Overview
This note presents Bank of Canada staff’s current assessment of the US and Canadian neutral rates of interest. The neutral rate is where the Bank expects the policy rate would settle once output is at its long-run potential level and inflation is at target, after the effects of all cyclical shocks have dissipated (Mendes 2014). The Bank does not target the neutral rate, but this is an important input for its economic projections.
We assess both the US and Canadian nominal neutral rates to be in the range of 2.25% to 3.25%, somewhat higher than the range of 2.0% to 3.0% in 2023. The assessed range is back to the level it was at in April 2019.
- A stronger outlook for potential output growth primarily explains the revision to the US neutral rate (Benmoussa et al. 2024).
- The revision to the Canadian neutral rate reflects a combination of the revised US neutral rate and key domestic factors, including stronger growth of trend labour input that is fully offset by weaker growth of trend labour productivity over the long term (Devakos et al. 2024).
The neutral rate is unobservable and inferred by assessing the evolution of the factors that influence it. Measurements of the neutral rate are subject to a considerable amount of uncertainty. The assessed ranges do not capture the full extent of uncertainties surrounding the neutral rate in the United States and Canada.
US neutral rate
The estimate of the US neutral rate—the Bank’s proxy for the global neutral rate—is based on the Bank’s view of US potential output growth and other factors that drive desired savings and investment in the United States, particularly inequality, macroeconomic risk and government debt.
We assess the US nominal neutral rate to be at the midpoint of a range from 2.25% to 3.25%, which is 25 basis points higher than in 2023 (Ahmed et al. 2023). The change mainly reflects the stronger outlook for potential output growth. This estimate of the US neutral rate is the same as the one presented in the April 2019 assessment (Carter, Chen and Dorich 2019).
New overlapping generations and term structure models
For this year’s assessment, we introduce two new models to our suite of approaches: a new overlapping generations (OLG) model of the US economy (Box 1) and a term structure model (Fontaine, Feunou and Krohn, forthcoming). Therefore, three models inform our assessment by capturing different drivers of the neutral rate:
- an OLG model that has the richest structure and accounts for several key drivers of the US neutral rate
- a risk-augmented neoclassical growth model that accounts for the tail risk channel, as explained in Bootsma et al. (2020)
- a term structure model that extracts information from financial markets1
Box 1: A new overlapping generations model
Box 1: A new overlapping generations model
We introduce a new overlapping generations (OLG) model this year for estimating the US neutral rate. The model is largely based on the one Kuncl and Matveev (2023) developed for assessing the Canadian neutral rate. In contrast to Canada, the United States is modelled as a closed economy where only domestic factors explain the neutral rate.
The new OLG model incorporates key drivers of the neutral rate that are discussed in the literature, particularly demographic trends, productivity growth, inequality and government debt (for example, see Platzer and Peruffo 2022; Marx, Mojon and Velde 2021; Gagnon, Johannsen and Lopez-Salido 2021; Mian, Straub and Sufi 2021; and Eggertsson, Mehrotra and Robbins 2019).
Compared with the previous OLG model introduced in Bootsma et al. (2020), our model includes additional features affecting the total supply of savings and total demand for investment in the US economy. These additions improve our estimation of the neutral rate. They include the following:
- Household heterogeneity within a generation captures the impact of inequality on the neutral rate. Introducing a bequest motive ensures that the model captures the effect of inequality on aggregate saving. All else being equal, an increase in inequality places relatively more resources in the hands of richer households with a higher propensity to save, putting downward pressure on the neutral rate.
- Changes to life expectancy capture the effect of longevity on the neutral rate. In the model, middle-aged households face a given probability of surviving into old age. As this probability rises in the model, so does life expectancy. Higher longevity means more households are expected to live beyond their working age and increase their savings to finance their retirement period. The additional savings put downward pressure on the neutral rate.
- Capturing the impact of government debt on the neutral rate is done through two dimensions. The first is the amount of debt issued to finance spending, which affects the total supply of safe assets in the economy. The second is spending on public pensions, which affects aggregate savings. All else being equal, upward pressure on the neutral rate comes from:
- a higher level of government debt, which implies a larger supply of safe assets
- a more generous public pension, which reduces the need for savings
Upward revision mainly due to a stronger outlook for potential output growth
Table 1 presents the estimated range for the neutral rate from each of the models above. All the models suggest the range for the neutral rate in 2024 increased by 25 basis points from 2023.2 As a result, our 2024 assessment is that the US neutral rate currently lies in the range of 2.25% and 3.25%.
