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| Nominal rigidity, also known as price-stickiness (and/or wage-stickiness), describes a situation in which the [[nominal price]] is resistant to change. Complete nominal rigidity occurs when a price is fixed in nominal terms for a relevant period of time. For example, the price of a particular good might be fixed at $10 per unit for a year. Partial nominal rigidity occurs when a price may vary in nominal terms, but not as much as it would if perfectly flexible. For example, in a regulated market there might be limits to how much a price can change in a given year.
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| If we look at the whole economy, some prices might be very flexible and others rigid. This will lead to the [[aggregate price level]] (which we can think of as an average of the individual prices) becoming "sluggish" or "sticky" in the sense that it does not respond to macroeconomic shocks as much as it would if all prices were flexible. The same idea can apply to nominal wages. The presence of nominal rigidity is an
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| important part of macroeconomic theory since it can explain why markets might not reach equilibrium in the short run or even possibly the long-run. In his [[The General Theory of Employment, Interest and Money]], [[John Maynard Keynes]] argued that nominal wages display downward rigidity, in the sense that workers are reluctant to accept cuts in nominal wages. This can lead to [[involuntary unemployment]] as it takes time for wages to adjust to equilibrium, a situation he thought applied to the [[Great Depression]] that he sought to understand.
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| ==Examples of stickiness==
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| Many firms, during [[recessions]], [[downsizing|lay off]] workers. Yet many of these same firms are reluctant to begin hiring, even as the economic situation improves. This can result in slow job growth during a recovery.
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| Wages, prices, and employment levels can all be sticky. Normally, a variable oscillates according to changing market conditions, but when stickiness enters the system, oscillations in one direction are favored over the other, and the variable exhibits "creep"—it gradually moves in one direction or another. This is also called the "ratchet effect". Over time a variable will have ratcheted in one direction.
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| For example, in the absence of [[competition]], firms rarely lower prices, even when production costs decrease (i.e. supply increases) or demand drops. Instead, when production becomes cheaper, firms take the difference as [[Profit (economics)|profit]], and when demand decreases they are more likely to hold prices constant, while cutting production, than to lower them. Therefore, prices are sometimes observed to be ''sticky downward'', and the net result is one kind of [[inflation]].
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| Prices in an [[oligopoly]] can often be considered sticky-upward. The [[kinked demand]] curve, resulting in elastic [[price elasticity of demand]] above the current market clearing price, and inelasticity below it, requires firms to match price reductions by their competitors to maintain market share.
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| ''Note: For a general discussion of asymmetric upward- and downward-stickiness with respect to upstream prices see [[Asymmetric price transmission]].''
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| ==Modeling sticky prices==
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| 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.
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| 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 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 }}</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.
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| The 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 firm 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-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+1)/2 (if you count the first period as 1).
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| In the Calvo 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-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-h)<sup>(i-1)</sup>, and the expected duration is h<sup>-1</sup>. For example, if h=0.25, then a quarter of firms will rest their price each period, and the expected duration for the price-spell is 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.
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| In state-dependent models the decision to change prices is based on changes in the market and are not related to the passage of time. Most models relate the decision to change prices changes to [[menu costs]]. 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 |first=Peter J. |last=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 }}</ref> Examples of state-dependent models include the one proposed by Golosov and Lucas<ref>{{cite journal |first=Mikhail |last=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 }}</ref> and one suggested by Dotsey, King and Wolman<ref>{{cite journal |last=Dotsey |first=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 }}</ref>
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| ==Significance in macroeconomics==
