Jeff FuhrerFederal Reserve Bank of Boston

May 29, 2014

This paper

• Looks at many of the difficult MP issues that CB’s have confronted over the past 5-7 years

• So it was fun to read (and re-live)!• Key topics:

I. Does raising πe at the ZLB work? (do i and πe enter “IS” curves with equal magnitude and opposite signs? Does πe enter at all?)

II. Is forward guidance a good idea? Effective? How is “anchoring expectations” working?

III. Asset purchases—how/do they work? Through term or risk premia?

IV. Aggregate supply issues (very briefly)• I will comment on pieces of I-III

2

I. Nominal or real rates?or how/does expected inflation affect real

activity?• Great question• Hard to answer• At the crux: Identification

– Carl has a lot of interesting empirical results

– I will argue that many of his results (which he doesn’t push too hard) are fraught with identification issues

– But I am still quite sympathetic to the hypothesis that nominal rates may be as important as real rates

3

1961:Q1 1966:Q1 1971:Q1 1976:Q1 1981:Q1 1986:Q1 1991:Q1 1996:Q1 2001:Q1 2006:Q1-1

-0.5

0

0.5Coeff. on 1-year Treasury rate

1961:Q1 1966:Q1 1971:Q1 1976:Q1 1981:Q1 1986:Q1 1991:Q1 1996:Q1 2001:Q1 2006:Q1-1.5

-1

-0.5

0

0.5

1Coeff. on lagged inflation

Rolling regression of R-S output gap equation with independent inflation effect40-quarter estimation window

1961:Q1 1966:Q1 1971:Q1 1976:Q1 1981:Q1 1986:Q1 1991:Q1 1996:Q1 2001:Q1-1

-0.5

0

0.5Coeff. on 1-year Treasury rate

1961:Q1 1966:Q1 1971:Q1 1976:Q1 1981:Q1 1986:Q1 1991:Q1 1996:Q1 2001:Q1-1

-0.5

0

0.5Coeff. on lagged inflation

Rolling regression of R-S output gap equation with independent inflation effect60-quarter estimation window

ID of any interest rate effects in the R-S model is dicey.

Do nominalRates matter?

Does expected inflation matter?

4

What should we expect to learn from reduced-form

regressions?• Consider a simple model (simpler than Iacoviello and

Neri)

• Compute analytical reduced-form coefficients for different values of γ0

• Exactly the same as the regression coefficients implied by the model • In general, will not retrieve the IS curve coefficients from these regressions

–Will be combination of Phillips, policy rule, etc.

1 1

*1 1 0 1

* * *1

= + (1- )E + y

y = y + (1- )E y - (ff -(1+ )E - )

ff = ff +(1- )(a ( - )+a y +( + ))

t t t t t

t t t t t t t

t t t y t

5

Analytical reduced-form

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1-0.15

-0.1

-0.05

0

0.05

0

Lagged inflation coefficient

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1-1

-0.8

-0.6

-0.4

-0.2

0

Lagged funds rate coefficient

Solution coefficients

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1-0.3

-0.2

-0.1

0

0.1

0.2

0

Lagged inflation coefficient

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

Lagged funds rate coefficient

Solution coefficients

SE’s dependon shock variances

and sample size;here we calibrate

to this sample

At γ0=0, structural coeffs. on (rt, Eπt+1) are (-σ, σ)RF coeffs. on lagged (r, π) are -0.6, -0.043

6

Conclusion: Be

careful what we

infer from

reduced-from

regressions about what’s

going on undernea

th

My DSGE estimatesIn this sample, id of γ0 is tough

1961:Q1 1966:Q1 1971:Q1 1976:Q1 1981:Q1 1986:Q1 1991:Q1-5

-4

-3

-2

-1

0

1

2

3

4

5

FIML estimates of 0, rolling samples 1961-2013

Sample size = 100 quarters

Full-sampleestimate (se’sindicated with

“+”

