Today, I was reading a survey paper on convex optimization in risk management (naturally, the applications were financial), when I started thinking about high-frequency trading and how to rationally design the exchange. From the game theoretic perspective, designing such an exchange becomes less than straightforward when the interaction of rational, self-interested buyers and sellers is taken into consideration. I decided to just do this "exercise" on the bus, on my way to Maju camp for RT. (Like many, I was unaware of the 3 month shift in the deadline for doing my IPPT. Still, the exercise would be good for me. My running has deteriorated to a sad state.)
High frequency trading entails computers making lightning-fast trades, and trading agents (such as brokerages) holding positions for as little as a few seconds. As of the end of last year, it accounted for about two-thirds of trades in the US and about half of those in Europe. Last year, the Singapore Exchange (SGX) launched a new trading engine called Reach, advertising it as the world's fastest. It is unfortunate that details on how trades are cleared are not readily available for scrutiny. While the potential harm of poorly designed exchange mechanisms is not huge, inefficiencies commensurate with the frequency of trading can arise.
My objective, here, is to design an exchange so buyers and sellers have incentives to truthfully declare the maximum they are willing to buy at and the minimum they are willing to sell at. This is because given a trading mechanism that is not "truthful", outcomes can be highly inefficient (and possibly ill-defined). Here, inefficiency means that trades that might benefit some buyer and some seller might not happen. With a truthful mechanism, efficient allocations can be made that "maximize social welfare". It was thus my objective to design a good trading mechanism without paying an untenable "price of truthfulness".
Now, on to the topic at hand. In a sense, a stock exchange is not very much different from a traders’ wet market. In fact, the technical difficulties of achieving efficiency in the wet market are more severe than in the high-frequency trading market place. This is a surprising plus of the latter over the former. (This will become clear later.)
In both cases, buy and sell quotes have to be matched and cleared. (And much faster in the electronic market place.) This is when game theory seems to rear its ugly ugly head. A theorem due to Roger Myerson and Mark Satterthwaite tells us that there is no "efficient" way to trade a good between two individuals unless the lowest amount the seller is willing to sell the good at exactly matches the highest amount the buyer is willing to pay for it (i.e.: there is no buyer or seller surplus and that trade leaves no one better off, a pointless trade). This means that there are incentives to posture, pretend and hide the maximum value that one is willing to pay or the minimum value that one is willing to sell at. Anyone who has been to a market in Bangkok or Bali sees this first hand. (My girlfriend loves bargaining. I however, do not have the taste for it, perhaps making me manifestly unsuitable for wheeling and dealing.)
This unfortunate fact has correspondingly unfortunate effects on clearing trades. Let us say that a trade is matched for 1 share and the buy bid is at B (say 10) and the sell bid is at S (say 5). It is clear that the buyer must pay at most B (10) and the seller must be paid at least S (5). If the exchange stipulates that the trade clears at the any number between B and S (say the mid-point), then incentives exist for buyers to shave down (and for sellers to inflate) their bids in order to get a better deal. This is unfortunate as we need true valuations to make good allocation decisions. (In this context, "allocation" refers to clearing trades and "welfare maximization" is desirable. Also, we are not concerned about buyers inflating their bids and for sellers to shave theirs down as more trades are encouraged, and possible real losses lead to a natural restriction of this.)
Let us take a step back and consider how we might obtain matching buy-sell bids to clear. For simplicity, we consider 1 share blocks. (Though it is trivial to execute with blocks of varying sizes.) From the perspective of economics, we would like to incentivize people to truthfully inform the exchange of the lowest price one is willing to sell at (for buyers) and highest price one is willing to pay (for sellers). This allows efficient allocations. This incentive can be built into the exchange by making it possible for buyers and sellers to capture more trade surplus (the difference between transacted price and one's valuation) by bidding truthfully.
Consider the following matching procedure: pick the highest buy bid and match it with the lowest sell bid and pass that match on to clearing. This means that matches, from the pool of unsatisfied bids, are made so as to maximize the total trade surplus of that match. So "potential trade surplus reaped" will be used as an incentive for all to bid truthfully. Tentatively we will leave this at that, noting that a payment rule (to determine the clearing price) is needed to make this precise. Before getting to that, we return to the apparently ugly problem mentioned above.
I made a number of mistakes on that bus. I've thought asymmetric buyer-seller rules would work (noting that agents would buy essentially as often as they sell); I thought randomization would save the day. All those would not work. It turns out that there is a direct cost to economic efficiency that has to be paid to ensure truthfulness. What would please the board of any exchange implementing this mechanism is that the exchange can pick up what is left on the table. Let me explain.
The key requirement for truthfulness is that, all other bids being fixed, a buyer and seller pair should not be able to affect their gains by changing their bids. Changing their bids should only affect whether their trade is cleared first, and it should be clear that trades cleared first generate more "potential trade surplus". Thus, given a top buy bid B1 and second highest buy bid B2, and lowest sell bid S1 and second lowest sell bid S2, the buy price and the sell price should be functions of B2 and S2, (B2+S2)/2 being the obvious choice. If these differ (albeit slightly), the exchange pockets the difference as a "facilitation" commission.
Now moving back to the matching rule, we see that the leading buyer has no incentive to bid anything other than the maximum he is willing to pay as that would not increase his expected trade surplus (and possibly decrease it). A similar case is true for leading sellers. Ostensibly, we have achieved incentive compatibility in high-frequency exchanges.
Unfortunately, it still is not clear cut as (1) "non-leading" buyers may raise their bids and "non-leading" sellers may lower their bids to get a better match, and (2) there may be a timing issue. Due to these limitations, quotes were added to the title and "incentive compatible" was used as opposed to "truthful". Yet, these issues are far from fatally damaging to the mechanism outlined above.
On (1), the problem is ameliorated by the fact that for approximately evenly spaced buy bids and similarly spaced sell bids, non-leading bidders stand to lose if they manipulate. In fact, it can be shown that if buy bids are evenly spaced and sell bids are evenly spaced with a different spacing, if a non-leading buyer raises his bid, he only stands to gain if the "sell-side spacing" is more than twice that on the "buy-side", which is highly unlikely to persist in sustained trading by the "symmetry" of buying and selling (i.e.: the use of similar models for asset valuation) and the price mechanics led by supply and demand. A similar argument holds for sellers hoping to gain by pretending to be willing to sell for less. On (2), An agent might wonder what if a lower sell bid comes in over the next second and by posting a buy bid now, it is missed? However, in so far as things are uncertain, and one expects to lose money by holding back, this problem is not so severe. (Woo! Hand-waving. Doesn't this take you back to your school days.)
This has been a fun exercise in mechanism design. (Writing this up took longer than thinking about it.) It is quite amusing that the incentive problems in a simple setting like a traders’ wet market are more intractable than in a high-frequency exchange. Hopefully, it has demonstrated the value of the marriage of economics and computer science in our world.
Postscript 1: I feel that mechanism design has an important role to play in the evolution of the public and private spheres in Singapore. As I am embarking on a PhD in Decision Sciences at NUS Business School, I hope that I’ll be able to make some contributions in this arena. It would be appropriate to thank David Parkes for introducing me to this wonderful field. The commute up north to take his class (and missing another class I wanted to take that was back-to-back with it) was well worth it.
Postscript 2: The aforementioned matching can be done efficiently using priority queues. Certain specialized implementations are blazingly fast.
Postscript 3: An electronic marketplace may become even more interesting if a combinatorial element is introduced. That is, if bundles of different stocks in some proportions have a synergistic value. This adds horrid computational issues, and may be of dubious value. One question might be: given that in general, trades like this cannot be cleared fast, is there a non-trivial restricted class of trades that can?
Afternote 1: If the exchange would like to obtain additional revenue from each transaction or a government would like to tax transactions, it should be done as a fixed proportion of the buyer-seller trade surplus. This will preserve incentive compatibility.
Afternote 2: One of thoughts that went through my mind on that bus ride was how to sensibly do short selling in high-frequency trades. Now that this post has evolved into what it has become, this is a little off-topic. While I do not see the grave dangers of naked short selling (selling shares one does not own without first having actual shares borrowed), I feel it distorts supply/demand signals in markets and can have ill-defined effects. I was thinking of an auction for loaning shares for shorting, where the price would be the interest rate or a rental rate. A simple sequential VCG auction might be used for this.
Afternote 3: Note that this does not maximize trading volumes. To maximize trading volumes, the lowest sell bid might be matched with the lowest feasible buy bid, but this destroys incentive compatibility. This loss of potential volume, might be an additional price of incentive compatibility. It is unclear which is more costly: the price of untruthfully higher sell bids and untruthfully lower buy bids, or the price of incentive compatibility. Yet, these are hypotheticals. What is certain is, the mechanism outlined above has nice revenue properties.
Afternote 4: In view of Postscript 1, it would be interesting to compare (in simulation) this mechanism and, supposing this is not how it is done now, existing trading mechanisms. The main thing to look out for would be the total (exchange-measured) trade surplus. To do this, asset prices might generated using a (possibly very) noisy factor model, and agent valuations might be generated using (possibly bad) estimates of the aforementioned factor model. Trading strategies may then be simulated given these synthetic pieces of information.
Afternote 5: In a purely symmetric buy-sell environment, this reduces to the median price mechanism, which is nice. It is also trivially efficient since whoever values the goods the most gets them first (and whoever values them the least get rid of them soonest).
Afternote 6: Obtaining full incentive compatibility may be a matter of selecting different prices for buyer and seller using distributions on the "enclosed" bidders. This becomes a matter of using the empirical distribution to compute adaptive probabilities of setting the buy price at B2 and the sell price at S2. In these cases, the "exchange" pockets the difference to enforce incentive compatibility.
Showing posts with label Policy Engineering. Show all posts
Showing posts with label Policy Engineering. Show all posts
Sunday, August 26, 2012
Sunday, July 15, 2012
Handling the Defence of Singapore in the 21st Century
(Note: Post backdated to date of original writing.)
Two articles were published on TOC in June, Conscription: Necessary Or Outdated? (Bryan Cheang, 20 June 2012) and Rethinking Singapore’s Defence Needs (Rajiv Chaudhry, 25 June 2012), which I found to be rather off the mark. Thankfully, soon after, another article which had, I feel, a more realistic perspective on things, Conscription: The Missing Perspective (Benjamin Cheah, 3 July 2012), was posted. I would like to comment on what has been said and add, what I hope is, a little more to the discussion.
A "New Normal"??
It is naive to think that "in this age of moderation" a "new normal" has emerged characterized by all manner of warm and fuzzy sounding buzz words. Rajiv Chaudhry and, to a lesser extent, Bryan Cheang seem to think that everyone else is good and just today. But look at the way children act when unsupervised, how often do you see bigger kids taking things away from the smaller ones. Similarly, big dogs steal food from smaller dogs. In fact, for most living X's, big X's steal food from small X's unless the small X's are able to secure protection for themselves. Similarly, defence solutions have to give tangible security guarantees.
It is notable that the United States has been rather consistent in offering assistance to victims of aggression only when its interests are at stake. Certainly, Singapore has substantial strategic value as a friend to the United States, however this value to the USA is positional and is the same even is Singapore becomes an island of bombed out ruins. In the grand scheme of things, our economy is of little value to the USA, and we should remember that. More generally, military alliances and pacts to offer assistance can be breached if they are not in the counter-party's interests to honour the terms. We have to be aware that military intervention involves real costs that have to be justified from the point of view of others.
Lee Kuan Yew has one thing right: the truth about inter-country relations is that we can be friends only if we respect each others' strength. If friendships between sentimental human beings can be ephemeral, how much more fleeting can "friendships" between unfeeling nations be? Presently, deterrence is the only real way to be sure that military capabilities that can otherwise be used as a means to expropriate our property and sovereignty are not.
