Natural rate estimates for the euro area: insights, uncertainties and shortcomings

Prepared by Claus Brand, Noëmie Lisack and Falk Mazelis

Estimates of the natural rate of interest, or r*, show trends that are of fundamental significance for monetary policy, but are subject to important caveats. r* is defined as the real rate of interest that is neither expansionary nor contractionary. Measures of r* are typically constructed as an equilibrium value towards which interest rates tend to gravitate in the medium to long term, as aggregate saving and investment imbalances abate and the inflationary or disinflationary pressures that may have developed as a consequence of those imbalances dissipate. These measures are also informative regarding the risk of short-term interest rates becoming constrained by their effective lower bound. However, available measures of r* are fraught with measurement and model specification challenges and are highly uncertain, reflecting, to different degrees, model, parameter, filter and real-time data uncertainty. While estimates of r* provide complementary information for monetary policy decisions and aid communication on the stance of monetary policy, these cannot be seen as a mechanical gauge of appropriate monetary policy at any point in time. In conducting monetary policy, there is no alternative to taking decisions on the basis of a comprehensive analysis of the data and their macroeconomic implications. In the euro area, in particular, the focus of such an assessment is threefold: the inflation outlook in light of the incoming economic and financial data, the dynamics of underlying inflation and the strength of monetary policy transmission.

Ranges of point estimates from different r* models indicate a very high degree of model uncertainty. Model uncertainty is the variability in estimates of r* that arises from using different models. Since r* is unobservable, economists rely on a range of models to estimate it. These models may incorporate different definitions of the benchmark rate, for example the instrument used by the central bank to conduct monetary policy. Different models may also rely on alternative determinants, such as measures of economic slack or the time horizons over which inflation eventually stabilises. Models can be clustered by type of measure – such as slow-moving equilibrium measures and cyclical inflation-stabilising measures. Slow-moving r* measures are anchored to long-run economic trends but may not capture short-term fluctuations. Cyclical r* measures reflect short-term dynamics and exhibit inflation-stabilising properties but can be sensitive to temporary shocks and are less stable. Balancing these trade-offs is challenging.

Chart A

Real natural rates of interest in the euro area

(percentages per annum)

Chart A shows a wide range of point estimates for the real natural rate. Following a modest post-pandemic increase, the updated range of point estimates of the real natural rate of interest for the euro area has remained broadly unchanged since the end of 2023 and is consistent with the estimates documented in Issue 1, 2024 of the Economic Bulletin.^[1] We distinguish between four categories of measures. The median from survey-based measures is indicated by the red line. Measures shown by the dark blue area are derived from models of the term structure of interest rates. Those derived from semi-structural models are shown by the dark yellow area. Finally, three estimates derived from the Holston-Laubach-Williams (HLW) model are shown separately, by the light yellow area. The latter measures are not available for the fourth quarter of 2024.^[2] Taking only the measures shown in the dark blue and dark yellow areas that were possible to update to the very end of 2024, the most recent estimates of real r* span a range between -½% and +½% (see the dark blue and dark yellow intervals corresponding to the fourth quarter of 2024 in Chart A).^[3] The way to translate those measures into their nominal counterparts is measure-specific. Some of the models produce both real and nominal versions of r*, while others estimate only one version. In the latter case, the missing value must be derived by adding or subtracting the ECB’s 2% medium-term inflation target or the model-consistent medium-term inflation expectations from the model estimate. When the three estimates derived from versions of the HLW model are factored in, the range of real r* is -½% to 1% and the corresponding nominal range is 1¾% to 3%.^[4] Referring only to those measures included in the dark blue and dark yellow areas for which an update to the end of 2024 is available, the estimates of the nominal r* from the most recent interval range between 1¾% and 2¼%. Given the estimation uncertainties highlighted in this box, such ranges should be viewed as merely indicative.

