Abstract

This blog post examines the effectiveness of real rate rules in stabilizing inflation expectations using quarterly data from 10-year Treasury yields and inflation data from 1988 to 2024.

We estimate the relationship between inflation deviations from the target and the expected average deviation of future inflation, following the methodology outlined in “Robust Real Rate Rules” by Bundesbank economist Tom D. Holden. Our findings indicate a significant and positive relationship, supporting the use of real rate rules for effective monetary policy.

Introduction

Inflation stability is a key objective for central banks worldwide. Real rate rules, which adjust nominal interest rates based on real rates and inflation deviations, have been proposed as robust tools for achieving this goal. This study extends the analysis by using 10-year Treasury yields and inflation expectations to estimate the impact of inflation deviations on future inflation expectations.

Data Sources and Methodology

Data Sources

The data used in this study are sourced from the Federal Reserve Economic Data (FRED) database, maintained by the Federal Reserve Bank of St. Louis. The datasets include the Consumer Price Index (CPI), 10-Year Treasury Constant Maturity Rate (DGS10), and 10-Year Expected Inflation (EXPINF10YR). The data are provided quarterly and cover the period from 1988 to 2024.

Model Specification

To reflect the 10-year expectations, we use a rolling window of 40 quarters (10 years) to calculate the expected deviation.

Note: To address an unusual spike in Q4 2018 due to technical factors related to the shock 10 years earlier (2008), we adjusted the yt​ value for Q4 2018 to the average of Q3 2018 and Q1 2019 values. This adjustment ensures the model’s stability and accuracy.

Results

Regression Summary

• Inflation Deviation Coefficient (θ): 0.0227 (statistically significant at the 0.000 level)
• R-squared (uncentered): 0.362
• F-statistic: 57.19 (p-value: 1.87e-11)

Diagnostic Tests

• Durbin-Watson Statistic: 2.033 (no significant autocorrelation)
• Omnibus Test: 5.378 (p-value: 0.068)
• Jarque-Bera Test: 6.501 (p-value: 0.0388)

Visual Analysis

The actual and predicted values of yt are plotted against the date, showing that the model captures the overall trends and significant deviations effectively.

Discussion

The results confirm a significant positive relationship between inflation deviation and future inflation expectations. The coefficient aligns with the findings in Holden’s study, validating the robustness of real rate rules. The R-squared value indicates that the model explains a substantial portion of the variation, though other factors may also influence inflation expectations.

Comparison with Holden’s Results

Holden’s study “Robust Real Rate Rules” provides a framework for understanding the relationship between inflation deviations and inflation expectations, primarily focusing on data from 2008 Q4 to 2023 Q2. Our study extends this analysis in several key ways:

1. Longer Time Period:
   • Holden’s Study: 2008 Q4 to 2023 Q2.
   • Current Study: 1988 to 2024.
   • Impact: By including a longer time period, our study captures a wider range of economic conditions, including multiple economic cycles and policy changes.
2. Data Frequency and Sources:
   • Holden’s Study: Uses quarterly data on CPI and TIPS breakeven inflation.
   • Current Study: Uses quarterly data on CPI, 10-Year Treasury yields, and 10-Year expected inflation rates from FRED.
   • Impact: The use of 10-Year Treasury yields and expected inflation rates provides a longer-term perspective on inflation expectations.
3. Key Findings:
   • Holden’s Study: Found a significant positive relationship between inflation deviation and future inflation expectations, with various coefficients for different models ranging from 0.033 to 0.130.
   • Current Study: Also finds a significant positive relationship, with a coefficient of 0.0227. This consistency reinforces the robustness of real rate rules.

Conclusion

This blog post reinforces the effectiveness of real rate rules in stabilizing inflation expectations using long-term data. The findings support the adoption of such rules for robust monetary policy, ensuring inflation targets are met under varying economic conditions.

References

• Holden, T. D. (2023). Robust Real Rate Rules. https://www.tholden.org/assets/files/RobustRealRateRulesOnlineAppendices.pdf
• U.S. Bureau of Labor Statistics, Consumer Price Index for All Urban Consumers: All Items [CPIAUCSL], retrieved from FRED, Federal Reserve Bank of St. Louis; https://fred.stlouisfed.org/series/CPIAUCSL, June 27, 2024.
• Board of Governors of the Federal Reserve System (US), 10-Year Treasury Constant Maturity Rate [DGS10], retrieved from FRED, Federal Reserve Bank of St. Louis; https://fred.stlouisfed.org/series/DGS10, June 27, 2024.
• Federal Reserve Bank of Cleveland, 10-Year Expected Inflation [EXPINF10YR], retrieved from FRED, Federal Reserve Bank of St. Louis; https://fred.stlouisfed.org/series/EXPINF10YR, June 27, 2024.

This blog post has been nearly entirely written by ChatGPT-4 based on my prompting and the output from the regression analysis I asked ChatGPT-4 to undertake.

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