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

2. 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. 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. 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. 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. 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. 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. 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. 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. 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. 11 Summary of Model Comparisons Lucas (1973) NKNIRB/ LDR Perfectly competitive market?yesno Flexible price?yesnoyesno Perfect (common) information?noyesno Infinite regress problem?no yes

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

13. 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. 14 Notations

15. 15 Higher-Order Expectations

16. 16 The Heterogeneous Information Phillips Curve

17. 17 Firms’ Perceived Law of Motion

18. 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. 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. 20 The Rational Believer Model In a special case that A,B,D are known a priori, and C=0 and Q 2 =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 Q 2 =0 means that firms receive signals on the actual price and nominal spending, but not on their higher- order expectations

21. 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. 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.)price eq. This is supported by the experimental evidence in Nagel (1995)

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

24. 24 The Impulse Response Functions Assume that firms receive signals on contemporaneous nominal spending and aggregate price level (Q 2 =0) Using the baseline parameter values from Woodford (2003)

25. 25 Baseline Inflation Response

26. 26 Baseline Real Output Response

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

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

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

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

31. 31 Response of all Models, for varying

32. 32 Response of all Models, for varying 

33. 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