belong to CSM, the latter conclusion has to be interpreted with caution. These differences in
most cases are statistically significant. Even though the grouping of retail stores leads to
significant differences in average price levels between groups, the variation within each group
still is substantial (often at the same level as for the total sample). The second row of Table 2
reports the standard deviation of prices. For instance, the standard deviation of beef prices for
the store types is between 239 and 444 German pennies per kg, the overall standard deviation is
299 German pennies per kg. Thus, the clustering by store types does not substantially reduce the
within group variation, meaning prices seem to vary as much within cluster as they do in the
entire sample. The reduction in variation by clustering in the case of beef is 11 %. For the other
products the cluster effect is between 2 % and 11 %. The reduction is higher for meat products
compared to fruits and vegetables. Interestingly, the clustering by retailer companies indicates
an even lower reduction in the within group variation even though the number of clusters is
increased by 2. In relative terms the standard deviation is between 20 to 30 % of the
corresponding average price level for all products. Even though some variation in this relative
measure can be observed, no systematic relationship with respect to either the type of the store,
the retailer chain, or the product type was found in the sample.
4. Empirical results
To begin, a measure of retail sales is defined. Given that available data contains no
indication of whether prices are sale prices, we define an indicator of “sale” status of a price
when the current price level is a significant, though temporary reductions in past price level. It
would be of interest to require such changes to be independent of cost changes; however, cost
information is not available in our sample.12 As a criterion for identifying a significant price
reduction, we set a standard of downward price changes that exceed 20 %.13 As an indicator of
whether the price change is related to cost changes we define “sale” prices as those that deviate
from price dynamics that are common across products by more than 20 %. To empirically
identify prices that are consistent with this definition of sales prices, the following procedure
was implemented. First unweighted average prices are calculated for each food item (see Figure
1). For most products, these series indicate a high correlation with a wholesale price series that
reflects underlying cost dynamics.14 Thus, each food price time series is compared to an
average price series adjusted for the deviation between its own and the mean of the individual
time series. Whenever the price of the individual time series is 20 % below the adjusted average
series, then this price is to be considered as a sale’s price. This procedure is used to differentiate
sales prices from those associated with persistent, low price strategies. Clearly, our approach is
compromised when sales between shops are highly synchronized for a particular food product.15
Nonetheless, our approach avoids errors associated with use of shop announcement of sales,
given that such announcements are often associated with reduced prices.
Based on our criterion for defining sales, Figure 2 presents the share of products that are
on put sale in each week for all shops and for SSM and BSM only. On average over the entire
Hosken and Reiffen (2001) circumvent the problem by implicitly judging every downward price change as
a sale and every upward price change as the return to the normal price.
We have also tested the robustness of results by varying this margin, for instance using also a 10 % and a
30 % threshold. The general conclusions are similar for these variations, detailed results can be obtained
from the authors.
Another interpretation is that this measure indicates a sale when a shop offers the product for a price that is
significantly lower than the price at competing shops. Store specific differences, for instance, in service or
convenience are considered by adjusting the average prices to the store specific mean price.
Considering the low correlation between prices, between price changes, and between sales, we do not see
this to be a problem fort he actual data set (see Loy and Weiss, 2003). This is confirmed by the results
from the study by Pesendorfer (2000).