The financial stability interest rate is a threshold above which the real interest rate in an economy triggers financial constraints and systemic instability. It is different from the natural rate of interest, which balances growth and inflation. Indeed, the relationship between the financial stability interest rate and the natural interest rate may be one of the most important predictors of medium-term market direction and future crisis risk. A low financial stability rate versus the natural rate will create a tendency for real interest rates to rise to levels that disrupt financial relations. Factors that lower the financial stability rate include leverage and asset quality in the financial system. It is possible to build time series of financial conditions and stability rates.

Akinci, Ozge, Gianluca Benigno, Marco Del Negro, and Albert Queralto (2021), “The Financial (In)Stability Real Interest Rate, R**,” International Finance Discussion Papers 1308. Washington: Board of Governors of the Federal Reserve System.

The below are quotes from the above paper. Emphasis, heads and text in brackets has been added for clarity.
The post ties up with this site’s summary on managing systemic risk.

What is the financial stability interest rate?

“The financial stability interest rate is the threshold interest rate that triggers…financing constraint [in an economy]…The core idea relies on determining the underlying level of real interest rate that might generate financial instability dynamics…[It] differs from the natural real interest rate and from the observed real interest rate reflecting a tension in terms of macroeconomic stabilization versus financial stability objectives.”

“We consider an environment in which some agents in the economy face a credit constraint that gives rise to debt-deflation or asset fire-sale dynamics. Importantly, the credit constraint is occasionally binding. This implies that the economy is characterized by two states: when the constraint is not binding the economy is in a normal state or tranquil period; when the constraint binds the economy is in a crisis mode and a financial instability dynamic arises. The financial stability real interest rate is the interest rate that, for a given state of the economy (for example for a given amount of private debt), would be consistent with the constraint being just binding.”

“The decline in global real interest rates [in past decades] has largely occurred in a context of relatively low and stable inflation suggesting that the drop in observed real interest rates reflects a fall in what researchers refer to as the ‘natural real interest rate’.”

“The natural real interest rate…is usually defined as the real rate consistent with real GDP equal to its potential in the absence of shocks to demand. In turn potential GDP is defined to be the level of output consistent with stable price inflation absent transitory supply shocks…In short, the concept of natural real interest rate is associated with the notion of macroeconomic stability…Just like the natural rate of interest provides a benchmark for monetary policy in terms of macroeconomic stability, the financial stability interest rate is meant to provide a benchmark for financial stability: if the real rate in the economy is at or above [the financial stability rate], the tightness of financial conditions may generate financial instability.”

“Like the natural interest rate, the financial stability real interest rate is state dependent: it evolves with the conditions of the economy, and in particular with the degree of imbalances in the financial system. Along a path of higher external debt and lower net worth, higher leverage of the banking sector is accompanied by a lower financial stability rate…Increasing the real interest rate might create episodes of financial turbulence.”

A model that explains the role of the financial stability interest rate

We use a particular model to illustrate how the financial stability rate is constructed…One of the virtues of using the…framework is that it allows to relate the concept of financial stability real interest rate also to key variables for financial intermediaries such as the net worth or the asset/liability ratio…Financial intermediaries channel funds from households to firms. The key imperfection is that banks have a limit in their ability to raise funds because of a moral hazard problem…After raising funds and buying assets…the banker decides whether to operate honestly or divert assets for personal use. This moral hazard problem gives rise to an incentive compatibility constraint that creates a link between the value of the bank and the value of the assets that can be diverted.”

“Banks are ‘specialists’ who are efficient at evaluating and monitoring non-financial firms and at enforcing contractual obligations with these borrowers…Banks make risky loans to non-financial firms and collect deposits from both domestic households and foreigners. Because of an agency problem, banks may be constrained in their access to external funds.”

“The banker managing the bank may decide to default on its obligations and instead transfer a fraction of assets to the households, in which case it is forced into bankruptcy and its creditors can recover the remaining funds. In recognition of this possibility, creditors potentially limit the funds they lend to banks. In our setup, banks may or may not be credit constrained, depending on whether or not they are perceived to have incentives to disregard their contractual obligations.”

“In normal, or ‘tranquil,’ times, banks’ constraints do not bind: credit spreads are small and the economy’s behavior is similar to a frictionless neoclassical framework. When the constraint binds the economy enters into financial crisis mode: credit spreads rise sharply, and investment and credit collapse, consistent with the evidence.”

The link between the financial stability interest rate and financial system leverage

“We characterize the financial stability interest rate in a calibrated version of our model…We first calculate the implied real interest rate in the economy that makes the constraint just binding. When the leverage constraint is slack, this implied real interest rate is a benchmark rate for financial stability: if the real rate is to increase beyond the financial stability rate the tightness of financial conditions would generate financial instability…Increasing imbalances in the financial sector measured by an increase in leverage are accompanied by a lower threshold that could trigger financial instability events.

“As one moves towards adverse values of endogenous state variables…given by, for example, lower values of asset quality of the banking sector or higher values of the banking sector debt or the increased indebtedness of the country, the banking sector net worth falls and eventually the leverage constraint starts binding…Along the path of deteriorating asset quality of the banking sector (or higher banking sector debt, or higher foreign indebtedness), we observe that the banking sector becomes more leveraged and the economy more vulnerable to financial instability dynamics, implying that the financial stability rate has to fall.”

Financial conditions are very interdependent in determining the level of the financial stability rate…[The figure below] displays the three dimensional policy functions for a given level of the banking sector debt and the quality of bank assets. The constrained region is not only characterized by very low values of asset quality or by very high values of banking sector debt, but also by a combination of relatively low values the former and relatively high values of the latter. The threshold of banking sector debt for which the constraint becomes binding, and hence the level of the financial stability rate, is a function of the level of asset quality.”

An implied financial conditions index

“We…construct a theoretical implied financial condition index and show how it is related to the gap between the natural and financial stability interest rates.”

We construct a theoretical financial conditions index (FCI) using the standardized volatility of banks net worth and standardized annualized credit spread from the simulated model. In the index, volatility of banks net worth is defined as the annualized standard deviation of percentage change of banks equity. The principal component analysis on these variables yields the theoretical financial conditions index. We normalize the financial conditions index I, so that zero indicates the average level of financial stresses in the economy while positive (negative) values are associated with levels of financial stresses in the economy higher (lower) than the average.”

“[The figure below] illustrates the relationship between a measure of financial stresses in the model economy and the gap between the natural and financial stability interest rates. [Lower financial stability rates versus natural rates have been associated bouts of financial instability]”