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| In macroeconomics, nominal rigidity is crucial in explaining how money can effect the real economy and why the [[classical dichotomy]] breaks down. If nominal wages prices were ''perfectly flexible'', they would always adjust so that there would be equilibrium in the economy. Thus, for example, monetary shocks would lead to changes in the level of nominal prices, leaving quantities - output, employment for example - unaffected (this is sometimes called [[monetary neutrality| the neutrality of money]]). For money to have real effects, some degree of nominal rigidity is required so that prices (and wages) do not respond immediately. Hence sticky prices play an important role in [[Keynesian]] macroeconomic theory and [[new Keynesian economics|new Keynesian thought]]. Keynesian macroeconomists suggest that markets fail to clear because prices fail to drop to [[market clearing]] levels when there is a drop in demand. Economists have also looked at sticky wages as an explanation for why there is unemployment. [[Huw Dixon]] and Claus Hansen showed that even if only part of the economy has sticky prices, this can influence prices in other sectors and lead to prices in the rest of the economy becoming less responsive to changes in demand.<ref>{{cite journal |last=Dixon |first=Huw |last2=Hansen |first2=Claus |title=A mixed industrial structure magnifies the importance of menu costs |journal=[[European Economic Review]] |year=1999 |volume=43 |issue=8 |pages=1475–1499 |doi=10.1016/S0014-2921(98)00029-4 }}</ref> Thus price and wage stickiness in one sector can "spill over" and lead to the economy behaving in a more [[Keynesian]] way.<ref name="Dixon1992">{{cite journal |last=Dixon |first=Huw |title=Nominal wage flexibility in a partly unionised economy |journal=The Manchester School of Economic and Social Studies |year=1992 |volume=60 |issue=3 |pages=295–306 |doi=10.1111/j.1467-9957.1992.tb00465.x }}</ref><ref>{{cite journal |last=Dixon |first=Huw |title=Macroeconomic Price and Quantity responses with heterogeneous Product Markets |journal=Oxford Economic Papers |year=1994 |volume=46 |issue=3 |pages=385-402 |jstor=2663572 }}</ref> | |
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| ===Mathematical example: a little price stickiness can go a long way.===
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| To see how a small sector with a fixed price can affect the way rest of the flexible prices behave, suppose that there are two sectors in the economy: a proportion '''a''' with flexible prices '''P<sub>f</sub>''' and a proportion '''1-a''' that are affected by menu costs with sticky prices '''P<sub>m</sub>'''. Suppose that the flexible price sector price '''P<sub>f</sub>''' has the market clearing condition of the following form:
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| :<math> \frac{P_f}{P}=\theta </math>
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| where <math>P=P_f^{a}P_m^{1-a} </math> is the aggregate [[price index]] (which would result if consumers had Cobb-Douglas preferences over the two goods). The equilibrium condition says that the real flexible price equals some constant (for example <math>{\theta}</math> could be real marginal cost). Now we have a remarkable result: no matter how small the menu cost sector, so long as '''a<1''', the flexible prices get "pegged" to the fixed price.<ref name="Dixon1992" /> Using the aggregate price index the equilibrium condition becomes
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| :<math> \frac{P_f}{P_f^{a}P_m^{1-a}}=\theta</math>
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| which implies that
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| :<math> P_f^{1-a}=P_m^{1-a}\theta</math>,
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| so that
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| :<math> P_f=P_m\theta^{\frac{1}{1-a}}</math>.
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| What this result says is that no matter how small the sector affected by menu-costs, it will tie down the flexible price. In macroeconomic terms all nominal prices will be sticky, even those in the potentially flexible price sector, so that changes in nominal demand will feed through into changes in output in both the menu-cost sector and the flexible price sector.
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| Now, this is of course an extreme result resulting from the [[real rigidity]] taking the form of a constant real marginal cost. For example, if we allowed for the real marginal cost to vary with aggregate output '''Y''', then we would have
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| :<math>P_f=P_m\theta(Y)^{\frac{1}{1-a}}</math>
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| so that the flexible prices would vary with output '''Y'''. However, the presence of the fixed prices in the menu-cost sector would still act to dampen the responsiveness of the flexible prices, although this would now depend upon the size of the menu-cost sector '''a''', the sensitivity of <math>{\theta}</math> to '''Y''' and so on.
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| ==Sticky Information==
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| Sticky information is a term used in macroeconomics to refer to the fact that agents at any particular time may be basing their behavior on information that is old and does not take into account recent events. The first model of Sticky information was developed by [[Stanley Fischer]] in his 1977 article.<ref>{{cite journal |last=Fischer |first=S. |year=1977 |title=Long-Term Contracts, Rational Expectations, and the Optimal Money Supply Rule |journal=[[Journal of Political Economy]] |volume=85 |issue=1 |pages=191–205 |jstor=1828335 }}</ref> He adopted a "staggered" or "overlapping" contract model. Suppose that there are two unions in the economy, who take turns to choose wages. When it is a union's turn, it chooses the wages it will set for the next two periods. In contrast to [[John B. Taylor]]'s model where the nominal wage is constant over the contract life, in Fischer's model the union can choose a different wage for each period over the contract. The key point is that at any time t, the union setting its new contract will be using the up to date latest information to choose its wages for the next two periods. However, the other union is still choosing its wage based on the contract it planned last period, which is based on the old information.
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| The importance of sticky information in Fischer's model is that whilst wages in some sectors of the economy are reacting to the latest information, those in other sectors are not. This has important implications for monetary policy. A sudden change in monetary policy can have real effects, because of the sector where wages have not had a chance to adjust to the new information.
