«CHINA'S LAND MARKET AUCTIONS: EVIDENCE OF CORRUPTION Hongbin Cai J. Vernon Henderson Qinghua Zhang Working Paper 15067 ...»
We then attempted to implement this idea econometrically, by looking at sales which ex ante are “almost certain” to be competitive. The difficulty is that as we make the margin of competition more intensive, we get fewer and fewer two stage auctions in the sample, so there are fewer and fewer cities left in the sample which use both auction types. Second our instruments loose their power and degree of variation as the sample shrinks and what we report is the best case—use of all 7 instruments. So, for example, even if we cut at the probability of being competitive at a relatively low level such as 0.7, the first stage probit drops all but 3 instruments (lack of variation in instruments under city and time fixed effects). And rather than a sample of 715 for sales where the probability of competition exceeds.7 (Table 7), we must work with a sample of 541 in terms of cities which still use both auction types. The improvement in the LLF from adding these instruments has a χ - statistic of 2.09 which falls far short of the critical value of 7.8 with 3 degrees of freedom, and the corresponding F-statistic is tiny. If we cut finer in terms of increased degree of competition, we loose most variation in instruments and the problem is worse.
The best we can do is cut at the margin of the probability of competition exceeding.6, which definitely falls short of identification-at-infinity. For these sales we have a sample 792 (out of possible 912 from Table 7) where 9 cities still have both auction types. While all 7 instruments have variability in the sample, the improvement in the LLF for the first stage probit on auction type of adding the instruments is now significant ( χ - statistic of 28.5) but the implied F- statistic indicates weak instruments.
For this sample, in the same type of price equation as used in Table 5, the coefficient on auction type under MLE Heckman estimation is -.31 and significant. There is no evidence of selection into auction type: rho equals.028 (and is insignificant) and the OLS coefficient is close to the Heckman one at -.29. The effect of auction type is now much smaller than the -.70 in Table 5, but it is not zero. Unfortunately we can’t use this approach to tease out the effect when we are at the margin of properties which are “almost certain” to sell competitively, to see if the effect goes to zero. Thus we turn to the more traditional parametric approach.
6.2 MLE estimation of the bivariate selection into competitive, two-stage auctions To the model in equations (8) – (11), we now add a third equation for price
corresponding bivariate recursive probit estimates from which Section 5 and Table 6’s marginal effects are calculated. The two sets of coefficients are very close.
Results on the price equation in Table 8, column 2 are similar to the OLS estimates without any sample corrections. The coefficient for the auction type effect on price in competitive auctions is fairly close to zero and insignificant, as hypothesized. 27 In the covariance structure, as before, there is strong positive selection into two-stage auctions. The error term on the price equation has low correlation with the error terms on the discrete events.
Summary. Whether we approach the problem as a parametric one with strong assumptions or use a more non-parametric approach (identification at infinity on raw price data or in a price equation with auction selection), it seems that, once auctions become competitive, price is not affected by auction format. Auction format matters at the margin of whether auctions are competitive or not, all consistent with the corruption signaling hypothesis associated with two stage auctions
6.3 Review gains from switching to English auctions What are the revenue gains if one was to require properties sold at two-stage auction to be sold at English auction, assuming that would solve the problem of potential corruption between the auctioneer and partner bidders. In our data the actual revenue from properties sold at two-stage auctions is 239.6 billion Yuan or about $34.2 billion.
This is modestly higher than the expected revenue for these properties which is predicted from the estimated model, indicating the issue with mediating unit sales price predictions by lot sizes to get sales revenue per property. This predicted revenue if these properties are still sold at two-stage auction is 227.7 billion Yuan, about 5% lower than the actual.
The unit sales price calculation is based on the predicted probability of selling competitively if sold at two-stage auction ( prob( sijt = 1 dijt = 1 ) times the predicted price if sold competitively, plus the predicted probability of selling non-competitively at two-stage auction times the reserve price. The predicted price if sold competitively is The results are the same if we use 7 instruments.
calculated from the usual price equation adjusted for the two selection terms as footnoted (using parameters from the MLE estimation). 28 We compare the revenue from selling properties by two stage auctions with the predicted revenue obtained if all properties sold by two stage auctions in the data were sold at English auctions. This is the predicted probability of these properties selling competitively if switched to English auction times the predicted price when sold competitively, plus the predicted probability of not selling competitively if switched to English auction times the reserve price. The predicted probability of selling competitively is enhanced by the treatment effect of English auction on competition. 29 The predicted revenue is 299.6 billion Yuan. This is 25% higher than the actual revenue and 32% higher than the model predicted revenue if sold by two-stage auction. Thus, use of twostage auction with the associated reduction in degree of competition (through potentially signaling a corrupt sale) deprives cities of significant revenues.
This gain in revenue is illustrated in Figure 3, which for two-stage auctions compares the predicted unit price in the model if sold by two-stage auction, with that if sold by English auction. The 45o line is for model predicted prices if sold still at twostage auction, while the scatter plot of points is for the predicted prices if these properties were sold by English auction. The difference reflects both the increase in probability of selling competitively for any property, as well as the fact that these properties have relatively good unobservables which enhances their competitive price.
