The four different r-stars
Ricardo Reis in this paper, presents a comprehensive analysis of four distinct long-run steady-state values for real interest rates. He distinguishes between four r-stars:
- m: The expected return on productive investment
- y: The expected return on unproductive savings (e.g., government bonds)
- ρ: The realized return on savings
- i: The monetary policy rate
Reis then develops a general equilibrium framework to explain the joint evolution of the four r-stars and their impact on inflation. There are four components to the model that allow for divergence between the four r-stars while maintaining their interconnectedness.
- Investment and savings
Investment curve: Negative relationship between capital (k) and return on productive investment (m).
Savings curve: Upward sloping in (k, m) space. - Productive and unproductive savings
Portfolio-Arbitrage relation: Links return on productive investment (m) to yield on government bonds (y).
Ramsey-Euler relation: Balances average return on savings with consumption growth and time preferences. - Realized returns and output gap
Aggregate Supply (AS) curve: Relates realized returns (ρ) to output relative to potential.
Policy Target (PT) curve: Represents how policymakers manage aggregate demand. - Monetary policy and inflation
PC-IS curve: Combines Phillips Curve and IS relation, showing how lower policy rates lead to higher inflation.
Taylor rule: Describes how policymakers adjust the policy rate in response to inflation.
Finally, Reis explores trends during two different periods namely 1995-2019 and 2021-2024 in the US. He argues that the divergence between m and y should be attributed to global imbalances, changes in savings patterns, and shifts in the perceived safety and liquidity of government bonds. The recent narrowing of the m-y gap is linked to changes in global capital flows and perceptions of government bond safety.
- Divergent trends (1995-2019):
– m (return on productive investment) remained largely constant.
– y (yield on government bonds) showed a significant downward trend.
– ρ (realized returns) initially fell but increased in the last 5 years of the sample.
– i (policy rate) fell decisively until 2015, then partially recovered. - Recent developments (2021-2024):
– The wedge between m and y has sharply narrowed.
– y has risen continuously since 2022.
– i has moved upwards since 2022 as monetary policy tightened.
– ρ was very negative for most of this period due to inflation and bond price declines.
Policy Implications:
The author outlines three potential future scenarios:
- Benevolent benchmark: Inflation stays on target, output at capacity, with higher policy rates and bond yields.
- Forever-higher inflation: Attempts to run the economy “hot” lead to persistently rising inflation.
- Double trap: Both monetary and fiscal policy become constrained, leading to below-capacity output and low inflation.
The Four R-stars: From Interest Rates to Inflation and Back
Author: Ricardo Reis
From: LSE
The r-star in the Euro Area
Christensen & Mouabbi estimate the r-star for the euro area. The authors use a finance-based model estimated directly on French OAT€ bond prices since 2002. The authors’ r-star is defined as the 5y5y forward average expected real short rate, chosen to capture persistent trends in the natural real rate. Christensen and Mouabbi’s definition of r-star is most closely related to Reis’s y (the expected return on unproductive savings), as both focus on government bond yields.
Key findings:
- R-star decline: The natural rate of interest in the euro area has fallen by approximately 2 percentage points since 2002.
- Current level: Despite a recent increase (much like Reis’s y in the US), the r-star in the euro-area remains negative as of July 2024.
- Future scenario: The model suggests that the r-star is likely to revert only very gradually towards its old mean in the coming years.
- Global Factors: The similar trends observed in U.S. and euro-area market-based estimates suggest that global factors are likely driving the decline in interest rates.
A European Star: The Natural Rate of Interest in the Euro Area
Authors: Jens Christensen, Sarah Mouabbi
From: Federal Reserve Bank of San Francisco, Banque de France
