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Supply side modeling and
New Keynesian Phillips
Curves
CCBS/HKMA May 2004
Structure
• Introduction: What is a Phillips Curve?
• UK Phillips Curve estimates – traditional
approach
• New Keynesian Phillips Curves
– Features of the model
• Modelling real disequilibria: Kalman Filter
example
– brief description of the model and approach used
What is a Phillips Curve?
• Definition:
– ‘Phillips Curve’ a term for models that relate nominal
price (or wage) inflation to some measure of excess
demand or real disequilibrium, conventionally
measured by either an unemployment or output “gap”
• Includes output gap/NAIRU/explicit expectations
models
• Key part of a fully specified macro-econometric
model
Phillips Curve: Some history
• Phillips (1958): money wage growth
negatively related to unemployment during
1861-1957
– Was there a trade-off?
• Modern expectations-augmented Phillips
curve, Friedman (1968), Phelps (1967)
– no long-run trade-off
Phillips Curve: Basic theory
• Simple Phillips curve may be written as:
 t   te   (ut  ut* )
• If inflation expectations are assumed to be
adaptive (for example, equal to last period’s
inflation), then the accelerationist Phillips
curve model
 t   t 1   (ut  ut* )
The relationship with structural
models
• Simple natural rate/accelerationist model
implies:
– Inflation only increases/decreases when
inflation is below/above natural rate
– Feed-through of excess demand to inflation
immediate
Empirical work – ‘Traditional’
approach
• In empirical work, the traditional Phillips curve that has
been estimated is often of the form:
i 4
 t    i t i   ( yt  yt* )
i 1
• Long-run Phillips curve is vertical if we impose dynamic
homogeneity:
i 4
 
i 1
i
t i
1
• In the short-run, may be away from equilibrium due to
nominal inertia in wage/price setting process
Example of traditional Phillips
Curve (TPC)
• Rudebusch and Svensson (1999) show that
a TPC with four lags of inflation fits US
data well
• Output gap (detrended log GDP) enters
significantly with a positive coefficient
• Accept dynamic homogeneity restriction –
implies no long-run trade-off (vertical
Phillips curve)
Empirical results (TPC)
Πt-1
US
0.602
Euro Area
0.520
UK
0.243
Πt-2
Πt-3
Πt-4
yt-1-yt-1*
0.041
0.152
0.155
0.192
0.233
-0.070
0.256
0.205
0.345
0.214
-0.041
0.096
Sample 1970-1999
• Source: Balakrishnan and Lopez-Salido (2002)
Bank of England working paper no. 164
Over-prediction of basic TPC
Performance of the basic R-S model (gdp deflator)
30
25
20
15
10
5
0
1970
1973
1976
1979
1982
1985
1988
1991
1994
1997
gdp deflator
fitted values
• Source: Balakrishnan and Lopez-Salido (2002)
Adding external factors
• Add world export prices or terms of trade
– Variables are positive and statistically
significant
• Helps to cure over-prediction problem
– Residuals less negative
Less Over-prediction with
augmented TPC
Performance of the augmented R-S model (gdp deflator)
30
25
20
15
10
5
0
1970
1973
1976
1979
1982
1985
1988
1991
1994
gdp deflator
fitted values
• Source: Balakrishnan and Lopez-Salido (2002)
1997
“Traditional” approach: limitations
• Empirical implementation has been ad-hoc:
inconsistent specification
• Useful forecasting tool but it is reduced
form - need information on structural
parameters
• Over-prediction of inflationary pressures in
the 1990s in many models
Modelling inflation dynamics
• Likely to be forward and backward-looking
• But backward-looking model may be
preferred because:
– Difficulties in measuring expectations
– May be adequate representation if no change in
policy regime or structure of economy
• If aim to examine credibility, these issues
are clearly important
New Keynesian Phillips Curve
(Roberts, 1995)
• NKPC highlight the importance of
expectations of future inflation, because
prices are sticky
• Roberts (1995) shows that the NKPC
captures the key elements of various models
(eg Rotemberg (1982), Calvo (1983) and
Taylor (1979)
• Common formulation is
pt  Et pt 1  c0    yt  yt*    t
Taylor (1979) wage contracting
-4
-3
-2
-1
1
2
3
4
group 1
group 2
group 3
group 4
• Four overlapping contracts in each period, but only one
contract is renegotiated
New Keynesian Phillips
Curves (NKPC)
• Attention has been placed on ensuring that the model
structure is consistent with the underlying behaviour of
optimising agents. Key elements:
–
–
–
–
intertemporal optimisation
rational expectations
imperfect competition and the goods (and/or labour) market
costly price adjustment
• The widely discussed ‘New Keynesian Phillips Curve’ is
based on this framework: Calvo (1983), Roberts (1995),
Galí and Gertler (1999) and Sbordone (1999)
Microfoundations (1)
• Households maximise the expected present
discounted value of utility:
 1
  M t i
i Ct  i

max Et   

1 1 b 

i 0
 Pt i


1b




N t1i 


1  

• Market Structure
– Monopolistic competition: Composite consumption
good consists of differentiated products produced by
monopolistically competitive firms.
Microfoundations (2)
• Households stage 1: optimally choose the
combination of individual goods that
minimises the cost of achieving level of
composite good
• Stage 2: choose consumption, employment
and money balances optimally
Microfoundations (3)
• Firms maximise profits subject to:
1) Production function
C jt  Zt N ajt ,
0  a  1, E(Zt )  1
2) Demand curve
C jt
 p jt

