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.
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 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.
Examples of stickiness
Many firms, during recessions, 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. 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.
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, 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.
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.
Note: For a general discussion of asymmetric upward- and downward-stickiness with respect to upstream prices see Asymmetric price transmission.
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 based on papers by John B. Taylor and Guillermo Calvo. In Taylor (1980), firms change prices every nth 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 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).
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 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. 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 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 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 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. 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 Pf and a proportion 1-a that are affected by menu costs with sticky prices Pm. Suppose that the flexible price sector price Pf 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
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 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. 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.
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; 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.
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