Taylor Principle & Fisher Relation

The paper begins by examining the short-run relationship between the nominal interest rate and inflation. The conventional view, supported by empirical work from Taylor (1999) and Clarida et al. (2000), interprets this relationship as a reflection of the central bank's interest rate rule or reaction function. An inflation coefficient less than one suggests that monetary policy responded too timidly to inflationary pressures, particularly noticeable in the macroeconomic instability before circa 1980, as shown by Clarida et al. (2000). However, the authors challenge this conventional interpretation. They highlight the work of Hetzel (2000), who cautions against interpreting reduced-form relationships as direct indicators of policymakers' underlying preferences. Cochrane (2011a) further emphasizes the difficulty in identifying suitable strategies to recover the coefficients of the reaction function, while Lucas (2003) contends that the Fisher relation already accounts for the observed empirical link. The initial analysis questions this conventional 'reaction function' interpretation, setting the stage for a more nuanced investigation of the short-run dynamics between the nominal interest rate and inflation. The study acknowledges that the short-run relationship may be more complex than simply reflecting central bank preferences, raising important questions about the reliability and accuracy of interpreting empirical findings on this relationship.

The analysis then shifts to the long-run relationship between the nominal interest rate and inflation, focusing on the Fisher relation (Crowder and Hoffman, 1996). In the long run, this relation suggests a one-to-one correspondence: the nominal interest rate adjusts to compensate investors for the erosion of purchasing power due to inflation. Crucially, the long-run Fisher relation is distinguished from a reaction function. The study acknowledges that nominal rigidities significantly impact the monetary policy transmission mechanism in the short run (Nelson, 2008a). However, in the long run, once these rigidities dissipate, the mechanism by which a central bank maintains a 'nominal anchor' for price level determination becomes uncertain. Nelson (2008a) argues that, given the empirical link between money growth and inflation at low frequencies, controlling the money supply provides a more plausible long-run solution. Thus, the paper delves into the long-run implications of the Fisher effect, contrasting it with short-run dynamics and highlighting potential limitations of using short-run relationships to infer long-term policy intentions. The different behavior and implications of the short-run and long-run relationships are central to the overall argument of the study.

The document contrasts the observed relationship between the nominal interest rate and inflation across different macroeconomic environments. Specifically, post-1980 U.S. data, corresponding to the Great Moderation period, exhibit a more-than-proportional relationship, aligning with the Taylor principle. In contrast, the period prior to 1980, characterized by significant macroeconomic instability and high inflation, shows a less-than-proportional relationship. This difference in observed relationships fuels the central question of the paper: are these variations a consequence of shifts in policymakers' preferences or a result of misspecified models? The conventional interpretation attributes the shifts to changes in monetary policy reaction functions (Taylor, 1999; Clarida et al., 2000). However, the study challenges this interpretation, suggesting that the discrepancies might not always accurately reflect changes in central bank behavior. It also touches upon alternate explanations related to investor behavior and rational expectations that account for the divergence from a simple, proportional relationship between inflation and interest rates over different time periods and macroeconomic environments. The analysis establishes a foundation for its later empirical work.

This section contrasts the use of interest rate rules and money supply rules in monetary policy. The preference for interest rate rules stems from their alignment with central bank communication strategies (Romer, 2000; Mehrling, 2006). The dependent variable in these rules, such as the Federal Funds Rate (US) or Bank Rate (UK), directly reflects announced policy actions, creating a clear link between theory and practice. Taylor (1993) further justifies interest rate rules by showing that fixed settings for monetary instruments are suboptimal, necessitating responses to changes in the price level or real GDP. However, the paper challenges the exclusive focus on interest rates, citing theoretical and empirical evidence that monetary relationships remain crucial. Nelson (2008a) points to the lack of a clear mechanism in the New Keynesian (NK) model for determining long-run inflation using only interest rates, suggesting that money supply control is a more natural candidate given the robust empirical link between money growth and inflation at low frequencies. This section sets the stage for a more thorough examination of the relative merits of both approaches, questioning the dominance of interest rate rules and highlighting the continuing importance of money supply considerations in monetary policy analysis.

