A Counterfactual Public Housing System and Its Outcomes

Today, I would like to examine a counterfactual. What if, in Singapore, public housing were more tightly controlled by HDB. In particular, what if purchase and sale transactions could only be performed with HDB itself and prices were controlled so as to preserve market forces based on location-based desirability while, at the same time, relieving speculative pressure. Let me elaborate on the basic mechanism behind this.

A Counterfactual Public Housing System
The sale price for a flat would be fixed upfront, 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 sale 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 sale 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, fixed sale 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). All this serve to 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 housing market, comprising the buyers, is best equipped to price this premium. Hence the auction mechanism. The premium paid over the sale 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 (the current legislation is not retroactive), (ii) begin a two-speed public housing market where the sale of all new flats are based on this paradigm and current flats can be sold to other buyers or to HDB at the aforementioned fixed price.

Step (ii) will result in a gradual conversion of the public housing market to the aforementioned system. 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 sale 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: An Attempt at an Auction Mechanism
I envision the conduct of regular auctions by district/sub-district and category (based on type, upgrading status, age bracket, size bracket, floor, etc.) with the reserve price on each flat set to the resale price. Interested buyers would first register with HDB and then be issued with accounts to bid for flats. (These accounts will be closed on the successful purchase of a flat.)

Before moving on, the auction described is probably not strategy proof. However, care was taken to reduce the potential gains of strategic manipulation to those reflecting personal preference by stratifying the flats on auction such that they have similar valuations. Having said that, auctions would be carried out as follows:

Each auction will be only for a certain by district/sub-district and category. Naturally, the number of flats will be known to all bidders as well as the reserve prices for each of the flats. The intent of conducting an auction by district/sub-district is to reduce the variation in valuation (resale price) each bidder holds for the available flats in the same category. (Note also the assumption of small per square foot prices.) Thus, bidders will specify a single (sealed) bid price. Each bidder will select only the available flats he/she desires (with reserve prices not exceeding his/her bid) and indicate a preference order on those.

The gist of the auction is that it is similar to the generalized second price auction. Readers for which the above is sufficient may skip the details and go on to the next paragraph. Now, onward. The winners of the auction will be selected in descending order of bid. While there are flats or bidders remaining in the auction, the following process takes place:

1. The question "Can parts of the auction be cleared at the reserve price?" is asked. Computationally, the set of bidders is partitioned into "bidder groups" such that for the bidders in a given group, all bidders there do not desire any flat selected by the bidders in all other groups. (This can be visualized by picturing the auction as a graph with bidders as nodes and edges corresponding to common demand for flats remaining in the auction.) For each bidder group, if all demand can be satisfied by allocating, ordered by descending bid price, the most desired remaining flat to all bidders, then all bidders in that group get their desired flats at the reserve price. (Note: "bidder groups" are recomputed at each step, as the removal of a flat can split groups, necessitating a re-check. Of course, a computational improvement can be made over this process.)
2. If the top bidder has no flats remaining on his/her list, remove him/her from the auction, doing this until the top bidder has a non-empty list.
3. The top bidder wins his/her most preferred flat remaining on his list at the price defined by the next highest bidder's bid or that flat's reserve price if he/she is the only bidder remaining.
4. The flat won is removed from all remaining bidders' lists and the current winning bidder is removed from the auction.

Bidders are obliged to take any flat they have selected and won. If a flat is declined without good reason, the buyer will be barred from bidding for some period of time.

The orchestration of the auctions, including the user interface, automation of bidding (such as bidding in a sequence of auctions until a flat is won) and other details can be ironed out at implementation.

Again, this is a sketch of a possible auction mechanism. Clearly it is an attempt, and a better mechanism may be developed. Perhaps with corrections for the (small) differences in flat valuation. (I attempted to incorporate this, but found I had to accept a mechanism with swapping of the order of awarding flats, thus I accepted non-Nash Equilibrium outcomes for comprehensibility.) Hopefully gaming this system would be more effort that it is worth. Perhaps a further analysis of the system would show that it admits epsilon-Equilibria as outcomes.