the world. Empirical research is a process of continuous learning and adaptation —fueled by perseverance. People come up with different approaches, and we learn from all of them. So, while we started with the problem of how to estimate r-star, it didn't end with that first Board memo. Rather, it opened the door to new questions, which led to further challenges and even more research. This is the legacy of Thomas Laubach, and it's what brings us all together today. Figures  1 John H. Williams. "The Monetary Doctrines of J. M. Keynes," The Quarterly Journal of Economics 45, no. 4 (August 1931): 547 – 587. 2 John B. Taylor. "Discretion versus Policy Rules in Practice," Carnegie-Rochester Conference Series on Public Policy, Vol. 39 (December 1993), pp. 195 – 214. 3 Athanasios Orphanides discovered that quote after we were already working on r-star. 4 Thomas Laubach and John C. Williams. Estimates of a Time-varying Equilibrium Real Federal Funds Rate.
But the editor cut it, leaving it "for future research." What's Past is Prologue Fast forward a decade, and an entirely new question about r-star arose: Why had estimates of r-star fallen so low? It's a topic Thomas and I explored in our "Redux" paper.8 And in 2017, Kathryn, Thomas, and I expanded the set of economies for which we estimated r-star.9 Indeed, before the pandemic, historically low estimates of r-star characterized advanced economies across the globe. This is illustrated by the Holston-Laubach-Williams (HLW) estimates of r-star for the United States and the Euro Area using data through 2019, shown in Figure 1. Both were around ½ percent before the onset of the pandemic, far lower than estimates from preceding decades. Back to the Future One of the features of the LW and HLW models is that both are designed to be flexible and to "let the data speak" in measuring changes in the natural rate of interest. Even this flexibility, however, has its limits. And the economic turmoil brought on by the COVID-19 pandemic went far beyond what the models were originally designed for. In particular, the pandemic violated two key assumptions about the nature of macroeconomic disturbances underlying the models.10 First, the Kalman filter statistical method that serves as the models' workhorse assumes random disturbances to the economy follow a normal, or bell-shaped, distribution. Relative to historical experience, COVID-19 represented an extremely rare tail event in terms of its effect on the economy.