The Need to Intelligently Provision for Defence
I am no big fan of the SAF and its (often sycophantic) "high potentials", but let us not kid ourselves. The SAF must be sufficiently provisioned to, at least, give the semblance of being a credible force with considerable sting. The sting must be sufficiently strong to skew the cost-benefit analysis of whether or not to infringe on our sovereignty towards a "no". However, this sting comes at a cost, and we have to obtain and sustain military capabilities cost effectively. Thus, it is important that senior officers in the SAF do not adopt a "don't ask me about money, I only train" attitude or a "I only need to manage my multi-year acquisition over my tenure of two years and look good before I post out" attitude. This is not a casual swipe at career soldiers, these attitudes are not uncommon and are highly costly to Singapore. Management of those managing the acquisition and operation of military systems needs to account for the prevailing incentives and structure remuneration and advancement in a manner that promotes military strength and cost effectiveness.
On the matter of manpower, I would argue that cutting the NS and reservist liabilities based on "what others are doing", as Rajiv Chaudhry suggests, is unthinking and silly. There are ways to do so intelligently but incrementally. Let me provide a simple example:
In the longer term, force structuring is the way forward to reducing ("right-sizing") the defence foot print. The ORBAT (Order of Battle) must be fluid, allowing reductions in some areas and increases in others. Capabilities will have to match the threat landscape, and capabilities that are less relevant have to be phased. Opposition to any reduction in command positions would reflect ego problems and rather than any substantive defence issue.
The Ability to Use Capabilities
The ability to effectively use equipment is crucial. The best soccer boots on an amateur team will not help them beat a barefoot Germany (because to use Brazil would simply be unfair). The man is more important than the machine.
During periods of tension, the best that can be done is to call men back for re-orientation with their equipment. How can it be expected that we will be able to use our equipment well. If technology is a force-multiplier, the lack of expertise in the use of that equipment is a force-divider. The natural question that arises is whether that number resolves to something greater or lesser than unity. Having this as the best option available to us seems to reflect a lack of foresight on the part of senior MINDEF/SAF officials/officers.
As equipment requires increasing amounts of practice and knowledge of its workings to use properly, the dictum that we do not want to have too many Singaporeans of working age tied up in the regular force has to be called into question. Economic output may suffer somewhat, but more soldiers will have the time required to build up their ability in the use of our high-tech equipment. This old assumption will have to be re-examined.
Conclusion
As Benjamin Cheah notes, the geography of the region puts us at a distinct strategic and tactical disadvantage. We have to be smart about how we handle defence. We must provision intelligently and ensure that our men have the ability to leverage our expensively obtained capabilities.
If we were to return to the issue of NS which started all this, in my mind, it would be appropriate to have a larger regular force for skill-development along with variable length NSF and reservist periods (based on demonstrated effectiveness). It might well turn out, that increased economic participation and longer economic life of Singapore males due to effective reductions in their NS liabilities more than pays for the increase in the size of the regular force.
Two articles were published on TOC in June, Conscription: Necessary Or Outdated? (Bryan Cheang, 20 June 2012) and Rethinking Singapore’s Defence Needs (Rajiv Chaudhry, 25 June 2012), which I found to be rather off the mark. Thankfully, soon after, another article which had, I feel, a more realistic perspective on things, Conscription: The Missing Perspective (Benjamin Cheah, 3 July 2012), was posted. I would like to comment on what has been said and add, what I hope is, a little more to the discussion.
A "New Normal"??
It is naive to think that "in this age of moderation" a "new normal" has emerged characterized by all manner of warm and fuzzy sounding buzz words. Rajiv Chaudhry and, to a lesser extent, Bryan Cheang seem to think that everyone else is good and just today. But look at the way children act when unsupervised, how often do you see bigger kids taking things away from the smaller ones. Similarly, big dogs steal food from smaller dogs. In fact, for most living X's, big X's steal food from small X's unless the small X's are able to secure protection for themselves. Similarly, defence solutions have to give tangible security guarantees.
It is notable that the United States has been rather consistent in offering assistance to victims of aggression only when its interests are at stake. Certainly, Singapore has substantial strategic value as a friend to the United States, however this value to the USA is positional and is the same even is Singapore becomes an island of bombed out ruins. In the grand scheme of things, our economy is of little value to the USA, and we should remember that. More generally, military alliances and pacts to offer assistance can be breached if they are not in the counter-party's interests to honour the terms. We have to be aware that military intervention involves real costs that have to be justified from the point of view of others.
Lee Kuan Yew has one thing right: the truth about inter-country relations is that we can be friends only if we respect each others' strength. If friendships between sentimental human beings can be ephemeral, how much more fleeting can "friendships" between unfeeling nations be? Presently, deterrence is the only real way to be sure that military capabilities that can otherwise be used as a means to expropriate our property and sovereignty are not.
The Need to Intelligently Provision for Defence
I am no big fan of the SAF and its (often sycophantic) "high potentials", but let us not kid ourselves. The SAF must be sufficiently provisioned to, at least, give the semblance of being a credible force with considerable sting. The sting must be sufficiently strong to skew the cost-benefit analysis of whether or not to infringe on our sovereignty towards a "no". However, this sting comes at a cost, and we have to obtain and sustain military capabilities cost effectively. Thus, it is important that senior officers in the SAF do not adopt a "don't ask me about money, I only train" attitude or a "I only need to manage my multi-year acquisition over my tenure of two years and look good before I post out" attitude. This is not a casual swipe at career soldiers, these attitudes are not uncommon and are highly costly to Singapore. Management of those managing the acquisition and operation of military systems needs to account for the prevailing incentives and structure remuneration and advancement in a manner that promotes military strength and cost effectiveness.
On the matter of manpower, I would argue that cutting the NS and reservist liabilities based on "what others are doing", as Rajiv Chaudhry suggests, is unthinking and silly. There are ways to do so intelligently but incrementally. Let me provide a simple example:
- Consider having only 7 compulsory ICTs, the last of which is an ATEC assessment. If the reservist battalion passes, they are done with their reservist liability and will transition into the MINDEF Reserve. Otherwise they will come back for the 8th, 9th and perhaps 10th re-test sessions. This gives the incentive to build competence and also cuts the effective liability.
In the longer term, force structuring is the way forward to reducing ("right-sizing") the defence foot print. The ORBAT (Order of Battle) must be fluid, allowing reductions in some areas and increases in others. Capabilities will have to match the threat landscape, and capabilities that are less relevant have to be phased. Opposition to any reduction in command positions would reflect ego problems and rather than any substantive defence issue.
The Ability to Use Capabilities
The ability to effectively use equipment is crucial. The best soccer boots on an amateur team will not help them beat a barefoot Germany (because to use Brazil would simply be unfair). The man is more important than the machine.
During periods of tension, the best that can be done is to call men back for re-orientation with their equipment. How can it be expected that we will be able to use our equipment well. If technology is a force-multiplier, the lack of expertise in the use of that equipment is a force-divider. The natural question that arises is whether that number resolves to something greater or lesser than unity. Having this as the best option available to us seems to reflect a lack of foresight on the part of senior MINDEF/SAF officials/officers.
As equipment requires increasing amounts of practice and knowledge of its workings to use properly, the dictum that we do not want to have too many Singaporeans of working age tied up in the regular force has to be called into question. Economic output may suffer somewhat, but more soldiers will have the time required to build up their ability in the use of our high-tech equipment. This old assumption will have to be re-examined.
Conclusion
As Benjamin Cheah notes, the geography of the region puts us at a distinct strategic and tactical disadvantage. We have to be smart about how we handle defence. We must provision intelligently and ensure that our men have the ability to leverage our expensively obtained capabilities.
If we were to return to the issue of NS which started all this, in my mind, it would be appropriate to have a larger regular force for skill-development along with variable length NSF and reservist periods (based on demonstrated effectiveness). It might well turn out, that increased economic participation and longer economic life of Singapore males due to effective reductions in their NS liabilities more than pays for the increase in the size of the regular force.
On Casino Entry: Lessons from Credit Card Approval Requirements
Earlier this month, Minister of State for Finance Josephine Teo revealed to Parliament that casino entry levy fees collected by the government in the past 18 months reached S$288 million. (A daily entry levy of S$100 and annual entry levy of S$2,000 is imposed on Singaporeans and permanent residents seeking to enter the casinos.)
It strikes me that while the casinos were advertised to be an additional draw in our tourism portfolio, with an "effective" barrier to locals frittering away their hard-earned (and low by international standards) salaries in the form of levies, they have nevertheless "been very effective at drawing locals".
I believe that this is undesirable and it is important that more effective barriers to entry be put up to prevent gambling-led destitution. One way to do this is hinted at by another, albeit more pleasant, route to ruinous debt: the credit card.
Under the Monetary Authority of Singapore (MAS) guidelines, to be eligible to apply for a credit card, one needs to be (i) at least 21 years old and (ii) earn an annual declared income of at least S$30,000 for citizens and S$45,000 for PRs. In addition to the minimum requirements set by the MAS, individual banks may impose additional requirements for card holding.
This regulation makes it more likely that card holders have the capacity to afford the easy spending that credit cards facilitate. Furthermore, ones monthly salary also goes into determining one's credit limit. Similar income based requirements would be more suitable than a flat S$100 daily levy.
Singapore Citizens and PRs who wish to gamble should first become "members" of the casino, with membership being granted on the basis of a minimum annual salary which should be checked on an annual basis (e.g. via CPF contributions). Furthermore, a "member's" annual salary should determine a monthly chip exchange limit.
This might let those between jobs slip through the cracks somewhat, but the regular CPF contribution checks should close the gap quickly enough.
At this point, I have no good answer for how to handle retirees. It may be too intrusive to look at entire CPF balances to determine chip exchange limits. However, annuity sizes might provide a guide for doing this.
I think we have to be smarter about dealing with the gambling problem. What we have is grossly insufficient.
It strikes me that while the casinos were advertised to be an additional draw in our tourism portfolio, with an "effective" barrier to locals frittering away their hard-earned (and low by international standards) salaries in the form of levies, they have nevertheless "been very effective at drawing locals".
I believe that this is undesirable and it is important that more effective barriers to entry be put up to prevent gambling-led destitution. One way to do this is hinted at by another, albeit more pleasant, route to ruinous debt: the credit card.
Under the Monetary Authority of Singapore (MAS) guidelines, to be eligible to apply for a credit card, one needs to be (i) at least 21 years old and (ii) earn an annual declared income of at least S$30,000 for citizens and S$45,000 for PRs. In addition to the minimum requirements set by the MAS, individual banks may impose additional requirements for card holding.
This regulation makes it more likely that card holders have the capacity to afford the easy spending that credit cards facilitate. Furthermore, ones monthly salary also goes into determining one's credit limit. Similar income based requirements would be more suitable than a flat S$100 daily levy.
Singapore Citizens and PRs who wish to gamble should first become "members" of the casino, with membership being granted on the basis of a minimum annual salary which should be checked on an annual basis (e.g. via CPF contributions). Furthermore, a "member's" annual salary should determine a monthly chip exchange limit.
This might let those between jobs slip through the cracks somewhat, but the regular CPF contribution checks should close the gap quickly enough.
At this point, I have no good answer for how to handle retirees. It may be too intrusive to look at entire CPF balances to determine chip exchange limits. However, annuity sizes might provide a guide for doing this.
I think we have to be smarter about dealing with the gambling problem. What we have is grossly insufficient.
Monday, July 9, 2012
Universal Healthcare: Its Importance to the Economy and Incentivising the Proper Uses of Funds
(Note: Post backdated to date of original writing.)
Those that feel that universal healthcare is a bad idea typically point to the high utilizations in some jurisdictions as "proof" that it would increase the incentive to go to the doctor unnecessarily and for doctors to overcharge. Their arguments typically end there.
It is unfortunate that those naysayers who oppose universal healthcare appear to be unable to or seem to not be bothered to think of a way to reduce healthcare finance risk for Singaporeans while ensuring that funds are not drained unnecessarily. This is why I am a fan of The SDP's Healthcare Plan. They have made an effort to create a comprehensive scheme for healthcare finance which precisely reduces the healthcare finance risk for Singaporeans. It can be improved a little though (which is the subject of the second part of this note).