Table 1: Summary of estimates of the US nominal neutral policy rate
| 2023 estimates | 2024 estimates | |
|---|---|---|
| New overlapping-generations model | 2.00–2.75 | 2.25–3.00 |
| Risk-augmented neoclassical growth model | 2.00–3.00 | 2.25–3.25 |
| Term structure model | 2.00–3.25 | 2.25–3.50 |
| Overall assessment | 2.00–3.00 | 2.25–3.25 |
Note: Rates are in nominal terms. All estimates have been rounded to the nearest 25 basis points. Reported ranges are constructed based on different counterfactuals with respect to key inputs.
A stronger outlook for potential output growth in the United States mainly explains the upward revision. This outlook is due to an increase in growth for both productivity and trend labour input (Benmoussa et al. 2024).
Counterbalancing the stronger outlook for potential output is an increase in the measure of perceived macroeconomic risk over the medium to long term, likely in response to the increasing frequency and duration of geopolitical tensions. This should lead to more precautionary savings and downward pressures on the neutral rate. Overall, the positive impact of a higher projected potential output growth outweighs the negative impact of higher macroeconomic risk. This leads to the upward shift in the 2024 assessment of the neutral rate.
US neutral rate back to the level presented in 2019
The neutral rate was revised down in 2020 due to economic factors related to the COVID-19 pandemic (Bootsma et al. 2020), particularly:
- a decline in expected potential output growth
- concerns about increased inequality due to the uneven negative impacts of the pandemic
- an increase in perceived macroeconomic risks
The estimate of the US neutral rate was revised up in 2022, and this year’s revision brings it back to the range assumed in the April 2019 assessment (Carter, Chen and Dorich 2019) (Chart 1). Upward pressure on the US neutral rate comes from:
- a rise in recent years in US government debt as a percentage of gross domestic product (GDP), also known as the debt-to-GDP ratio
- stronger projected growth in productivity and population growth compared with pre-pandemic estimates
However, an increase in macroeconomic tail risk roughly offsets these effects.
Chart 1: Evolution of the range of the US neutral rate since 2019
Canadian neutral rate
We assess that the Canadian neutral rate has increased by 25 basis points relative to the level in the 2023 assessment, and now lies in the range of 2.25% to 3.25%. The change is driven by a higher estimate of the US neutral rate and domestically by higher long-term trend labour input growth that is offset by lower long-term trend labour productivity growth. The estimated range for the Canadian neutral rate is based on the results from five assessment methods (Table 2):3
- an interest rate parity approach
- a term structure model
- a reduced-form model
- a risk-augmented neoclassical growth model
- an OLG model
Table 2: Summary of estimates of the Canadian nominal neutral rate
| 2023 estimates | 2024 estimates | |
|---|---|---|
| Interest rate parity approach | 2.00–3.00 | 2.25–3.25 |
| Term structure model | 1.75–3.00 | 2.00–3.25 |
| Reduced-form model | 2.25–2.75 | 2.25–3.00 |
| Risk-augmented neoclassical growth model | 2.50–3.00 | 2.25–2.75 |
| Overlapping-generations model | 2.25–3.00 | 2.25–3.25 |
| Overall assessment | 2.00–3.00 | 2.25–3.25 |
Note: Rates are in nominal terms. All estimates have been rounded to the nearest 25 basis points. Reported ranges are constructed based on different counterfactuals with respect to key inputs.
Interest rate parity approach
The interest rate parity model assumes that the Canadian neutral rate equals the global neutral rate. We continue to use estimates of the US neutral rate as a proxy for the global neutral rate. The upward revision to the estimate of the US neutral rate implies that the Canadian rate is between 2.25% and 3.25%.
Term structure model
This year, we supplement our estimates of the neutral rate by estimating the term structure model of interest rates jointly for the United States and Canada. We do this in a way that matches estimates with the evolution of the exchange rate between the Canadian and US dollars (Fontaine, Feunou and Krohn, forthcoming). This approach builds on the benchmark of Bauer and Rudebusch (2020) by examining the implications of any deviation from neutral rate parity on the exchange rate.
The results show an increase of 25 basis points, comparable to what we obtained from the interest rate parity approach. This similarity arises because the currency risk premium, which can drive a wedge between the neutral rates in each country, has declined over the last decade and is currently estimated to be close to zero.