7. Summary To the best of our knowledge, this paper is the first to investigate empirically corruption in auctions beyond simple price-fixing among bidders, to allow corrupt auctioneers and signaling activity. This complements the recent increased interest in the theoretical literature on corruption in auctions (see, e.g., Burguet and Che, 2004, Compte, O., A.
Lambert-Mogiliansky and T. Verdier, 2005, Menezes and P. K. Monteiro, 2006). But our paper differs also from this theoretical literature. Corruption in our context takes the form of auction choice, while these theoretical papers consider corruption in a given auction format. Another difference is that both English and two stage auctions are open (that is, all bids are observable to all participants), while the existing literature considers first price sealed bid auctions (so that the corrupt auctioneer can manipulate bids).
In this setting, we show that after controlling for observable land characteristics (and location and time trends), two stage auctions lead to less competitive bidding and thus substantially smaller revenue than English auction in China’s land market. We further demonstrate that land bureau officials in Chinese cities divert hotter properties to two stage auctions that are more corruptible. Since urban land in large Chinese cities is hugely valuable and revenue from land auctions accounts for a large portion of city fiscal revenue, such corruption activities result in large losses of potential public funds. And the losses from this type of corruption are not merely transfers from city coffers to the corrupt officials and developers. This type of corruption also leads to misallocations, as honest developers with higher valuations are deprived of the chances to develop the land.
these entry threshold valuations reflects the entry deterrence effect of bidder 1’s signaling.
For V1 ∈ [V,V], if bidder 1 makes a bid of B and is believed by the other potential bidders as having a valuation of V1, his expected payoff is U(V1,V1, B) = F(VS (V1 ))N −1(V1 − B) − C.
ˆ Clearly this payoff function is increasing in bidder 1’s true valuation V1 and the belief of the other potential bidders V1, but decreasing in his bid B.
In equilibrium, bidder 1 should “tell the truth” by bidding his equilibrium bid B(V1 ), which reveals to the other potential bidders that his true type is V1. For a strictly monotonic bidding schedule to satisfy this truth-telling constraint (or incentive compatibility constraint), bidder 1’s above expected payoff function must satisfy the single crossing condition, so lower valued bidders have no incentive to misrepresent their valuations. It can be checked that this condition is indeed satisfied, because the slope of the indifference curve
is clearly increasing in V1.
From the truth-telling constraint, we can derive the differential equation that
characterizes the strictly increasing bidding schedule as follows:
2. Comparing the English and two stage auctions without corruption: a numerical example Because a general comparison of the expected revenue between English and two stage auctions is too difficult, we use a simple numerical example to show that the expected revenue is higher for an English auction than for a two stage auction when the land is “hot,” and vice versa. We normalize parameters by setting v0 = 0, C=1. Let r =2.
Consider the case of N = 2, and each bidder’s valuation is uniform on [0,V ], where V r + C = 3. A cold property occurs when V is relatively small, while the property is hot when V is relatively large.
For an English auction, from equation (1) it can be shown that the entry threshold valuation is V = 0.5r + (0.25r 2 + CV )0.5. The probability of no entry (hence no sale) is ˆ (V V )2 ; the probability of only one bidder entering is 2 V (V − V ) V, in which case the ˆ ˆ ˆ land will be sold at the reserve price. The probability of competitive bidding is (V − V ) 2 V, in which case the expected revenue is the expected lower valuation of the ˆ two bidders (by revenue equivalence with the second price auction).
For the two stage auction, we have two scenarios: low valuation scenario and high valuation scenario. The low valuation scenario occurs when V ≤ r + 2C ; then bidder 2 will not enter at all as long as bidder 1 has entered. So bidder 1’s entry threshold valuation is V = r + C, and if he does not enter, bidder 2 will enter if his valuation is above r + C. In this scenario, the probability of no entry (no sale) is (r + C ) 2 V 2 ; the probability of only one bidder entering is 1 − (r + C ) 2 V 2, in which case the sales price is the reserve price. Note that in this low valuation scenario there will be no competitive bidding.
In the high valuation scenario of the two stage auction ( V r + 2C ), if bidder 1 does not enter, then bidder 2 should enter with a bid at the reserve price when V2 ≥ VNS = r + C. If bidder 1 enters with a signaling bid, bidder 2 will enter only if his ˆ valuation V2 ≥ VS (V1 ) = V1 + C. From equation (2), it can be shown that bidder 1’s entry ˆ threshold valuation is given by V = 0.5(r − c) + [0.25(r + C ) 2 + CV ]0.5. In this scenario, the probability of no entry (no sale) is V (r + C ) V 2. There are two cases that result in only one bidder entering: (i) bidder 1 enters with a signaling bid and bidder 2 does not enter, which happens with probability of [(V − V )(0.5V + 0.5V + C ) − 0.5C 2 ] V 2 and with a sales price equal to bidder 1’s signaling bid; and (ii) bidder 1 does not enter and bidder 2 enters with a bid at the reserve price, which happens with probability of V (V − r − C ) V 2. The remainder of the probability goes to the case of competitive bidding.