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  • Writer's pictureSergio Focardi

The natural interest rate

Today Focus Risparmio Magazine, publishes an article I have written on the subject of the natural rate of interest. The article is written in Italian. It can be read at the following address:

Given the interest of the subject at a moment when central banks are raising interest rates I provide here an English translation of my article.

Sergio Focardi

The natural interest rate: reality or fiction?

June 16, 2022


4 min

It is very difficult to hazard a critique of methods used by entities and people of great credibility such as central banks and their economists. Yet it is useful to do so. Perhaps it helps to separate the purely conceptual aspect from the practical aspect related to the decision-making processes of central banks and their objectives.

Sergio Focardi

The concept of a natural interest rate, today often called a neutral interest rate or even r* (R-star) in academic works, is due to the Swedish economist Knut Wicksell. In an 1898 paper, Wicksell defined the natural interest rate as the interest rate that allows an economy to function with full employment at the maximum of its productive capacities with a small constant inflation.

Wicksell was a brilliant economist and had many insights that proved fundamental to the development of economic theory. For example, he created the theory of an economy based only on credit and argued that credit creates purchasing power. Addressing the "Towards a Sustainable Financial System" conference at the Stockolm School of Economics on September 12, 2013, Adair Turner argued that many of Wicksell's insights into the role of credit in economics have been forgotten by modern economists.

Wicksell in the modern world

Wicksell's work was ignored for a long time: written in German, it was translated only in 1936. Above all, until the 90s central banks did not actively manage interest rates. It was believed that the main task of central banks was to control the quantity of money in circulation but not to control interest rates. Beginning in the 90s, however, central banks began to manage interest rates. Renewed interest in interest rates led to a close look at Wicksell's work. When interest rates reached zero, central banks concluded that it was necessary to understand what the correct value of interest rates was.

The natural interest rate, or r*, is a theoretical concept and not an observable variable. Central banks' growing interest in the natural rate, seen as a kind of constant of nature, has produced an offer of models for estimating the r* rate. The best-known models are the Laubach-Williams model (LW model, 2003) and the newer Holston-Laubach-Williams model (HLW model, 2017). These models obviously cannot be subjected to empirical verification, or at least not to direct empirical verification. In fact, the r* rate represents the short-term rate of a highly idealized economy. From a methodological point of view, the r* rate is analogous to the theoretical price of a share.

So, since central banks consider the r* rate an important indicator, let's try to understand what its usefulness and its connection with empirical reality really is. First of all, it is necessary to understand what the causal relationships are. Central banks have shifted their focus to interest rates because they believe that interest rates can act as regulators of an economy. Central banks act on the theory that raising interest rates has a depressing effect on the economy while reducing interest rates is a stimulus for the economy. In parallel, a depressing effect on the economy is believed to curb inflation while a stimulus effect may lead to an increase in inflation. Interest rates are therefore used as regulators of inflation. [1]

LW and HLW models are theoretical macroeconomic models that estimate r* based on various parameters in particular the growth rate of an economy's output. The r* rate does not remain constant over time but changes as a function of technological and structural changes that affect the output. The r* rate is believed to have fallen significantly over the past three decades.

Now it is very difficult to hazard a critique of methods used by entities and people of great credibility such as central banks and their economists. Yet it is useful to do so. Perhaps it helps to separate the purely conceptual aspect from the practical aspect related to the decision-making processes of central banks and their objectives.

The actuality of Wicksell's thought

Wicksell wrote his essay on the neutral rate 120 years ago. Advanced economies then were very different from those of today. Agriculture still employed half the population and industry was linked to large investments in heavy machinery. The evolution of products and services was slow. It could reasonably be assumed that in the first approximation an economy was a homogeneous entity capable of reaching a state of equilibrium. One could also accept that concepts such as output and inflation could represent an approximation of economic reality.

Today, advanced economies are complex evolutionary systems. Products and services are constantly evolving and the very structure of institutions is evolving. As I have written in other articles from the pages of this newspaper, it is impossible to aggregate economic output so as to arrive at a physical measure of output. The only possible aggregation is through the price forming the GDP, the sum of all final transactions. But GDP is a monetary quantity that depends on monetary factors and is subject to a process of inflation.

However, calculating the inflation of products and services subject to qualitative innovation is partly arbitrary as it involves deciding "the price of quality". In some papers we have suggested dividing goods and services into two categories, high and low innovation. For low-innovation products, inflation is calculated using classical methods, but we stipulate that the inflation of high-innovation products is zero. We choose highly innovative products and services using a complexity index.

Another critical point is full employment. The classical notion that employment is linked to output no longer applies to complex, evolutionary economies. In fact, automation, the growing symbolism of products and services, and the dislocation of productive activities have disconnected employment and output. In addition, the creation of monetary profit is linked to the indebtedness of workers and the actions of the Central Bank. I have covered these points in two articles on Social Europe[2].

Then we must ask ourselves the question of whether it makes sense to hypothesize and calculate a neutral rate, r*, in a high-innovation, high-level automation economy with a credit-based money creation mechanism. If we ignore the complexities, calculate inflation as usual, the interest rate may or may not have an expansionary effect on the economy. In this sense, the r* rate is a theoretical equilibrium point.

However, if we look closely at the economy as a complex evolutionary system, we see that the employment-GDP-inflation relationship is very complex. The reduction in employment and the emergence of large sections of the population employed for primitive and underpaid jobs is an example of the complexity of these relationships.

The r* rate is calculated using highly idealized models that are estimated using data such as real GDP, i.e. discounted nominal GDP to account for inflation. In a complex evolutionary system this strategy is, at least in part, arbitrary. Real GDP is not an observable is a theoretical term that depends on the method of calculating inflation.

From the point of view of central banks, the r* rate provides guidance for stimulating real GDP or contracting inflation, where real GDP and inflation are calculated by classical methods. But what are the real consequences of these decisions? Raising interest rates in a generalized way to reduce inflation risks counteracting the inevitable creative effort of industry to increase the quality of products and services without increasing their "material footprint" that is, their impact on the environment. The consequences on the work can be serious for the reasons we have indicated before related to automation and the profit circuit.

Advanced economies today are complex systems that must adapt to producing quality rather than quantity: economic policy measures that do not recognize the essential complexity of the economy risk being very negative.

* Sergio Focardi teaches "Economics of Complexity" at Franklin University Switzerland in Lugano, Switzerland.

[1] Holston, Kathryn, Thomas Laubach, John C. Williams. 2016. "Measuring the Natural Rate of Interest: International Trends and Determinants." Federal Reserve Bank of San Francisco Working Paper 2016-11.

[2] Focardi Sergio M. 2018, "Do Capitalists Still Need Consumers?", appeared in Social Europe, 18 September, 2018 (; Focardi Sergio M. 2018, "Symbolic Growth and Stagnant Wages", appeared in Social Europe, 31 May, 2018 (

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