Data and computational requirements 5.4
The implementation of price correlation tests requires time series of data which have at least 20 observations.92 It is customary to compute the correlation coefficient using the natural logarithm (log) of the price series, both due to efficiency reasons and because the first log difference is an approximation of the growth rate. Equal changes in the log represent equal percentage changes in price. Correlations should always be computed both between levels and differences in the log prices. The computational requirements to carry out the test are minimal; all statistical and econometric packages and most spreadsheets have in-built routines to compute correlation coefficients. Packages such as SPSS also provide results from significance tests on the estimated correlation coefficients.
Interpretation 5.5
Stigler and Sherwin93 argued that given time series price data for two products or areas, the correlation coefficients between their levels and first differences can be used to determine whether these products or areas are in the same market. 94 Prices can differ because of transport and transaction costs or because of temporary demand or supply shocks, so that the correlation coefficients will be less than 1 even in a perfect market. It is however impossible to determine how big the correlation coefficient needs to be in order for the analysis to conclude that two areas or products are in the same market. Stigler and Sherwin 95 ‘... believe that no unique criterion exists, quite aside from the fact that the degree of correspondence of two price series will vary with the unit and duration of time, the kind of price reported, and other factors’. In other words, even if the estimated correlation coefficient is statistically different from zero, the economic interpretation of the test is not straightforward. This is due to the lack of an obvious cutoff point where it can be decided whether the estimated degree of interdependence between the prices can be taken as an indication of price uniformity.
5.6
A further problem with the use of the correlation coefficient is that if there are common factors influencing prices this statistic can lead to erroneous conclusions. 96 To see why, consider the case of two producers using the same input, so that the prices of their products are highly correlated with the input price. The analyst will find a high
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Computing correlation coefficients with less than 15 observations is meaningless from a statistical point of view. Stigler, G.J. and Sherwin, R.A., 1985, op. cit. See Waverman, L., 1991, Econometric Modeling of Energy Demand: When are Substitutes Good Substitutes, in D. Hawdon (ed.), Energy Demand: Evidence and Expectations. Academic Press. ibid, p 562. Stigler G.J. and R.A. Sherwin, 1985, op. cit., are aware of this problem, and discuss the possible solutions.
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