Healthcare Risk and the Larger Economy
It is certainly good to reduce one's the healthcare finance risk. But to see how it is important and not simply a "good to have", compare the following two lotteries (which are equal in expectation):
Supporting stability is one of the justifications that the Singapore government has given for all manner of political abuses. Yet while they wax lyrical about human resources being our most important resource, they hypocritically deny that resource the stability on which to build their lives. How then can a vibrant economy, based on enterprising Singaporeans, grow from the absence of personal stability?
Incentivising the Proper Use of Funds
Economic commentary aside, I would like to describe a simple framework for thinking about the usage of funds. I will acknowledge that uncontrolled availability of funds provides incentives to go the doctor unnecessarily and for doctors to overcharge. A fixed ratio co-payment scheme does not provide a complete answer as the co-payment is so small in some cases that unnecessary visits still occur (say, for the purposes of getting "medical leave"). The same fixed ratio may also result in an onerous payment should a necessary medical expense have a high base cost.
Now what is onerous and what is trivial depend on the size of the expense, its necessity and the income level of the one paying. If one earns less than $1000 a month, one would be careful not to waste $5 on an unnecessary medical co-payment (but would probably be willing to pay it out if actually sick). On the other hand, someone earning $5000 a month would gladly shell out the same $5 for a day of "medical leave". For the individual earning $1000 a month, a $2000 medical co-payment for a major procedure is extremely onerous. For the individual earning $5000 a month, it means forgoing a spa package: just a pinch. It is thus useful for co-payments to vary with (i) income levels and (ii) the size of the expense. I would add on to that set of criteria, (iii) the type of ailment being treated.
The why of (i) and (ii) should be clear. Small payments are not huge downsides that people have to be protected against. (And unnecessary trivialities are what the healthcare system should not be loaded with.) In contrast, large downsides have to be smoothed out.
On (iii), using the type of ailment as a criterion for determining the percentage of the co-payment can be explained based on the undesirability of various ailments. While NSFs have been known to eat toothpaste in the hope of contracting a "fever" to skive out of a 3-day outfield training exercise, I know of no one who willingly contracts diabetes or cancer. Co-payments should be lower for ailments which are "less likely to be abused". Notably, (iii) is far less important as a consideration than (i) and (ii), but it is included for "completeness".
An economist might call a scheme built using the above framework a "progressive incentive compatible co-payment scheme". These are nice sounding words: "progressive" refers to lower income individuals paying less for the same treatment and "incentive compatible" refers to the incentives to use the system only with necessary/the disincentives to use the system when unnecessary.
I will stop short of proposing co-payment percentages as it demands knowledge of how individuals at various income levels use their earnings, how serious various ailments are, as well as a number of other matters that I do not possess the relevant domain knowledge to comment on.
Summary
The level of healthcare finance risk is an important element determining individual economic stability. It is thus important to broadly reduce healthcare finance risk, as its reduction will give individuals more capacity to pursue ventures as opposed to locking money down to protect themselves against financial downsides associated with healthcare.
While cutting healthcare finance risk for individuals is important. It is important that state resources are used prudently. I have proposed a framework for developing co-payments that are progressive and "incentive compatible" to address this question. Comments on the framework are very much welcome.
Those that feel that universal healthcare is a bad idea typically point to the high utilizations in some jurisdictions as "proof" that it would increase the incentive to go to the doctor unnecessarily and for doctors to overcharge. Their arguments typically end there.
It is unfortunate that those naysayers who oppose universal healthcare appear to be unable to or seem to not be bothered to think of a way to reduce healthcare finance risk for Singaporeans while ensuring that funds are not drained unnecessarily. This is why I am a fan of The SDP's Healthcare Plan. They have made an effort to create a comprehensive scheme for healthcare finance which precisely reduces the healthcare finance risk for Singaporeans. It can be improved a little though (which is the subject of the second part of this note).
Healthcare Risk and the Larger Economy
It is certainly good to reduce one's the healthcare finance risk. But to see how it is important and not simply a "good to have", compare the following two lotteries (which are equal in expectation):
- 99% of the time you pay out $100, 1% of the time you pay out $100000
- 99% of the time you pay out $1000, 1% of the time you pay out $10900
Supporting stability is one of the justifications that the Singapore government has given for all manner of political abuses. Yet while they wax lyrical about human resources being our most important resource, they hypocritically deny that resource the stability on which to build their lives. How then can a vibrant economy, based on enterprising Singaporeans, grow from the absence of personal stability?
Incentivising the Proper Use of Funds
Economic commentary aside, I would like to describe a simple framework for thinking about the usage of funds. I will acknowledge that uncontrolled availability of funds provides incentives to go the doctor unnecessarily and for doctors to overcharge. A fixed ratio co-payment scheme does not provide a complete answer as the co-payment is so small in some cases that unnecessary visits still occur (say, for the purposes of getting "medical leave"). The same fixed ratio may also result in an onerous payment should a necessary medical expense have a high base cost.
Now what is onerous and what is trivial depend on the size of the expense, its necessity and the income level of the one paying. If one earns less than $1000 a month, one would be careful not to waste $5 on an unnecessary medical co-payment (but would probably be willing to pay it out if actually sick). On the other hand, someone earning $5000 a month would gladly shell out the same $5 for a day of "medical leave". For the individual earning $1000 a month, a $2000 medical co-payment for a major procedure is extremely onerous. For the individual earning $5000 a month, it means forgoing a spa package: just a pinch. It is thus useful for co-payments to vary with (i) income levels and (ii) the size of the expense. I would add on to that set of criteria, (iii) the type of ailment being treated.
The why of (i) and (ii) should be clear. Small payments are not huge downsides that people have to be protected against. (And unnecessary trivialities are what the healthcare system should not be loaded with.) In contrast, large downsides have to be smoothed out.
On (iii), using the type of ailment as a criterion for determining the percentage of the co-payment can be explained based on the undesirability of various ailments. While NSFs have been known to eat toothpaste in the hope of contracting a "fever" to skive out of a 3-day outfield training exercise, I know of no one who willingly contracts diabetes or cancer. Co-payments should be lower for ailments which are "less likely to be abused". Notably, (iii) is far less important as a consideration than (i) and (ii), but it is included for "completeness".
An economist might call a scheme built using the above framework a "progressive incentive compatible co-payment scheme". These are nice sounding words: "progressive" refers to lower income individuals paying less for the same treatment and "incentive compatible" refers to the incentives to use the system only with necessary/the disincentives to use the system when unnecessary.
I will stop short of proposing co-payment percentages as it demands knowledge of how individuals at various income levels use their earnings, how serious various ailments are, as well as a number of other matters that I do not possess the relevant domain knowledge to comment on.
Summary
The level of healthcare finance risk is an important element determining individual economic stability. It is thus important to broadly reduce healthcare finance risk, as its reduction will give individuals more capacity to pursue ventures as opposed to locking money down to protect themselves against financial downsides associated with healthcare.
While cutting healthcare finance risk for individuals is important. It is important that state resources are used prudently. I have proposed a framework for developing co-payments that are progressive and "incentive compatible" to address this question. Comments on the framework are very much welcome.
Friday, July 6, 2012
Conceptual Learning vs Skills
I am convinced of the need for comprehensive conceptual learning in schools as a pre-requisite for skill acquisition of good quality. Conceptual learning opens up the mind to possibilities and is more mentally intensive due to the need to tear-down and re-build internalized conceptions of how the world works or should work.
It is typically very difficult to successfully facilitate conceptual learning in a 5 day course unless it is particularly intensive or students are particularly open intellectually. Thus, in order for students to eventually develop updated skills, it appears that current and cutting edge thought should be imparted to them at schools. In that way, by the time cutting edge transits from "experimental prototype" to "advanced technology", students would have the proper intellectual structures to grasp the skills needed to use the said technology. Given today's rapid transition from research to industry, this is not entirely unreasonable as students will not be taught skills they cannot for the next 10 years.
There is a clear tension between the long term and the short term. Focusing on skills and neglecting newer paradigms leads to structural problems in the economy in the long term. Focusing on concepts and neglecting skills leads to workers that have a longer lead time to doing useful work.
Naturally, conceptual learning and skills are complements that reinforce each other. Concepts present an intellectual frame which helps in the understanding of skills. Skills can be inductively mined for concepts. However the relationship is not symmetric. The former is far easier and more comprehensive than the latter.
Thus, I believe that the balance should tilt towards the conceptual and the skills imparted should be those that best facilitate the learning of advanced concepts. A lead time reduction in one's early career of a few months is not sufficient to outweigh a decade or so of facility in picking up new skills.
It is typically very difficult to successfully facilitate conceptual learning in a 5 day course unless it is particularly intensive or students are particularly open intellectually. Thus, in order for students to eventually develop updated skills, it appears that current and cutting edge thought should be imparted to them at schools. In that way, by the time cutting edge transits from "experimental prototype" to "advanced technology", students would have the proper intellectual structures to grasp the skills needed to use the said technology. Given today's rapid transition from research to industry, this is not entirely unreasonable as students will not be taught skills they cannot for the next 10 years.
There is a clear tension between the long term and the short term. Focusing on skills and neglecting newer paradigms leads to structural problems in the economy in the long term. Focusing on concepts and neglecting skills leads to workers that have a longer lead time to doing useful work.
Naturally, conceptual learning and skills are complements that reinforce each other. Concepts present an intellectual frame which helps in the understanding of skills. Skills can be inductively mined for concepts. However the relationship is not symmetric. The former is far easier and more comprehensive than the latter.
Thus, I believe that the balance should tilt towards the conceptual and the skills imparted should be those that best facilitate the learning of advanced concepts. A lead time reduction in one's early career of a few months is not sufficient to outweigh a decade or so of facility in picking up new skills.
Thursday, June 28, 2012
Operationalizing HDB Balloting with Multiple Selections
Some thoughts:
Suppose we add 2 shoebox variants, 2rm+, 3rm+, 4rm+, actual 5rm+ for a new total of 11 flat types. Taking the shoeboxes out (shoeboxes relate more to "lifestyle choice" than "income"), we have 8 flat types that allows for better pegging to income level due to less "sandwiching".
Now there is a new problem of how to handle balloting since the number of flats per type becomes much smaller. It is no longer practical to ask for applicants to indicate only a single flat type. The reality is, it probably is more sensible to ask applicants to indicate 2 to 4 choices (in the same development) in order of preference. How to implement the balloting process now becomes the problem.
Given a few ballot orders and the preferences of balloters, how do we allocate flats well. Can we obtain an allocation where no two balloters would be willing to perform mutual swaps of numbers for one or more of their choices? (The "no-envy" condition.)
Let me describe a simple process that provides a result that satisfies that "no-envy" condition.
(If there are theoretical questions on the resulting ballot numbers I think I can answer them. Like given a set of ballot orders and preferences, is the "no envy" allocation generated from this random process unique? The answer to that one is no due to the random comparison order. So it is not "optimal" in a sense, though "optimal" is hard to quantify rigorously due to the number of conflicting interests. We'll leave theory to another day, if there is interest.)
On the other hand, if it is desirable to pare down the number of appointments on paper, it can be done, but the algorithm I can think of is not so rigorous. (A better way is to incentivize people to give up the appointments they do not really need through a small price discount, say $500 per appointment dropped.)
In any event, it is not hard to give those balloting for flats more choices. Why can't someone's application read:
- What kind of housing comfortably houses 1 person? What kind of housing comfortably houses 2 people? What kind of housing comfortably houses 2+1? And 2+2? How about 2+3? Is 2+4 even advisable given it is public housing?