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| The idea of Sticky information was later developed by [[N. Gregory Mankiw]] and [[Ricardo Reis]].<ref>{{cite journal |last=Mankiw |first=N. G. |first2=R. |last2=Reis |year=2002 |title=Sticky Information Versus Sticky Prices: A Proposal To Replace The New Keynesian Phillips Curve |journal=[[Quarterly Journal of Economics]] |volume=117 |issue=4 |pages=1295–1328 |doi=10.1162/003355302320935034 }}</ref> This added a new feature to Fischer's model: there is a fixed probability that you can replan your wages or prices each period. Using quarterly data, they assumed a value of 25%: that is, each quarter 25% of randomly chosen firms/unions can plan a trajectory of current and future prices based on current information. Thus if we consider the current period: 25% of prices will be based on the latest information available; the rest on information that was available when they last were able to replan their price trajectory. Mankiw and Reis found that the model of sticky information provided a good way of explaining inflation persistence.
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| ===Evaluation of sticky information models===
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| Sticky information models do not have nominal rigidity: firms or unions are free to choose different prices or wages for each period. It is the information that is sticky, not the prices. Thus when a firm gets lucky and can re-plan its current and future prices, it will choose a trajectory of what it believes will be the optimal prices now and in the future. In general, this will involve setting a different price every period covered by the plan.
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| This is at odds with the empirical evidence on prices.<ref>{{cite journal |first=V. V. |last=Chari |first2=Patrick J. |last2=Kehoe |first3=Ellen R. |last3=McGrattan |year=2008 |url=http://www.minneapolisfed.org/research/sr/sr409.pdf |title=New Keynesian Models: Not Yet Useful for Policy Analysis |work=Federal Reserve Bank of Minneapolis Research Department Staff Report 409 }}</ref><ref name="Knotec2010">{{cite journal |first=Edward S. II |last=Knotec |year=2010 |title=A Tale of Two Rigidities: Sticky Prices in a Sticky-Information Environment |journal=Journal of Money, Credit and Banking |volume=42 |issue=8 |pages=1543–1564 |doi=10.1111/j.1538-4616.2010.00353.x }}</ref> There are now many studies of price rigidity in different countries: the US,<ref name="KlenowKryvtsov2008" /> the Eurozone,<ref>{{cite journal |first=Luis J. |last=Álvarez |first2=Emmanuel |last2=Dhyne |first3=Marco |last3=Hoeberichts |first4=Claudia |last4=Kwapil |first5=Hervé |last5=Le Bihan |first6=Patrick |last6=Lünnemann |first7=Fernando |last7=Martins |first8=Roberto |last8=Sabbatini |first9=Harald |last9=Stahl |first10=Philip |last10=Vermeulen |first11=Jouko |last11=Vilmunen |year=2006 |title=Sticky Prices in the Euro Area: A Summary of New Micro-Evidence |journal=[[Journal of the European Economic Association]] |volume=4 |issue=2-3 |pages=575-584 |doi=10.1162/jeea.2006.4.2-3.575 }}</ref> the UK <ref>{{cite journal |first=Philip |last=Bunn |first2=Colin |last2=Ellis |year=2012 |title=Examining The Behaviour Of Individual UK Consumer Prices |journal=[[The Economic Journal]] |volume=122 |issue=558 |pages=F35-F55 |doi=10.1111/j.1468-0297.2011.02490.x }}</ref> and others. These studies all show that whilst there are some sectors where prices change frequently, there are also other sectors where prices remain fixed over time. The lack of sticky prices in the sticky information model is inconsistent with the behavior of prices in most of the economy. This has led to attempts to formulate a "dual Stickiness" model that combines sticky information with sticky prices.<ref name="Knotec2010" /><ref>{{cite journal |first=Bill |last=Dupor |first2=Tomiyuki |last2=Kitamura |first3=Takayuki |last3=Tsuruga |title=Integrating Sticky Prices and Sticky Information |journal=[[Review of Economics and Statistics]] |year=2010 |volume=92 |issue=3 |pages=657-669 |doi=10.1162/REST_a_00017 }}</ref>
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| ==See also==
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| *[[Real rigidity]]
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| *[[Menu costs]]
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| ==References==
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| {{reflist|30em}}
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| ==Further reading==
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| *{{cite book|last1=Arrow|first1=Kenneth J.|authorlink1=Kenneth Arrow|last2=Hahn|first2=Frank H.|authorlink2=Frank Hahn|year=1973|<!-- chapter=Introduction to stability analysis, Stability with recontracting, Trading out of equilibrium: A pure exchange economy, The Keynesian model -->|title=General competitive analysis|publisher=North-Holland|<!-- pages= -->|series=Advanced textbooks in economics|volume=12|edition=1980 reprint of (1971) San Francisco, CA: Holden-Day, Inc. Mathematical economics texts. '''6'''|location=Amsterdam|isbn=0-444-85497-5|mr=439057|ref=harv}}
