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«CHINA'S LAND MARKET AUCTIONS: EVIDENCE OF CORRUPTION Hongbin Cai J. Vernon Henderson Qinghua Zhang Working Paper 15067 ...»

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To see that a revenue maximizing auctioneer prefers a two stage auction over an English auction for cold properties, consider first the low valuation scenario when V is close to r + 2C. In our numerical example, this means that V ≈ r + 2C = 4. Then in an English auction the entry threshold is V ≈ 3.24, the probability of no sale is about 0.656, the probability of one bidder entering is about 0.308 and that of competitive bidding is less than 0.04. Since the sales price in competitive bidding is less than 4, the expected revenue is no more than 0.776. For a two stage auction, the probability of no sales is 0.563, and the probability of having one bidder enter is 0.438. Thus, the expected revenue of a two stage auction is 0.875, higher than that of an English auction. Because the expected revenue is continuous inV, we conclude that for cold properties a two stage auction generates greater expected revenue than an English auction.

Now consider the other extreme case in which V is large, e.g., V = 24. Then in an English auction the entry threshold is V = 6, the probability of no sale is 0.0625, the ˆ probability of one bidder entering is 0.375 and that of competitive bidding is 0.563. It can be shown that the total expected revenue of an English auction is 7.5. For a two stage auction, the threshold valuation for bidder 1 is 5.62 and the probability of no sale is about

0.03. The probability of only bidder 2 entering is about 0.205, generating an expected revenue of 0.41. From the preceding Appendix, bidder 1’s signaling bidding function is B = (0.5V12 − 2.55) (V1 + 1) starting at B = r = 2 when V1 = V = 5.62. It can be checked that the event of only bidder 1 entering generates an expected revenue of about 3.88, and the event of competitive bidding generates an expected revenue of 2.99. Thus, the total expected revenue of a two stage auction is 7.28, which is less than that of an English auction.

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strategy of waiting to see whether there is a corrupt developer who submits a bid at reserve price at the start of the auction, a non-corrupt bidder with valuation V obtains an expected payoff of (1 − p )U (V ), where U (V ) is his expected payoff in the two stage auction without corruption. Note that when p is close to one and κ is large, p* is close to one. Then the snapping strategy will give a non-corrupt bidder too low an expected payoff.

Data appendix.

Comparing the estimating sample with samples of unsold properties and properties with incomplete information

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* significant at 10% level; ** significant at 5% level or higher The table above explores the differences in means of variables for the estimating sample versus other listings. A comparison of columns I and II (with tests of differences given in column IV) suggests unsold properties are more distant from the CBD with a lower reserve price; and are more likely to have been offered at English auction. A probit of auction type on sold or not, with controls for property characteristics including reserve price and city and year fixed effects, suggests two stage auctions have a.076 higher probability of a sale. A comparison of columns I and III (with tests of differences given in column V) suggests sales with missing sale or reserve price data are similar to those in our estimating sample. They have similar auction type and use proportions and when data is available have similar reserve and sales unit prices.

MLE appendix.

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Figure 1. Distribution of unit sales prices by auction type Orange (solid) is two stage auction; white (blank) is English auction Percent

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Figure 3. For 2-stage auction sales: predicted unit price if sold by 2-stage (45o line) versus switching to English auction Predicted price when switching to English auction

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