Suppose we add 2 shoebox variants, 2rm+, 3rm+, 4rm+, actual 5rm+ for a new total of 11 flat types. Taking the shoeboxes out (shoeboxes relate more to "lifestyle choice" than "income"), we have 8 flat types that allows for better pegging to income level due to less "sandwiching".
Now there is a new problem of how to handle balloting since the number of flats per type becomes much smaller. It is no longer practical to ask for applicants to indicate only a single flat type. The reality is, it probably is more sensible to ask applicants to indicate 2 to 4 choices (in the same development) in order of preference. How to implement the balloting process now becomes the problem.
Given a few ballot orders and the preferences of balloters, how do we allocate flats well. Can we obtain an allocation where no two balloters would be willing to perform mutual swaps of numbers for one or more of their choices? (The "no-envy" condition.)
Let me describe a simple process that provides a result that satisfies that "no-envy" condition.
- Balloters get numbers for all the flats types that they have indicated a preference for. (Recall these are in the same development.)
- Pairs of balloters are compared in a random order to make them happier by mutual swaps of their ballot numbers. At the end of this process, the "no envy" condition will be satisfied.
(If there are theoretical questions on the resulting ballot numbers I think I can answer them. Like given a set of ballot orders and preferences, is the "no envy" allocation generated from this random process unique? The answer to that one is no due to the random comparison order. So it is not "optimal" in a sense, though "optimal" is hard to quantify rigorously due to the number of conflicting interests. We'll leave theory to another day, if there is interest.)
On the other hand, if it is desirable to pare down the number of appointments on paper, it can be done, but the algorithm I can think of is not so rigorous. (A better way is to incentivize people to give up the appointments they do not really need through a small price discount, say $500 per appointment dropped.)
In any event, it is not hard to give those balloting for flats more choices. Why can't someone's application read:
- Geylang (4 rm)
- Kallang (4 rm)
- Hougang (4 rm)
Wednesday, June 20, 2012
Illegal Subletting and Deterrent Penalties
Illegal subletting of HDB flats should be punished. Severely. It is a violation of the spirit of public housing. The question is, what is the appropriate penalty in monetary terms?
This is the expected number of months of rent that an illegal subletter expects to get:
This expression may not quite look right, but I assure you it can be obtained by summing
This, multiplied by the monthly rental, is the minimum fine that should be levied to make illegal subletters indifferent between obeying the law and trying their luck. Raising it a bit more would tip the scales in favour of the law.
Since the rental life of flats tend to be long, for any small probability of getting caught in any given month, the expected number of months of rental accrued is very high. For instance, if the probability of not getting caught in a given month is 0.995, then for a flat with a rental life of 20 years, the probability of not getting caught at all is about 0.3 (and the expected number of months of rent accrued is 139.94).
At a glance:
To use these tables, one might first make a ballpark estimate of the probability of an illegal subletter never getting caught given he/she illegally rents out part of his/her flat for some number of years. Using the second table, a value for p can be estimated. Then the first table can be used to identify the right ballpark of a deterrent fine.
In any event, all this tells us that since it is very unlikely to ever get caught, the rental that an illegal subletter expects to accrue is extremely high. Therefore, unless there are stiff penalties such as large enough fines or repossession of the flat by HDB, illegal subletters will continue to ply their trade.
This is the expected number of months of rent that an illegal subletter expects to get:
- (1-p12N)/(1-p)
This expression may not quite look right, but I assure you it can be obtained by summing
- Sum[k=0 to 12N-1] (k+1) pk(1-p)
- Sum[k=12N to ∞] 12N pk(1-p)
This, multiplied by the monthly rental, is the minimum fine that should be levied to make illegal subletters indifferent between obeying the law and trying their luck. Raising it a bit more would tip the scales in favour of the law.
Since the rental life of flats tend to be long, for any small probability of getting caught in any given month, the expected number of months of rental accrued is very high. For instance, if the probability of not getting caught in a given month is 0.995, then for a flat with a rental life of 20 years, the probability of not getting caught at all is about 0.3 (and the expected number of months of rent accrued is 139.94).
At a glance:
| Expected Months of Rental Collected | Rental Life N (years) | ||||
|---|---|---|---|---|---|
| 5 | 10 | 15 | 20 | ||
| p | 0.9975 | 55.7815 | 103.784 | 145.0924 | 180.6402 |
| 0.995 | 51.9478 | 90.4027 | 118.8694 | 139.9422 | |
| 0.9925 | 48.4603 | 79.3076 | 98.9434 | 111.4425 | |
| 0.99 | 45.2843 | 70.062 | 83.6192 | 91.0371 | |
| 0.9875 | 42.3889 | 62.3175 | 71.6868 | 76.0916 | |
| 0.985 | 39.7462 | 55.796 | 62.277 | 64.8941 | |
| 0.9825 | 37.3314 | 50.2742 | 54.7615 | 56.3172 | |
| 0.98 | 35.1223 | 45.5731 | 48.6828 | 49.6081 | |
| 0.9775 | 33.0989 | 41.5482 | 43.7051 | 44.2557 | |
| 0.975 | 31.2434 | 38.083 | 39.5803 | 39.9081 | |
| 0.9725 | 29.5396 | 35.083 | 36.1233 | 36.3185 | |
| 0.97 | 27.9731 | 32.4714 | 33.1947 | 33.311 | |
| 0.9675 | 26.5311 | 30.1855 | 30.6888 | 30.7582 | |
| 0.965 | 25.2019 | 28.174 | 28.5246 | 28.5659 | |
| 0.9625 | 23.9751 | 26.395 | 26.6392 | 26.6639 | |
| 0.96 | 22.8412 | 24.8136 | 24.9839 | 24.9986 | |
| 0.9575 | 21.7919 | 23.4011 | 23.5199 | 23.5287 | |
| 0.955 | 20.8194 | 22.1337 | 22.2166 | 22.2219 | |
| 0.9525 | 19.9171 | 20.9914 | 21.0493 | 21.0525 | |
| 0.95 | 19.0786 | 19.9576 | 19.998 | 19.9999 | |
| Probability of Non-detection | Rental Life N (years) | ||||
|---|---|---|---|---|---|
| 5 | 10 | 15 | 20 | ||
| p | 0.9975 | 0.8605 | 0.7405 | 0.6373 | 0.5484 |
| 0.995 | 0.7403 | 0.548 | 0.4057 | 0.3003 | |
| 0.9925 | 0.6365 | 0.4052 | 0.2579 | 0.1642 | |
| 0.99 | 0.5472 | 0.2994 | 0.1638 | 0.0896 | |
| 0.9875 | 0.4701 | 0.221 | 0.1039 | 0.0489 | |
| 0.985 | 0.4038 | 0.1631 | 0.0658 | 0.0266 | |
| 0.9825 | 0.3467 | 0.1202 | 0.0417 | 0.0144 | |
| 0.98 | 0.2976 | 0.0885 | 0.0263 | 7.84E-3 | |
| 0.9775 | 0.2553 | 0.0652 | 0.0166 | 4.25E-3 | |
| 0.975 | 0.2189 | 0.0479 | 0.0105 | 2.30E-3 | |
| 0.9725 | 0.1877 | 0.0352 | 6.61E-3 | 1.24E-3 | |
| 0.97 | 0.1608 | 0.0259 | 4.16E-3 | 6.69E-4 | |
| 0.9675 | 0.1377 | 0.019 | 2.61E-3 | 3.60E-4 | |
| 0.965 | 0.1179 | 0.0139 | 1.64E-3 | 1.93E-4 | |
| 0.9625 | 0.1009 | 0.0102 | 1.03E-3 | 1.04E-4 | |
| 0.96 | 0.0864 | 7.46E-3 | 6.44E-4 | 5.56E-5 | |
| 0.9575 | 0.0738 | 5.45E-3 | 4.03E-4 | 2.97E-5 | |
| 0.955 | 0.0631 | 3.98E-3 | 2.52E-4 | 1.59E-5 | |
| 0.9525 | 0.0539 | 2.91E-3 | 1.57E-4 | 8.46E-6 | |
| 0.95 | 0.0461 | 2.12E-3 | 9.78E-5 | 4.50E-6 | |
To use these tables, one might first make a ballpark estimate of the probability of an illegal subletter never getting caught given he/she illegally rents out part of his/her flat for some number of years. Using the second table, a value for p can be estimated. Then the first table can be used to identify the right ballpark of a deterrent fine.
In any event, all this tells us that since it is very unlikely to ever get caught, the rental that an illegal subletter expects to accrue is extremely high. Therefore, unless there are stiff penalties such as large enough fines or repossession of the flat by HDB, illegal subletters will continue to ply their trade.
Tuesday, June 19, 2012
Creating a Support Structure for the Poor
I just read The Malay Underclass, an essay by some final year students from NTU about the socio-economic challenges facing lower income Malays.
(Actually, I realize I forgot to post this from some time ago.)
I believe that we can provide an additional support structure for low-income families. Let me describe what I have in mind. It all begins with the schools. I propose that primary and secondary schools provide additional tuition to kids from low-income families for most days of the school week (all for primary school kids). Meals should be provided (lunch and dinner). This allows the parents to work to support their families while their kids are under supervision. For the older kids (sec 1 and above), they should not be going through "tuition" every day, but rather, helping out at the sessions for the younger children.
Thus, kids from low-income families will be learning under some supervision and learning responsibility. The younger ones will have role models to look up to. Given this, it is far more likely that these children will be able to achieve better educational outcomes and learn some life skills that will stand them in good stead when it comes to tertiary education and the working world. In addition, those who are going through tertiary education should volunteer a few days a month to help out as well. I think of this as a socially meaningful form of "national service", but one where Kids first receive "full time" care and then come back as "reservists" to pay it forward. Furthermore, each kid gets a concrete sense that he/she is doing good for someone else. (To reinforce this, the parents of kids under full time care should be asked to attend a biannual ceremony to thank the teachers and students who have given up time and energy to help out in the program.)
Perhaps with programs like that in place, we can provide better and more effective support for low income families. In time, hopefully the program will no longer be necessary. Eventually only being preserved in the fond memories of graduates of the program who remember how their seniors paid it forward.
(Actually, I realize I forgot to post this from some time ago.)
I believe that we can provide an additional support structure for low-income families. Let me describe what I have in mind. It all begins with the schools. I propose that primary and secondary schools provide additional tuition to kids from low-income families for most days of the school week (all for primary school kids). Meals should be provided (lunch and dinner). This allows the parents to work to support their families while their kids are under supervision. For the older kids (sec 1 and above), they should not be going through "tuition" every day, but rather, helping out at the sessions for the younger children.
Thus, kids from low-income families will be learning under some supervision and learning responsibility. The younger ones will have role models to look up to. Given this, it is far more likely that these children will be able to achieve better educational outcomes and learn some life skills that will stand them in good stead when it comes to tertiary education and the working world. In addition, those who are going through tertiary education should volunteer a few days a month to help out as well. I think of this as a socially meaningful form of "national service", but one where Kids first receive "full time" care and then come back as "reservists" to pay it forward. Furthermore, each kid gets a concrete sense that he/she is doing good for someone else. (To reinforce this, the parents of kids under full time care should be asked to attend a biannual ceremony to thank the teachers and students who have given up time and energy to help out in the program.)
Perhaps with programs like that in place, we can provide better and more effective support for low income families. In time, hopefully the program will no longer be necessary. Eventually only being preserved in the fond memories of graduates of the program who remember how their seniors paid it forward.
Tuesday, June 5, 2012
On Effective Incentives at Universities
University faculty members have different profiles. Simplistically, there are (i) those focused on research and/or industrial collaboration, (ii) those who emphasize teaching, and (iii) some who blend the two in a relatively balanced ratio. Both the functions of (i) and (ii) are important, but the former is seen as the more glamorous among faculty members and university promotion boards and search committees. Coming from the perspective of the university as a tool to support a nation's sustained competitive advantage, teaching edges out research and industrial collaboration in importance.