• Hard to reject the classic real-rate version of the model

• Not conclusive, but an indication of robustness issues

Beginning of estimation sample 7

FIML estimates of γ0, rolling samples 1961-2013Sample size = 100 quarters

Bayesian estimates of the simple model

Just for completeness—same results

8

0 0.5 1 1.50

1

2

3

4

5

mu

Posterior

Prior

-0.2 0 0.2 0.4 0.60

10

20

30

40

gam-0.2 0 0.2 0.4 0.60

5

10

15

20

sig1

-4 -2 0 20

0.5

1

1.5

2

lam00 2 4 6

0

1

2

3

4

rhobar0 0.5 1 1.5

0

5

10

15

20

rho

0 2 4 60

0.5

1

1.5

2

api0 5 10

0

0.5

1

1.5

2

pibar0 2 4 6

0

1

2

3

4

ay

Posterior parameter distributions400000 replications

0

Estimated parameter distributions

9

Why ID is hard:AUTOCORRELATION FUNCTION for Carl’s VAR

0 10 20 30-1

0

1

Y w lags of Y0 10 20 30

-1

0

1

Y w lags of 0 10 20 30

-1

0

1

Y w lags of r0 10 20 30

-1

0

1

Y w lags of E0 10 20 30

-1

0

1

Y w lags of pcom

0 10 20 30-1

0

1

w lags of Y0 10 20 30

-1

0

1

w lags of 0 10 20 30

-1

0

1

w lags of r0 10 20 30

-1

0

1

w lags of E0 10 20 30

-1

0

1

w lags of pcom

0 10 20 30-1

0

1

r w lags of Y0 10 20 30

-1

0

1

r w lags of 0 10 20 30

-1

0

1

r w lags of r0 10 20 30

-1

0

1

r w lags of E0 10 20 30

-1

0

1

r w lags of pcom

0 10 20 30-1

0

1

E w lags of Y

0 10 20 30-1

0

1

E w lags of 0 10 20 30

-1

0

1

E w lags of r

0 10 20 30-1

0

1

E w lags of E0 10 20 30

-1

0

1

E w lags of pcom

0 10 20 30-1

0

1

pcom w lags of Y0 10 20 30

-1

0

1

pcom w lags of 0 10 20 30

-1

0

1

pcom w lags of r0 10 20 30

-1

0

1

pcom w lags of E0 10 20 30

-1

0

1

pcom w lags of pcom

ALL neg. correls.

among Y, r, π

Pos. struc.

correls. must arise from policy rule,

Phillips shocks

10

Need serious identify

ing assump

s. to identify

the underly

ing structure from the raw correls.

Conclusion on E(π) issue

• The DSGE estimates are probably of more interest, as they hold greater promise of identification

• And they say that– It depends on how you do it– The strongest result you can get is at the 10%

confidence level– So it’s not clear that inflation acts differentially

from its role in defining the real interest rate• So the results aren’t clear• What to do?

– Examine more detailed micro data, sectorally disaggregated models and data?

11

II. Forward guidance: How to think about this?

• Carl employs a useful framework:

• Which implies Fed can guide by– Providing information about the outlook (term

3)– Engineering an increase in inflation

expectations during the ZLB period (term 1, i = 0 to S)

– Changing expectations about the length of the ZLB period (change S)

– Reducing expectations about real rates once ZLB is over (term 2)

1 10 1 0

( )S

Nt t t i t i t i t i

i i S i

c E i r

12

1. Real rate at ZLB2. Real rate after ZLB3. Natural rate(proxy for outlook)

Another way to look at this:Why would we ever need forward

guidance?• If Fed behaves systematically, following a rule,

then only a few things can change guidance– Change in the outlook for inflation and output

• Can an increase in inflation expectations be separated from changes in the outlook? Changes in Fed policy/goals?

– Change in the inflation goal– Change in policy preferences, as reflected in α and

δ– Change in estimates of the equilibrium funds rate

or equilibrium output

max{ ( ) ( ) ,0}t t t tff y y ff

13

But both are pretty simple frameworks

• In most normal cases, I agree with Carl that the desire to manipulate expectations may be ill-founded– Better to discuss the outlook, policy preferences, etc.—the

inputs to expectations• But the world can be a bit more complicated, especially

recently• How so?

– Heightened uncertainty in the wake of the recession• About the structure of the economy—supply side, interest rate

effects, credit supply effects, QE effects, etc.• About the nature and persistence of unusual shocks (financial

crisis)• About the shape and nature of nonlinearities in the policy “rule”• About whether the Fed believes there is value in considering

policies that might deviate from the rule, e.g. Woodford– May be that forward guidance helps to clarify the Fed’s

views on some of these margins, and also their intentions, which may be difficult to forecast from simple rules in these special circumstances 14

Some complications with forward guidance

• Temporarily higher inflation versus change in long-run target– Hard to communicate the distinction

• Promises without actions (as Carl points out)– Our forward guidance was always coupled with QE—helpful? Did QE

do all the signaling? Only signaling?

• Distinguishing statements about policy from statements about the outlook (Classic problem, not unique to current circumstances)– Heightened by perception that the Fed has an information advantage

• Mitigants– Most often a temporary problem– FOMC forecasts help (although the structure is certainly not perfect)– We have LOTS of other opportunities to clarify our intentions

regarding outlook, policy

15

On “anchored expectations”1. Empirics

• While long-run expectations are remarkably stable, do they anchor actual inflation?

