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Discussion of The Bond Premium in a DSGE Model
with Long-Run Real and Nominal Risks
David VestinMonetary and Economic
Department Views expressed are those of the
author and not necessarily those of the BIS.
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What does the paper do?

• Examine the average size and time-varying
  properties of the term-premium in a DSGE model

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How does the paper do it?

• Extends the standard NK model with EZ preferences
• Introduces two sources of long-run risk-
  inflation target- very persistent technology

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What does the paper find?

• EZ breaks the link between inter-temporal
  elasticity of consumption and risk aversion.
• Can explain the size of the average term premium
  without sacrifice to fit of macro variables
• Long-run risk allows reducing risk-aversion
• Model falls a bit short on explaining time
  variation in premia

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Deserved Praise

• This is a very good and important paper
• Bridges finance (endowment) approach and DSGE
  successfully
• The minimum modification of the standard
  framework is sure to be well received among
  large-scale modellers

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Background equity premium

• Equity premium puzzle
• The high risk-aversion needed to fit the equity
  premium generates a huge short term interest rate
  in the standard CRRA model
• Reason elasticity of substitution inverse of
  risk-aversion
• Solution in that literature EZ preferences

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Background finance approach

• Assume a process for consumption that fits
  historical patterns
• Assume a utility function that implies a ratio of
  marginal utilities over time, eg.E
  (Ct1/Ct)-g(Mt1-Rt1)0
• Use data on M and the assumed process to find g

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DSGE Lucas critique?

• When we vary utility function parameters, the
  implied behaviour for consumption should also
  change!
• Indeed, an early DSGE result was that if you
  increase risk-aversion and reduce el. of
  substitution then consumption became too
  smooth.
• Well, depends on what we want to do. If we only
  want to recover preferences, we should be fine
  since history is given...

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Some issues

• What kind of time variation do we want?
• Hard to assess if implied risk-aversion is
  plausible
• Where to go from here?

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The three facts

• The term-structure is upward-sloping on average?
• Long-term bond yields are about as volatile as
  short ones
• There seems to be time-variation in the way the
  expectations hypothesis fails

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Long-term bond yields

• Long yield E(average short yield) premia
• A model explaining changes in long-rates could
  can rely on1. changing expectations about the
  future short2. change premia
• Need very persistent factors to affect long-end
• CS regressions tells us that the expectations
  hypothesis does not hold hence 1 must be
  supplemented by 2

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10Y Risk-premia (Kim and Wright)?
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Forward rates 10Y and 1Y (Kim and Wright)?
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Changes in interest rates and premia
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Suggestions

• Decompose your forward-yields and show how much
  of the movement at various maturities are
  explained by changes in expectations vs. changes
  in premia
• Relate this to Kim and Wright
• Decompose real and nominal term-premia important
  because the long-run inflation premia is
  substantial (will affect BEIRs...)

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Issues plausibility of risk-aversion

• In the standard model, risk-aversion equals the
  inverse of the elasticity substitution. Hence,
  high risk-aversion means low willingness to
  substitute over time.
• One take is to view plausibility on the basis of
  counterfactual implications in old model, high
  gamma meant too low substitution hence
  implausible
• New model circumvents this by breaking the link -
  but maintains the high risk aversion

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Implications of EZ

• First-order approximation is unaffected
• Higher order have (possibly) implications for1.
  dynamics2. risk premia
• If effect on 1 is negligable, then risk-aversion
  can be selected to fit one risk-premium (authors
  focus on the 10Y term premium)?
• Would be interesting to see several yields, to
  see if all premia are fitted as well with that
  value. Would also be interesting to see how the
  reported value fares with equity returns (using
  the reduced form of the model, the pricing kernel
  and returns data rather than computing
  endogenous stock returns!)?

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Implications

• Modelling macrodynamics this is perfect!
• We fit bond yields and can hence discuss and
  relate market expectations to economic
  fundamentals
• Zero cost in terms of loss of performance of the
  macro part of the model
• Does the latter mean that there are no
  macro-implications? No once we consider
  counter-factual (in particular optimal) monetary
  policy...
• Also steady state effects... in particular if
  there is capital

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Assessing the high risk-aversion

• Consumption gamble 1 rise or fall with 50-50
  chance
• What certain level of consumption is equivalent
  in terms of u?

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Assessing the high risk-aversion

• Suggestion Calculate a measure of how much the
  consumer is willing to give up to eliminate the
  uncertainty more generally
• For example, a Lucas calculation of the cost of
  business cycle fluctuations.
• Tallerini, 2000, finds very large costs in his
  model when risk is high.

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Assessing the high risk-aversion

• This points out that if our models are unable to
  price risky assets, they may be inappropriate for
  welfare analysis
• Negative people with very strong priors on these
  costs (based on good or bad evidence) will not
  find explanations based on too-high
  risk-aversion acceptable.
• But then again, it takes a model to beat a
  model...

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Where to go from here?

• Think about the role of bonds and different
  maturities.
• Think about implications for optimal monetary
  policy
• Size of the commitment problem
• Etc...

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No debt

• Complete markets ensures that the type of assets
  does not matter
• Once model is solved, anything can be priced, but
  there is no intrinsic role for difference in
  maturity
• Could be especially special here If long-rates
  matters directly, risk-premia would affect
  dynamics... and hence possibly break the
  convenient independence of dynamics from risk
  aversion.
• Would introduce the maturity-transforming role of
  banks/FIs that are at the hart of the current
  crisis

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Wrapping up

• Again Very nice paper
• Opens a host of interesting issues that will keep
  us occupied