To develop effective incentives, we have to be a little hard nosed and be willing to bruise a few egos. We must face the fact that the "university system" has used the inventions and discoveries of a few talented individuals to justify the "contemplative life" for manifold numbers of others. The proliferation of uninteresting journal articles and conference papers is but a symptom of this.
"Research" takes pole position in universities as search and promotion preferences make clear. Those with personal leanings towards teaching advanced subjects effectively are edged out of the faculty or are forced to do "research" that turns out to be uninteresting (and they probably never get tenure anyway).
In Singapore, government ownership of universities allows changes to be made to align incentives in universities with national economic objectives. One way is to allow all faculty members to do what they do best. There are two related ways of measuring performance: absolute and relative (rank order). Additionally, there are different metrics by which performance can be measured. For instance, (i) the research productivity-industrial grants ruler, (ii) the teaching evaluation-student performance (in later courses) ruler, and hybrid metrics. Faculty members should be evaluated on all measures in absolute terms, and also have his/her rank on each measure computed. Remuneration and promotion should be based on all those measures.
To give a sense of what I am alluding to, consider the following. In principle we want to reward the top ranked performers, but at the highest levels of academic research performance, rank means little, so all top tier researcher (by absolute performance) should be rewarded highly regardless of rank; rank should only come in at the "lower" tiers. This conduces to the creation of a group with many top tier researchers and encourages faculty to move into the top rung. On teaching, similar incentives should be in place. Appropriate performance measurement logic should be there to "determine" the "role" each faculty member has crafted for himself/herself and use only the appropriate performance metrics.
The illustration in the above paragraph may seem a bit sketchy, but should give a flavor of what I am thinking. Incentives should be there to encourage faculty members to perform at the highest levels of performance of research and/or teaching. Staff who are mediocre at both over a sustained period should be let go. The university system should not be a place where only the forms of research are aped and knowledge is purported to be transferred. It should be a place where research is done and knowledge is transferred effectively.
---
Postscript: I'm writing this while "stuck in Rome". My passport was stolen from my left pant pocket on a crowded train 4h before my flight. The embassy was closed, and the police report was not accepted as a valid document for traveling out of Europe. When I got in touch with MFA, and through them the local Singapore consulate, it turned out the Italian Honorary Consul General had died and consular authority was transferred to Geneva. I was stunned to hear that. It all made things more surreal. Even stranger was when, today, I got an SMS from DBS Cards telling me that "I" had charged $15xx.xx for a United Airlines flight from the Las Vegas, Nevada branch. Woo.
To develop effective incentives, we have to be a little hard nosed and be willing to bruise a few egos. We must face the fact that the "university system" has used the inventions and discoveries of a few talented individuals to justify the "contemplative life" for manifold numbers of others. The proliferation of uninteresting journal articles and conference papers is but a symptom of this.
"Research" takes pole position in universities as search and promotion preferences make clear. Those with personal leanings towards teaching advanced subjects effectively are edged out of the faculty or are forced to do "research" that turns out to be uninteresting (and they probably never get tenure anyway).
In Singapore, government ownership of universities allows changes to be made to align incentives in universities with national economic objectives. One way is to allow all faculty members to do what they do best. There are two related ways of measuring performance: absolute and relative (rank order). Additionally, there are different metrics by which performance can be measured. For instance, (i) the research productivity-industrial grants ruler, (ii) the teaching evaluation-student performance (in later courses) ruler, and hybrid metrics. Faculty members should be evaluated on all measures in absolute terms, and also have his/her rank on each measure computed. Remuneration and promotion should be based on all those measures.
To give a sense of what I am alluding to, consider the following. In principle we want to reward the top ranked performers, but at the highest levels of academic research performance, rank means little, so all top tier researcher (by absolute performance) should be rewarded highly regardless of rank; rank should only come in at the "lower" tiers. This conduces to the creation of a group with many top tier researchers and encourages faculty to move into the top rung. On teaching, similar incentives should be in place. Appropriate performance measurement logic should be there to "determine" the "role" each faculty member has crafted for himself/herself and use only the appropriate performance metrics.
The illustration in the above paragraph may seem a bit sketchy, but should give a flavor of what I am thinking. Incentives should be there to encourage faculty members to perform at the highest levels of performance of research and/or teaching. Staff who are mediocre at both over a sustained period should be let go. The university system should not be a place where only the forms of research are aped and knowledge is purported to be transferred. It should be a place where research is done and knowledge is transferred effectively.
---
Postscript: I'm writing this while "stuck in Rome". My passport was stolen from my left pant pocket on a crowded train 4h before my flight. The embassy was closed, and the police report was not accepted as a valid document for traveling out of Europe. When I got in touch with MFA, and through them the local Singapore consulate, it turned out the Italian Honorary Consul General had died and consular authority was transferred to Geneva. I was stunned to hear that. It all made things more surreal. Even stranger was when, today, I got an SMS from DBS Cards telling me that "I" had charged $15xx.xx for a United Airlines flight from the Las Vegas, Nevada branch. Woo.
Wednesday, May 2, 2012
A "New" Paradigm for Rental
Much has been said about how ballooning rentals for business premises strangles businesses and curtails real economic growth. We could ask for lower rentals, but should rentals be lowered, spaces would then be under-priced and business owners would reap windfalls instead, leading to disgruntled landlords.
I'd like to briefly talk about a "new" paradigm for rental. The prohibition against usury in Islam has led to the creation of a set of investment principles called "Islamic banking". In Islamic banking, the lender also takes equity in the venture that money is being loaned out for. In modern parlance, we might say that borrower and lender are now "in it together", and the lender now has the incentive to provide support to the borrower to help the borrower to succeed.
Rentals can be formulated in a similar way. Rentals to be paid might be a ("low") flat rental rate with additional profit sharing. That way tenants need not fear poor business as the rental to be paid corresponds to how much revenue is collected. In addition, the owner of a building becomes more responsive to the needs of tenants and does not have to wait till the tenant's tenure is over to jack up rents.
How profit sharing takes place is an important detail. One possibility is for payment support to be provided by the landlord (credit card accounts, cash registers, etc.) and revenues to be recorded. This is not at all onerous for the owner of a building, and can make for stronger bargaining power with banks for the terms of payment services. (Ok, I'm aware that even the aggregation of all Capitaland malls is unlikely to make Visa or Mastercard budge.) Paranoid landlords can also have cameras installed watching the cash boxes to record possible cheating on the part of tenants. In any event, financial risk is reduced for both tenant and landlord (though admittedly more for the tenant). Furthermore, under such a system, landlords might obtain valuable information about consumption patterns that will certainly come in handy when, say, determining the tenant mix of a new mall.
On a more philosophical note, it may be time for the rentier capitalist economy of Singapore to transform into one where renter and borrower are in it together.
(Those familiar with the econo-operations management literature, might see this as a form of supply chain coordination that seeks to ameliorate the effects of "double marginalization" that leads to supply chain inefficiency.)
I'd like to briefly talk about a "new" paradigm for rental. The prohibition against usury in Islam has led to the creation of a set of investment principles called "Islamic banking". In Islamic banking, the lender also takes equity in the venture that money is being loaned out for. In modern parlance, we might say that borrower and lender are now "in it together", and the lender now has the incentive to provide support to the borrower to help the borrower to succeed.
Rentals can be formulated in a similar way. Rentals to be paid might be a ("low") flat rental rate with additional profit sharing. That way tenants need not fear poor business as the rental to be paid corresponds to how much revenue is collected. In addition, the owner of a building becomes more responsive to the needs of tenants and does not have to wait till the tenant's tenure is over to jack up rents.
How profit sharing takes place is an important detail. One possibility is for payment support to be provided by the landlord (credit card accounts, cash registers, etc.) and revenues to be recorded. This is not at all onerous for the owner of a building, and can make for stronger bargaining power with banks for the terms of payment services. (Ok, I'm aware that even the aggregation of all Capitaland malls is unlikely to make Visa or Mastercard budge.) Paranoid landlords can also have cameras installed watching the cash boxes to record possible cheating on the part of tenants. In any event, financial risk is reduced for both tenant and landlord (though admittedly more for the tenant). Furthermore, under such a system, landlords might obtain valuable information about consumption patterns that will certainly come in handy when, say, determining the tenant mix of a new mall.
On a more philosophical note, it may be time for the rentier capitalist economy of Singapore to transform into one where renter and borrower are in it together.
(Those familiar with the econo-operations management literature, might see this as a form of supply chain coordination that seeks to ameliorate the effects of "double marginalization" that leads to supply chain inefficiency.)
On "Economic Flexibility"
Being pinned down is no fun. It can be tremendously suffocating knowing that you are trapped and there is no way out. This is really the situation that many Singaporeans find themselves in. Young Singaporeans find themselves in low income jobs (as benchmarked to comparable work overseas). The necessity of a roof over their heads leads into expensive mortgages for houses whose title deeds their names are not on. It is a rut. A sad, sad rut.
The financial burden often deals a death blow to any enterprise that would entail risk. Aspirations are killed and with them, the possibility of a stronger, more vibrant, more productive economy. This may seem to be quite a logical leap, but it most assuredly does follow.
We are in need of new enterprises that generate real-value to rejuvenate our economy. The Singapore government knows this and is already gambling on what might generate, in public service lingo, the next S-curve. These businesses we need are certainly not the “safe” businesses that exploit the socio-politico-economic system to extract rents (or isomorphically, protection money). The desirable businesses will create goods and services that add-value to the lives of people or facilitate the conduct of people’s lives or businesses. Barring the most brilliant insights into consumer needs, almost all value-adding businesses will carry considerable financial risk as they will have to be operational before they can be revenue generating. The founders will have to raise capital by debt or (in the fortunate but rarer cases) issuing equity while running the risk of failure.
Many young people leave school with a different perspective on how things might be done. They have learnt about possibly new ways of doing things in school and after a year or two of hands-on work, they are ready to combine the updated perspective from the academy with their knowledge of current practices into a business. Unfortunately, the vicissitudes of the Singapore system catch up with them. Already a few hundred thousand in debt after paying for the lease of a HDB flat, the capacity to take on the additional risks of starting a business is lost.
What I hope for Singaporeans is Economic Flexibility. It is being released from the economic coercion of debt and financial risk and being able to pursue experiences and/or enterprises. While there is something primordially irreducible in start-up costs for businesses, we can do something about the financial burden that young Singaporeans are forced to shoulder. Possible angles of attack for this problem, which might yield huge dividends, are the cost of housing and the financial outcomes associated with the risk of medical disaster.
The SDP has published a proposal for a national healthcare insurance system and it looks good. In fact, I’m told that a number of doctors thanked the authors of the proposal for bringing up that important issue. Should that proposal or a variant of it be implemented, perhaps 90% of Singaporeans will have a substantial fraction of the financial risk associated with medical issues reduced.
From the housing angle, the first question to be asked is whether public housing has to cost so much. It turns out that construction costs are not as outrageous as HDB flat prices are. This is because flat prices consist of the construction cost, cost of overheads, and the cost of land. Based on the fact that flat prices have essentially doubled since 2005, while construction costs cannot be said to have increased by much, it then follows that land costs, which reflect market prices, must make up a large fraction of HDB flat prices. I’ve written about how we can create a public housing system that better meets the needs of Singaporeans without destabilizing the present housing market. (Tentatively, the reader may ignore the pricing recommendation. I've had a lot of push-back from people on the matter of pricing with auctions so it may detract from the point I'm trying to make here. The auction is for allocative efficiency and represents pure consumption of households. The article may be read as if a fixed price were recommended.) I’ve also written about how land pricing can be done on a rational basis which will enable shorter lease (hence, cheaper) flats to become attractive (LINK). In a nutshell, it is possible to quickly reduce the financial burden associated with housing costs without destabilizing the housing market.
Dealing with both healthcare and housing would certainly unshackle Singaporeans who will then be free to venture into business, invest, or pursue experiences. Economic flexibility is not just about money, it is about having flexibility in living life. This is a compelling vision for the future and I hope that we, as a nation, can get there.
