Economic Models at Central Banks
Jeffrey C. Fuhrer
Director of Research
Federal Reserve Bank of Boston
1
A Brief History of the Evolution of Models
used by Central Banks
(A decidedly US-centric view)
• Once upon a time …
– There was the MPS model (MIT-Penn-SSRC)
– In its own way, it incorporated the latest theory
• Life-cycle/permanent income consumers
• Modified neoclassical investment (Bischoff)
• Accelerationist Phillips curve wage-price block
– Expectations?
• Proxies—largely distributed lags
• Muddled with other sources of lags in the model
– Stability?
• Often required “special” policy assumptions
2
A typical block of the old-style model:
Consumption spending
• Disaggregation: durables, nondurables,
services
• Durables were—and still are—a “service flow”
concept (consequently so is total consumption)
• Typical distributed-lag equation:
trans
prop
Stk
non−stock
Ct = ∑ai ytlabor
+
b
y
+
c
y
+
dW
+
eW
∑ i t−i ∑ i t−i ∑ i t−i ∑ i t−i
−i
i
i
i
i
i
• Expectations? Adjustment costs? Micro
foundations? Cointegration?
3
The new FRB/US model
• Typical equation: consumption spending
Table 3 from Brayton and Tinsley, eds., “A Guide to FRB/US,” FEDS 1996-42, October 1996.
4
Why did the models change?
• Couldn’t answer questions of increasing
importance
– What are markets expecting CB to do?
– How much do expectations of income, tax policy,
spending/hiring/pricing/asset pricing decisions?
– How do inflation targets, other CB communications
and strategies affect expectations/spending/asset
pricing?
– Optimal monetary policy: What’s the welfare
function?
• Interaction with academia spurred, developed
these discussions
5
In short, what was needed:
• Identification
• Identification
• Identification
6
Interaction with academia
• Has been beneficial in both directions
– Academics have a more realistic depiction of the
monetary policy process, both instrument
endogeneity and transmission mechanisms
– Central banks have better-identified macro models
for forecasting and policy analysis
– Issues that might not have arisen in academic
literature without interaction:
•
•
•
•
Importance of communications, transparency
Real-time data issues
Policy under various strata of uncertainty
Trade-offs between data consistency and theoretical rigor
7
Interaction with academia, cont’d.
• Example 1: an early 1980s academic depiction
of the monetary transmission channel:
Yt = a (m t − pt )
• Interaction between academics and central
bank economists led to the modern “I-S”
curve:
Y t = µ Y t − 1 + ( β − µ ) E tY t + 1 − a ( R t − R )
R t = g ( E t [ it + i , π t +1+ i ] )
M =
Not terribly important
8
Interaction with academia, cont’d
• Example 2: The interaction contributed to the
gradual evolution and adaptation of the supply
Increasing
dataside
consistency
and micro
foundations
– From the early “Lucas supply” curve
pt = t −1 p + α ( yt − y )
e
t
*
– To the later Calvo/Rotemberg price specification
π t = Et −1π t +1 + α ( yt − y )
*
t
– To the modern “hybrid” NKPC
π t = µπ t −1 + (1 − µ ) Et −1π t +1 + α st
9
Interaction with academia, cont’d
• Example 3: Endogenous monetary policy via a
“Taylor rule” with interest rate instrument it
it = sit −1 + (1 − s )( aπ [π t − π t ] + a y y% t + i )
– where we don’t exactly know why there’s an s>0
– or whether it should be instead (e.g. Rudebusch)
εt
it = aπ [π t − π t ] + a y y% t + i +
1− ρL
10
Current practice: Different models for
different purposes
• Models for Forecasting
– Board of Governors:
• “Judgmental” sector forecasts
• Combined via Human Gauss-Seidel (HGS)
– FRB Boston
• Small “translation” model to convert highfrequency indicator data into current-quarter
GDP forecast
• Larger structural model to forecast further out
11
Current practice: Different models for
different purposes
• Models for Policy Analysis:
– BOG:
• FRB/US: Expectations options (VAR, RE)
– FRB Boston
• Small structural models with explicit RE, more overidentifying restrictions, etc.
– ECB
• Country models; Euro region model
– Bank of Canada
• QPS model
– Bank of England
• VARs, structural DSGE model
– You?
12
Why the dichotomy?
