III. A SSESSING P RICE R IGIDITY : T HREE I NDICATORS
3.1. First Indicator: Comparing the Frequency and Magnitude of Changes for Prices and
Consider a situation when prices are fully flexible. Then they fully and immediately adjust to changes in the optimal frictionless price. This means that both the frequency and the size of changes in the actual price are the same as the frequency and the size of changes in the optimal price. Thus:
( ) ( ) and
freq p freq p p p (1)
Where p denotes the price, p* denotes the (unobserved) optimal frictionless price and x is the first difference xt – xt-1.
However, the number of markets where prices are fully flexible is quite limited. In most markets, price adjustment is costly. From the discussion above, it follows that a natural way to measure price rigidity is to compare the frequency and magnitude of price changes with those of the underlying costs and/or mark-ups as measured by p*.
The literature about adjustment costs focuses on two polar cases: fixed costs and quadratic costs. In the former case, prices (p) change less often than the optimal (frictionless) price
p*. The standard representation of this behaviour is the (S,s) model where the price of a specific product i is changed to its optimal value when its price in period t-1, pi,t-1, deviates
from the optimal (frictionless) price level, p*it, by an amount larger than an inaction band
sit. The inaction band depends in particular on the costs incurred by adjusting prices, on
those induced by not adjusting prices but also on the "usual" magnitude of shocks (e.g. see Dixit, 1991):
1 if 1 otherwise i t i t it it it it p p p s p p (2)
Given a constant inaction band, s, such price-setting behaviour implies periods of price inaction, as described in Figure 3.1.
Figure 3.1: The (S,s) Price Setting Model
-0.6 0 0.6
b. Deviations from optimal price a. Actual price -2 -1.5 -1 -0.5 0 0.5 -0.6 0 0.6
b. Deviations from optimal price a. Actual price -2 -1.5 -1 -0.5 0 0.5
As can be seen in Figure 3.1, such a model generates periods of price inaction during which the price is kept constant for different periods of time, depending on the evolution
of the optimal price and whether or not the discrepancy between this optimal price and the current price is larger or smaller than si. When prices are changed, the magnitude of the
change is larger than the current change in p*. Therefore, for the fixed cost case, the frequency of changes of the nominal price is smaller, and the size is larger, than the frequency and size of changes of the optimal price:
Fixed costs freq p( ) freq p( ) and p p (3)
The other often used form of adjustment costs is a quadratic cost, where the cost is increasing in the size of adjustment. This means that the total cost of two small changes is less than the cost of one large change.53 In this case, after a shock to costs or demand, firms may find it too costly to make a full adjustment to the new optimal price and instead proceed to undertake several small changes. Therefore, in the quadratic cost case, the frequency of changes of the nominal price is larger, and the size is smaller, than the frequency and size of the changes of the optimal price:
Quadratic costs freq p( ) freq p( ) and p p (4)
Following these considerations, we define the first indicator of price rigidity as:
2
1 ( ( ) ( )) ( )
RigidA freq p freq p p p 2 (5)
Products/sectors with flexible prices would have low values of this indicator while products with rigid prices should have high values of this indicator, regardless of the nature of underlying rigidity.
Given the difference in the size of the frequencies and magnitude of price changes, these measures can be standardized by dividing the differences by the averages:
2 2 1 1 2 2 ( ) ( ) 2 ( ( ) ( )) ( ) p p freq p freq p RigidA freq p freq p p p (6) 53
Although this is not the most frequently observed pattern of price changes, at least at the consumer level, its relevance may nevertheless be explored for some products. For example, an agreement has been signed in France between oil companies and the government to smooth the impact of crude oil price rises by staggering price increases over time. Even though prices are changed frequently, this situation is characterized by rigidity since oil companies are constrained in their ability to adjust prices to changes on the crude oil market. However, consumers often consider than, at the opposite, price increases are fully and rapidly transmitted to prices while crude oil decreases are staggered over time. Then, despite the numerous price increases and decreases we observe, it is not certain that gas prices are as flexible as we might think by just looking at the frequencies.
A simple modification of the second indicator allows the identification of the type of adjustment costs underlying the price rigidity. This is obtained by computing the following indicator: 1 1 2 2 ( ) ( ) 3 ( ( ) ( )) ( ) p p freq p freq p RigidA freq p freq p p p (7)
If the rigidity is mostly due to fixed costs, we should obtain RIGIDA3 < 0 since
freq(p) < freq(p*) and |p| > |p*|. On the other hand, a positive value for RIGIDA3
would correspond to quadratic costs as, in this case, freq(p) > freq(p*) and |p| < |p*|. In order to implement these indicators, we need to measure changes in the optimal price,
p*. For consumer prices, we assume that a proxy for the optimal price of a given product is obtained from its manufacturing production cost. The frequency and magnitude of producer price changes as compared to those observed at the retail level determine the relative rigidity rankings across products. In other words, we assume that other retailer costs (wages, rents, transportation costs) affect consumer prices of all final products in roughly the same proportion and thus do not affect the rankings obtained with the producer price changes.
The conversion table between the consumer goods and services categories (the COICOP grouping) and the producer goods categories for which the necessary information about price changes is available (the NACE 2 digit) is given in appendix A. The construction of the conversion table requires a few assumptions and simplifications. As a (simple) example, the COICOP category ‘Food products and non-alcoholic beverages’ is linked with NACE 15, ‘Manufacture of food products and beverages’ despite the fact that the latter also includes alcoholic beverages.
Due to data limitations, it is more difficult to assess the degree of rigidity of producer prices themselves. Indeed, for the set of countries and sectors for which the PPI analyses have been made, we do not have much information about the variations of costs and demand underlying the variations in the optimal (unobserved) producer prices. However, it is possible to make use of the input-output tables in order to determine the influence of price changes of important inputs on the frequency of price changes (see section 6.4.) Availability of data on producer price changes required by RigidA2 and RigidA3 indicators
(i.e. their frequency and magnitude), allows computing these indicators for only four countries: Belgium, France, Germany and Spain. The analysis concentrates on prices of goods as the information on cost changes is not available for services.