correlation coefficient between the prices of the two products: that is because both their prices are influenced by the input price, not because they are interdependent. Unless the influence of common factors is purged, the use of the correlation coefficient as a test of price interdependence leads to wrong conclusions, regardless of the size or the statistical significance of the estimate. This is especially the case when the series cover periods of high inflation and are therefore trended, or when the data is seasonal. The influence of common factors can be purged by de-trending all the variables first or by using regression analysis: the price is regressed on the influencing factor (input price, or a time trend, or seasonal dummies, etc), and the residuals from that regression are taken to represent the purged series. 5.7
A further problem with using correlation analysis lies in the fact that price responses for some products, and in some areas, might be delayed. This would be the case when, for instance, prices are negotiated at discrete time intervals which are not synchronised: the analyst could find a very low correlation when in fact the series are highly correlated in the long run. A visual inspection of the plotted price series can be of help in such cases. Another instance when prices of products that are closely related have low correlation is when the products are good substitutes and their supply is elastic.
Application: wholesale petrol markets in the US 5.8
Stifler and Sherwin97 have used correlation analysis to test whether the cities of Chicago, Detroit and New Orleans are in the same market for wholesale petrol. They correlate monthly fuel prices in the three cities during the period 1980-82 inclusive. Stigler and Sherwin98 eliminate the effect of serial correlation by taking the first difference on every third price. They also remove the effect of common factors, which is a very important step in the analysis of petrol prices, as fluctuations in the price of crude oil tend to influence the price of refined petrol quite heavily. The results are taken by the authors as indicating that the correlation coefficients are very high: the coefficient between New Orleans and Chicago is 0.792; that between New Orleans and Detroit is 0.967; and that between Chicago and Detroit is 0.77. These results indicated to the authors, that the three cities are in the same economic market. However, correlation analysis, as the sole means of reducing market breadth, is no longer considered a sufficiently robust approach.
97 98
Ibid. Ibid.
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