The section delves into the Taylor rule (Taylor, 1993), a pivotal interest rate rule, discussing its various extensions. These extensions encompass forward-looking elements (Clarida et al., 1998, 2000; Batini and Haldane, 1999; Mehra, 1999), econometric estimation procedures rather than calibration (Taylor, 1999; Clarida et al., 1998, 2000; Rudebusch, 2009), interest rate smoothing to account for lagged dependent variables (Carlstrom and Fuerst, 2008), and the inclusion of variables beyond inflation and the output gap, such as unemployment (Mankiw, 2001; Clarida et al., 2000; Rudebusch, 2009). The flexibility of the Taylor rule framework allows for such modifications. However, the paper contrasts this exogenously specified rule with implicit interest rate rules derived from underlying structural models. Implicit rules are equilibrium conditions of a model, often under alternative monetary regimes like a constant money growth rule. The paper notes that these implicit rules place constraints on their coefficients, questioning the ability of empirical studies to definitively reveal policymakers' true 'reaction functions' solely through aggregate data. This lays the foundation for the subsequent empirical analysis, which will directly address the capabilities and limitations of various modelling approaches.

The text explores the decreased emphasis on monetary aggregates in monetary policy analysis, alongside the rise of interest rate rules. The New Keynesian (NK) model, often considered a complete representation of the economy (Woodford, 2008), can be solved without referencing money, partially explaining this theoretical marginalization. This is also reflected in practical central banking, with many advanced economies de-emphasizing monetary aggregates in recent decades (Bernanke, 2006). One practical justification for this shift centers on the perceived instability of money demand (Goldfeld, 1976; Goldfeld and Sichel, 1990). The difficulty in accurately modeling money demand, along with sudden shifts in the velocity of money (Beck and Wieland, 2008), are cited as key challenges for traditional monetary targeting. However, this view is not universally held. The European Central Bank (ECB), Bundesbank, and Swiss National Bank retain the view of inflation as a monetary phenomenon (Bordo and Filardo, 2007), maintaining the importance of monetary aggregates. Even within central banks primarily focused on interest rates, concerns remain about frameworks devoid of money (King, 2002). Empirical studies supporting the continued relevance of money are also reviewed, suggesting that the debate over the role of money in monetary policy remains unresolved and that ignoring monetary aggregates may lead to incomplete and potentially misleading analysis.

This section details the empirical investigation of the Taylor principle using simulated data from the Benk et al. model. The Taylor condition, derived from the model, is used to create various estimating equations, including misspecified versions. To isolate high-frequency fluctuations reflecting business cycles (Christiano and Fitzgerald, 2003), the simulated data is filtered using Hodrick-Prescott and band-pass filters. Three econometric techniques—Ordinary Least Squares (OLS), Two-Stage Least Squares (2SLS), and Generalized Method of Moments (GMM)—are employed to estimate the coefficients. The GMM method is favored for its precision. The results generally support the Taylor principle (inflation coefficient > 1) when using filtered data, indicating a more-than-proportional relationship between the nominal interest rate and inflation. Critically, the study highlights that restricting the estimating equation or using unfiltered data leads to coefficient estimates that violate the Taylor principle. This finding underscores the importance of proper model specification and data pre-processing in accurately assessing monetary policy. The exercise emphasizes that inferences about policymakers' preferences should not be drawn solely from estimates of a misspecified model.

This section focuses on the empirical analysis of the Fisher relation using actual US data from 1960 to 2011. The analysis aims to determine whether the data supports a stable real rate plus inflation premium, as per the Fisher relation, or a central bank's policy response to inflation, as suggested by Lucas (2003). The study uses an error correction model, a common technique in Fisher relation literature (Arnwine and Yigit, 2008), treating the augmented Fisher relation as a long-run equilibrium condition. The model incorporates lagged dependent and independent variables to describe short-run deviations from this equilibrium. Initial results using various econometric techniques and filters, such as those designed to extract medium-term cycles (Comin and Gertler, 2006), are reported. The analysis addresses the non-stationary nature of the data, a concern raised by Siklos and Wohar (2005) and Österholm (2005), and uses error correction methods. The results from this section are compared to those obtained with simulated data and used to make inferences about the correspondence between various interest rate rules and the Fisher relation over different time periods. The focus is on identifying the appropriate empirical model for accurately representing the underlying economic relationships.