Reduced-form model
In this model, we use a regression framework to consider the effects of both global and domestic factors on the Canadian neutral rate. These factors are captured by the US neutral rate and long-run potential output growth in Canada, respectively. Long-run potential output growth that is lower than in the 2023 assessment mitigates the upward push on the neutral rate implied by a higher estimate of the US neutral rate.
Results from the model suggest an increase of 25 basis points in the upper bound of the neutral rate estimates compared with the 2023 estimates. Thus, this model implies a nominal neutral rate in the range of 2.25% to 3.00%.
Risk-augmented neoclassical growth model
This model is a closed-economy general equilibrium model with aggregate uncertainty. It assumes that only domestic factors affecting households’ consumption and saving decisions drive the neutral rate. Higher population growth than in the 2023 assessment puts upward pressure on the Canadian neutral rate but is more than offset by the downward revision of long-term productivity growth. This leads to a downward revision of 25 basis points to the range of estimates. Thus, this model implies a nominal neutral rate in the range of 2.25% to 2.75%.
Overlapping-generations model
This is an open-economy general equilibrium model that was significantly extended for the 2022 assessment (for details, see Kuncl and Matveev 2023). Among the models used to evaluate the range of the neutral rate, the OLG model has the richest structure and encompasses most of the factors they capture.
In this model, international and domestic factors drive the Canadian neutral rate. The global neutral rate captures the international factors. Domestic factors include changes in:
- the growth rates of long-run labour input and productivity
- longevity
- government debt
- inequality
Our analysis this year updates the global neutral rate as well as domestic government debt and the growth rates of long-run labour input and productivity. As in previous assessments, we treat the US neutral rate as a proxy for the global neutral rate. The upward revision of the US neutral rate pushes up the Canadian neutral rate.
Domestically, higher growth in long-run labour input exerts upward pressure on the Canadian neutral rate. In the OLG model, population growth matters through the impact on both labour force growth—as in the neoclassical growth model—and the composition of borrowers and savers. A fast-growing population increases the proportion of young borrowers relative to middle-aged and older savers, putting upward pressure on the neutral rate. However, offsetting this upward pressure is lower growth in long-run productivity.
Furthermore, we revise up our assumption for the long-run level of the net public debt-to-GDP ratio in line with federal debt projections from the Government of Canada’s 2023 Fall Economic Statement. This revision to the debt-to-GDP ratio puts further upward pressure on the Canadian neutral rate. Overall, the upper bound of the range of estimates is revised up by 25 basis points. As a result, the model implies a nominal neutral rate in the range of 2.25% to 3.25%.
Assessment of the Canadian neutral rate
We estimate that the Canadian neutral rate likely lies in a range of 2.25% to 3.25% based on the combined result from a suite of approaches. This estimate is higher than the range from 2% to 3% reported in the 2023 assessment. The increase is mainly driven by:
- the upward revision in the US neutral rate
- higher long-term population growth in Canada that is offset by lower long-term productivity growth
The Canadian neutral rate was revised down in 2020 (Chart 2). This was due to a fall in the global neutral rate, a decline in potential output growth and an increase in the perceived level of macroeconomic risk (which boosts savings). In this assessment, the range of estimates of the neutral rate is back to its pre-pandemic level. This is partly explained by reconsidering the long-term effects of the pandemic on our estimate of the US neutral rate. Domestically, potential output growth and the net government debt-to-GDP ratio are close to their pre-pandemic levels.
Chart 2: Evolution of the range of the Canadian neutral rate since 2019
Conclusion
We assess the US and Canadian nominal neutral rates to be in the range of 2.25% to 3.25% in 2024, above the estimated range of 2.0% to 3.0% in 2023.
Inevitably, uncertainty surrounds estimates of an unobservable variable such as the neutral rate of interest. While the ranges presented in this note reflect the sensitivity of our estimates to different models and their inputs, these ranges are narrower than what econometric models would suggest (Cacciatore, Feunou and Ozhan, 2024).
References
Ahmed, S., A. Avshalumov, T. Chaar, E. Ekanayake, H. Lao, L. Poirier, J. Rolland-Mills, A. Toktamyssov and L. Xiang. 2023. “Assessing Global Potential Output Growth and the US Neutral Rate: April 2023.” Bank of Canada Staff Analytical Note No. 2023-5.