• Because there’s a trade-off between two goals
13
The trade-off (courtesy of Bank of England)
Theoretical
consistency
(Identification)
0
0
Data coherence
(Forecasting)
Adapted from figure 2.1 from The Bank of England Quarterly Model, Harrison et al, 2005.
14
Why the dichotomy?
• Because there’s a trade-off between two goals
– Trade-off between forecasting ability and identification
– Well-identified, restricted models generally forecast poorly
– Pure forecasting models can’t answer certain questions, and
are (perhaps rightly) assumed unstable in the presence of
significant policy shifts
• At present, I’m comfortable with the split
– Because I think there’s little alternative
• At some point, it would be nice to integrate the
two classes of models
15
FRB Boston forecasting model
A Four-Equation Version of the Model
• Monetary Policy Reaction Function:
rt = f ( yt − ytpot , π t , rt −1 )
• Demand Equation (actually disaggregated):
yt − y
pot
t
= f ( yt−1 − y ,πt−1, rt−1)
pot
t −1
• Okun’s Law:
ut − u
NAIRU
t
• Supply Equation:
= f ( yt − y )
pot
t
π t = f (π t −1 , ut − u
NAIRU
t
)
16
FRB Forecasting Model: General Features
• No explicit forward-looking relationships
– Do forward-looking terms matter, esp. for IS and Phillips?
– Reduced-form of a model with forward-looking elements?
• Output is demand-determined
– Spending components include
•
•
•
•
Consumer goods excl. MV, MV, Services,
Res. structures, Nonres. structures, Equip. and Software spending
Federal, S&L govt.,
Exports, imports, foreign GDP
• Each equation of the model is estimated separately by
OLS
– Using simultaneous equations methods (FIML) leads to
very similar point estimates
– Concern for structural stability: the equations are usually
estimated from 1980 on
17
The Importance of Initial Conditions
• The “jumping-off point” for the forecast
matters
– This may be the source of forecasting prowess in
the Board staff’s “Greenbook” inflation forecast,
for example
• We have a separate “translation” model to
forecast current quarter GDP components
– Use high-frequency monthly and weekly source
data
– Know how the BEA puts GDP together
– Get a pretty good read on current-quarter real GDP
18
FRB Boston Policy Analysis Model
• Policy rule
rt = ert −1 + (1 − e)( f y [ yt − ytpot ] + fπ [π t − π ] + ρ + π )
• “I-S” relation
pot
yt − ytpot = a( yt−1 − ytpot
)
+
(1
−
a
)
E
(
y
−
y
−1
t
t +1
t +1 ) − b(ρt − ρ )
• Term structure relation
ρ t = ωρ t +1 + (1 − ω )(it − Etπ t +1 )
• Phillips curve
π t = cEtπ t +1 + (1 − c)π t −1 + d ( yt − ytpot )
19
Even the policy model embodies the trade-off
• Not a pure theory model
• Incorporates “hybrid” terms in both “I-S” and
supply specification
• Essentially ad hoc descriptions of the
fundamental inertia in these data series
20
What about welfare analysis?
• Models that are currently useful:
– Depends on how you wish to define welfare
• Variance measures—many models
• Utility-based measures—none that I trust yet
• Why is that?
– The cost of inflation in the models is poorly
motivated
– Cost of imperfect competition with positive inflation
is distortionary? Real money balance smoothing?
– Versus: Stories we normally tell students/the public
• Stability/predictability is really the key
• Interaction with tax code in many countries
21
Some Recent Modeling Conundrums
• “Frictions” versus “Structure”
• Dynamics from errors versus behavior
• Costs of inflation in the models
• Technique over substance
22
Frictions versus Structure
• Observation: Without frictions, the specification
unravels
– Well-established by now that the simple model
π t = β Etπ t +1 + γ xt + et fails miserably
– How to fix?
• Add a fraction of backward-indexing price-setters
• Add a fraction of backward-looking price-setters
• Add something that gets lagged inflation in there
– A problem?
• To the extent that the lag becomes the model, the structure
goes out the window; so does the welfare analysis
• To what extent is the lag the whole model?
23
Example of the importance of frictions:
The Hybrid NKPC
π t = ( β − µ ) Etπ t +1 + µπ t −1 + γ yt + et ; yt = ρ yt −1 + ut
µ=.6
24
Dynamics from Errors?
• Now quite fashionable
– Smets-Wouters
– Onatski-Williams
– Christiano, Eichenbaum, Evans
• Is this a problem?