This section discusses important methodological considerations and addresses concerns about the empirical analysis. The study acknowledges the critique of Hetzel (2000) and Lucas (2003) regarding the interpretation of reduced-form relationships as policy rules and the identification problem in the NK model (Cochrane, 2011a). The authors emphasize the necessity of using a structural model to accurately understand the relationships underpinning reduced-form expressions. The analysis acknowledges the non-stationary nature of the nominal interest rate and inflation series over the long sample period, a common issue in time-series econometrics, and employs appropriate econometric methods such as cointegrating regressions and error correction models to address this. Furthermore, the impact of tax adjustments to the nominal interest rate is investigated. The study also notes how the choice of empirical proxies for the nominal interest rate (e.g., effective federal funds rate vs. 3-month Treasury bill rate) can affect results and that various econometric techniques (OLS, 2SLS, GMM) provide different insights, which highlights the importance of methodological rigor in drawing reliable conclusions from the data.

The research findings raise significant questions about the conventional interpretation of empirical results concerning the Taylor rule. The study demonstrates that the seemingly inconsistent variations in inflation coefficients observed in historical data, often attributed to changes in policymakers' preferences (Clarida et al., 2000), might instead stem from model misspecification. The analysis shows how the inclusion or exclusion of variables like the velocity of money can drastically alter the estimated inflation coefficients, even leading to violations of the Taylor principle. Therefore, concluding that a central bank's behavior shifts because empirical estimates violate the Taylor Principle may be premature and inaccurate. The findings suggest a need for greater methodological rigor when employing the Taylor rule empirically, particularly concerning the careful selection of variables and appropriate econometric techniques. The research also highlights that the empirical success of the Taylor rule in certain periods might be coincident with a well-managed money supply, rather than solely reflecting the effectiveness of the interest rate targeting regime. The paper suggests a closer examination of the link between interest rate rules and money supply management in future research.

The empirical investigation supports the Fisher relation in the long run, finding a one-to-one relationship between the nominal interest rate and inflation. However, achieving this result required the use of error correction models to address the non-stationary nature of the data and an adjustment for tax effects on capital income. This finding suggests that previous empirical studies which focused solely on shorter-term relationships might have overlooked essential factors like tax rates when assessing the validity of the Fisher relation. The inclusion of tax effects can explain why the coefficient on inflation in empirical studies may exceed unity, contrary to a simple interpretation of the Fisher relation which predicts a coefficient of 1. The study emphasizes the importance of considering tax implications when analyzing the connection between nominal interest rates and inflation. The research underlines the importance of understanding how various modeling choices and data limitations influence the interpretation of the Fisher relation, emphasizing the need for more robust and comprehensive empirical methodologies in this area of research.

In conclusion, the research challenges the simplistic interpretation of empirical results obtained from applying the Taylor rule and suggests a more nuanced approach to monetary policy analysis. The paper highlights the limitations of models that neglect monetary aggregates and advocates for incorporating money supply considerations to better understand both short-run and long-run macroeconomic dynamics. The study's findings underscore the crucial role of accurate model specification and appropriate econometric techniques when drawing policy inferences from empirical data. A key result is the demonstration that the Benk et al. model incorporates both the short-run Taylor principle and the long-run Fisher relation. The study implicitly suggests the need for more sophisticated models that can capture the complex interplay between interest rates, money supply, and inflation, especially when assessing the effectiveness of various monetary policy approaches. The study's limitations—such as using actual data in unfiltered form and maintaining rational expectations—are acknowledged, pointing towards avenues for future research to refine the current approach.