Imperfect Common Knowledge, Price Stickiness, and Inflation Inertia

1. Imperfect Common Knowledge, Price Stickiness, and Inflation Inertia Porntawee Nantamanasikarn University of Hawai’i at Manoa November 27, 2006

2. Introduction • The standard New Keynesian (NK) model does a poor job explaining observed inflation inertia (e.g. Mankiw, 2001) • Inflation response jumps immediately at the time of monetary shocks, because • price, but not inflation, is sticky, and • the representative agent is purely forward looking

3. Other Studies’ Proposed Solutions • Backward looking behavior • Fuhrer and Moore (1995), Gali and Gertler (1999) • Limited or bounded rationality • Roberts (1997), Ball (2000) • Automatic indexation to past inflation • Yun (1996), Christiano et al. (2005)

4. Other Studies’ Proposed Solutions • Information stickiness • Mankiw and Reis (2002, 2003) • Implementation lags • Cochrane (1998), Bernanke and Woodford (1997) • Habit persistence • Fuhrer (2000), Smets and Wouters (2003)

5. The Noisy Information (NI) Model • Woodford (2003) assumes monopolistic competitive market in Lucas’s (1973) island model to generate inflation inertia • Firms have heterogeneous subjective perceptions of current conditions (imperfect common knowledge) • Inflation responds sluggishly to monetary shock because higher-order expectations are slow to adjust

6. The NI Model’s Problems • Prices are fully flexible • Implication: credible future policy change does not affect current decisions • Can generate inflation persistence only if the monetary shock is persistent • Implication: inflation inertia is the result of external drivers, not internal propagation mechanism

7. The NI Model’s Problems • Firms have (noisy) information only on exogenous nominal spending, not on the endogenous aggregate price level • Agents’ perceptions are not affected by others’ current decisions

8. Research Objective • Develop models that • credible future policy can affect current decisions • can generate inflation inertia, even if monetary shock is not very persistent • others’ decisions simultaneously affect perceptions • How: assume imperfect CK and price stickiness • Challenge: the infinite regress problem

9. The Infinite Regress Problem • Dating back to Pigou (1929), Muth (1960) • The recursive representation of the system requires infinite number of state variables • When agents must forecast the forecasts of others (which is unobserved), it is necessary for them to keep track of infinite history of observable variables

10. The Infinite Regress Problem • Some proposed “solutions”: • Townsend (1983), Lucas (1975) • The NI model avoids this problem because there is no feedback from pricing decisions to the source of signals • I propose two alternative models for how expectations are formed: • The Rational Believer (RB) Model • The Limited Depth of Reasoning (LDR) Model

11. Summary of Model Comparisons

12. Model Setup • Firm i ’s optimal flexible price • Aggregate demand equation • Central bank’s policy

13. Adding Price Stickiness • Firms have a constant probability of (1-) to adjust price in each period (Calvo 1983) • If able to adjust price, a forward looking firm will set the new price, according to • The aggregate price is

14. Notations

15. Higher-Order Expectations

16. The Heterogeneous Information Phillips Curve

17. Firms’ Perceived Law of Motion

18. Firms’ Signal Equation • Each firm receives idiosyncratic signal of the state variables according to is mean-zero Gaussian white noise error terms, distributed independently both of the history of fundamental disturbance and of the observation errors of all other agents

19. The Kalman Filter Updating Algorithm • Firms form minimum MSE estimates of the state variables, according to where K is a matrix of Kalman gain • The equilibrium objects are L,M,N, which result in a fixed point of mapping from the perceived law of motion to the actual one when firms’ updating algorithm is the above equation

20. The Rational Believer Model • In a special case that A,B,D are known a priori, and C=0 and Q2=0, the equilibrium matrices L,M,N are exactly identified. Otherwise, there are more unknown variables than the number of equilibrium conditions • C=0 means that firms (mistakenly) believe that the actual aggregate price and nominal spending do not depend on their higher-order expectations • Q2=0 means that firms receive signals on the actual price and nominal spending, but not on their higher-order expectations

21. The Rational Believer Model • The RB model assumes that firms believe and know that others also believe the economy evolves according to the full-info NK model • But they are unaware that their own decisions affect the aggregate outcome • Misperception persists because firms’ information set consists of only a history of contaminated signals, which cannot be used to prove that the NK model is actually wrong

22. The Limited Depth of Reasoning Model • Firms are aware that their own decisions affect the aggregate outcome • But they can form expectations of others’ forecasts only for a finite (k) number of iterations (see the price eq.) • This is supported by the experimental evidence in Nagel (1995)

23. The Limited Depth of Reasoning Model • Suppose that k=3, that is, firms assume that the 4th order expectation is the same as the 3rd • The state vector is • Limited depth of reasoning means

24. The Impulse Response Functions • Assume that firms receive signals on contemporaneous nominal spending and aggregate price level (Q2=0) • Using the baseline parameter values from Woodford (2003)

25. Baseline Inflation Response

26. Baseline Real Output Response

27. Inflation Response of the LDR Model, for varying k

28. Real Output Response of the LDR Model, for varying k

29. Inflation Response of the NI Model, for varying 

30. Real Output Response of the NI Models, for varying 

31. Response of all Models, for varying

32. Response of all Models, for varying 

33. Conclusion • The models can generate inflation inertia, even when monetary shocks are not persistent, esp. the LDR model • But it is necessary that we make assumptions about how expectations are formed to “solve” the infinite regress problem • Extension: endogenize price stickiness