The Number of Bids Received per U.S. Offshore Oil and Gas Lease Offered: More or Less?
Authors: Dougherty Elmer L. , Lohrenz John 
Published: December 2007

First, we develop a distribution giving the frequency with which U.S. offshore oil and gas leases have received 0, 1, 2, . . ., bids per lease offered. Then, we use that distribution to assess whether leases offered under different bidding alternatives actually received more bids or less.If there were M potential bidders for a lease, each of whom bids with probability, p, the expected number of bids would be pM, and the frequency with which a lease received 0, 1, 2, . . ., bids would be given by the binomial distribution. If M is large and p is small, the binomial distribution can be approximated by the Poisson distribution. Poisson distribution. The binomial or Poisson distribution may not always describe the variation in the number of bids received for a lease in U.S. offshore oil and gas lease sales. For example, the Louisiana sale held Dec. 15, 1970, shows multiple modes. This observation led us to consider a mixture of distributions.We considered the following mixture of three Poisson distributions:
(1)
F1 is the fraction of leases offered on which no bidder considered bidding, F2 is the fraction that received modest bidder attention, and F3 is the fraction that attracted the greatest interest. There are five unknown parameters in Eq. 1: F1, F2, F3, n2, and n3, among parameters in Eq. 1: F1, F2, F3, n2, and n3, among which there are two constraints:
(2)(3) We determined the parameters under these constraints so that
(4)
was minmized for each U.S. offshore oil and gas lease sale. Low, noise bids were deleted in each sale.
Table 1 shows results for selected sales. Note that for the sale held Dec. 15, 1970, the parameter values are
n2 = 3.0 and n3 = 9.9. Fig. 1 compares Pn*, shown as data points, and Pn for this sale.Table 1 also shows cases in which F3 = 0, with no leases appearing to draw the strong bidder interest. The Oregon/Washington sale held Oct. 1, 1964, is an example. Table 1 also shows a case, the California sale held May 14, 1963, in which F1 = F3 = 0 with the bid variation being described by a single Poisson distribution.We cannot prove Eq. 1 is supported statistically by the data. However, we cannot disprove it either. For example, using the Kolmogorov-Smirnov one-sample test, the maximum deviation of the sale held Dec. 15, 1970, is 5%. The allowable maximum deviation is 35% at the 1% level of significance (n = 21). These values soundly reject the hypothesis that the results in Fig. 1 could be a statistically "lucky" fit.
Our probability model (Eq. 1) can be used to analyze bidding for leases offered under different bidding alternatives, seven of which are cited in the Outer Continental Shelf Lands Act Amendments of 1978. Which bidding alternative tends to attract more bids? We presume that more bids would be advantageous to the presume that more bids would be advantageous to the seller (the government). Indeed, the Federal Trade Commission has concluded that the applicable statutes and regulations "reflect a policy that the number of bidders at a sale be as large as possible."
P. 697