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Exploring Imperfect Common Knowledge and Price Stickiness in the Context of Inflation Inertia

This research delves into issues with existing models and proposes solutions by incorporating imperfect common knowledge and price stickiness to explain inflation inertia. It examines the challenges of infinite regress problem and offers alternative models like the Rational Believer and Limited Depth of Reasoning. The study aims to develop models where current decisions are influenced by future policy credibility and perceptions, even in non-persistent monetary shocks scenarios. The proposed models address the need for accurate forecasting in economic decision-making by considering imperfect information and price adjustments.

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Exploring Imperfect Common Knowledge and Price Stickiness in the Context of Inflation Inertia

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  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

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