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Description
This paper studies the consequences of a lack of common knowledge in the transmission of monetary policy by integrating the Woodford (2003a) imperfect common knowledge model with Taylor-Calvo staggered price-setting models. The average price set by monopolistically competitive firms depends on their higher-order expectations about not only the current state of the economy but also about the states in the future periods in which prices are to be fixed. This integrated model provides a plausible explanation for the observed effects of monetary policy: it shows analytically how price adjustments are delayed and how the response of output to monetary disturbances is amplified.
JEL codes: D82, E30
Keywords: imperfect common knowledge, higher-order expectations, public and private information, staggered price setting.
MODERN MACROECONOMIC THEORY provides two main explanations for why monetary policy has real effects in the short run: imperfect information about the policy shocks and short-run rigidity in price or wage adjustment. The imperfect information approach was originally developed by Phelps (1970) and Lucas (1972) in the era in which the traditional output-inflation relationship collapsed. Their arguments, however, were criticized for their practical irrelevance: the Phelps-Lucas models imply that the real effects of monetary policy only last while the precise public information about aggregate disturbances is unavailable, which seems to contradict the observed persistence of business fluctuations despite the availability of macroeconomic data with little delay. To analyze the persistent real effects of monetary policy, many current monetary models of business fluctuations assume short-run rigidity in price or wage adjustment, typically by incorporating staggered price setting as in Taylor (1980) or Calvo (1983).
Recently, some authors have reconsidered the imperfect information approach. Mankiw and Reis (2002) consider sticky information rather than sticky prices, which means some price setters cannot choose their prices based on current information. Woodford (2003a) considers imperfect common knowledge about nominal disturbances in an environment among monopolistically competitive suppliers. These models can generate persistent real effects of monetary policy. Moreover, they can also explain the observed delay in the monetary policy effect on inflation, which implies they overcome a major problem faced by the Taylor-Calvo staggered price-setting models.
These imperfect-information models, however, still leave the original problem in the Phelps-Lucas models unsolved. The source of persistence of the real effects of monetary policy in the Mankiw-Reis model is the outdated information that influences current price setting. In their model, there are always some suppliers who set their prices based on very old information because the probability of obtaining new information in each period is constant and identical for all suppliers however recent their last updates. In the Woodford model, suppliers choose their prices solely on the basis of the history of their subjective observations that contain idiosyncratic perception errors. They never obtain, nor pay attention to, precise information about aggregate demand and even about the actual quantities they sold at their chosen prices. In both models, there would be no persistent real effects of monetary policy if the true state of the economy were revealed to all suppliers with a delay of only one period. These models do not explain why price setters fail to use widely and readily available macroeconomic data. (1)
In this paper, we develop a model that integrates Woodford's imperfect common knowledge model with Taylor-Calvo staggered price-setting models in order to overcome the problems in each of them and explain plausibly the observed effects of monetary policy. The model is based on the standard monopolistic competition framework as in Blanchard and Kiyotaki (1987). Following Woodford, we assume that price setters can only observe the state of the economy through noisy private signals. Their optimal pricing strategy depends not only on their own estimates of the aggregate demand but also on their expectations of the average estimates by other price setters. In such an environment, the overall price level is determined by a weighted sum of price setters' "higher-order expectations," that is, what others expect about what others expect... about aggregate demand. (2) Meanwhile, we drop Woodford's unrealistic assumption by assuming that the true state of the economy is revealed to all price setters with a delay of one period. Given staggered price setting, however, the model can generate persistent real effects of monetary policy. The average price chosen in each period depends on higher-order expectations about not only the current state of the economy but also about the states in the future periods in which prices are to be fixed. For simplicity, we assume that half of the price setters in the economy set their prices fixed until the next period, namely two-period staggered price setting. Our model of imperfect common knowledge, however, can be integrated with more general price setting that allows for multiple-period staggered price setting (3) including the one analogized with Calvo-type price setting. (4) Despite the complexity in those dynamic and staggered higher-order expectations, the model can be solved analytically by virtue of the assumption that the true current state becomes common knowledge in the subsequent period.
The main results of the model are as follows. The noisier are the private signals, the more sluggish is the initial response of prices to a monetary disturbance. The response that operates through dynamic and staggered higher-order expectations is, in many cases, more sluggish than the one that operates through static and simultaneous higher-order expectations under flexible prices. Following this initial response, price adjustments are delayed and inflation may peak later than in the corresponding full-information staggered price-setting model. The response of output is amplified by the lack of common knowledge and continues to exceed the response in the full-information model. Even a small amount of noise in the private signals may significantly delay the adjustment of prices and amplify the response of output. The model nests the full-information staggered price-setting model as one limit case. As another limit case, it also nests the predetermined-prices model, in which all firms either have no information about the current aggregate disturbances or are simply assumed to set their prices one period in advance. (5) The case of imperfect common knowledge is between these two limit cases and explains endogenously how price adjustments are delayed.
We extend the above baseline model by introducing a noisy public signal in addition to the private signals and study the consequences of a more general information structure following Hellwig (2002) and Amato and Shin (2003). These authors emphasize the separation of information into public and private signals and criticize the Woodford model for focusing only on private signals and for lacking considerations of problems involving informational interaction between decision makers. As they argue, in an economy in which decision makers' information sets are heterogeneous, public information has disproportionately large effects on their decisions. Whereas Amato and Shin assume that price setters never obtain precise information as in the Woodford model, we retain the assumption that the true state of the economy is revealed to all price setters with a delay of one period. The public signal in our extended model, then, may represent preliminary data that is to be revised or noisy information promptly provided by the media, the government, and so on. When it is interpreted as a communication tool of the monetary authority, the model has interesting implications for the conduct of monetary policy involving, for example, transparency.
We first show that provision of the public signal alleviates the effects of monetary disturbances. The noisier is the public signal, as are the private signals, the more sluggish is the initial response of prices. Compared with the baseline model without the public signal, which corresponds to the case with an infinite amount of noise in the public signal, the initial response of prices is less sluggish and the response of output is less amplified. Meanwhile, the provision of the public signal exposes firms to an additional aggregate disturbance, namely, noise in the public signal itself. For example, a negative informational disturbance, that is, downwardly biased information about current aggregate demand, generates delayed inflation... |
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