Nominal rigidity

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. 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 (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. 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 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 index. 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 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 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. 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 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 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.