A Counterfactual Public Housing System (Revised)

(This is a revised version of a previous post containing a revised auction mechanism with nice properties, including strategy-proof-ness. An edited version of this was published at NewAsiaRepublic.)

I would like to examine a counterfactual. What if, in Singapore, public housing were more tightly controlled by HDB in the following fashion:

1. purchase and sale transactions could only be performed with HDB itself,
2. prices were controlled so as to preserve only market forces based on location-based desirability to individual buyers while, at the same time, removing the speculative component.

Let me elaborate on how this might be achieved.

A Counterfactual Public Housing System

The resale price (back to HDB) for a flat would be set according to its type and floor area. Thus, a 1000 square feet four-room flat in Marine Parade would be sold back to HDB for the same amount as a 1000 square feet four-room flat in Pasir Ris. Furthermore, these resale prices would be kept low. (This may be tweaked to account for age and recent upgrading work.) The purchase of flats would be done by sealed-bid auction, with the previously mentioned resale price as the reserve price. (The details of the auction mechanism will be outlined in the Annex.) In addition, if an owner of a HDB flat comes to own any private property in Singapore (through purchase or bequest), that person must dispose of either the HDB flat (to HDB) or the private property.

Due to the low resale prices, there would be no incentive to purchase HDB flats for speculative purposes. Presently, there is a loophole where some foreign nationals (PRs and those with dual citizenships) are essentially able to buy to rent, reducing the strained public housing supply and profiting off the misery of the "flat-less". Measures to plug that loophole will be outlined in the next paragraph. On the other hand, to avoid market distortions where a flat is priced at the same amount as a less desirable one, sale of flats will be done by (country-wide) auction (with a reserve price dictated by the nature of the flat). It is intended that buyers make bids for available flats of all types in all locations so as to eliminate dillemas of whether to participate in an auction for flats of a second choice type or in a second choice location. All this would serve to "defragment" the public housing market and ensure that the premium paid over the reserve price reflects desirability due to location, and does not contain a component pricing potential future speculative profit.

To reduce actual foreign speculative pressure, consider requiring all flat owners holding any foreign citizenships (non-citizens and citizens with dual citizenships) to certify their occupancy of their flats by certifying, in person, every quarter (or some suitable time interval), their occupancy of their flat at their local town council. This will not be onerous as town councils are typically located close by.

The philosophy behind this counterfactual system is that residents derive value from public housing based on the housing space and the location. The actual public housing market, comprising the buyers, is best equipped to price this premium. Hence the auction mechanism. The premium paid over the resale price would reflect the value derived from the flat consumed by the owner over the tenure of residence and, as such, would not be returned when the flat is sold back to HDB.

Implications for Economic Vibrancy and Investment

It follows that without a concomitant increase in prices and without an accompanying fall in wages, lower housing prices will result in higher household savings. (The former two do not appear to follow from lower housing prices.)

The upshot of this is that funds would be available for the enterprising to start businesses. The less entrepreneurial would have funds to invest in those new businesses. With less funds tied up in property, the economic landscape would be fertile enough to encourage new businesses to spring forth and be nourished by the increased availability of funds.

It is not too much of a stretch to project that a number of these new businesses would introduce innovative business models and new uses of technology, thus bringing a new vibrancy to the economy. With this, investment in Singapore will no far less property driven, but rather, innovation led, as befits a knowledge economy.

Closing Remarks

The counterfactual public housing system I have proposed has a number of positive features. However, the problem is how to get from the present state to this one. In my mind, the way forward entails a number of steps (i) legislate that the divestment requirement for all public housing to take effect in a number of years (as existing current legislation to that effect is not retroactive), (ii) begin a two-speed public housing market where the resale of all new flats will be based on this paradigm and current flats can be sold to other buyers or to HDB at the aforementioned resale price.

Step (ii) will result in a gradual conversion of the public housing market to the aforementioned counterfactual system. In decades to come, as newer, more desirable, flats are rolled out, the prices of current flats will naturally decline due to the greater availability of cheaper flats, as well as their age. Eventually they will be sold back to HDB at the dictated resale price, reducing the share of flats held in the old housing system.

Will this take place? It depends on the priorities of the government and the electorate.

Annex: Remarks on the Merits of Using Auctions for Allocating Public Housing

At first glance, it might appear that the use of auctions would punish poorer Singaporeans based on the historical use of auctions for selling collectors' items. However, auctions are a direct mechanism to mark to market. Auctions have been used for certain types of items that are difficult to properly value a priori, such as collectors' items whose market value is uncertain. Homes are similar to an extent. HDB and banks cannot properly assess how much value a flat has to a buyer as work location, residents of friends and family, and a host of other factors contribute to this.

It might be argued that current market prices cannot be said to be true free market prices. They are essentially monopoly prices set by the "housing establishment" which includes developers and banks who both profit from "high valuations". Current prices also include premiums for potential future gains.

In contrast, if buyers know they cannot resell flats to HDB for much more than the set resale price (as only small corrections are made due to inflation), then the premium they would indicate that they are willing to pay over the reserve prices would really comprise just the benefit derived from the availability of the flat to them for their planned time horizon.

Furthermore, a bidder pays at most the bid price, and in subsets of an issue which are not oversubscribed, essentially everyone (bidding for flats in those subsets) pays the reserve price. Only when there are wildly oversubscribed segments can prices get high, and only for flats in those segments.

The reserve price is intended to be a statement by HDB of cost or cost+, and that HDB will not sell for anything less than that. It should reflect the economies of scale associated with good contracting practice and good management of outsourcing contracts (i.e. costs should be low).

