–
– –
Even if this framework is OK we have to deal with the fact that we never see the value at which the highest bidder would drop out.
However, we would see all but the first order statistic, which is a lot of information really. That said, you have to be very careful: order statistics loose their independence if you do not observe all of them and, in an ascending auction, but construction you do not observe them all (see the Athey Haile survey paper for more). So overcoming the mechanical loss of independence due to the data generating process is a central issue. Sometimes you can get around this, more often it is a technical issue that can kill a paper. Compare to Haile Tamer to follow.
The key thing from theory, regardless of approach used is that bidders never bid more than they are willing to pay, and never let anyone win with a price they are willing to beat.
Identification and Estimation of FPSB PV Auctions
Early work by Harry Paarsch and others in the early 1990s explored ways of estimat- ing using bid functions and imposing parametric forms on the distribution of private information.
Other work by Laffont, Ossard and Vong (in various combinations), and Pat Bajari tried other approaches using different theoretical ‘handles’
The literature seems to have converged on the following basic line of attach due to Guerre, Perrigne and Vong (2000).