The financial burden often deals a death blow to any enterprise that would entail risk. Aspirations are killed and with them, the possibility of a stronger, more vibrant, more productive economy. This may seem to be quite a logical leap, but it most assuredly does follow.
We are in need of new enterprises that generate real-value to rejuvenate our economy. The Singapore government knows this and is already gambling on what might generate, in public service lingo, the next S-curve. These businesses we need are certainly not the “safe” businesses that exploit the socio-politico-economic system to extract rents (or isomorphically, protection money). The desirable businesses will create goods and services that add-value to the lives of people or facilitate the conduct of people’s lives or businesses. Barring the most brilliant insights into consumer needs, almost all value-adding businesses will carry considerable financial risk as they will have to be operational before they can be revenue generating. The founders will have to raise capital by debt or (in the fortunate but rarer cases) issuing equity while running the risk of failure.
Many young people leave school with a different perspective on how things might be done. They have learnt about possibly new ways of doing things in school and after a year or two of hands-on work, they are ready to combine the updated perspective from the academy with their knowledge of current practices into a business. Unfortunately, the vicissitudes of the Singapore system catch up with them. Already a few hundred thousand in debt after paying for the lease of a HDB flat, the capacity to take on the additional risks of starting a business is lost.
What I hope for Singaporeans is Economic Flexibility. It is being released from the economic coercion of debt and financial risk and being able to pursue experiences and/or enterprises. While there is something primordially irreducible in start-up costs for businesses, we can do something about the financial burden that young Singaporeans are forced to shoulder. Possible angles of attack for this problem, which might yield huge dividends, are the cost of housing and the financial outcomes associated with the risk of medical disaster.
The SDP has published a proposal for a national healthcare insurance system and it looks good. In fact, I’m told that a number of doctors thanked the authors of the proposal for bringing up that important issue. Should that proposal or a variant of it be implemented, perhaps 90% of Singaporeans will have a substantial fraction of the financial risk associated with medical issues reduced.
From the housing angle, the first question to be asked is whether public housing has to cost so much. It turns out that construction costs are not as outrageous as HDB flat prices are. This is because flat prices consist of the construction cost, cost of overheads, and the cost of land. Based on the fact that flat prices have essentially doubled since 2005, while construction costs cannot be said to have increased by much, it then follows that land costs, which reflect market prices, must make up a large fraction of HDB flat prices. I’ve written about how we can create a public housing system that better meets the needs of Singaporeans without destabilizing the present housing market. (Tentatively, the reader may ignore the pricing recommendation. I've had a lot of push-back from people on the matter of pricing with auctions so it may detract from the point I'm trying to make here. The auction is for allocative efficiency and represents pure consumption of households. The article may be read as if a fixed price were recommended.) I’ve also written about how land pricing can be done on a rational basis which will enable shorter lease (hence, cheaper) flats to become attractive (LINK). In a nutshell, it is possible to quickly reduce the financial burden associated with housing costs without destabilizing the housing market.
Dealing with both healthcare and housing would certainly unshackle Singaporeans who will then be free to venture into business, invest, or pursue experiences. Economic flexibility is not just about money, it is about having flexibility in living life. This is a compelling vision for the future and I hope that we, as a nation, can get there.
Friday, April 6, 2012
Measuring the Efficacy of Education: A Possible Methodology
Given the mission of education to enable upward mobility, an obvious methodology for measuring the efficacy of education suggests itself: measure the decrease in the level of correlation of student performance on family background from primary 6 to secondary 4/5.
It goes without saying that student performance at Primary 6 is strongly related on family background. Given that secondary school is a substantial part of the Singapore education experience, where academic preferences are formed, the Secondary 4/5 level is a good time to make the comparison. In fact, a first reading may be obtained at the end of Primary 1/2, which will be very strongly related to family background.
Any competent econometrician would be ale to do the analysis given the data. We should be measuring this and using it as a KPI.
It goes without saying that student performance at Primary 6 is strongly related on family background. Given that secondary school is a substantial part of the Singapore education experience, where academic preferences are formed, the Secondary 4/5 level is a good time to make the comparison. In fact, a first reading may be obtained at the end of Primary 1/2, which will be very strongly related to family background.
Any competent econometrician would be ale to do the analysis given the data. We should be measuring this and using it as a KPI.
Sunday, March 11, 2012
A Practical Approach to Balancing the GST Burden
One way of making GST less regressive would be to simply make it progressive along the lines of income tax. (As an amusing side effect, children would be exposed to how to calculate income taxes.)
Consider the following (consumption) tax rate scale:
In this tax regime, it makes sense to levy taxes at the "item level", meaning that a multi-item purchase would have tax assessed on items individually before everything is aggregated to give the final payment amount. This would enable sticker prices to continue to make sense, and would prevent perverse incentives to perform "purchase splitting".
Consider the following (consumption) tax rate scale:
- First $5 at 4.0% (Up to $5; GST up to $0.20)
- Next $5 at 4.5% (Up to $10; GST up to $0.43)
- Next $5 at 5.0% (Up to $15; GST up to $0.68)
- Next $5 at 5.5% (Up to $20; GST up to $0.95)
- Next $30 at 6.0% (Up to $50; GST up to $2.75)
- Next $50 at 6.5% (Up to $100; GST up to $6.00)
- Next $400 at 7.0% (Up to $500; GST up to $34.00)
- Next $500 at 7.5% (Up to $1000; GST up to $71.50)
- Next $1000 at 8.0% (Up to $2000; GST up to $151.50)
- Next $1000 at 8.5% (Up to $3000; GST up to $236.50)
- Next $2000 at 9.0% (Up to $5000; GST up to $416.50)
- Next $5000 at 9.5% (Up to $10000; GST up to $891.50)
- Item value above $10000 taxed at 10.0%
- Fairprice Kaya (400g) costing $2.40: $2.40 at 4.0%, GST $0.10.
- McSpicy Double Meal (Upsized) costing $8.80: $0.20 on first $5, remaining $3.80 at 4.5%, GST $0.37 (Effective rate: 4.22%).
- Dell UltraSharp U2412M 24" LED Widescreen Monitor costing $299.00: $6.00 on first $100, remaining $199.00 at 7.0%, GST $19.93 (Effective rate: 6.67%).
- Kate Spade Signature Spade costing $429.00: $6.00 on first $100, remaining $329.00 at 7.0%, GST $29.03 (Effective rate: 6.77%).
- XFX Radeon 7970 Black Edition 3GB costing $938.00: $34.00 on first $500, remaining $438.00 at 7.5%, GST $66.85 (Effective rate: 7.13%).
- Qatar Airways Economy SG to Paris, Rome to SG (incl. taxes) costing $1030.30: $71.50 on first $1000, remaining $30.30 at 8.0%, GST $73.92 (Effective rate: 7.17%).
- iPad with Wi-Fi + 4G 64GB (3rd generation) costing $1088.00: $71.50 on first $1000, remaining $88.00 at 8.0%, GST $78.54 (Effective rate: 7.22%).
- Hermes HER Bag costing $1690.00: $71.50 on first $1000, remaining $690.00 at 8.0%, GST $126.70 (Effective rate: 7.50%).
- Hermes Picotin Bougainviller costing $3690.00: $236.50 on first $3000, remaining $690.00 at 9.0%, GST $298.60 (Effective rate: 8.09%).
- Toyota Prius 1.8 costing $170k: $891.50 on first $10k, remaining $160k at 10.0%, GST $16891.50 (Effective rate: 9.94%).
In this tax regime, it makes sense to levy taxes at the "item level", meaning that a multi-item purchase would have tax assessed on items individually before everything is aggregated to give the final payment amount. This would enable sticker prices to continue to make sense, and would prevent perverse incentives to perform "purchase splitting".
Cutting the NS Outlay while Improving "Readiness"
I would like to add detail to a previous post on revising National Service in view of the intent behind its original design and the strategic picture of defence today.
We can reduce the reservist cycle and at the same time increase our "readiness". In so far as "readiness" is positively associated with how seriously our reservists take their training, there is an obvious way to do both things simultaneously. Suppose we cut the reservist cycle down to 8 mandatory in-camp training sessions with at least 5 high-key sessions (down from 7), with up to 2 more high-key ICTs should performance in the ATEC appraisals not be satisfactory. (These appraisals are are done by assessors outside the unit in question.)
The incentives are clear. Soldiers will train hard for themselves and their friends to avoid the two possible "remedial training" sessions. By and large, we would expect to cut down the reservist cycle down to 8 in-camp sessions (down by 2 high-key ICTs) and experience an improvement in training standards. This is a win for the public purse, a win for the soldiers, and a win for national defence.
Once again, let me reiterate that cutting the cycle is realistic given the realities of modern warfare. The reader may refer to the previous article for the (short) argument. Now let me move to estimates of the potential annual cost savings.
With 35000 per cohort of NSFs/reservists, expected to be earning $3000 per month by the time they have served 8 ICTs, and given that a high-key ICT takes up at least 40% of the days of a month, the reduction will save about $84M. This is not too shabby, but it is only about 0.7% of the defence budget.
We can reduce the reservist cycle and at the same time increase our "readiness". In so far as "readiness" is positively associated with how seriously our reservists take their training, there is an obvious way to do both things simultaneously. Suppose we cut the reservist cycle down to 8 mandatory in-camp training sessions with at least 5 high-key sessions (down from 7), with up to 2 more high-key ICTs should performance in the ATEC appraisals not be satisfactory. (These appraisals are are done by assessors outside the unit in question.)
The incentives are clear. Soldiers will train hard for themselves and their friends to avoid the two possible "remedial training" sessions. By and large, we would expect to cut down the reservist cycle down to 8 in-camp sessions (down by 2 high-key ICTs) and experience an improvement in training standards. This is a win for the public purse, a win for the soldiers, and a win for national defence.
Once again, let me reiterate that cutting the cycle is realistic given the realities of modern warfare. The reader may refer to the previous article for the (short) argument. Now let me move to estimates of the potential annual cost savings.
With 35000 per cohort of NSFs/reservists, expected to be earning $3000 per month by the time they have served 8 ICTs, and given that a high-key ICT takes up at least 40% of the days of a month, the reduction will save about $84M. This is not too shabby, but it is only about 0.7% of the defence budget.
How Singapore's Sovereign Wealth Funds Should Invest
More strategic, less opportunistic. This spells things out simply. (I intend for this to be a very short blog post.)
We should not be doing too many investments of the opportunistic variety, such as taking apparently cheap equity in struggling banks. (Look where that has got us. I do not plan to look for where and how much the losses are. Suffice to say that they have amounted to billions over a very short time frame.)
Strategic investments in the obvious technologies of the future and the maturing technologies of tomorrow (... or next week) would make more sense from the point of view of national sustainability (also known as "relevance to the world").
With strategic investments in relatively young firms, growth potential exists. Furthermore, there is scope to use our large stakes to steer those firms towards collaborations with, or investments (building plants) in Singapore.
While this would remain a hit and miss process, any hit would increase our relevance to the world by putting us among other world leaders in the roll-out of some eventually ubiquitous technologies. As we have seen in the past years, capabilities spawn services. Our small size allows for an agility in roll-out that would allow our services sector to build and grow quickly locally with respect to a given capability. The next step: the world (or at least South East Asia).
In this respect, we need fewer "quantitative finance types", who mostly see value and risk as plain vanilla numbers handling our investments (this is harsh and pejorative but not too far off the mark). We need more technologists and academics, who would have a more strategic view of desired capabilities and technologies that might enable them, advising on acquisitions.
(It is my belief that fund managers with a risk profile featuring a high upside and no downside should not be running a national sovereign wealth fund.)
Our sovereign wealth funds have a unique opportunity to play a major role in bolstering our nation's future relevance to the world. Let us not throw that opportunity away.