Natural rate estimates are further surrounded by uncertainties in model parameters. Point estimates typically display an outcome that is conditional on a single estimate of the model parameters – commonly the “most likely” value. However, the econometric methods used to estimate the model parameters generate a whole set of plausible alternative estimates. Bayesian estimation techniques, for example, concentrate on the probability distributions of parameters rather than on their fixed-point estimates. Embracing this approach allows the use of a distribution of values for each model’s r* estimate, which reflects the statistical uncertainty affecting the estimation of that model’s parameters. Taking one semi-structural model whose point estimate is included in the range shown in Chart A (the model by Brand and Mazelis, 2019), it can be seen that the parameter uncertainty surrounding each of the point estimates for r* can be quite large (Chart B, dark blue range).

Chart B

Parameter and filter uncertainty around the real natural rate estimates in the model by Brand and Mazelis

(percentages per annum)

An additional source of uncertainty comes from the fact that r* is an unobservable variable that must be inferred from observable data – a challenge known as filtering. Since r* cannot be observed directly, we must deduce it from the economic data that we can measure. Accordingly, additional filter uncertainty is associated with obtaining an informative signal from the data. Like parameter uncertainty, the filter uncertainty range is time-varying. Cumulatively, parameter and filter uncertainty together can span up to several percentage points (Chart B, light blue range) even for a single model.^[5]

Different data samples and revisions in backdata amplify the impact of filter uncertainty, leading to large ex post variations in in-sample point estimates of r* and adding yet another layer of uncertainty. Model-specific estimates of r* can vary significantly when observations are added or backdata are revised.^[6] Chart C illustrates the considerable extent of this sensitivity using the widely referenced approach of Holston, Laubach and Williams (2023). Over time, as updates become available, revisions in previously obtained estimates can be as large as 1 percentage point. Most recently, end-of-sample point estimates have varied by similar magnitudes from one quarter to the next.

Chart C

Vintages of point estimates of the real natural rate of interest for the euro area from the model by Holston, Laubach and Williams

(percentages per annum)

Despite the uncertainties involved, tracking broad movements in the natural rate over time provides qualitative insights into underlying economic trends. Notwithstanding the uncertainties associated with estimating r*, its trends contain information about developments in saving-investment imbalances that may create inflationary or disinflationary pressures, as well as about the extent to which the short-term interest rate might become constrained by the lower bound. The persistently low estimates of r* over the period 2015-22 displayed in Chart A, for example, reflect the persistent weakness in aggregate demand at the time and the low inflationary pressures that it generated. While in the post-pandemic environment estimates suggest some increase in r*, current estimates continue to be measurably below those prevailing before the global financial crisis, pointing to still lingering lower-bound risks in the event of sufficiently large disinflationary shocks.

The inherent uncertainties as well as conceptual shortcomings limit the usefulness of available natural rate estimates for conducting monetary policy in real time. Because of the multiple types of uncertainty and the focus on the short-term interest rate instrument – as opposed to broader measures of financing conditions, which can have a stronger impact on spending – the usefulness of r* as an indicator to support the calibration of the monetary policy stance is greatly limited, making it difficult to use as a rate-setting norm at policy meetings. Many models used do not construe r* as stabilising inflation in line with target but as merely indicating levels towards which interest rates gravitate over the longer term. As a function of historical shocks, such “equilibrium” interest rate measures are also largely backward-looking. By the time that equilibrium level is expected to be reached, the economy may well have already been exposed to further shocks, possibly causing the equilibrium rate of interest to drift and requiring monetary policy to offset these shocks. Furthermore, the connection between an r* defined in terms of the short-term interest rate instrument of monetary policy and the broader economy may itself change, as monetary policy transmission depends on a broader set of financing conditions – including the cost and availability of bank credit, and prices in a range of asset markets. The link between the short-term interest rate instrument and broader indicators for monetary policy is state-contingent and typically not stable. Accounting for these conceptual shortcomings and uncertainties is crucial for interpreting r* estimates.