## The Term Structure of Interest Rates and Macrofinancial Dynamics

_IMF News, August 17, 2017_

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## Bibliographic details
- Authors: Tobias Adrian
- Published: August 17, 2017

---

### Overview
- Speaker: Tobias Adrian, Financial Counsellor, Director of the Monetary and Capital Markets Department, IMF.
- Venue: Bank of Canada Conference on Advances in Fixed Income and Macro-Finance Research, Vancouver.
- Date: August 17, 2017.
- Objective: Lay out a path to modeling macrofinancial dynamics using a recent approach and illustrate usefulness with a term structure application.

### Four important aspects of interest rates examined
- The level of the 10-year yield.
- The term premium embedded in the 10-year yield.
- Interest rate volatility as measured by the MOVE index.
- The natural real rate r*.
- Definitions:
  - Term premium: investors’ compensation for the risk that interest rates do not evolve as expected.
  - Natural rate of interest r*: the real interest rate that prevails when monetary conditions are neutral.

Key empirical observations:
- Nominal rate rose from 4 percent in 1961 to a peak of 15 percent in 1982, before declining to below 2 percent in 2016.
- Term premium rose from around 0 percent in 1961 to above 5 percent in 1985, and fell back to below 0 percent in 2016; it spiked in 2008.
- Movements in volatility are tightly linked to movements of the term premium.
- Estimated level of the neutral rate exhibits a long term downward trend and is only tightly linked to the level of interest rates in recent years.

### The need for macrofinancial modeling — empirical motivation
- Traditional macro models often assume constant term premium and interest rate volatility (examples: standard New Keynesian (NK) model; Christiano, Eichenbaum and Evans, 2005; Smets and Wouters, 2007).
- Popular term structure models are reduced form and often omit macroeconomic inputs (examples: Kim and Wright, 2005; Adrian, Crump, Moench, 2013).
- Linearized NK models lack features to match macroeconomic and bond market moments; some nonlinear approaches imply implausible parameter estimates (Rudebusch and Swanson, 2012).

Evidence on explanatory power of macro vs financial variables for yield-curve PCs:
- Table 1 (macroeconomic variables explaining yield-curve principal components):
  - Level (PC1) explained: 13%
  - Slope (PC2) explained: 5%
  - Curvature (PC3) explained: 18%
  - (Panel details: Production & income 0% for PC1; Employment, unemployment, & hours 1% for PC1 etc. — overall R-squares above.)
  - Source factors: yield curve PCs from Gurkaynak, Sack, Wright (2006); macro factors are the four most significant factors of the Chicago Fed economic conditions index.

- Table 2 (financial conditions explaining yield-curve principal components):
  - Level (PC1) explained: 42%
  - Slope (PC2) explained: 25%
  - Curvature (PC3) explained: 33%
  - Average R-squared using financial conditions: 33 percent, compared to 12 percent for macroeconomic variables.
  - Source factors: yield curve PCs from Gurkaynak, Sack, Wright (2006); financial conditions factors are the four most significant factors of the Chicago Fed financial conditions index.

- Table 3 (both macroeconomic factors and financial conditions):
  - Average R-squared increases to 43 percent when both sets of variables are used.
  - Interpretation: financial conditions are quantitatively more important determinants of the term structure than macroeconomic variables in linear regressions; linear approaches likely miss nonlinear linkages.

Additional empirical findings:
- Financial conditions are highly significant predictors of the conditional distribution of GDP: at one-quarter or one-year horizons, tight financial conditions forecast low GDP growth and high GDP variance, shifting the conditional GDP distribution left.
- Conditional mean, variance, skewness, and kurtosis of GDP depend significantly on financial conditions; movements in the first and second moments tend to be more important than movements in the third and fourth moments.
- Negative dependence of conditional GDP mean and conditional GDP volatility: when financial conditions deteriorate, mean declines and volatility increases; right tail of GDP distribution relatively stable because mean and volatility effects offset for upper quantiles.
- These empirical approaches are designed to capture nonlinear effects; evidence points to nonlinear macrofinancial linkages and the importance of financial cycle for output risk.

### A different modeling approach (Adrian and Duarte 2016)
Model ingredients:
- Start from a standard New Keynesian model augmented with a financial intermediary (banking) sector subject to an occasionally binding Value-at-Risk (VaR) constraint.
- Effective risk aversion is time varying as a function of the tightness of the VaR constraint.
- Intermediary preference shocks induce shifts in pricing of risk.
- Aggregate demand from household intertemporal consumption-saving (IS curve); aggregate supply from standard Phillips curve.

