Measuring the Natural Rate of Interest
 
DOWNLOADS LW Estimation Real-time estimates Current estimates Replication code
HLW Estimation Real-time estimates Current estimates Replication code
 
The Laubach-Williams (“LW”) and Holston-Laubach-Williams (“HLW”) models provide estimates of the natural rate of interest, or r-star, and related variables. Their approach defines r-star as the real short-term interest rate expected to prevail when an economy is at full strength and inflation is stable.

R-STAR FOR THE UNITED STATES
LW Estimation



The Laubach-Williams (2003) model uses data on real GDP, inflation, and the federal funds rate to extract trends in U.S. economic growth and other factors influencing the natural rate of interest. Link through the main navigation tabs above to a data visualization.

Download Data Series and Code for LW Estimation
Real-time estimates (based on vintage data)
Current model estimates (previously labeled "updated estimates"; data include parameter estimates)
Replication code (as of 11/1/19)
Notes on the August 31, 2018, estimates
Adapting the Laubach and Williams and Holston, Laubach, and Williams Models to the COVID-19 Pandemic (May 27, 2020)
Replication code for COVID-adjusted LW model (as of 6/16/2020)

Reference
Laubach and Williams. 2003. “Measuring the Natural Rate of Interest,” Review of Economics and Statistics 85, no.4 (November): 1063-70.

Working paper version: “Measuring the Natural Rate of Interest”

2020 Release Dates*
February 28
May 29
August 28
* Owing to the extraordinary volatility in GDP related to the COVID-19
pandemic, we are suspending until further notice the posting of regular
updates of the LW and HLW model estimates. (November 30, 2020)

Note: The New York Fed does not offer individualized services to readers, such as custom charts or analysis.

The replication code zip files shared above contain programs to prepare and manage data series used in LW and HLW estimation. They do not, however, contain the input data. Consult the code guides in the zip packages as well as the scholarly references on this web page for information on the data series used to run the models and their sources.

The Laubach-Williams and Holston-Laubach-Williams estimates were previously published on the Federal Reserve Bank of San Francisco’s website. No aspects of the methodology changed when publication moved to the Federal Reserve Bank of New York. See our “Notes” summarizing the effects of the 2018 National Income and Product Account (NIPA) revisions on our estimates of r-star and related variables above.

How to cite this report: Federal Reserve Bank of New York, Measuring the Natural Rate of Interest, https://www.newyorkfed.org/research/policy/rstar/overview.

Contact: research.publications@ny.frb.org


Disclaimer: The Laubach-Williams and Holston-Laubach-Williams estimates are not official forecasts of the Federal Reserve Bank of New York, its president, the Federal Reserve System, or the Federal Open Market Committee.

R-STAR FOR ADVANCED ECONOMIES
HLW Estimation



The Holston-Laubach-Williams (2017) model extends this analysis to other advanced economies, estimating r-star and related variables for the United States, Canada, the Euro Area, and the United Kingdom. Link through the main navigation tabs above to a data visualization.

Download Data Series and Code for HLW Estimation
Real-time estimates
Current model estimates
Replication code (as of 11/1/19)
Adapting the Laubach and Williams and Holston, Laubach, and Williams Models to the COVID-19 Pandemic (May 27, 2020)
Replication code for COVID-adjusted HLW model (as of 6/16/2020)

Reference
Holston, Laubach, and Williams. 2017. “Measuring the Natural Rate of Interest: International Trends and Determinants,” Journal of International Economics 108, supplement 1 (May): S39–S75.

Working paper version: “Measuring the Natural Rate of Interest: International Trends and Determinants”

2020 Release Dates*
March 2
May 29
August 31

* Owing to the extraordinary volatility in GDP related to the COVID-19
pandemic, we are suspending until further notice the posting of regular
updates of the LW and HLW model estimates. (November 30, 2020)
R-star is the real interest rate expected to prevail when the economy is operating at its full sustainable level, while the output gap measures the extent to which the economy is currently operating above or below this sustainable level. Using the Laubach-Williams model, we calculate these estimates for the United States, along with estimates for trend growth—a source of change driving r-star.
  • Source: Calculations use the methodology outlined in Laubach and Williams (2003).
  • Note: The shaded areas indicate periods designated as recessions by the National Bureau of Economic Research.
  • 1 "One-sided" refers to the Kalman filter estimates of the state variables (r-star, trend growth, and the output gap), that is, the "one-sided" estimate of the time t value of r-star is conditional on observations dated 1 through t.
  • 2 "Two-sided" refers to the Kalman smoother estimates of the state variables. The "two-sided" estimate of the time t value of r-star is conditional on all the available observations.
Holston, Laubach, and Williams estimate the natural rate of interest, trend growth, and the output gap for four economies—the United States, Canada, the United Kingdom, and the Euro Area—using a version of the Laubach-Williams model. For each economy, the analysis employs data on real GDP, inflation, and a short-term interest rate to extract trends in economic growth and other factors influencing r-star.
  • Source: Calculations use the methodology outlined in Holston, Laubach, and Williams (2017).
  • Notes: All estimates are one-sided, and constructed as Kalman filter estimates of the state variables (r-star, trend growth, and the output gap). For example, the “one-sided” estimate of the time t value of r-star is conditional on observations dated 1 through t. Data for the Euro Area are available beginning in 1972.
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