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Discussion of „The Bond Premium in a DSGE Model with

Long-Run Real and Nominal Risks”

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David Vestin*Monetary 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 [(Ct+1/Ct)

-g(Mt+1-Rt+1)]=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)

0

0.5

1

1.5

2

2.5

3

3.5

Kolumn A

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Forward rates: 10Y and 1Y (Kim and Wright)

0

1

2

3

4

5

6

7

8

9

10

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Changes in interest rates and premia

-0,4 -0,3 -0,2 -0,1 0 0,1 0,2 0,3 0,4-0,4

-0,3

-0,2

-0,1

0

0,1

0,2

0,3

0,4

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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 for

1. 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?

0 2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 00 .6 5

0 .7

0 .7 5

0 .8

0 .8 5

0 .9

0 .9 5

1

R elative risk -avers ion

Con

sum

ptio

n eq

uiva

lent

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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