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Wolman, Alexander L.. "Sticky Prices, Marginal Cost, and the Behavior of Inflation." Economic Quarterly. Federal Reserve Bank of Richmond. 1999. HighBeam Research. 20 Jul. 2018 <https://www.highbeam.com>.
Wolman, Alexander L.. "Sticky Prices, Marginal Cost, and the Behavior of Inflation." Economic Quarterly. 1999. HighBeam Research. (July 20, 2018). https://www.highbeam.com/doc/1G1-63973152.html
Wolman, Alexander L.. "Sticky Prices, Marginal Cost, and the Behavior of Inflation." Economic Quarterly. Federal Reserve Bank of Richmond. 1999. Retrieved July 20, 2018 from HighBeam Research: https://www.highbeam.com/doc/1G1-63973152.html
A principal goal of economic modeling is to improve the formulation of economic policy. Macroeconomic models with imperfect competition and sticky prices set in a dynamic optimizing framework have gained wide popularity in recent years for examining issues involving monetary policy. For example, Rotemberg and Woodford (1999b) and McCallum and Nelson (1999) examine the behavior of model economies under a variety of monetary policy rules; Ireland (1995) examines the optimal way to disinflate; and Benhabib, Schmitt-Grohe, and Uribe (forthcoming) and Wolman (1998) study the monetary policy implications of the zero bound on nominal interest rates. [1] Nevertheless, serious questions remain as to whether these models accurately describe the U.S. economy, and therefore as to how one should interpret the results of this research.
One criticism of optimizing sticky-price models is that the relationship between output and inflation they generate is inconsistent with the behavior of these variables in the United States. [2] However, recent research by Sbordone (1998) and Gal[acute{i}] and Gertler (1999) has breathed new life into these models by shifting attention away from the relationship between output and inflation and toward one between marginal cost and inflation--the latter being a more fundamental relationship in the models. If firms have some market power, as under imperfect competition, the behavior of their marginal cost of production is an important determinant of how they set prices. In turn, the overall price level and inflation rate are determined by aggregating individual firms' pricing decisions. There is then a clear relationship between the behavior of individual firms' marginal cost and the behavior of inflation. Sbordone (1998) and Gal[acute{i}] and Gertler (1999) use this relationship to estimate and evaluate optim izing sticky-price models. [3] They find that such models can accurately replicate the observed behavior of inflation.
In this article, we work through the details of a sticky-price model, making explicit the relationship between marginal cost and inflation just described. We then offer a criticism of the specific form of price stickiness used by Sbordone and Gal[acute{i}] and Gertler; essentially, they let prices be implausibly sticky. Plausible forms of price stickiness generate fundamentally different inflation dynamics and hence will be more difficult to reconcile with the behavior of marginal cost and inflation in the United States. However, the methodology introduced by Sbordone (1998) and Gal[acute{i}] and Gertler (1999) remains a promising approach for evaluating sticky-price models. We suggest two ways in which this research agenda can continue progressing.
We concentrate on partial equilibrium analysis. The analysis takes as given the average inflation rate and the behavior of demand and real marginal cost. A complete general equilibrium version of our sticky-price framework would include descriptions of factor markets, consumer behavior, and monetary policy. In a general equilibrium, marginal cost and inflation would be endogenous; conditional on private behavior, policy would determine the behavior of inflation. Nonetheless, even in a general equilibrium, one would observe the relationship between marginal cost and inflation that is the focus of this article.
1. FROM INDIVIDUAL FIRMS' PRICING TO AGGREGATE INFLATION
Two central components comprise most of the recent optimizing sticky-price models: (1) monopolistic competition among a large number of firms producing differentiated products and (2) limited opportunities for price adjustment by individual firms. Monopolistic competition makes it feasible for some firms not to adjust their price in a given period; under perfect competition, only firms that charged the lowest price would sell anything. Limited price adjustment means that real and nominal variables interact; output and real marginal cost--both real variables--affect individual firms' pricing decisions, which in turn affect the price level and inflation.
Monopolistic Competition
The first component is monopolistic competition. The monopolistic competition framework most common in recent models is that of Dixit and Stiglitz (1977). The large number of firms mentioned above is represented mathematically by a continuum, and the firms are indexed by z [in] (0, 1). Assume that these firms' differentiated products can be aggregated into a single good, interpreted as final output. If [y.sub.t](z) is the amount produced by firm z, final output is
[y.sub.t] = [[lgroup][[[integral of].sup.1].sub.0] [y.sub.t][(z).sup.([varepsilon]-1)/[varepsilon]]dz[rgroup].sup.[varep silon]/([varepsilon]-1)]. (1)
With this aggregator function and market structure, demand for the good produced by firm z is given by
[y.sub.t](z) = [[lgroup][frac{[P.sub.t](Z)}{[P.sub.t]}][rgroup].sup.-[varepsilon]] [y.sub.t], (2)
where [P.sub.t](z) is the nominal price of good z, and [P.sub.t] and the price of one unit of [y.sub.t]. According to (2), demand for good z has a constant elasticity of -[varepsilon] with respect to the relative price of good z, and given the relative price, demand is proportional to the index of final output ([y.sub.t]). The Appendix contains a detailed derivation of the demand function (2) and shows that the price index ([P.sub.t]) is
[P.sub.t] = [[lgroup][[[integral of].sup.1].sub.0] [P.sub.t][(z).sup.1-[varepsilon]][rgroup].sup.[frac{1}{1 - [varepsilon]}]]. (3)
The price index has the property that an increase in the price of one of the goods has a positive but not necessarily one-for-one effect on the index. If that good's nominal price is lower (higher) than the price index, an increase in its price raises the price index more (less) than one-for-one, because the good has a relatively high (low) expenditure share.
Limited Price Adjustment
Limited opportunities for price adjustment constitute the second important component of our representative model. We assume that any firm z [in] (0, 1) faces an exogenous probability of adjusting its price in period t and that the probability may depend on when the firm last adjusted its price. The probability of adjusting is non-decreasing in the number of periods since the last adjustment, and we denote by J the maximum number of periods a firm's price can be fixed. [4] The key notation describing limited price adjustment will be a vector [alpha]; the [j.sup.th] element of [alpha], called [[alpha].sub.j], is the probability that a firm adjusts its price in period t, conditional on its previous adjustment having occurred in period t - j.
From the vector [alpha] we derive the fractions of firms in period t charging prices set in periods t-j, which we denote by [[omega].sub.j]. To do this, note that
[[omega].sub.j] = (1 - [[alpha].sub.j])[[omega].sub.j-1], for j = 1,2,...,J - 1,
and
[[omega].sub.0] = 1 - [[[sum].sup.J-1].sub.k=1] [[omega].sub.k]. (4)
This system of linear equations can be solved for [[omega].sub.j] as a function of [alpha]. The most common pricing specifications in the literature are those first described by Taylor (1980) and Calvo (1983). Taylor's specification is one of uniformly staggered price setting: every firm sets its price for J periods, and at any point in time a fraction I/J of firms charge a price set j periods ago. The (J - 1)-element vector of adjustment probabilities for the Taylor model is [alpha] = [0,...,0], and the J-element vector of fractions of firms is [omega] = [1/J, 1/J, . …
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