«CHINA'S LAND MARKET AUCTIONS: EVIDENCE OF CORRUPTION Hongbin Cai J. Vernon Henderson Qinghua Zhang Working Paper 15067 ...»
Comparison: English versus two stage auction ˆ ˆ ˆ Since V V and VNS V, the probability of no sale is lower in a two stage auction than in an English auction. Since bidder 1 can discourage entry by other potential bidders with his early bid, he is more likely to enter in a two stage auction than in an English auction.
And when bidder 1 does not enter, other bidders still are more likely to enter a two stage auction than an English auction. The intuition is that the simultaneous entry game in an English auction suffers from coordination failure: one bidder’s entry creates a negative externality for others. Thus, bidders may not enter the auction even when their valuation is significantly higher than the reserve price plus entry cost, for fear of being outbid by others. In contrast, bidder 1 in the sequential entry game of a two stage auction does not suffer from negative externalities from other bidders, thus having a stronger incentive to enter the auction. The flip side of this is that the probability of competitive bidding (two or more active bidders) is lower in a two stage auction than in an English auction, because the early entrant may deter later entrants.
In terms of expected revenue, the comparison between two stage and English auctions is ambiguous in general. The intuition is that while a two stage auction has a higher probability of sale, the likelihood of competitive bidding is smaller than in an English auction. Thus, depending on parameter values, the expected revenue of the two stage auction can be greater or smaller than that of an English auction.
In the Appendix, we show in a numerical example that the expected revenue of a two stage auction is greater than that of an English auction when V is low, and vice versa.
We conjecture that when land is “cold,” in the sense that the valuation is likely to be low ( e.g., low V ) or the potential demand ( N ) is small, a sale and some revenue is more likely under a two stage auction. We note N is unobserved in our data (as is V ). With cold properties which in an English auction might generate no active bidders, a two stage auction may generally be a better choice of auction for a revenue-maximizing land bureau, since the threshold valuations for entry are lower. If land is “hot” so an English auction is likely to attract many bidders, English auctions will tend to generate more revenue since two stage auctions may lead to entry deterrence. Thus we might expect a revenue-maximizing land bureau to steer hot properties towards English auctions. Thus overall, there would be negative selection on unobservables into two stage auctions.
2.3 Effect of corruption Suppose corruption arises in the following way. Under a corrupt sale, a government official reaches an implicit agreement with a particular developer, say, developer 1, so that if he wins the land auction, she will provide special help (which could include weaker enforcement of development constraints or greater government investment in relevant infrastructure), in exchange for a bribery payment. Let Q be the value of the government official’s help to developer 1, and let q ≤ Q be the bribery payment developer 1 makes to the government official, if he wins the auction. Define κ ≡ Q − q as the net benefit to developer 1 from having an under-the-table deal with the government official.
Assume the corrupt government official’s payoff function is given by ER + λq, where ER is the expected revenue from the land auction (that goes to the city coffers) and λ measures how corrupt the government official is. When λ = 0, the government official is non-corrupt, as in the situation we discussed above. When λ becomes larger, the government official cares more about her own bribery income and less about the city’s fiscal revenue. Assume the government official is corrupt with probability of p.
This depends on the likelihood the government official in charge of the land is intrinsically corrupt and the likelihood that she has a “partner” developer who is interested in the land and they trust each other. If the government official is corrupt, only she and her partner developer know about their implicit agreement; no other potential bidders know about it. The only thing the other potential bidders know is that with probability p the government official and a developer have an under-the-table deal.
What might be the impact of such corruption under the two auction formats?
English auction Under an English auction, all potential bidders make entry decisions simultaneously in the entry stage and then the active bidders make bidding decisions in the auction stage.
Let bidder 1 be the potential partner developer with the government official, so with probability of p her total valuation is V1 + κ, and with probability of 1 − p her valuation ˆ ˆ is V1. Let V1P be the valuation threshold for entry for bidder 1, and let V−1 be the
where the bracketed expression on the left hand side represents a non-corrupt bidder’s expected rent (conditional on there being no other active non-corrupt bidder) in each of three cases: (1) he outbids the corrupt bidder 1; (2) the corrupt bidder 1 does not enter;
and (3) bidder 1 is not corrupt and does not enter. Note that the above equation assumes
we solved in the previous section. 10 The reason is as follows. Thanks to the favor from the government official, the corrupt developer 1 can afford bidding more aggressively and thus has a better chance of winning the auction. So she is more likely to enter. Facing the possibility that bidder 1 may be favored, the other potential bidders are less likely to win and thus are less likely to enter.