– Not to have some structure in errors
– But need a diagnostic that shows how much of
model behavior comes from errors
– A goal, in my view, is to have a relatively small
fraction come from errors
25
An Example of a Diagnostic Tool
Comparison of autocovariance Functions:
VAR versus Rotemberg-Woodford with iid errors
From NBER Macroeconomics Annual 1997
26
Cost of inflation in the models
• Money in the utility function
M t (it )
U = U (Ct ,
)
pt
– Provides a motive for keeping inflation low and stable, as
agents prefer smooth real money balances
– Also a motive for smoothing nominal interest rates
– Is this empirically important (currency share very small)?
• The Woodford/Calvo trick
– We have backed our way into using the monopolistically
competitive Calvo framework as a source of inflation
distortions
– I don’t think this has much to do with the concerns of the CB
27
More on the Woodford/Calvo trick
• Cost of inflation
– Price dispersion, proportional to output dispersion, arising
from imperfect competition with sticky prices, causes
welfare loss
– In special cases, it is proportional to the variance of
inflation—look at this link empirically in a moment
• In Woodford (2002), the loss function is
κ
Lt = π + ( xt − xt* ) 2
θ
2
t
• Note that the relative contributions to the loss function as originally
calibrated are greater than 10:1 for inflation relative to output
• Evidence on price dispersion and inflation variance?
28
Inflation Variance and Relative Price Variability
0.0008
10
Relative Price Variability, Excl. Fuels
9
Inflation variance, 24-month window
0.0007
Correlation, 1969-2002: 0.66
Correlation, 1985-2002: 0.47
0.0006
0.0005
8
7
6
0.0004
5
4
0.0003
3
0.0002
2
0.0001
1
0
0
1969:Jan
1973:Jan
1977:Jan
1981:Jan
1985:Jan
1989:Jan
1993:Jan
1997:Jan
2001:Jan
Relative price variability = expenditure-weighted average of 24-month centered moving variance of CPI component
relative prices, including meats, fruits, other food, shelter, household furnishings, apparel, MV, and MV maintenance
29
and parts, medical care, and other goods. Sums to 83.5% of overall CPI consumption basket.
Inflation variance and relative price
dispersion
• At least they appear to be somewhat correlated
• The correlation has declined somewhat since 1985,
but still significant
• What does the correlation mean?
• Which way does causation run?
• How is this related to the more classical argument
about relative price confusion?
– How much of relative price variation is signal versus noise?
– How much is anticipated versus unanticipated?
30
The “New Neoclassical Synthesis”
or the “New Keynesian Synthesis”
•
•
•
•
New Keynesian Phillips curve plus
New Keynesian IS curve plus
Identified policy rule plus
Other assorted features (sometimes capital,
sometimes habits, sometimes wages,
sometimes correlated errors, sometimes other
frictions) =
• The Synthesis
– The micro-foundations are complete!
31
Bob Hall:
(NBER Reporter, Fall 1999)
“The long-sought
microeconomic foundations for
the field [of macroeconomics]
have been built.”
… perhaps a touch of hyperbole here?
32
Why is this a problem?
• We over-apply our technique on this model
– Thousands of optimal policy papers
– Optimal policy with “super-inertial” rules
(Woodford)
– “Timeless” optimal policy from model’s FOC
(Woodford)
– Optimal policy with filtering, given data
uncertainty (Svensson and Woodford)
– Optimal policy under uncertainty (model,
parameter, data)
• Possibly at the expense of better fundamental
understanding of consumption, investment,
financial markets, labor markets
33
Summary: Where Are We?
• It’s a good time to be a modeler
–
–
–
–
More data!
Better theory—explicit expectations, optimizing!
More analytical tools!
More computing power!
• Models are better than they used to be
– Explicit expectations
– More concern about underlying foundations
– Easier to develop and implement diagnostics and
model selection criteria
– There were frictions in earlier models, too!
34
Challenges: We got plenty
• Is RE a good approximation? If not, what?
• Is the “representative agent” a good approximation?
– Is LC/PI a good approximation?
• Is there any good approximation for aggregate capital
formation?
• How to approximate economic welfare?
– Why is inflation costly? Build models closer to our stories?
• Asset prices—how to model, how to respond?
• Why is inflation inertial/prices sticky?
– Interesting ECB work on this
• Why is monetary policy inertial?
• How does fiscal policy work?
35