Bidding models: testing the stationarity assumption

Abstract

With notably few exceptions, bidding models contain probability distributions with parameters that are assumed to be fixed, or stationary, over time. Some methods of method of testing the tenability of this assumption are examined and applied to eight datasets. Of particular interest is the statistical significance of two types of periodicity; (1) that bidders gradually reduce their bids prior to winning a contract and (2) that bidders have periods in which they are more competitive and periods in which they are less competitive. To test (1), McCaffer and Pettitt’s (1976) cusum method is used and shown to have a limited interpretation in this context. McCaffer’s ‘deficit’ statistic is then used in conjunction with a one-way analysis of variance (ANOVA) and shows (1) to be untenable for the samples involved. To test (2), the deficit statistic is again used with an ANOVA to examine all possible sub series of bids.