• Japan:

• Is the problem that folks don’t believe the Fed will ultimately return inflation to 2%? Probably not.– Expectations are anchored. The question is whether

those long-run expectations exert a strong pull on current inflation and short-term expectations

– The answer to that question is not clear just yet16

1980 1985 1990 1995 2000 2005 2010 2015-10

-5

0

5

10

Core CPI

Total CPIOutput gap

1985 1990 1995 2000 2005 2010-2

-1

0

1

2

3

4

Year (semi-annual data)

Core CPI

1-yr. forecast6-10 yr. forecast

Key Japanese data

The good and not so good news on that front for the US

2000 2002 2004 2006 2008 2010 2012 2014

1.4

1.6

1.8

2

2.2

2.4

2.6

Year

4-qtr.

10-year

SPF inflation expectationsGDP deflator

Long-run (SPF) expectations may

~anchor short-run expectations 17

2000 2002 2004 2006 2008 2010 2012 20140.8

1

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

Year

10-year

Actual inflation

Long-run expectations and realized inflationGDP deflator

The anchoring of actual inflation is less obvious, but perhaps it will

manifest itself soon.

1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 201475

80

85

90

95

100

105

110

115

Year

Another way of looking at this

Notional 2% lineindexed to 1994:Q1core PCE value

Actual Core PCE

6% gap

Expectations have been AT LEAST 2% throughout this 20-year period. But we have not attained an average inflation rate of 2%

18SO: Expectations anchored, but inflation

not so much?

What do we mean by “anchored expectations?”

2. Theory• Which model do we have in mind?

• First is often used as shorthand, but has little/no theoretical basis (πt=c + εt)

• Second is getting closer to a conventional model

• Third is a conventional model, but won’t usually have the same implications as first or second model

1 1 1 1

=

= ( )

- ( - ) (1 )( - ) ( )

( );

LRt t t

LRt t t t t

LR LR LRt t t t t t t t t t

LR CB CBt

y y

E y y

f

19

Description of the data

Bow toward theory (what happened to Eπt+1?)

Carl’s section 3 model• His model posits a link between short-run expectations

and the CB’s target inflation rate:

– This is good as an expository device, but is it a model?– If δ=1, expectations are always equal to πT? Why would they

be?– No theory basis for this kind of expectations formation

• Rational expectations are already perfectly “anchored to the target”– Double-anchoring? Belt and suspenders?– May be better to use this kind of apparatus for

characterizing deviations of trend inflation/long-run expectations from πT?

• Practical matter: How much attention do price-setters pay to πT?

• → Forward guidance may not be about this kind of anchoring, but about clarifying uncertainties discussed earlier?

1 1(1 )e Tt t tE

20

“Anchoring” in an RE model

• How quickly Etπt+1→π*

– Depends on all key parameters [μ, σ, ρ, aπ, ay]

• Example:• How else can we “anchor” expectations in

this sense (i.e. ensure reasonably quick return to π*?)

21

1 1

*1 1 1

* * *1

= + (1- )E + y

y = y + (1- )E y - (ff -E - )

ff = ff +(1- )(a ( - )+a y +( + ))

t t t t t

t t t t t t t

t t t y t

0 2 4 6 8 10 12 14 16 18 200.45

0.5

0.55

0.6

0.65

0.7

0.75

0.8

a

Rate

of

converg

ence

Rate of convergence as a function of aπ

III. Identification issues apply to the term/risk premium

analysis in section 4• Identification in “forecasting equations” is weak

– Makes results hard to interpret

• That said, it might help to disaggregate further– For example: 10-year Treasury has an effect on

mortgage rates (in many CB models and in the real world)

– Mortgage rates affect residential investment

• Perhaps both term spreads and risk spreads matter, once properly identified

• Look at some evidence, both RF and structural

22

Evidence in support of this hypothesis:

A disaggregated forecasting regression

23

And some more structural estimates of risk versus term

spread (still a bit ad hoc)

• Results favor the term premium

• Certainly not conclusive, but

again, a test of robustness, id,

etc.

*1 1 1

1 1 1 2 1 1

y = y + (1- )E y - (ff -E - )

-S ( 10 ) ( 10 )t t t t t t t

t t t tR ff S RBAA R

24

+ rest of DSGE

Summary

• Huge number of topics in this paper• They’re all important• Key issues

– Empirical: Identification of the real/expected inflation rate effects is problematic, so conclusions are murky

– Forward guidance: motivations may lie well outside the model, and outside most of historical experience

• Anchored expectations: What it means theoretically, how to model it require more serious attention

– Term/risk premia: ID an issue here, too. More disaggregated work might provide more compelling empirical evidence, as might more structural modeling

25