Integrating the Structural Auction Approach and Traditional Measures of Market Power

M2 are similar to M3 except that M1 does not include HHIjt, and M2 does not include
bid1, bid2, and bid3. Variance components model (M3) was estimated via maximum
likelihood (ML) using the NLMIXED Procedure in SAS 9.1 (SAS 2001-2003).

There are two null hypotheses of interest in model M3. The first null hypothesis
is that the coefficients for bid1, bid2 and bid3 are jointly zero (H₀₁ : ω₁₄ = ω₁₅ = ω₁₆ = 0).
The second null hypothesis is that the coefficient for HHI is zero (H02 : ω₁₇ = 0). If both
H01 and H02 are rejected, then number of bidders and the number of firms contain unique
information, and suggest an encompassing model (M3) rather than either model M1 or
M2. If both H01 and H02 are not rejected, then the number of bidders and the number of
firms contain the same information and either aggregate or disaggregate model could be
used. If only H01 is rejected then a disaggregate model is favored, while if only H02 is
rejected an aggregate model is favored.

Estimation of a Structural Auction Model

This section reports the procedures used to estimate packer’s bid shading using the
structural auction model represented by equation (2.4a). The estimate of the auction
model is compared with an estimate of price markdowns computed directly from the data.
The estimation considers the number of potential bidders rather than the actual number of
bidders. This was due to the presence of numerous transactions where only one bidder
submitted a bid, which precluded estimation of bid shading using equation (2.4a).

The estimation of packer’s bid shading in equation (2.4a) uses the nonparametric
approach for estimating the structural auction model proposed by Guerre et al. (2000).
As equation (2.4a) shows, packer’s bid shading is the ratio of the bid probability
distribution F(p_ij^f ) to the product between bidders’ density function f ( p_ij^f ) and the

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