|
Article Excerpt
This article examines the price formation process under small numbers competition using data from Singapore land auctions. The theory predicts that bid prices are less than the zero-profit asset value in these first-price sealed-bid auctions. The model also shows that expected sales price increases with the number of bidders both because each bidder has an incentive to offer a higher price and because of a greater likelihood that a high-value bidder is present. The empirical estimates are consistent with auction theory and show that the standard land attributes are reflected in auction prices as expected.
**********
This article examines the price formation process under small numbers competition. The neoclassical competitive bid price model envisions an implicit auction in which the highest bidding land use obtains the land and competition among atomistic agents drives profits to zero. The model provides the foundation for modern land use theory and underlies most applied property markets analysis. The framework is easy to apply and capable of predicting how a variety of factors, including risk, affect the market price of land. The question of price formation, however, is subsumed within the competitive zero profit condition and therefore, by construction, the standard bid price model is not designed to evaluate the consequences of situations in which finite numbers of agents interact.
The literature has taken several alternative paths to study price formation in real estate markets. One approach focuses on the search and matching aspect of many property markets (particularly the housing market), an extensive line of literature that is growing rapidly. A second approach focuses on the negotiation process often observed in face-to-face real estate market transactions, typically relying on Nash bargaining or similar equilibrium constructs to model price formation. The empirical evidence in this line of literature is much less extensive, depending as it does upon data that is not widely available. These two approaches are similar in that they diverge from the standard competitive bid price equilibrium assumption, but differ in the market dimension upon which they focus; the role of search versus bargaining power in determining selling price. The third approach studies the performance of structured markets, like formal auctions, in which price formation is determined by well-defined rules governing bidding and acceptance by finite numbers of buyers and sellers. (1)
This article takes the third approach to studying price formation under small numbers competition. It begins with the recognition that the neoclassical bid price model depicts prices "as if" determined by auctions (although the structure of the implicit auction is not spelled out in any but the vaguest terms). It follows the logical connection of the implicit bid price-auction market nexus, beginning with a formal model of an auction process that yields the bid price formulation as a limiting case, and then using the model to study the properties of the expected auction outcome as the finite number of participants varies.
Even though there are not many empirical studies of real estate auctions, the few that have been published are beginning to build a picture of regularities and anomalies. For example, open-bid real estate auctions often restrict bidding by potential buyers to take place in a fixed location during a limited time period. There is a growing consensus that real estate sold in such auctions appears to sell at a discount relative to full exposure to a market comprising searching buyers who are free to make offers on a specific property as long as it remains unsold (Ashenfelter and Genesove 1992, Mayer 1998, Allen and Swisher 2000, Ching and Fu 2003). Other aspects of open-bid real estate auctions, however, are not so clear-cut. For example, while Lusht (1994) and Mayer (1998) find that auction prices tend to decline for units sold later during a sequential auction of multiple units, (2) Allen and Swisher (2000) find that selling prices tend to increase for properties sold in sequence as the auction proceeds.
Of course, analyzing auctions requires data, and the paucity of such data has stymied the empirical study of real estate auction markets. Singapore's Sale of Sites (SOS) program presents an opportunity to study price properties in an actual auction market. While there are relatively few empirical studies of real estate auctions in general, first-price sealed-bid auctions of single properties like Singapore's have been virtually ignored. (3) Thus, one contribution of this article is that it presents empirical evidence regarding a type of auction largely overlooked in the real estate literature. A second contribution arises from the type of property being auctioned. While several of the existing studies of real estate auctions pertain to property offered for sale as the result of foreclosure or seller liquidation due to financial duress, factors that can by themselves affect the auction outcome (Ong, Lusht and Mak 2005), our sample consists of land offered under normal market conditions. Finally, each auction in our data set consists of a single fully assembled land parcel offered for sale by the Singapore Government. This auction structure avoids introducing the pricing anomalies related to the sales sequence and property heterogeneity found in auctions that consecutively offer multiple individual units for sale during a single auction session, as found by Allen and Swisher (2000), Lusht (1994) and Mayer (1998).
The discussion is organized as follows. The next section presents a simple sealed-bid private value model corresponding to the Singapore land auction system and uses the model to show how different factors affect bidding strategies and the resultant land price. The third section offers a brief description of the Singapore SOS auction program. The empirical analysis of the set of individual Singapore land auctions is reported in the fourth section and the last section concludes.
Bidding for Land in a Sealed-Bid Auction
This section presents a simple auction model adapted from received theory. (4) The purpose of this discussion is to link the observable characteristics of winning bidders and land to the observed auction prices in our empirical study. This is a model of a first-price sealed-bid auction with private values. There is a single seller offering one parcel of land for sale in the auction. A (known) finite number of interested buyers determine their bids and then simultaneously present them to the seller. The seller awards the land to the highest bidder at that bid price.
Potential bidders for the specific parcel of land are identified by their private value, the expected value they attach to the land, which is the net return to the bidder in its developed use, v. This value can be thought of as a potential bidder's estimate of the present value of returns (discounted at the risk-free rate) from the bidder's best use. Different potential buyers will generally have different ranges of the types of projects in which they specialize, depending upon their experience and expertise. Therefore, the variable v reflects in part the type of development envisioned by the bidder mediated by his ability. Different types of bidders have different expected v values. Unless otherwise stated, however, all potential bidders are identical except for their land valuation v; we will introduce other differences in firm characteristics in what follows. The distribution of bidder types is given by G(v) continuously defined over the range of property values [[v.sub.l], [v.sub.u]]. Intuitively, each bidder represents a different development configuration or use for the land parcel being offered; viewed this way, the individual bidders in this auction are the analogues to competing bids from alternative land uses in the neoclassical bid price model of the competitive land market.
The realized net return to the winning bidder is uncertain ex ante and equals v + [epsilon], where the stochastic term [epsilon] is distributed with mean zero and finite variance, var([epsilon]). (5) It is important to note that v indicates bidder type, while the stochastic term [epsilon] captures the net return riskiness or uncertainty that all potential buyers confront. The [epsilon] term introduces an additional source of uncertainty confronting bidders; not only are they uncertain about the competing bids that will be forthcoming, they are also uncertain about the net returns from their proposed development project when offering their bids.
This is a private value auction modeled as a private information game. While a given bidder i knows his own type (v) and the number of other bidders who will make offers for the property, bidder i does not know the underlying v value the other participating bidders have for the property. Each bidder does know, however, that the population of potential bidders from which the N participating bidders are drawn is distributed G(v).
Consider bidder i, whose expected value of the land is [v.sub.i]. Given that the ex post net return is distributed F([epsilon]), the individual bidder's problem is to offer the bid [b.sub.i] that maximizes the expected utility from the land. Define p as the probability of bidder i winning the auction. The probability of the single bidder making a high enough bid to obtain the land, given the potential bids from others, is increasing in the own bid, p'([b.sub.i]) > 0. Given the stochastic return to other investments or development projects of the bidder is [omega], the expected utility is Eu([omega] + [v.sub.i] - [b.sub.i] + [epsilon]) when i offers the highest bid and wins the auction and Eu([omega]) when he does not. For bidder i the expected utility from the auction is
EV = p([b.sub.i])Eu([omega] + [v.sub.i] - [b.sub.i] + [epsilon]) + (1 - p([b.sub.i]))Eu([omega]), (1)
where the expectation operator is understood to be taken with respect to [omega] and [epsilon].
Because...
|
