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:

• If inflation expectations are assumed to be adaptive (for example, equal to last period’s inflation), then the accelerationist Phillips curve model

)( *1 tttt uu

)( *tt

ett uu

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:

• Long-run Phillips curve is vertical if we impose dynamic homogeneity:

• In the short-run, may be away from equilibrium due to nominal inertia in wage/price setting process

4

1

1i

iiti

4

1

*)(i

ittitit yy

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)

• Source: Balakrishnan and Lopez-Salido (2002) Bank of England working paper no. 164

US Euro Area UK

Πt-1 0.602 0.520 0.243

Πt-2 0.041 0.233 0.345

Πt-3 0.152 -0.070 0.214

Πt-4 0.155 0.256 -0.041

yt-1-yt-1* 0.192 0.205 0.096

Sample 1970-1999

Over-prediction of basic TPC

• Source: Balakrishnan and Lopez-Salido (2002)

gdp deflator

fitted values

Performance of the basic R-S model (gdp deflator)

1970 1973 1976 1979 1982 1985 1988 1991 1994 19970

5

10

15

20

25

30

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

• Source: Balakrishnan and Lopez-Salido (2002)

gdp deflator

fitted values

Performance of the augmented R-S model (gdp deflator)

1970 1973 1976 1979 1982 1985 1988 1991 1994 19970

5

10

15

20

25

30

“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 *

1 0t t t t t tp E p c y y

Taylor (1979) wage contracting

-4 -3 -2 -1

1 2 3 4

group 1group 2group 3group 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:

• Market Structure– Monopolistic competition: Composite consumption

good consists of differentiated products produced by monopolistically competitive firms.

111max

111

0

it

b

it

itit

i

it

N

P

M

b

CE

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

2) Demand curve

1)( 1,a0 , tajttjt ZENZC

tt

jtjt C

P

pC

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:

11

1*1 1 ttt PpP

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:

• where is the firm’s mark-up

nktt

kt

kt mcEp

,

0

* 1log

Marginal cost in the NKPC (3)

• Obtain the NKPC (after some re-arranging):

• where is real marginal cost, expressed as a percentage deviation around its steady state value.

• May also express NKPC in terms of the output gap

tttt E ˆ~1

t̂

Derivation of the New Keynesian Phillips Curve (1)

• Firm’s maximisation problem:

where the stochastic discount factor is:

and real marginal costs are

iti it

jtit

it

jtiti

it

C

CP

p

P

pE

0

1

,max

)/(, tit

iiti CC

1

/ajtt

ttt NaZ

PW

Derivation Of The New Keynesian Phillips Curve (2)

• Optimal relative price:

• 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

1

0

1

0

1

*

)1(

t

it

iit

iit

t

itit

iit

iit

t

tt

P

PCE

P

PCE

P

pX

ttt

t

P

P

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:

• Dixit-Stiglitz aggregator

11

1*1 1 ttt PPP

Derivation of the New Keynesian Phillips Curve (4)

• If we use the log-linearised (4) & (5), we obtain the NKPC (after some re-arranging):

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

tttt E ˆ~1

11t̂

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

ttbttft mcE ~11

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:

• Broad Consensus: the hybrid-NKPC fits the data well. The coefficient on the backward-looking component is statistically significant, so reject the ‘pure’ NKPC

1*

1 ttbt pp

Empirical results (NKPC)

• Source: Batini, Jackson and Nickell (2000)

Bank of England External MPC Unit paper no. 2

Πt+1 0.69 0.48 0.68

Πt-1 0.15 0.32

Labour share

0.16 0.17 0.08

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 cross-

check 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