 P
 t





Ct
Microfoundations (4)
• 3) Constraint that some firms cannot change
prices, for example Calvo (1983) model
– Each period there is a constant probability that
the firm will have the opportunity to adjust
– Firms adjust their prices infrequently
– Some alternative models use Rotemberg (1982)
or Taylor (1980) style contracting (see Ascari,
2000)
Marginal cost in the NKPC (1)
• Galí and Gertler (1999): Aggregate price
level is an average of the price charged by
those firms setting their price in that period
and the remaining firms who set prices in
earlier periods:
1
t
P
 
 1    p
* 1
t
1
t 1
 P
Marginal cost in the NKPC (2)
• Galí and Gertler show that if a firm can change its
price, then it maximises expected discounted
profits given technology, factor prices and the
constraint on price adjustment.
• The optimal reset price is set according to:


p  log   1      Et mctn,t  k
*
t
k
k 0
• where  is the firm’s mark-up

Marginal cost in the NKPC (3)
• Obtain the NKPC (after some re-arranging):
  E   ~ˆ
t
t
t 1
t
• where ̂t is real marginal cost, expressed
as a percentage deviation around its steady
state value.
• May also express NKPC in terms of the
output gap
Derivation of the New
Keynesian Phillips Curve (1)
• Firm’s maximisation problem:
 p jt
i
Et    i ,t i 
max
C
 Pt i
i 0

1



 p jt
 t i 
 Pt i





Ct i

where the stochastic discount factor is:
i ,t i   i (Ct i / Ct ) 
and real marginal costs are
t 
Wt / Pt
aZ t N ajt1
Derivation Of The New
Keynesian Phillips Curve (2)
• Optimal relative price:

 Pt i 
i
i 1


E


C

t
t i
t i 
*
p

i 0
 Pt 
Xt  t 
 1

Pt
(  1)


P
Et   i  i Ct1i  t i 
i 0
 Pt 

• Constant markup over a weighted average of
marginal costs over the duration of price contracts
• When ω = 0 the firm sets its price as a markup
over nominal marginal costs
 Pt *    

t  t
 P 

 t    1 
Derivation of the New
Keynesian Phillips Curve (3)
• Aggregate Price Level is an average of the
price charged by those firms setting their
price in that period and the remaining firms
who set prices in earlier periods:
1
t
P
 
 1    Pt
* 1
• Dixit-Stiglitz aggregator
 Pt11
Derivation of the New
Keynesian Phillips Curve (4)
• If we use the log-linearised (4) & (5), we obtain
the NKPC (after some re-arranging):
 t  Et t 1  ~ˆt
 
1   1    
where
and ̂ is real

marginal cost, expressed as a percentage deviation
around its steady state value.
• May also express NKPC in terms of the output
gap
t
How well does the NKPC
perform? (1)
• ‘Reconciling the new Phillips curve with
the data, has not proved to be a simple task’
(Galí and Gertler, 1999)
• NKPC suggests that the current change in
inflation should depend negatively on the
lagged output gap. Estimates tend to show a
positive coefficient on the output gap
How well does the NKPC
perform? (2)
• Real marginal costs used instead (labour
share) - more sensible results, see Galí and
Gertler (1999) and Sbordone (1999)
• Pure forward-looking specification does not
fit the data well- does not account for
inflation inertia - Galí and Gertler (1999)
suggest a ‘hybrid’ NKPC
 t   f Et t 1   b t 1  ~mct
Hybrid NKPC Specification
• Modify pricing rule so that some of the firms that
can change prices set prices optimally using all of
the available information (à la Calvo), but some
instead use a simple, but ad-hoc, rule of thumb
based on recent price behaviour:
b
*
pt  pt 1   t 1
• Broad Consensus: the hybrid-NKPC fits the data
well. The coefficient on the backward-looking
component is statistically significant, so reject the
‘pure’ NKPC
Empirical results (NKPC)
Πt+1
0.69
Πt-1
Labour
share
0.16
0.48
0.68
0.15
0.32
0.17
0.08
• Source: Batini, Jackson and Nickell (2000)
Bank of England External MPC Unit paper no. 2
Hybrid NKPC Specification
• But forward-looking component is
dominant
– Galí, Gertler and Lopez-Salido (2001) suggest
that about 1/3 backward-looking and 2/3
forward-looking in US
– Also true for UK, elsewhere?
• Use of real marginal cost in the NKPC is
critical for the empirical success
Robustness of the NKPC
• Several papers have questioned the robustness of
the NKPC estimates: Rudd and Whelan (2001),
and Linde (2002)
• Galí, Gertler and Lopez-Salido (2003) argue that
their earlier results are robust
– They argue that the Rudd and Whelan work, which
solves for the closed form of the pure forward-looking
model and then appends lagged inflation terms, is
inconsistent with the hybrid model, the most
appropriate model
• Problem: ad-hoc nature of hybrid model
Conclusion (1)
• Many of the traditional Phillips curve
models over-predict inflation in the 1990s
– May need external variables (terms of trade,
world prices)
• Triangle model with time-varying NAIRU
fits the data well, but model not based on
optimising behaviour
Conclusion (2)
• New Keynesian Phillips Curves are a good
alternative
– Advantage: based on optimising behaviour.
– Disadvantage: pure forward-looking model is
rejected by the data and there are concerns
about the motivation for the hybrid model.
– Also, results are often unfavourable when
output gap is used (‘filtered’ gap may not be
good measure of true gap)
Conclusions (3)
• Phillips curve are a key part of model
• Various alternatives may provide a useful crosscheck for forecasts from model
– Can help to identify other factors driving the model
– Phillips curve structure common to variety of structural
models, robustness checks
• Simplicity and transparency
– Useful framework for policy discussions