The Term Structure of Interest Rates and Macrofinancial Dynamics

IMF News, August 17, 2017

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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.