Methodological contribution:
- Derive the nonlinear equilibrium in closed form; then linearize first and second moments separately.
- Rationale: first and second moments’ evolution as functions of state variables drive nonlinear macrofinancial dynamics; linearizing them separately yields tractable approximations.
- Applicable to a wide range of macro-finance models.

Mechanisms and dynamics:
- VaR constraint links conditional means and conditional volatilities, producing feedback between financial premia (conditional volatilities) and expected levels of real macro variables (conditional means).
- Monetary policy movements in the real rate shift the intertemporal savings decision and affect VaR-tightness, thus moving the price of risk.
- Optimal monetary policy analytically derived: conditions on output gap, inflation, and pricing of risk (vulnerability).

Model-generated features:
- When financial conditions are easy (price of risk compressed): expected GDP growth high, conditional GDP volatility low.
- When financial conditions are tight: expected growth low, conditional volatility high.
- Volatility paradox: easy conditions → buildup of intermediary leverage → vulnerability → adverse shocks induce balance-sheet contraction → lower asset prices → higher realized volatility → tighter VaR → amplification; good times followed by bad times on average.
- Cycle in pricing of risk drives financial cycle; amplification mechanisms present despite market completeness.
- Vulnerability breaks the "divine coincidence" of NK models: zero mean and zero volatility of the output gap are no longer simultaneously attainable.
- Macroprudential policies can further improve welfare.

### Macrofinancial dynamics and term structure implications — simulation evidence
- Simulations use Adrian and Duarte (2016) model with only shocks to intermediaries’ risk appetite (shifts in pricing of risk).
- Principal components extracted from simulated yields and regressed on output gap, inflation, and the price of risk (financial conditions within model context).
- Nonlinear equilibrium dynamics generate multiple significant principal components despite a single underlying risk factor.

Table 4 (simulated regressions of first three yield-curve PCs on macroeconomic and financial variables):
- Panel A: Monetary policy that ignores financial conditions (Taylor rule coefficients: 1 for output gap, 2 for inflation, 0 for vulnerability)
  - Inflation and output gap: 22%
  - Financial conditions: 35%
  - Additional reported values: 28%, 26% (as in source table layout)
- Panel B: Monetary policy that responds to financial conditions (Taylor rule coefficients: 1 for output gap, 2 for inflation, 2 for vulnerability)
  - Reported R-squares: 39%, 41%, 32%

Interpretation of simulation results:
- Simulated R-squares comparable to observed data even though model has only one risk factor.
- Three principal components explain the vast majority of variation in simulated yields, yet are only loosely related to macroeconomic variables.
- Optimal monetary policy that incorporates financial conditions generates larger R-squares and mitigates GDP skewness.
- Nonlinear macrofinancial dynamics can jointly explain:
  - Macroeconomic and financial variables driven by same factors but related nonlinearly.
  - Term structure well described by a small number of yield factors.
  - Yield-curve factors only loosely related to macroeconomic variables.

Modeling implications for term-structure methods:
- An affine term structure model would perform well in the data but is misspecified relative to underlying nonlinearity.
- A CIR-type model allowing for conditional heteroscedasticity is a better approach.
- Linearizing conditional mean and conditional volatility separately can produce a CIR-type pricing kernel.
- The model has potential to parsimoniously explain joint evolution of r*, term premium, interest rate volatility, and the nominal yield curve.

### Policy implications and recommendations
- Monetary policy should condition on vulnerability (pricing of risk) in addition to output gap and inflation.
- Optimal monetary policy differs from standard NK prescriptions: it must account for the interplay between means and volatilities driven by financial conditions.
- Macroprudential policies can improve welfare by addressing amplification mechanisms and vulnerabilities.
- Monitoring pricing of risk and levels of vulnerabilities is critical for quantifying financial stability and mitigating tail risk.
- The IMF will provide financial stability assessment of these risks in the upcoming Global Financial Stability Report in October.

### Current macrofinancial environment (brief comments)
- In the United States, Germany, and Japan:
  - Unemployment rates close to historical lows.
  - Core inflation below target.
  - Path of monetary tightening (yield curve adjusted for term premia) is shallow; market perceives that interest rates will rise only gradually.
  - Estimates of r* are close to zero in all three regions.
  - Market pricing implies a low likelihood of near-term recession and low observed market volatility — a benign phase of the financial cycle.
- Policy implication: benign times often coincide with buildup of financial vulnerabilities; monitoring financial stability remains key.

_The Term Structure of Interest Rates and Macrofinancial Dynamics, By Tobias Adrian, Financial Counsellor, Director of the Monetary and Capital Markets Department, IMF, Bank of Canada Conference, August 17, 2017._

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## References

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