March Madness in the Classroom

Bid Price Determination

Using regression analysis instructors and students may use the auction data to determine what factors determine the final bid price. A team’s past performance and the winning bidder’s valuation of the team are typically important factors. The analysis may even be used to test whether the “declining price phenomenon” occurred in the auction. Typically at an auction for multiple goods, the prices of identical goods decline as the auction progresses. The rational is that potential buyers with higher valuations leave the auction once they have made a purchase.

The March Madness in the Classroom exercise was conducted at Mount Saint Mary’s University in Emmitsburg, Maryland. Students received the Sagarin ratings (a widely accepted computer rating system that the NCAA uses to seed the tournament teams) to represent past performance and students developed expected valuations of all the tournament teams.

The bid price [OPENPRICE] in the open outcry auction is expected to be a function of [RATING] the Sagarin rating, [VALUATION] the winning bidder’s valuation of the team, and [ORDER #] the order number of the team that indicates when it was auctioned off. The following is the result of OLS Regression using Microsoft Excel.

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.87
R Square	0.76
Adjusted R Square	0.74
Standard Error	32010.86
Observations	64
ANOVA
	df	SS	MS	F	Significance F
Regression	3	1.91E+11	6.35E+10	61.9829	0.00
Residual	60	6.15E+10	1.02E+09
Total	63	2.52E+11
	Coefficients	Standard Error	t Stat	P-value
Intercept	-259000	78745.09	-3.29	0.00
RATING	3312.84	957.21	3.46	0.00
ORDER #	224.44	243.83	0.92	0.36
VALUATION	1.45	0.21	6.86	0.00

With an R-squared of 0.76, the model does a fairly good job of estimating the bid price. By examining the data, however, one can clearly see that the relationship between the Sagarin rating and the bid price is not linear. As the Sagarin rating increases, the marginal change in the bid price is increasing as well. The OLS technique is one that the Managerial Economics students are most familiar with. It is used for discussion purposes, and the limitations of the model specification are clearly explained.

The results indicate that the Sagarin rating and the Winning Bidder’s valuation are significant. According to the model, bidders paid $3,313 more per Sagarin rating point. Bidders also 45% more than their valuation due to the learning and competition that occurred during the open outcry auction. The coefficient on [ORDER #] is positive suggesting that prices in the auction increase as the auction progresses. This might occur as students become worried that they may not initially own any sponsorship rights. However, the coefficient on [ORDER #] is not statistically significant.

A similar analysis may be conducted using the results of the first-price sealed bid auction. There is no [ORDER #] in the sealed bid auction, so the bid price [SEALEDPRICE] in the sealed bid auction is expected to be a function of [RATING] and [VALUATION]. The following is the result of OLS Regression using Microsoft Excel.

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.99
R Square	0.99
Adjusted R Square	0.99
Standard Error	1828.80
Observations	64
ANOVA
	df	SS	MS	F	Significance F
Regression	2	6.82E+10	3.41E+10	10192.67	0.00
Residual	61	2.04E+08	3344521
Total	63	6.84E+10
	Coefficients	Standard Error	t Stat	P-value
Intercept	-8073	4838.32	-1.67	0.10
RATING	89.20	62.18	1.43	0.16
VALUATION	0.96	0.01	85.12	0.00

From the results of this model, it is clear that the students used their valuations to determine their sealed bid price. The [VALUATION} variable is extremely significant and bidders shaded their bids to 96% of their valuation. The Sagarin ratings were less important in determining the bid price as [RATING] was not statistically significant.