The Relationship between Wholesale and Consumer Prices

Abstract

Historically there are two aggregate measures of prices in the United States, the Wholesale Price Index (WPI) which measures the price of goods at the first commercial transaction in the economy and the Consumer Price Index (CPI) which measures the price of goods and services at the retail level. The general public and some economists commonly believe that current changes in the WPI are followed automatically by future changes in the CPI. This view depends on two factors: The fact that the transaction at the wholesale level occurs before the retail sale and that people believe that all wholesale price changes are transmitted through the distribution system and are contained in the final retail price. There is some support, however, for the opposite viewpoint, that is, that there is no statistical relationship between changes in the WPI and the CPI. The basis for this view is that the two indexes are different samples from different universes of prices and that there is no a priori reason to assume that changes in one universe will occur in or be transmitted to the other. Some support for this second view, the contents of the indexes, and their relationship to each other are discussed in Bechter and Pickett [2]. While both of these views have been expressed, neither has been supported by an examination of the data by thorough statistical analysis. It is reasonable to hypothize that the relationship between changes in the WPI and CPI is described by a distributed lag model since CPI changes are expected to occur over time after and in response to WPI changes. This paper explores the hypothesis that the relationship between wholesale (producer) price changes as measured by the WPI and consumer price changes as measured by the CPI is described by the distributed lag model suggested by Solow [10]. This model assumes that the lag coefficients of the model follow a Pascal distribution. The Pascal distribution was selected for its ability to provide both a lag distribution with geometrically declining weights, the well known Koyck model, and a unimodal lag distribution where the maximum lagged effect may be in a later time period. The results of the analysis support the hypothesis that there exists a significant relationship between changes in the two indexes and the Pascal distribu-