Nominal rigidity, also known as price-stickiness or wage-stickiness, is a situation in which a
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.
If one looks at the whole economy, some prices might be very flexible and others rigid. This will lead to the
aggregate price level
The general price level is a hypothetical measure of overall prices for some set of goods and services (the consumer basket), in an economy or monetary union during a given interval (generally one day), normalized relative to some base set. ...
(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 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
''The General Theory of Employment, Interest and Money'' is a book by English economist John Maynard Keynes published in February 1936. It caused a profound shift in economic thought, giving macroeconomics a central place in economic theory an ...
'',
John Maynard Keynes
John Maynard Keynes, 1st Baron Keynes, ( ; 5 June 1883 – 21 April 1946), was an English economist whose ideas fundamentally changed the theory and practice of macroeconomics and the economic policies of governments. Originally trained in ...
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.
Evidence
There is now a considerable amount of evidence about how long price-spells last, and it suggests that there is a considerable degree of nominal price rigidity in the "complete sense" of prices remaining unchanged. A price-spell is a duration during which the nominal price of a particular item remains unchanged. For some items, such as gasoline or tomatoes, prices are observed to vary frequently resulting in many short price spells. For other items, such as the cost of a bottle of
champagne
Champagne (, ) is a sparkling wine originated and produced in the Champagne wine region of France under the rules of the appellation, that demand specific vineyard practices, sourcing of grapes exclusively from designated places within it, ...
or the cost of a meal in a restaurant, the price might remain fixed for an extended period of time (many months or even years). One of the richest sources of information about this is the price-quote data used to construct the
Consumer Price Index (CPI). The statistical agencies in many countries collect tens of thousands of price-quotes for specific items each month in order to construct the CPI. In the early years of the 21st century, there were several major studies of nominal price rigidity in the US and Europe using the CPI price quote microdata. The following table gives nominal rigidity as reflected in the frequency of prices changing on average per month in several countries. For example, in France and the UK, each month on average, 19% of prices change (81% are unchanged), which implies that an average price spell lasts about 5.3 months (the expected duration of a price spell is equal to the reciprocal of the frequency of price change if we interpret the empirical frequency as representing the
Bernoulli probability of price change generating a
negative binomial distribution
In probability theory
Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expr ...
of durations of price-spells).
The fact that price spells last on average for 3.7 months does not mean that prices are not sticky. That is because many price changes are temporary (for example sales) and prices revert to their usual or "reference price".
Removing sales and temporary price cuts raises the average length of price-spells considerably: in the US it more than doubled the mean spell duration to 11 months. The reference price can remain unchanged for an average of 14.5 months in the US data.
Also, it is prices that we are interested in. If the price of tomatoes changes every month, the tomatoes price will generate 12 price spells in a year. Another price that is just as important (for example, canned tomatoes) might only change once per year (one price spell of 12 months). Looking at these two goods prices alone, we observe that there are 13 price spells with an average duration of (12+13)/13 equals about 2 months. However, if we average across the two items (tomatoes and canned tomatoes), we see that the average spell is 6.5 months (12+1)/2. The distribution of price spell durations and its mean are heavily influenced by prices generating short price spells. If we are looking at nominal rigidity in an economy, we are more interested in the distribution of durations across prices rather than the distribution of price spell durations in itself. There is thus considerable evidence that prices are sticky in the "complete" sense, that the prices remain on average unchanged for a prolonged period of time (around 12 months). Partial nominal rigidity is less easy to measure, since it is difficult to distinguish whether a price that changes is changing less than it would if it were perfectly flexible.
Linking micro data of prices and cost, Carlsson and Nordström Skans (2012), showed that firms consider both current and future expected cost when setting prices. The finding that the expectation of future conditions matter for the price set today provides strong evidence in favor of nominal rigidity and the forward looking behavior of the price setters implied by the models of sticky prices outlined below.
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 and
Guillermo Calvo. In Taylor (1980), firms change prices every ''n''th period. In Calvo (1983), price changes follow a
Poisson process
In probability, statistics and related fields, a Poisson point process is a type of random mathematical object that consists of points randomly located on a mathematical space with the essential feature that the points occur independently of one ...
. In both models the choice of changing prices is independent of the inflation rate.
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 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-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).
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)
(i-1), and the expected duration is h
−1. 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.
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 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.
Examples of state-dependent models include the one proposed by Golosov and Lucas and one suggested by Dotsey, King and Wolman.
Significance in macroeconomics
In macroeconomics, nominal rigidity is necessary to explain how money (and hence monetary policy and inflation) can affect the real economy and why the
classical dichotomy breaks down.
