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by: Clifford Mertz


Clifford Mertz
Texas A&M
GPA 3.72


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This 6 page Study Guide was uploaded by Clifford Mertz on Wednesday October 21, 2015. The Study Guide belongs to AGEC 695 at Texas A&M University taught by Staff in Fall. Since its upload, it has received 39 views. For similar materials see /class/225925/agec-695-texas-a-m-university in Agricultural & Resource Econ at Texas A&M University.

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Date Created: 10/21/15
Lecture Four Ximing Wu 34 Reserve prices and parametric estimation 0 When there is a reserve price the number of bidders is endogenous and the resulting value distribution is truncated o The nonparametric methods discussed above do not address this truncation issue We now resort to parametric methods 0 Assume a value distribution FV and N potential bidders There are three possibilities regarding the outcome of an auction The good is unsold The probability is FV rN The good is sold at the reserve price which indicates there is only one bidder with value equal to or higher than 7 The probability is NFV7N11 FV 74 The good is sold at a price above 7 indicating there are at least two bidders with value equal to or higher than 7 The winning bid is the second order statistics denoted here by w with a density function NW 1 Fv MN 2 lt1 Fv ltwgtgt fv w lt1 This density is derived in Appendix using a limit argument Note that we can derive it directly The probability that the second order statistics is no greater than w is FV UM NFV 111W 1 1 FV 111 2 Taking derivative of 2 with respect to w and rearranging terms yields 1 0 Assuming the value distribution comes from a parametric famin FV u 60 where 60 are the unknown true parameters Let N be the number of actual bidders Further define D0 1 if N 0 and 0 otherwise D1 1 if N 1 and 0 otherwise The density function of a winning bid w is D0 D1 fW w aw Fv 7 M NFV76N11 FV 7 an N N 1 FV 1M 2 1 FV w 9 fV w 01D0D1 Given a sample of auctions with number of bidders NZh and winning bids 1111 we can then estimate the model using MLE by maximizing T 10ng m 61V 11 The sample is censored in this case See Figure 31 in textbook for this mixed discretecontinuous density of winning bid With loss of generality we can set w 0 when N 0 Why Assuming there are no ties in potential bidders39 valuations To avoid confusion we can define alternatively D0 1 if w 0 and 0 otherwise and D1 1 if w 7 and 0 otherwise Now the likelihood function contains only 111 instead of w and Ni 0 Suppose only auctions with the good sold were reported or observations with 4 Ni 0 are not included in the sample In this case we have a truncated sample The likelihood function of a winning bid conditioning on N gt 0 is now given by NFvr0N 11 FV r 6 D1 fWNwngt06J 7 7 1 Fv lt7 6W NlNlvalwN21 Fvw6fvw6 1 1 Fv 7 6N 39 This model is estimated using MLE by maximizing T 2109 fWN wiln gt Lav 2391 35 Policy application See textbook p6577 and Paarsch 1997


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