Two stage auction In the two stage auction, if the government official is corrupt and has reached an implicit agreement with her partner developer, bidder 1, he should know about the auction beforehand and can act right after it is started. Since both would like to let all other potential bidders know that this land is “claimed,” a simple and natural way to send that signal is for bidder 1 to obtain qualification quickly (potentially with the government official’s help) and make a bid right after the auction is started, before other potential bidders are granted qualification to bid, and perhaps even before they know that the auction has actually started. Since bidder 1 is only signaling that he has the agreement This assumption holds when ex ante no one knows the identity of the potentially corrupt bidder, so that all potential bidders are symmetric if the government official is not corrupt. If everyone knows that bidder 1 is the only possible developer who can have a deal with government official, he is more likely to enter than other bidders (having a lower threshold) even when in fact he does not have a deal. This is because only bidder 1 knows that no one else is corrupt and all other bidders are worried that bidder 1 is corrupt. This latter case is not that realistic and the analysis will not change much if we allow for this possibility.
Clearly by comparing equations (3) and (4) we must have V1 p V−1. If V−1 ≥ V1 p + κ, then equation (4) ˆ ˆ ˆ ˆ
with the government official, bidder 1 only needs to signal that, by bidding just the reserve price (to increase the rent from winning the auction). When κ is relatively large, such signaling by bidder 1, if believed by other bidders, will seriously deter entry by other bidders since they see little hope of outbidding bidder 1.
If a bid at the reserve price submitted right after the auction start date is perceived as a signal of having an insider agreement, a bidder without such an agreement may be tempted to mimic such behavior to scare away other bidders. However, this snapping strategy is not likely to work, even if the snapper knows the time when the auction starts and is granted qualification in advance. If the snapper manages to make a bid at the reserve price before the true corrupt developer, the latter is likely to make a higher bid in order to reclaim the land as long as p is close to one and κ is relatively large. In such a case, the snapper will lose the auction and waste his entry cost. In the Appendix, we illustrate this argument in a simple example. 11 We consider the following equilibrium. Let VC be the minimum threshold in which bidder 1 will send a signal by bidding the reserve price. If seeing that bidder 1 bids at the reserve price right after the auction is announced, all the other potential bidders understand that bidder 1’s valuation is V1 + κ, where V1 ∈ [VC,V ]. Then they decide simultaneously whether to enter. Let V0 be the valuation threshold for all other potential bidders. Then it must satisfy 12
Even if a non-corrupt bidder will try the snapping strategy, he will do so only when his valuation is very high for fear of being outbid by a corrupt bidder. It is possible that in equilibrium, a non-corrupt bidder with very high valuation and a corrupt bidder are pooled in using the same strategy of bidding at the reserve price at the start of the auction (whoever manages to be the first is immaterial). In such an equilibrium, a corrupt bidder who does not get the chance to submit a first bid will try to outbid the non-corrupt bidder only when he also has a quite high valuation. What is important, however, is that in such a pooling equilibrium, other bidders are seriously discouraged to enter, either by a very high valuation non-corrupt bidder or by a corrupt bidder.
This assumes that, when their valuations are sufficiently high, other non-corrupt bidders may still enter the auction after seeing that corrupt bidder 1 has entered. Otherwise, the corrupt bidder 1’s signaling can completely prevent entry by other bidders, and the difference between the English and two stage auctions in terms of entry will be larger.
ˆ And VC must satisfy an equation similar to equation (4) with VC replacing V1P and V0 ˆ replacing V−1. Below we argue that this entry threshold for other bidders in a two stage auction, V0, is greater than that under an English auction.
When no one bids at the reserve price right after the auction is announced, then bidders understand that the government official is not corrupt. In this case our previous analysis of the two stage auction under no corruption is valid.
Comparison of English and two stage auctions under corruption It can be verified that upon seeing a first day bid at the reserve price, all other potential bidders’ valuation threshold for entry V0 in a two stage auction will be significantly ˆ greater than the threshold in the case of an English auction, V−1. 13 This occurs because in the case of an English auction, the other potential bidders do not know whether bidder 1 is corrupt. They only know that he is corrupt with probability p. However, in the two stage auction, the other potential bidders know for sure whether bidder 1 is corrupt or not.
When he is corrupt, the other potential bidders have a much smaller chance of winning the auction since bidder 1 has substantial advantages from having a higher expected valuation from government help and having made the first bid. This greatly reduces the incentives to enter for other potential bidders.
It can also be shown that the corrupt bidder is more likely to enter a two stage ˆ auction than an English auction, that is, VC is smaller than V1P. Because other potential bidders are less likely to enter the two stage auction, the corrupt bidder sees less risk of losing the auction and thus is more motivated to enter a two stage auction (by posting a bid at the reserve price right after the auction starts) than an English auction.
That the corrupt bidder is more likely but other potential bidders are less likely to enter a two stage auction implies that the corrupt bidder has a much better chance to win the land in a two stage auction than in an English auction. Since the corrupt government official can get the bribery income only if the corrupt developer wins, she would favor a
(counterfactually) V0 ≤ V−1, then it can be shown that the left hand of equation (5) is less than that of ˆ equation (3), which yields a contradiction (since the right hands of two equations are the same).