We should not be doing too many investments of the opportunistic variety, such as taking apparently cheap equity in struggling banks. (Look where that has got us. I do not plan to look for where and how much the losses are. Suffice to say that they have amounted to billions over a very short time frame.)
Strategic investments in the obvious technologies of the future and the maturing technologies of tomorrow (... or next week) would make more sense from the point of view of national sustainability (also known as "relevance to the world").
With strategic investments in relatively young firms, growth potential exists. Furthermore, there is scope to use our large stakes to steer those firms towards collaborations with, or investments (building plants) in Singapore.
While this would remain a hit and miss process, any hit would increase our relevance to the world by putting us among other world leaders in the roll-out of some eventually ubiquitous technologies. As we have seen in the past years, capabilities spawn services. Our small size allows for an agility in roll-out that would allow our services sector to build and grow quickly locally with respect to a given capability. The next step: the world (or at least South East Asia).
In this respect, we need fewer "quantitative finance types", who mostly see value and risk as plain vanilla numbers handling our investments (this is harsh and pejorative but not too far off the mark). We need more technologists and academics, who would have a more strategic view of desired capabilities and technologies that might enable them, advising on acquisitions.
(It is my belief that fund managers with a risk profile featuring a high upside and no downside should not be running a national sovereign wealth fund.)
Our sovereign wealth funds have a unique opportunity to play a major role in bolstering our nation's future relevance to the world. Let us not throw that opportunity away.
Sunday, March 4, 2012
On "Land Costs" in Public Housing
Land costs are included in the price of Housing Development Board (HDB) flats to price the use of land over the tenure of the estate. The principle is sound as the occupancy of the land by the residents of that estate deprives others of the land over the span of their tenure. It recognizes that land is scarce and scarcity comes with an economic price. Thus, on top of construction costs and HDB's operational overhead, a component for the cost of land is included in the cost of flats.
Shorter Leases v.s. The Profit Motive
In Feb 2012, National Development Minister Khaw Boon Wan had said in a reply to Parliament in January that cutting short the lease of new flats to bring prices down may not be suitable for the needs of young couples. In fact, some young couples were lukewarm about the idea as well. One, who recently bought a Build-to-Order four-room flat in Sengkang for $320,000 and hopes to make at least a 10 per cent profit if they sell it, was quoted as saying:
This profit motive on the part of new flat owners is not unexpected, but it is both unreasonable and unsustainable. It is unreasonable to expect high risk-less returns, and rising housing prices that outstrip income growth impoverish younger generations and are, as such, unsustainable. To see why, first recognize that wages cannot grow faster than the general market, to have housing prices grow faster than that means both high resale profit and increasing unaffordability of housing.
The sale of a flat is termed "unlocking value". That itself is a figure of speech that precisely illustrates inaccessible value that cannot be directly used to achieve market outcomes like starting a business or funding the expansion of an existing one. A mindset shift on the part of Singaporeans must take place. Singaporeans should ask for low-cost housing without the expectation of capital gains, doing so with a mind to using the increased savings for entrepreneurial activity or investment. Singaporeans should expect to apply themselves in order to realize financial gain. This is important for our nation's future.
Pricing Shorter Leases: "Current Methods"
A senior real estate professional, quoted in the Straits Times this month, estimated that the price of a four-room Built-to-Order flat in Punggol with a 99-year lease would fall from $300k to $230k (by about 20%) if its lease were shortened to 60 years, and that the same flat would cost about $140k with a 30 year lease.
At first glance, the reduction in cost is too low to account for the much larger reduction in lease length. These figures were probably furnished to the couples that the Straits Times interviewed. With this in mind, it is retrospectively obvious that none would have been interested in such a raw deal.
Going back to that estimate, if one considers straight line depreciation with no residual value (both flat and land lease), and reads off the total value up to 60 years and 30 years respectively, it turns out that this means a discount rate of about 1.41%. Furthermore, this is uncannily accurate noting that we do have "more equations than unknowns" to work with.
Pricing Shorter Leases: A More Principled Method
It is agreeable the value of the flat should be depreciated over time. Not necessarily linearly, as flats are relatively well maintained in the early years, but the general idea is sound.
On the other hand, I believe that straight line depreciation with discounting should not be the basis the way land is priced. (I recognize that SLA may not actually price in this manner and the numbers might just happen to point to it, but when I see a bird that walks like a duck and swims like a duck and quacks like a duck, I call that bird a duck.)
The basis on which a land lease is priced is the degree to which it deprives other worthy purposes of the use of that land. This is an inherently probabilistic question not unlike those in risk analysis.
It stands to reason that the longer the lease, the more likely that some high value uses beyond the horizon are denied use of that land. Furthermore, it is reasonable to postulate that future land use possibilities would increase in value. In accordance with the history of technological progress, this should be exponential in the distance to the future. (Suggesting a geometric random walk with positive drift. This is geometric growth which is in contrast with the geometric decay of straight line depreciation with discounting.) As such, short leases should carry a disproportionately low price, while long leases should carry disproportionately higher prices. [Edit: An alternate perspective would be to note that the value of land uses grows roughly in tandem with the general stock market, which in turn, on average, grows at a rate much faster than general interest rates which tends to be the ball park of the discount rates used in discounted cash flow analyses.]
There is also a reasonably good analogy to cutting fixed price contracts with suppliers. In this context, one considers risk. Suppliers might be willing to commit to a certain price for a short time frame (say 5 years), but would be unwilling to do so over longer periods like (10 years) unless there is a substantial price premium. This is due to the increasingly higher uncertainty of market conditions as the period of commitment extends farther.
Under "future use/uncertainty pricing", the lease pricing outcome would be the opposite from what arises in straight line depreciation (with discounting over time). With straight-line depreciation and discounting, periods of flat ownership closer to the present day carry a larger portion of the "land cost". Under this principle of pricing, periods of flat ownership closer to the present day carry a smaller portion of the "land cost". (Subsequently, we will term this "Accelerating depreciation".)
This has large implications for the pricing of HDB flats, lease top-up pricing following en-bloc sales, and many other transactions. My interest, however, lies in how this, more principled, approach to pricing land impacts the viability of short tenure flats.
The following diagram illustrates the outcome of such a pricing method. It will be termed Hybrid pricing (Straight Line Depreciation for the flat and "Accelerating" Depreciation for the land) where the intermediate lease is priced. For simplicity, the cost of the flat and the cost of land for the 99-year lease are the same, and the discount rate is the same as the "rate of acceleration" for land depreciation.
Consulting Figure 1, for 30 year leases, the price of the 4-room BTO flat would be about $97k (compared to $140k), and for 60 year leases the price would be about $180k (compared to $230k). This looks like a much better deal. If the "rate of acceleration" were twice as high, the respective prices would be about $84k and about $159k. (Different rates may be set for different land uses based on historical trends in technology.) [Edit: The graph above presents a "market growth rate" only 1.41% faster than the interest rate. This is a gross underestimate by any account. If the difference were 3%, a 50 year lease would be priced at 20% of the 99 year lease. Why should this be so? Land pricing is about pricing lock-in.]
Given various lease lengths, an average monthly rent is implied. This is shown in Figure 2.
Notably, the main mechanism for the initial decline of the "Average Monthly Rent" is the initial rapid fall in value of the flat (and land in the standard case) due to depreciation and discounting. To reiterate a point made earlier, it does not make much sense to depreciate land.
To briefly digress (to make a polemical statement), studio apartments are 35 sq m to 45 sq m flats costing between $61,000 and $106,000. In contrast, four-room flats typically have a floor area of 90 sq m. Considering the preceding discussion, studio apartments are clearly disproportionately expensive, and it is now somewhat clear why they are priced this way. In view of the foregoing discussion, the present pricing scheme (or the apparent pricing scheme) is one that bilks seniors of their hard earned savings. This is not right.
It should be noted that there is room for confusion in the application of this concept. A partially used lease cannot be reasonably resold on this basis. Ostensibly, it is not equitable if the seller uses the cheaper part of the lease and leaves the buyer with the more expensive part. Examining the matter a bit more deeply, the original basis for pricing the land was, from the perspective of the state, a matter of optimal land use. The tenant of the land has no such considerations, and to him/her the land lease is depreciating capital and may be priced accordingly.
Economic Outcomes
Now, $97k for a 30 year lease is less than 16 months of income for the median household ($6307, including employer CPF contributions, monthly in 2011). For such a household, this is not very much and can be paid off in 3 years comfortably. Relatively early on one's life, one becomes debt free and gains the capacity to take on more debt financing to start a business (for the majority of start-ups that are unable to obtain VC funding).
It is important that people are given the freedom to flex their entrepreneurial muscle when they are young, or they, as many stories of regret will affirm, will find venturing out of their comfort zones too risky when they can. Financial security is a huge concern for a family with children. All things accounted for, the Singapore economy may be losing hundreds of millions in GDP each year due to the new value that would have been created.
Conclusion
A more principled way of pricing land would make shorter lease flats viable. Shorter lease flats would most likely be attractive to those of a more entrepreneurial bent, enabling them to quickly gain the capacity to start business ventures. This would increase the economic vibrancy of Singapore.
While less money would flow into state coffers, increased numbers of people (with some work experience under their belt) will start businesses. Presumably, these people would be aware of the current state of practice, and have enough drive to create businesses that implement better. This will strengthen the economy due to the successive creation of more-productive-than-average businesses.
Increased economic vibrancy has a strongly positive security implication. High productivity means relevance to the world. And relevance is something that we, as a "small resource-poor nation" that is generally represented in red on cartological depictions, cannot do without.
[Edit: In addition, it would be important for the SLA to gain clarity on how to price land using a value-centred approach. Where competition is available in the form of direct competitive bidding that might suffice, but when land is sold to other government agencies for uses like housing and education, then a more nuanced approach is necessary. Anything else might be harmful.]
Shorter Leases v.s. The Profit Motive
In Feb 2012, National Development Minister Khaw Boon Wan had said in a reply to Parliament in January that cutting short the lease of new flats to bring prices down may not be suitable for the needs of young couples. In fact, some young couples were lukewarm about the idea as well. One, who recently bought a Build-to-Order four-room flat in Sengkang for $320,000 and hopes to make at least a 10 per cent profit if they sell it, was quoted as saying:
- "I may pay less for a flat with shorter lease, but I don't want to be stuck with the property which will not be worth much 10 or 20 years down the road."
This profit motive on the part of new flat owners is not unexpected, but it is both unreasonable and unsustainable. It is unreasonable to expect high risk-less returns, and rising housing prices that outstrip income growth impoverish younger generations and are, as such, unsustainable. To see why, first recognize that wages cannot grow faster than the general market, to have housing prices grow faster than that means both high resale profit and increasing unaffordability of housing.
The sale of a flat is termed "unlocking value". That itself is a figure of speech that precisely illustrates inaccessible value that cannot be directly used to achieve market outcomes like starting a business or funding the expansion of an existing one. A mindset shift on the part of Singaporeans must take place. Singaporeans should ask for low-cost housing without the expectation of capital gains, doing so with a mind to using the increased savings for entrepreneurial activity or investment. Singaporeans should expect to apply themselves in order to realize financial gain. This is important for our nation's future.
Pricing Shorter Leases: "Current Methods"
A senior real estate professional, quoted in the Straits Times this month, estimated that the price of a four-room Built-to-Order flat in Punggol with a 99-year lease would fall from $300k to $230k (by about 20%) if its lease were shortened to 60 years, and that the same flat would cost about $140k with a 30 year lease.
At first glance, the reduction in cost is too low to account for the much larger reduction in lease length. These figures were probably furnished to the couples that the Straits Times interviewed. With this in mind, it is retrospectively obvious that none would have been interested in such a raw deal.
Going back to that estimate, if one considers straight line depreciation with no residual value (both flat and land lease), and reads off the total value up to 60 years and 30 years respectively, it turns out that this means a discount rate of about 1.41%. Furthermore, this is uncannily accurate noting that we do have "more equations than unknowns" to work with.