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| *{{cite book|first=F. M.|last=Fisher|authorlink=Franklin M. Fisher|title=Disequilibrium foundations of equilibrium economics|location=New York|publisher=Cambridge University Press|series=Econometric Society Monographs|year=1983|edition=1989 paperback|isbn=978-0-521-37856-7|pages=248|ref=harv}}
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| *{{cite book|last=Gale|first=Douglas|authorlink=Douglas Gale|title=Money: <!-- lower case "in" --> in equilibrium|location=Cambridge, U.K.|publisher=Cambridge University Press|year=1982|volume=2| series=Cambridge economic handbooks|isbn=978-0-521-28900-9|pages=349|ref=harv}}
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| *{{cite book|last=Gale|first=Douglas|<!-- authorlink=Douglas Gale -->|title=Money: <!-- lower case "in" --> in disequilibrium|location=Cambridge, U.K.|publisher=Cambridge University Press|year=1983|volume=| series=Cambridge economic handbooks|isbn=978-0-521-26917-9|pages=382|ref=harv}}
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| *{{cite book|title=Money and value: A reconsideration of classical and neoclassical monetary economics|first=Jean-Michel|last=Grandmont|authorlink=Jean-Michel Grandmont|series=Econometric Society Monographs|volume=5|isbn=978-0-521-31364-3|year=1985|pages=212|ref=harv|publisher=Cambridge University Press|mr=934017}}
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| *{{cite book|title=Temporary equilibrium: Selected readings|editor-first=Jean-Michel|editor-last=Grandmont|series=Economic Theory, Econometrics, and Mathematical Economics|volume=|isbn=978-0-12-295146-6|year=1988|pages=512|publisher=Academic Press|ref=harv|mr=987252 }}
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| *Herschel I. Grossman, 1987.“monetary disequilibrium and market clearing” in ''[[The New Palgrave: A Dictionary of Economics]]'', v. 3, pp. 504–06.
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| *''[[The New Palgrave Dictionary of Economics]]'', 2008, 2nd Edition. Abstracts:
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| :[http://www.dictionaryofeconomics.com/article?id=pde2008_M000409&q=monetary%20overhang&topicid=&result_number=1 "monetary overhang"] by Holger C. Wolf.
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| :[http://www.dictionaryofeconomics.com/article?id=pde2008_N000153&edition=current&q=Monetary-disequilibrium&topicid=&result_number=47 "non-clearing markets in general equilibrium"] by Jean-Pascal Bénassy.
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| :[http://www.dictionaryofeconomics.com/article?id=pde2008_F000141&edition=current&q=Monetary-disequilibrium&topicid=&result_number=48 "fixprice models"] by Joaquim Silvestre. [http://www.dictionaryofeconomics.com/article?id=pde2008_I000272 "inflation dynamics"] by Timothy Cogley.
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| :[http://www.dictionaryofeconomics.com/article?id=pde2008_T000040&edition=current&q=Monetary-disequilibrium&topicid=&result_number=41 "temporary equilibrium"] by J.-M. Grandmont.
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| *{{cite book |first=David |last=Romer |authorlink=David Romer |chapter=Nominal Rigidity |title=Advanced Macroeconomics |edition=Fourth |location=New York |publisher=McGraw-Hill |year=2011 |pages=238–311 |isbn=978-0-07-351137-5 }}
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| *{{cite book|title=General equilibrium models of monetary economies: Studies in the static foundations of monetary theory|series=Economic theory, econometrics, and mathematical economics|editor-first=Ross M.|editor-last=Starr|editor-link=Ross Starr|publisher=Academic Press|year=1989|isbn=978-0-12-663970-4|pages=351|ref=harv}}
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| * {{cite book|title = Why Wages Don't Fall during a Recession|last = Bewley|first = Truman|publisher = Harvard University Press|year = 1999|isbn = 978-0674009431|authorlink = Truman Bewley}}
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| ==External links==
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| *[http://www.nber.org/papers/W9741 NBER (2006) "Why Are Prices Sticky? The Dynamics of Wholesale Gasoline Prices."]
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| *[http://www.economist.com/research/Economics/alphabetic.cfm?TERM=STICKY%20PRICES#stickyprices Economics A-Z: Sticky Prices]
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| {{Macroeconomics}}
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| [[Category:Economics terminology]]
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| [[Category:New Keynesian economics]]
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| [[Category:Keynesian economics]]
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