Supply side modeling and New Keynesian Phillips Curves

1. Supply side modeling and New Keynesian Phillips Curves CCBS/HKMA May 2004

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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)

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

10. Source: Balakrishnan and Lopez-Salido (2002) Over-prediction of basic TPC

11. 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

12. Less Over-prediction with augmented TPC • Source: Balakrishnan and Lopez-Salido (2002)

13. “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

14. 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

15. 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

16. Taylor (1979) wage contracting • Four overlapping contracts in each period, but only one contract is renegotiated

17. 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)

18. 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.

19. 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

20. Microfoundations (3) • Firms maximise profits subject to: 1) Production function 2) Demand curve

21. 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)

22. 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:

23. 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

24. 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

25. Derivation of the New Keynesian Phillips Curve (1) • Firm’s maximisation problem: where the stochastic discount factor is: and real marginal costs are

26. 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

27. 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

28. 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

29. 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

30. 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

31. 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

32. Empirical results (NKPC) • Source: Batini, Jackson and Nickell (2000) Bank of England External MPC Unit paper no. 2

33. 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

34. 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

35. 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

36. 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)

37. 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