«CHINA'S LAND MARKET AUCTIONS: EVIDENCE OF CORRUPTION Hongbin Cai J. Vernon Henderson Qinghua Zhang Working Paper 15067 ...»
-.40. These are still at least twice the OLS estimate. 19 In terms of issues of selection, the fact that the treatment effect coefficients are significantly larger than under OLS suggests positive selection: not accounting for selection understates the size of the treatment effect. Correspondingly, for direct evidence on selection, the correlation coefficient in the MLE results is positive and significant, as is the 2-step Heckman estimate of the Mills’ ratio coefficient. The theory section suggested positive selection would be a marker of corruption, and the results indicate that positive selection into two stage auctions is a significant force.
We also examined the validity of instruments to the extent any tests are persuasive. A Sargan p-value of.15 while acceptable is low. We believe this is due to model specification error (see next) rather than unsuitability of instruments per se. If we add to column 1 (the OLS specification) our 4 instruments as covariates, the coefficient on auction type goes from -.1697 to -.1624, a tiny change. If instruments were correlated with unobservables affecting sale prices, assuming that auction type is correlated with unobservables, the added instruments should absorb some of the correlation of unobservables with auction type, affecting its coefficient. That the coefficient is unchanged and instruments are definitely correlated with auction type suggests that the instruments are orthogonal to unobservables.
Finally, we note if we drop the reserve price variable and use property characteristics (and city and time fixed effects) to represent both common value and demand considerations, all coefficients become much more negative. 20 For example, the OLS coefficient goes from -.17 (with a reserve price control) to -.34 (without a reserve price control); the Heckman 2-step and MLE rise in absolute value to -.81 and -.92 respectively; and the LIML coefficient goes to -.80. The lambda in the Heckman 2-step rises to.27, while the rho in the Heckman MLE falls to.37. Thus, the results without a reserve price control also suggest positive selection.
With use of all 7 instruments, the MLE and 2-step Heckman results are almost the same (-.69 and -.46 respectively). The LIML estimates are higher in absolute value when using either a first stage probit or linear probability model (-.526 and -.893 respectively). All coefficients are significant.
These reported results are for 7 instruments.
4.4 The problem with the baseline approach: “Kink/discontinuity” in the price equation We speculate that if multiple entrants emerge in the second stage of a two stage auction, the outcomes for English and two stage auctions for that property will be similar.
In both cases once into the English auction portion, the sales price will simply be the valuation of the second highest valuation bidder. Corruption more likely takes the form of inducing non-corrupt entrants to stay out of the two stage auction, with the result that sales are at reserve prices. Of the 2302 auctions upon which estimation is based, only 1235 are ex post competitive, or have more than one bidder as inferred from the degree of spread. A non-competitive auction means sales price equals reserve price, so reserve price tells us sales price. We already saw in Table 3 from the raw data that the significant overall unit price differences between English and two stage auctions for the overall sample become insignificant once we look just at auctions which are competitive.
To explore these issues, we examine the two components. How does auction type affect the probability that an auction will be competitive or not? Second, if auctions are competitive does the choice of auction format still affect sales price? The answers to these questions will help us study the revenue losses from use of two stage auctions.
5. The effect of auction type on competition What is the effect of auction type, on whether an auction will be competitive or not, defined as whether there appears to be more than one bidder because spread exceeds 1.005? A simple probit of competitive or not with auction type as a potentially endogenous dummy variable faces the same selection problem as in the sales price estimation. Properties may be negatively or positively selected into two stage auctions, and such selection itself will affect the potential for competition. The literature handles this in different ways. We use the bivariate recursive probit (Greene, 1998, Evans and Schwab, 1995), as an MLE solution. As a robustness check we also performed regular IV estimation in a linear probability model (Angrist, 1999), where we instrument for auction type with Z’s. Here, the marginal 2-stage auction effects are even stronger than we will report below—reducing the probability of competition by.75. 21 These results are based on use of 7 instruments, under LIML estimation.
The bivariate recursive probit is a two equation MLE model where we model action type as a dummy endogenous variable which is a function of X and Z, with auction type affecting the event: competition or not. That is,
where dijt denotes whether an auction is two-stage (1), or not (0), and sijt denotes whether an auction is competitive (1) or not (0). The X’s include city fixed effects, time dummies, seasonal dummies, and ln(ask price) in all equations (cf, equation 7). The recursive structure allows identification in a standard bivariate probit framework (Greene, 1998). In the next section we will add a continuous equation, for sales price in competitive auctions; at that point we will offer more details on estimation.
Results are in Table 6. For the bivariate recursive probit, we show marginal direct and indirect effects. For the variable of interest, two stage auction, there is only a direct auction effect. In the ordinary probit, the marginal effect of two stage auction on the probability of being competitive is -.34, consistent with the raw data in Table 3. In the bivariate recursive formulation that marginal effect is 26% stronger, at -.43. 22 This is again suggestive of positive selection into two stage auctions: the two stage auction’s negative effect on competition is understated because properties with better unobservables are selected into two stage auctions. Consistent with this, the rho measuring the degree of correlation between the error terms is positive (.38), and significant. Properties with better unobservables are more likely to be competitive, and more likely to be assigned to two stage auction.
