Yu Binbing, Gastwirth Joseph L
Laboratory of Epidemiology, Demography and Biometry National Institute on Aging, National Institutes of Health, Bethesda, MD 20904, U.S.A.
Stat Sin. 2010 Apr;20(2):837-852.
Art auction catalogs provide a pre-sale prediction interval for the price each item is expected to fetch. When the owner consigns art work to the auction house, a reserve price is agreed upon, which is not announced to the bidders. If the highest bid does not reach it, the item is brought in. Since only the prices of the sold items are published, analysts only have a biased sample to examine due to the selective sale process. Relying on the published data leads to underestimating the forecast error of the pre-sale estimates. However, we were able to obtain several art auction catalogs with the highest bids for the unsold items as well as those of the sold items. With these data we were able to evaluate the accuracy of the predictions of the sale prices or highest bids for all item obtained from the original Heckman selection model that assumed normal error distributions as well as those derived from an alternative model using the t(2) distribution, which yielded a noticeably better fit to several sets of auction data. The measures of prediction accuracy are of more than academic interest as they are used by auction participants to guide their bidding or selling strategy, and similar appraisals are accepted by the US Internal Revenue Services to justify the deductions for charitable contributions donors make on their tax returns.
艺术品拍卖目录会为每件预计拍出的物品提供一个售前预测区间。当所有者将艺术品委托给拍卖行时，会商定一个保留价，该保留价不会向竞拍者公布。如果最高出价未达到保留价，该物品将被撤回。由于只有已售出物品的价格会公布，分析人员因这种选择性销售过程只能得到一个有偏差的样本用于研究。依赖已公布的数据会导致低估售前估价的预测误差。然而，我们得以获取了几本包含未售出物品以及已售出物品最高出价的艺术品拍卖目录。利用这些数据，我们能够评估从假设误差分布为正态的原始赫克曼选择模型得出的所有物品售价或最高出价预测的准确性，以及从使用t(2)分布的替代模型得出的预测准确性，后一种模型对几组拍卖数据的拟合效果明显更好。预测准确性的衡量标准不仅具有学术意义，因为拍卖参与者会用它们来指导自己的竞拍或销售策略，而且美国国税局也认可类似的评估，用于证明捐赠者在纳税申报单上为慈善捐款所做扣除的合理性。
