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Description
I. INTRODUCTION
Empirical studies suggest that inflation adjusts gradually after a monetary policy shock, with the peak occurring several quarters later. (1) Most theoretical models, however, generate an inflation response that peaks on impact. Nelson (1998) finds that even the introduction of sticky prices does not help solve that problem. Mankiw and Reis (2002) argue that the key to generating a substantial lag in the peak inflation response is the introduction of sticky information, not sticky prices, in a model.
The premise in Mankiw and Reis (2002) is that the slow dissemination of information on macroeconomic conditions is responsible for the sluggish adjustment in inflation. In their study, the gradual flow of information is incorporated into a partial equilibrium model via a Fischer (1977)--style price-setting rule. (2) This rule assumes that every firm adjusts its price each period, but the expectations of current and future economic conditions used to set that price are updated infrequently. Hence, information and not prices tends to be sticky. Mankiw and Reis (2002) show that a sticky information model, in contrast to a standard sticky price model, can generate a substantial lag in the inflation peak after a monetary disturbance. These results lead Mankiw and Reis (2002) to conclude that sticky information should replace sticky prices in New Keynesian models of the business cycle.
This article begins by using Mankiw and Reis' (2002) partial equilibrium model to reproduce their finding that inflation responds with a significant lag in a sticky information model but adjusts rapidly in a sticky price model. Uncertainty about the parameterization of one of the equations in their model, however, persuades us to examine the robustness of their results. A sensitivity analysis shows that the lagged peak in inflation occurs anywhere from one to seven periods after a monetary disturbance depending on the parameterization of the model. In order to determine a plausible parameterization for their model, we integrate a sticky information rule into a dynamic stochastic general equilibrium (DSGE) model where the monetary authority follows a money growth rule as in Mankiw and Reis (2002). In our model, inflation peaks one period after a monetary policy shock, which is consistent with a parameterization of the partial equilibrium model different from the one used by Mankiw and Reis (2002). We then conduct a second sensitivity analysis to determine whether the addition of more real rigidities and changes to the monetary policy rule can assist our DSGE model with sticky information in producing results consistent with Mankiw and Reis (2002). (3) Our findings demonstrate that a considerable amount of real rigidities are necessary if a DSGE model with sticky information is going to generate the seven-period lag in the peak inflation rate produced in Mankiw and Reis (2002). When the monetary instrument is the nominal interest rate instead of the money growth rate, we show that a DSGE model with sticky information, like the standard sticky price model, produces an immediate inflation peak after a monetary policy shock. Those results suggest that a sticky information model can produce more plausible inflation responses than a sticky price model if the model includes important real rigidities and a money growth policy rule. The inflation behavior in the two models, however, is similar when the policy instrument is the nominal interest rate.
The rest of the article is arranged as follows. Section II introduces the partial equilibrium model used by Mankiw and Reis (2002) and replicates inflation's response to a monetary policy shock with both sticky prices and sticky information. Then, a sensitivity analysis is conducted to determine the robustness of those results to different parameterizations of both models. Section III examines inflation's response to a monetary policy shock when a sticky information price-setting rule is incorporated into a DSGE model. Inflation's response in the DSGE model is compared with its behavior in the partial equilibrium model. Section IV presents a sensitivity analysis of inflation's response to different parameterizations of the DSGE model. Section V concludes.
II. PARTIAL EQUILIBRIUM APPROACH
In an influential study, Mankiw and Reis (2002) use a partial equilibrium model to show that a sticky information model can generate a gradual inflation response that peaks several quarters after a monetary policy shock, while a sticky price model produces an inflation response that peaks on impact. The result leads Mankiw and Reis (2002) to conclude that New Keynesian business cycle models should be specified routinely with a sticky information rule, as opposed to a sticky price rule. Given the potential implications of such a conclusion, we begin by examining the robustness of Mankiw and Reis' (2002) inflation responses in their sticky price and sticky information models.
A. The Model
The sticky price and sticky information models used by Mankiw and Reis (2002) comprise five equations. Of the five equations, four are common to both models, while only the price-setting equation is unique to each model. Since the models share most of the same equations, we present one common model but specify it with a sticky price and a sticky information price-setting rule.
In every period t, each firm prefers to set a price, [P.sup.*.sub.t], that is a function of the price level, [P.sub.t], and output, [y.sub.t]:
(1) log([P.sub.*.sub.t]/[P.sub.*]) = log([P.sub.t]/P) + [gamma]log([y.sub.t]/y),
where [gamma] > is the sensitivity of a firm's price to output, and a variable without a time subscript represents a steady-state value. Although Equation (1) is not determined by solving a profit-maximizing problem, a similar equation can be derived using the Dixit and Stiglitz (1977) methodology of monopolistically competitive firms. The difference between the pricing rule in Mankiw and Reis (2002) and a rule derived by solving a profit-maximizing problem is that in a profit-maximizing framework [P.sub.*.sub.t] depends on marginal cost and not output. Mankiw and Reis (2002), however, argue that output is a sufficient proxy for marginal cost because the demand pressures for additional output cause marginal cost to rise. While output and marginal cost move together over the business cycle, the relative volatility of marginal cost to output influences the similarity between those two pricing rules. (4) This distinction is important because firm pricing decisions directly influence inflation's response to a monetary policy shock. A comparison of the impact of these two pricing rules on inflation is discussed in more detail in Section III.
Sticky price and sticky information models differ by the method in which firms set their prices. In the sticky price model, a fraction of the firms each period can select a new price, [X.sub.t,0], while the remaining firms can only adjust their price by the steady-state inflation rate. Hence, the price charged by a firm that last selected a new price j periods ago is [X.sub.t,j] = [[pi].sup.j] [X.sub.t-j,0], where [pi] is the gross steady-state inflation rate. Based on Calvo (1983), the conditional probability that a firm can pick a new price in any period is [eta], while the conditional probability it must adjust its price by the steady-state inflation rate is (1 - [eta]). Since price-selecting opportunities are infrequent, a price-changing firm sets a price equal to the weighted average of its optimal prices until its next expected pricing opportunity:
(2) log([X.sub.t,0]/X) = [eta][[infinity].summation over (j=0)] [(1 - [eta]).sup.j]
[E.sub.t][log([P.sup.*.sub.t+j]/([[pi].sup.j] [P.sup.*]))].
In the sticky information model, every firm can adjust its price each period, but the expectations used to set that price is updated sporadically. Utilizing Calvo's (1983) model of random adjustment, each firm's conditional probability that it can adjust its expectations is [eta], while the remaining fraction of firms, (1 - [eta]), must set their prices based on expectations last adjusted j periods ago. Hence, each firm sets its price, [P.sup.*.sub.t,j], equal to its expectation of the optimal price formed j periods ago:
(3) log([X.sub.tj]/X) = [E.sub.t-j][log([P.sup.*.sub.t]/[P.sup.*])].
A common characteristic of sticky price and sticky information models is that the adjustment rate in prices or expectations, [eta], is constant. Thus, the fraction of firms that last adjusted their prices or expectations j periods ago is [eta][(1 - [eta]).sup.j]. The calculation of the price level, which is the average of all prices in the economy, then is identical for both models:
(4) log([P.sub.t]/P) = [eta] [[infinity].summation over (j=0)] [(1 - [eta]).sup.j]log([X.sub.t,j]/X).
To complete the model, we identify an aggregate demand equation and a monetary policy rule. A simple equation of exchange is specified for aggregate demand:
(5) log([y.sub.t]/y) + log([P.sub.t]/P) = log([M.sub.t/M),... |
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