Bauer, M. and G. Rudebusch. 2020. “Interest Rates Under Falling Stars.” American Economic Review 110 (5): 1316–1354.
Benmoussa, A. A., R. Dastagir, J.-D. Guenette, H. Lao, J. Rolland-Mills, A. Spencer and L. Xiang. 2024. “Assessing Global Potential Output Growth: April 2024.” Bank of Canada Staff Analytical Note No. 2024-10.
Bootsma, J., T. J. Carter, X. S. Chen, C. Hajzler and A. Toktamyssov. 2020. “2020 US Neutral Rate Assessment.” Bank of Canada Staff Discussion Paper No. 2020-12.
Cacciatore, M., B. Feunou and K. Ozhan. 2024. “The Neutral Interest Rate: Past, Present and Future. A Thematic Review.” Bank of Canada Staff Discussion Paper No. 2024-3.
Carter, T. J., X. S. Chen and J. Dorich. 2019. “The Neutral Rate in Canada: 2019 Update.” Bank of Canada Staff Analytical Note No. 2019-11.
Devakos, T., C. Hajzler, S. Houle, C. Johnston, A. Poulin-Moore, R. Rautu and T. Taskin. 2024. “Potential Output in Canada: 2024 Assessment.” Bank of Canada Staff Analytical Note No. 2024-11.
Eggertsson, G. B., N. R. Mehrotra and J. A. Robbins. 2019. “A Model of Secular Stagnation: Theory and Quantitative Evaluation.” American Economic Journal: Macroeconomics 11 (1): 1–48.
Fontaine, J.-S., B. Feunou and I. Krohn. Forthcoming. “Twin Stars: Neutral Rates and Currency Risk Premiums.” Bank of Canada Staff Working Paper.
Gagnon, E., B. K. Johannsen and D. Lopez-Salido. 2021. “Understanding the New Normal: The Role of Demographics.” IMF Economic Review 69 (2): 357–390.
Kuncl, M. and D. Matveev. 2023. “The Canadian Neutral Rate of Interest Through the Lens of an Overlapping-Generations Model.” Bank of Canada Staff Discussion Paper No. 2023-5.
Marx, M., B. Mojon and F. R. Velde. 2021. “Why Have Interest Rates Fallen Far Below the Return On Capital?” Journal of Monetary Economics 124: S57–S76.
Mendes, R. R. 2014. “The Neutral Rate of Interest in Canada.” Bank of Canada Discussion Paper No. 2014-5.
Mian, A. R., L. Straub and A. Sufi. 2021. “What Explains the Decline in R*? Rising Income Inequality Versus Demographic Shifts.” University of Chicago, Becker Friedman Institute for Economics Working Paper No. 2021-104.
Platzer, J. and M. Peruffo. 2022. “Secular Drivers of the Natural Rate of Interest in the United States: A Quantitative Evaluation.” International Monetary Fund Working Paper No. 2022/030.
Endnotes
- 1. Details on the approach are included in the section on the Canadian neutral rate.[←]
- 2. The new OLG model includes the main drivers of the neutral rate captured in the heterogeneity- and liquidity-adjusted semi-open economy model, or HALO for short. However, results from the HALO model would also yield an upward revision of 25 basis points.[←]
- 3. These models were first established in Mendes (2014) and recently updated in Carter, Chen and Dorich (2019) and Kuncl and Matveev (2023). See these papers for detailed descriptions of the methods.[←]
Acknowledgements
We thank José Dorich, Stefano Gnocchi, Marc-André Gosselin, Harriet Jackson, Sharon Kozicki, Rhys Mendes and Subrata Sarker for their insightful conversations and feedback. We thank Jean-Sébastien Fontaine for useful inputs. Aviel Avshalumov and Argyn Toktamyssov provided useful input for the assessment of the US neutral rate. We also thank Maren Hansen and Jordan Press for their editorial assistance and Maxime Beaudet and Sylvie Vancappel for their help translating this note into French.
Disclaimer
Bank of Canada staff analytical notes are short articles that focus on topical issues relevant to the current economic and financial context, produced independently from the Bank’s Governing Council. This work may support or challenge prevailing policy orthodoxy. Therefore, the views expressed in this note are solely those of the authors and may differ from official Bank of Canada views. No responsibility for them should be attributed to the Bank.
DOI: https://doi.org/10.34989/san-2024-9