Bidding models_ testing the stationarity assumption

Bidding models_ testing the stationarity assumption -...

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Bidding models: testing the stationarity assumption MARTIN SKITMORE 1 * and GORAN RUNESON 2 1 School of Urban Development, Queensland University of Technology, Australia 2 Faculty of Design, Architecture and Building, University of Technology, Sydney, Australia Received 24 February 2005; accepted 2 March 2006 With notably few exceptions, bidding models contain probability distributions with parameters that are assumed to be fixed, or stationary, over time. Some methods 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. Keywords: Bidding, behaviour, parameters, cusum method, deficit statistic Background The data demands of bidding models are such that a trade-off is needed between the flexibility of the models and the accuracy of the estimates of the parameters of the models. Apart from a few notable exceptions (Beeston, 1983; Morin and Clough, 1969) this has resulted in models being built on the assumption that bidders behave in a consistent, if probabilistic, way over a reasonably long period of time regardless of changing conditions (Runeson and Skitmore, 1999). In particu- lar, stationarity is assumed, that is that the probability distributions used to model the bids have parameters whose values are fixed over this time. The tenability of this assumption has been questioned on theoretical grounds—standard economic theory predicts that, for example, changing workloads and market conditions must have a destabilising influence over time (Flanagan and Norman, 1983; Harris and McCaffer, 1983, p. 219; Runeson and Skitmore, 1999)—and it is likely that new models will be needed if real-world bidding offers a significant departure Whether or not the stationarity assumption is reasonable in practice is likely to depend on several factors. One is the extensive use of subcontracting in the industry, which protects main contractors to some extent from workload problems. Another is that the conditions of uncertainty involved in estimating both price and cost levels may make significant systematic adjustments in competitive behaviour difficult, if not impossible. Of the little empirical research to date aimed at establishing the extent to which stationarity exists in practice , Skitmore (1981, 1987) and Rawlinson and Raftery (1997) have identified some significant yearly changes in the moments of the overall aggregated
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This note was uploaded on 05/06/2011 for the course ETHICS 234 taught by Professor Shah during the Spring '11 term at Birla Institute of Technology & Science, Pilani - Hyderabad.

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Bidding models_ testing the stationarity assumption -...

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