Annex: Remarks on Managing the Cost of Public Housing

Procurement and the management of outsourcing contracts must improve to ensure that costs to HDB, and hence flat buyers, do not increase in an unwarranted fashion. Public officials in such roles should have their incentives explicitly linked to ensuring that costs do not go up (or go down due to productivity improvements). This is aimed at eliminating the mentality that as long as the lowest cost alternative in the tender gets the award, the job is done. Such a mentality demonstrates the "not my own money" view of using public money and should be eliminated using proper incentives.

Public officials in such roles should be rewarded for keeping costs in place, and given large bonuses when costs go down (as they have generated huge value for the public). These officials should be replaced when cost increases are not supportable by market conditions. Furthermore, exclusion clauses should exist to prevent them, for a period of time, from working for construction firms, firms in closely related industries, companies linked by a parent company or in a parent-child relationship with such firms. All this serves to prevent collusion that harms the public.

Annex: An Attempt at an Auction Mechanism

I envision the conduct of regular auctions of all available flats in Singapore with the reserve price on each flat set to the aforementioned resale price. Interested buyers would first register with HDB and then be issued with accounts to bid for flats. They would then place bids for each flat they are interested in.

This is my third attempt. The first attempt at a mechanism is featured at the previous post. It was not satisfactory. The second was online just briefly, but was taken down because I realized that an aspect of the proof of strategy-proof-ness was wrong and it couldn't be fixed. (I found a clear counterexample.) This auction mechanism will stand up easily to scrutiny because it is based on a well-known (and well-studied) family of mechanisms called Vickrey-Clarke-Groves (VCG) Mechanisms.

In the auction, each bid price is intended to be the maximum amount the relevant bidder is willing to pay for a flat of a particular type in a particular location. Bidders will make bids for every type of flat they are interested in. The beauty of VCG mechanisms is that the optimal bidding strategy is for a bidder to truthfully bid the actual maximum value he is willing to pay for a flat, the auction mechanism will not use this information to extract additional revenue from him. This is in contrast to situations where perfect price discrimination is possible and buyers have an incentive to hide information on exactly how much they are willing to pay.

To jump the gun, the allocation portion of the auction seeks to maximize allocative efficiency, which is quantified by the total value of the allocation to the bidders defined by the sum of bid prices for all allocated flats (including unallocated flats which are valued at the reserve price. The pricing portion charges each bidder allocated a flat a price which represents "the social cost to society of him having been allocated the flat". Imprecisely speaking, this social cost typically entails the loss to someone else who would have been allocated a flat, and as such, is typically the bid price of the bidder "next in line" to be allocated a flat (the first among the losing bidders). More accurately, the price charged for each allocated flat is precisely the lowest amount the respective bidder could have bid and been allocated the flat.

To give a concrete (albeit simple) example, if only 800 bidders compete for an issue of 1000 "identical" flats, regardless of how wildly high some bidders might bid, all bidders bidding at least the reserve price pay the reserve price for their flat. In contrast, if 1800 bidders compete for an issue of 1000 "identical" flats, the 1000 winning bidders would end up paying the 1001-st highest bid price. In the setting of auctioning identical items, the VCG auction reduces to the k-th price auction. One might visualize the results to be exactly "intersecting the demand curve with the supply curve" to determine the equilibrium price. This justifies the claim that such a mechanism is a direct (and accurate) means to price flats through the free market.

One criticism of the VCG Mechanism turns out to be a strength for allocating public housing: revenue from VCG-based auctions compares poorly to that from other auction forms. This arises as VCG enforces the property of truthfulness by charging winning bidders the lowest amount they could have bid and been allocated a flat, an amount typically much lower than the amount bid. Since the mission of HDB is to "provide affordable homes of quality and value", it may be said that selling flats at the reserve price is a mark of successfully meeting housing demand in an affordable fashion and low revenue from the auction is not, in fact, a problem.

If this takes off, there will probably be a short lived cottage industry of housing agents offering bidding services for flats, but with proper communication of what the optimal bidding strategy is, this market inefficiency (due to lack of awareness) will disappear.

In the future, I will probably post examples of the VCG auction at work.

Annex: The Allocation Model for the VCG Auction

v_ij: Bid price of bidder i for a flat of category j

x_ij: Boolean variable defining whether bidder i was allocated a flat in category j (for the bidder representing HDB, this is a not a boolean variable, but rather a non-negative integer variable)
n_j: Number of available flats in category j

maximize Sum[over i and j] v_ij x_ij
subject to:

Sum[over flat categories j] x_ij <= 1 for each bidder i except HDB (1) Sum[over bidders i] x_ij = n_j for each flat category j (2)

Note that HDB bids the reserve price for each category. Also, bidders not bidding for a flat category bid zero.

The set of constraints (1) mean that each bidder (other than HDB) may be allocated at most 1 flat. The set of constraints (2) mean that all flats are allocated.

One can prove that if the bid prices (other than HDB's) are all not equal (and another non-equal "difference" condition holds), this integer optimization problem can be relaxed to a linear optimization problem and yield the same solution. (This can be easily engineered and implies big computational savings, which will be necessary for quickly producing an allocation and pricing the allocated flats.) Such a scenario can be engineered by requiring minimal bid increments (of say $100) and incorporating random tie breaking by doctoring bids by random values smaller than the bid increment. This practical measure is similar to allocating flats by ballot, but differs in that it first takes allocative efficiency into account.