Editing Nominal rigidity (section)

==Modeling sticky prices==
Economists have tried to model sticky prices in a number of ways. These models can be classified as either time-dependent, where firms change prices with the passage of time and decide to change prices ''independently'' of the economic environment, or state-dependent, where firms decide to change prices ''in response to changes'' in the economic environment. The differences can be thought of as differences in a two-stage process: In time-dependent models, firms decide to change prices and then evaluate market conditions; In state-dependent models, firms evaluate market conditions and then decide how to respond.

In time-dependent models price changes are staggered exogenously, so a fixed percentage of firms change prices at a given time. There is no selection as to which firms change prices. Two commonly used time-dependent models are based on papers by [[John B. Taylor]]<ref>{{cite journal |last=Taylor |first=John B. |year=1980 |title=Aggregate Dynamics and Staggered Contracts |journal=[[Journal of Political Economy]] |volume=88 |issue=1 |pages=1–23 |jstor=1830957 |doi=10.1086/260845|s2cid=154446910 }}</ref> and [[Guillermo Calvo]].<ref>{{cite journal |last=Calvo |first=Guillermo A. |year=1983 |title=Staggered Prices in a Utility-Maximizing Framework |journal=Journal of Monetary Economics |volume=12 |issue=3 |pages=383–398 |doi=10.1016/0304-3932(83)90060-0 }}</ref> In Taylor (1980), firms change prices every ''n''th period. In Calvo (1983), price changes follow a [[Poisson process]]. In both models the choice of changing prices is independent of the inflation rate.

The [[Taylor contracts (economics)|Taylor model]] is one where firms set the price knowing exactly how long the price  will last (the duration of the price spell). Firms are divided into cohorts, so that each period the same proportion of firms reset their price. For example, with two-period price-spells, half of the firms reset their price each period. Thus the aggregate price level is an average of the new price set this period and the price set last period and still remaining for half of the firms. In general, if price-spells last for ''n'' periods, a proportion of 1/''n'' firms reset their price each period and the general price is an average of the prices set now and in the preceding ''n''&nbsp;−&nbsp;1 periods. At any point in time, there will be a uniform distribution of ages of price-spells: (1/''n'') will be new prices in their first period, 1/''n'' in their second period, and so on until 1/''n'' will be ''n'' periods old. The average age of price-spells will be (''n''&nbsp;+&nbsp;1)/2 (if the first period is counted as&nbsp;1).

In the Calvo [[Calvo (staggered) contracts|staggered contracts]] model, there is a constant probability h that the firm can set a new price.  Thus a proportion h of firms can reset their price in any period, whilst the remaining proportion (1&nbsp;−&nbsp;''h'') keep their price constant. In the Calvo model, when a firm sets its price, it does not know how long the price-spell will last. Instead, the firm faces a probability distribution over possible price-spell durations.  The probability that the price will last for ''i'' periods is (1&nbsp;−&nbsp;''h'')<sup>''i''−1</sup>, and the expected duration is ''h''<sup>−1</sup>.  For example, if ''h''&nbsp;=&nbsp;0.25, then a quarter of firms will rest their price each period, and the expected duration for the price-spell is&nbsp;4. There is no upper limit to how long price-spells may last: although the probability becomes small over time, it is always strictly positive.  Unlike the Taylor model where all completed price-spells have the same length, there will at any time be a distribution of completed price-spell lengths.

In state-dependent models the decision to change prices is based on changes in the market and is not related to the passage of time. Most models relate the decision to change prices to [[menu cost]]s. Firms change prices when the benefit of changing a price becomes larger than the menu cost of changing a price. Price changes may be bunched or staggered over time. Prices change faster and monetary shocks are over faster under state dependent than time.<ref name="KlenowKryvtsov2008">{{cite journal |first2=Oleksiy |last2=Kryvtsov |first1=Peter J. |last1=Klenow |year=2008 |title=State-Dependent or Time-Dependent Pricing: Does It Matter For Recent U.S. Inflation? |journal=[[The Quarterly Journal of Economics]] |volume=123 |issue=3 |pages=863–904 |doi=10.1162/qjec.2008.123.3.863 |citeseerx=10.1.1.589.5275 }}</ref>  Examples of state-dependent models include the one proposed by Golosov and Lucas<ref>{{cite journal |first1=Mikhail |last1=Golosov |first2=Robert E. Jr. |last2=Lucas |year=2007 |title=Menu Costs and Phillips Curves |journal=[[Journal of Political Economy]] |volume=115 |issue=2 |pages=171–199 |doi=10.1086/512625 |citeseerx=10.1.1.498.5570 |s2cid=8027651 }}</ref> and one suggested by Dotsey, King and Wolman.<ref>{{cite journal |last1=Dotsey |first1=Michael |last2=King |first2=Robert G. |last3=Wolman |first3=Alexander L. |title=State-Dependent Pricing and the General Equilibrium Dynamics of Money and Output |journal=[[The Quarterly Journal of Economics]] |volume=114 |issue=2 |pages=655–690 |doi=10.1162/003355399556106 |year=1999|s2cid=33869494 }}</ref>