If nominal wages and prices were not sticky, or ''perfectly flexible'', they would always adjust such that there would be equilibrium in the economy. In a perfectly flexible economy, monetary shocks would lead to immediate changes in the level of nominal prices, leaving real quantities (e.g. output, employment) unaffected. This is sometimes called
monetary neutrality or "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 all mainstream macroeconomic theory:
Monetarists,
Keynesians and
new Keynesians all agree that markets fail to clear because prices fail to drop to
market clearing levels when there is a drop in demand. Such models are used to explain unemployment.
Neoclassical models, common in
microeconomics, predict that involuntary unemployment (where an individual is willing to work, but unable to find a job) should not exist, as this would lead employers to cut wages; this would continue until unemployment was no longer a problem. While such models can be useful in other markets where prices adjust more readily, sticky wages are a common way to explain why workers cannot find jobs: as wages cannot be cut instantaneously, they will sometimes be too high for the market to clear.
Since prices and wages cannot move instantly, price- and wage-setters become forward looking. The notion that expectations of future conditions affect current price- and wage-setting decisions is a keystone for much of the current monetary policy analysis based on Keynesian macroeconomic models and the implied policy advice.
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. Thus price and wage stickiness in one sector can "spill over" and lead to the economy behaving in a more
Keynesian way.
Mathematical example: a little price stickiness can go a long way
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
f and a proportion 1-a that are affected by menu costs with sticky prices P
m. Suppose that the flexible price sector price P
f has the market clearing condition of the following form:
:
where
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
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.
Using the aggregate price index the equilibrium condition becomes
:
which implies that
:
,
so that
:
.
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.
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
:
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
to Y and so on.
Sticky information
In macroeconomics, sticky information is old information used by agents as a basis for their behavior—information that does not take into account recent events. The first model of sticky information was developed by
Stanley Fischer
Stanley Fischer ( he, סטנלי פישר; born October 15, 1943) is an Israeli American economist who served as the 20th Vice Chair of the Federal Reserve from 2014 to 2017. Fisher previously served as the 8th governor of the Bank of Israel ...
in his 1977 article. 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 setting its wage based on the contract it planned last period, which is based on the old information.
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.
The idea of sticky information was later developed by
N. Gregory Mankiw and
Ricardo Reis. 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, and 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.
Evaluation of sticky information models
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.
This is at odds with the empirical evidence on prices.
There are now many studies of price rigidity in different countries: the US,
the Eurozone,
the UK
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.
Sticky inflation assumption
The sticky inflation assumption states that "when firms set prices, for various reasons the prices respond slowly to changes in monetary policy. This leads the rate of inflation to adjust gradually over time."
[Charles I. Jones, Macroeconomics, 3rd edition. Text (Norton, 2013) p.309.]
Additionally, within the context of the short run model there is an implication that the classical dichotomy does not hold when sticky inflation is present. This is the case when monetary policy affects real variables. Sticky inflation can be caused by expected inflation (e.g. home prices prior to the recession), wage push inflation (a negotiated raise in wages), and temporary inflation caused by taxes. Sticky inflation becomes a problem when economic output decreases while inflation increases, which is also known as
stagflation
In economics, stagflation or recession-inflation is a situation in which the inflation rate is high or increasing, the economic growth rate slows, and unemployment remains steadily high. It presents a dilemma for economic policy, since actio ...
. As economic output decreases and
unemployment
Unemployment, according to the OECD (Organisation for Economic Co-operation and Development), is people above a specified age (usually 15) not being in paid employment or self-employment but currently available for work during the refer ...
rises the standard of living falls faster when sticky inflation is present. Not only will inflation not respond to monetary policy in the short run, but monetary expansion as well as contraction can both have negative effects on the standard of living.
See also
*
Shapiro–Stiglitz theory
References
Further reading
*
*
*
*
*
*
*Herschel I. Grossman, 1987.“monetary disequilibrium and market clearing” in ''
The New Palgrave: A Dictionary of Economics'', v. 3, pp. 504–06.
*''
The New Palgrave Dictionary of Economics
''The New Palgrave Dictionary of Economics'' (2018), 3rd ed., is a twenty-volume reference work on economics published by Palgrave Macmillan. It contains around 3,000 entries, including many classic essays from the original Inglis Palgrave Diction ...
'', 2008, 2nd Edition. Abstracts:
"monetary overhang"by Holger C. Wolf.
"non-clearing markets in general equilibrium"by Jean-Pascal Bénassy.
"fixprice models"by
Joaquim Silvestre"inflation dynamics"by Timothy Cogley.
"temporary equilibrium"by J.-M. Grandmont.
*
*
*
External links
*
Economics A-Z: Sticky Prices
{{Keynesians
Monetary economics
New Keynesian economics
Keynesian economics