The New Keynesian Phillips Curve and Staggered Price and ...
Supply side modeling and New Keynesian Phillips Curves
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Supply side modeling and New Keynesian Phillips
Curves
CCBS/HKMA May 2004
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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
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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
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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
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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
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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
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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
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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)
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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
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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
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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
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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
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“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
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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
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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 *
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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
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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)
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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.
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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
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Microfoundations (3)
• Firms maximise profits subject to:
1) Production function
2) Demand curve
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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)
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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:
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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
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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
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Derivation of the New Keynesian Phillips Curve (1)
• Firm’s maximisation problem:
where the stochastic discount factor is:
and real marginal costs are
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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)
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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