In terms of other variables, relative to the base case of commercial use, sales of residential and mixed use land are likely to be more competitive, while large properties Use of 7 instruments further increases the strength of the negative effect to -.49.
away from the city center are less likely to have competitive bidding. Total marginal effects on competition or not include direct effects 23 and then indirect effects 24 through the effect of covariates on auction type and hence competition. Indirect effects seem strongest for land use variables, reinforcing the fact that commercial use properties face fewer takers and are less likely to be competitive. Removal of reserve price as a covariate in both equations has little effect on results, consistent with the fact that its coefficient is insignificant in Table 6.
6. Effect of auction format on sales prices, for competitive sales If properties sell competitively, is there a remaining effect of auction type on sales price?
A naive way of looking at this is to ask, conditional on a property selling competitively, ex post does auction type affect price for such properties? That is interesting information.
If we examine the sample of 1235 properties for which spread exceeds 1.005, OLS results in column 1 of Table 8 below show no effect of auction type, a coefficient of -.03.
This OLS estimate of auction effect on price faces two problems. First there is the auction selection problem discussed earlier, but now there is a second selection issue. Being competitive is endogenous, and there is selection on unobservables into competition that are surely correlated with price. Such selection is mediated by the auction process, so it is not the standard problem in Lee, Maddala and Trost (1980), but rather one modeled in the labor literature (Fraker and Moffitt 1988, Goux and Maurin, 2000) and more recently in firm growth models (Reize, 2001).
We tackle the problem in two ways. First, as a less parametric approach, we utilize the ideas from the literature on identification-at-infinity (Heckman, 1990), by examining auction effects for samples where the predicted probability of a noncompetitive sale is small. This isolates a sample where, ex ante, we expect sales to be Marginal direct effects are calculated based on the estimated coefficients in the second equation of the bivariate recursive probit, as well as the predicted probability of being competitive at the mean level of covariates, i.e., P=0.4817. For a continuous variable, its marginal effect is equal to the product of the density of normal distribution at P=0.4817 and its estimated coefficient. For a discrete variable, its marginal effect is equal to Φ (arg Φ (0.4817) + θ ) − 0.4817, where Φ (⋅) (or arg Φ (⋅) ) is the cdf (or inverse of cdf ) of the normal distribution and θ is the estimated coefficient.
The marginal indirect effect of each covariate is obtained from the product of the estimated coefficient of 2-stage auction in the second equation of the biprobit regression and the estimated coefficient of this covariate on auction type in the first equation. We calculate the standard errors using the delta method approach. The variance-covariance matrix is obtained through post-estimation of the biprobit model.
competitive regardless of auction type; and asks whether, for this sample, there is an effect on sales price of two stage auctions. The main issue with moving to such samples is that, especially when we want to still correct for selection into auction type, we start to run out of cities which have competitive sales in both auction formats.
6.1 Selection into being competitive Identification-at-infinity Similar to Mulligan and Rubinstein (2007), for each auction type separately, we estimate the probability that an auction is competitive; specifically that the spread (ratio of sales to reserve price) is greater than 1.005. The covariates are the X’s including reserve price and city fixed effects, but not the instruments (which don’t affect competition per se). We then created different samples: for example all properties where the probability of competition ex ante is predicted to be greater than 0.5, 0.6, 0.7, and so on. Patterns in the raw data are most instructive in terms of how the samples, mix of competitive to non-competitive auctions, and price differences change across auction types as we move to more and more competitive margins.
Table 7 shows the patterns. In Table 7 we distinguish 7 samples, all observations and then 6 samples distinguished by increasing degrees of predicted competitiveness of the auctions. We have three sets of columns. In the first we show that as the degree of predicted competitiveness increases, the ratio of (remaining) two-stage to English auctions declines precipitously. For the full sample the ratio is 2.6; for the most competitive it is 0.06. The result suggests that finding a sufficient sample of two stage auctions that are very likely to be competitive is not easy. The second set of columns shows that as we increase the margin on being competitive, the percentage of auctions with spread rises and converges for the two auction types. This of course follows from the nature of the exercise (creating samples by how competitive they are predicted to be);
but it shows the exercise is working.
The third set of columns in Table 7 contains the key results. It examines the pattern of spread (sales to reserve price) for English versus two stage auctions.
Significant differences in both median and ranks of spread exist at low levels of competition between the two auction types, but diminish as competition increases and disappear by a predicted probability of competition in excess of 0.7. Typically, for identification-at-infinity, a margin of.8 or greater is used. The raw data suggest that at such margins, English and two stage auctions yield similar outcomes.