Pricing Shorter Leases: A More Principled Method
It is agreeable the value of the flat should be depreciated over time. Not necessarily linearly, as flats are relatively well maintained in the early years, but the general idea is sound.
On the other hand, I believe that straight line depreciation with discounting should not be the basis the way land is priced. (I recognize that SLA may not actually price in this manner and the numbers might just happen to point to it, but when I see a bird that walks like a duck and swims like a duck and quacks like a duck, I call that bird a duck.)
The basis on which a land lease is priced is the degree to which it deprives other worthy purposes of the use of that land. This is an inherently probabilistic question not unlike those in risk analysis.
It stands to reason that the longer the lease, the more likely that some high value uses beyond the horizon are denied use of that land. Furthermore, it is reasonable to postulate that future land use possibilities would increase in value. In accordance with the history of technological progress, this should be exponential in the distance to the future. (Suggesting a geometric random walk with positive drift. This is geometric growth which is in contrast with the geometric decay of straight line depreciation with discounting.) As such, short leases should carry a disproportionately low price, while long leases should carry disproportionately higher prices. [Edit: An alternate perspective would be to note that the value of land uses grows roughly in tandem with the general stock market, which in turn, on average, grows at a rate much faster than general interest rates which tends to be the ball park of the discount rates used in discounted cash flow analyses.]
There is also a reasonably good analogy to cutting fixed price contracts with suppliers. In this context, one considers risk. Suppliers might be willing to commit to a certain price for a short time frame (say 5 years), but would be unwilling to do so over longer periods like (10 years) unless there is a substantial price premium. This is due to the increasingly higher uncertainty of market conditions as the period of commitment extends farther.
Under "future use/uncertainty pricing", the lease pricing outcome would be the opposite from what arises in straight line depreciation (with discounting over time). With straight-line depreciation and discounting, periods of flat ownership closer to the present day carry a larger portion of the "land cost". Under this principle of pricing, periods of flat ownership closer to the present day carry a smaller portion of the "land cost". (Subsequently, we will term this "Accelerating depreciation".)
This has large implications for the pricing of HDB flats, lease top-up pricing following en-bloc sales, and many other transactions. My interest, however, lies in how this, more principled, approach to pricing land impacts the viability of short tenure flats.
The following diagram illustrates the outcome of such a pricing method. It will be termed Hybrid pricing (Straight Line Depreciation for the flat and "Accelerating" Depreciation for the land) where the intermediate lease is priced. For simplicity, the cost of the flat and the cost of land for the 99-year lease are the same, and the discount rate is the same as the "rate of acceleration" for land depreciation.
Figure 1: Comparison of Lease Pricing Methods
Consulting Figure 1, for 30 year leases, the price of the 4-room BTO flat would be about $97k (compared to $140k), and for 60 year leases the price would be about $180k (compared to $230k). This looks like a much better deal. If the "rate of acceleration" were twice as high, the respective prices would be about $84k and about $159k. (Different rates may be set for different land uses based on historical trends in technology.) [Edit: The graph above presents a "market growth rate" only 1.41% faster than the interest rate. This is a gross underestimate by any account. If the difference were 3%, a 50 year lease would be priced at 20% of the 99 year lease. Why should this be so? Land pricing is about pricing lock-in.]
Given various lease lengths, an average monthly rent is implied. This is shown in Figure 2.
Figure 2: Equivalent Monthly Rentals for Different Lease Pricing Methods
Notably, the main mechanism for the initial decline of the "Average Monthly Rent" is the initial rapid fall in value of the flat (and land in the standard case) due to depreciation and discounting. To reiterate a point made earlier, it does not make much sense to depreciate land.
To briefly digress (to make a polemical statement), studio apartments are 35 sq m to 45 sq m flats costing between $61,000 and $106,000. In contrast, four-room flats typically have a floor area of 90 sq m. Considering the preceding discussion, studio apartments are clearly disproportionately expensive, and it is now somewhat clear why they are priced this way. In view of the foregoing discussion, the present pricing scheme (or the apparent pricing scheme) is one that bilks seniors of their hard earned savings. This is not right.
It should be noted that there is room for confusion in the application of this concept. A partially used lease cannot be reasonably resold on this basis. Ostensibly, it is not equitable if the seller uses the cheaper part of the lease and leaves the buyer with the more expensive part. Examining the matter a bit more deeply, the original basis for pricing the land was, from the perspective of the state, a matter of optimal land use. The tenant of the land has no such considerations, and to him/her the land lease is depreciating capital and may be priced accordingly.
Economic Outcomes
Now, $97k for a 30 year lease is less than 16 months of income for the median household ($6307, including employer CPF contributions, monthly in 2011). For such a household, this is not very much and can be paid off in 3 years comfortably. Relatively early on one's life, one becomes debt free and gains the capacity to take on more debt financing to start a business (for the majority of start-ups that are unable to obtain VC funding).
It is important that people are given the freedom to flex their entrepreneurial muscle when they are young, or they, as many stories of regret will affirm, will find venturing out of their comfort zones too risky when they can. Financial security is a huge concern for a family with children. All things accounted for, the Singapore economy may be losing hundreds of millions in GDP each year due to the new value that would have been created.
Conclusion
A more principled way of pricing land would make shorter lease flats viable. Shorter lease flats would most likely be attractive to those of a more entrepreneurial bent, enabling them to quickly gain the capacity to start business ventures. This would increase the economic vibrancy of Singapore.
While less money would flow into state coffers, increased numbers of people (with some work experience under their belt) will start businesses. Presumably, these people would be aware of the current state of practice, and have enough drive to create businesses that implement better. This will strengthen the economy due to the successive creation of more-productive-than-average businesses.
Increased economic vibrancy has a strongly positive security implication. High productivity means relevance to the world. And relevance is something that we, as a "small resource-poor nation" that is generally represented in red on cartological depictions, cannot do without.
[Edit: In addition, it would be important for the SLA to gain clarity on how to price land using a value-centred approach. Where competition is available in the form of direct competitive bidding that might suffice, but when land is sold to other government agencies for uses like housing and education, then a more nuanced approach is necessary. Anything else might be harmful.]
Saturday, January 28, 2012
Implementing Proportional Representation within the GRC System
While it may not be popular to support the existence of GRCs, there are administrative arguments for the grouping of constituencies into GRCs in Singapore. However, the current implementation of the administrative grouping is poor. Parliamentary Elections for GRC seats are akin to a high stakes game where large fractions constituents of constituents will be disenfranchised. (e.g.: in a 55% - 45% result, 45% of the constituents are not represented by the team they voted for.)
Now, unless candidates from political parties are of such atrociously low quality as to be unable to work together with each other, there is a strong case for the use of Proportional Representation in Singapore. Having representatives from various political parties ensure that each constituents can be represented by the party they believe in (if that party has sufficient support for at least one representative to enter parliament).
Who Gets How Many Seats
In a Proportional Representation system for GRCs, voters vote for parties. There are various variants of Proportional Representation, but we shall adopt one where each party selects which of its candidates take the seats It wins. This variant is selected to address the legacy of race in Singapore politics. But before getting to that, an important aspect of implementing Proportional Representation should be dealt with.
The chief issue with Proportional Representation where there are small numbers of seats (less than 7, for instance) is how to allocate seats to parties in response to the realized vote-share realized by the participating parties. In principle, the number of seats each party wins in a GRC should be the fraction of votes won multiplied by the total number of seats available in that GRC. In practice, however, these numbers are never prefect whole numbers. Thus, it is important to deal with this matter in as fair a manner as possible.
This means that the objective is to use a rule of seat allocation that, in all cases, under-represents as few voters as possible, and over-represents as few voters as possible.
Going back to the example of the 55% - 45% result, if there were only a single seat (or the winning party took all seats), 55% of the constituents would be 81% over-represented and the remaining 45% would be unrepresented (infinitely under-represented/disenfranchised). In the case where there are two seats and one went to each party, the 55% would be 9% under-represented and the 45% would be 11% over-represented. This is a much better result. Now, in the case where there are three seats and 2 went to the party with a 55% vote-share and 1 went to the other party, the 55% would be 21% over-represented and the 45% would be 26% under-represented. Flipping this around, in the case where there are three seats and 1 went to the party with a 55% vote-share and 2 went to the other party, the 55% would be 39% under-represented and the 45% would be 48% over-represented.
Now, I would like to propose a truly optimal rule, so like many academics, I will shift the goal posts slightly. Philosophically, we might say that each constituent is allocated a representative holding a seat, and each representative in a GRC with K seats may be allocated to at most 1/K of all constituents. It is clear that almost always, even in the best case, some constituents will be allocated to a representative whose party he/she did not vote for. Now, we would like the number of such consituents to be as small as possible. With such an objective, it is easy to propose an optimal rule.
Now, suppose the vote share of each party i is given by v(i) and the total number of seats is N. Then the number of seats that party should get (in a world where seats are infinitely dividable) is f(i)=v(i)×N. Since this is not to be, each seat is to be taken by a single representative from some party. Now, party i is initially allocated a number of seats equal to f(i) rounded down. The remaining seats are allocated in order of how close each f(i) is to "the smallest whole number greater than f(i)" (a.k.a.: f(i) rounded up if f(i) is not a whole number, and f(i)+1 if f(i) is a whole number).
Using this rule, it is obvious that as few as possible voters are left unhappy ("allocated to a representative from a party they did not vote for"). This is because we made "unallocated" groups of voters "happy" in order of size. So the left over ("unhappy") groups are, thus, the smallest ones.
Before dealing with another important issue, here is a worked example. The vote share of three parties are 25%-45%-30% in a 6 seat GRC. This means 1.5-2.7-1.8 fractional seats. So the initial allocation is 1-2-1 seats with 2 balance seats. Now, 1.5 is 0.5 less than 2, 2.7 is 0.3 less than 3, and 1.8 is 0.2 less than 2. So, the third and then the second party are allocated an additional seat each, resulting in a 1-3-2 seat allocation. This means that (1.5-1)/6=0.5/6=8.33% of the electorate are left "unhappy". In a majority takes all system, 55% would be left "unhappy".
A Legacy Issue: Dealing with the Race
Now, race is a legacy issue that Singaporeans have to deal with. The ethnic integration policy that the PAP government implemented in 1989 to prevent the formation of racial enclaves led to the concern that minorities would be disenfranchised as they would not have the critical mass to vote minority candidates into parliament in a first-past-the-post voting system. While it is my hope that, eventually, race becomes a non-issue, I felt it necessary to have a reasonable answer to the question of how to deal with it.
Now, disenfranchisement is not a purely philosophical issue, and to resolve it in a Proportional Representation system one would have to argue that representation at a national-level is a sign of enfranchisement, and the lack absence of minority candidates at a local-level does not affect the level of aid that minorities receive. I will not bother to make the argument for the latter as other commentators have already made it for me, and the former is self-evident.
Now, Singapore's resident population is 74% Chinese. It would be reasonable, then to require that political parties to, of all the candidates they send to parliament over all GRCs, send at least one minority candidate for each four Chinese beyond the first four Chinese candidates. Arithmetically speaking, if the number of candidates that a party sends to parliament is greater than four, the ratio of Chinese candidates minus 4 to minority candidates sent to parliament should not be greater than 4. (e.g.: 4C, 3C+3M, 8C+1M are ok; 5C, 9C+1M are not ok.)
The above system is not perfect. It will fail in the event that the political landscape is so fragmented that small parties with small vote shares all put non-minority candidates into parliament. Thankfully, the political landscape in Singapore is far from being like that (so we can cross the bridge when we get there).
A more major problem would occur when the best candidates of political parties are non-minorities. As such, these candidates would effectively be the ones who carry the ground. Now, if this system results in any of the top candidates not being sent to parliament, then in a sense, voters would have been cheated. On the flip side, such a system would spur all parties to cultivate high-quality minority candidates, ensuring effective representation for minorities in the long run.
Conclusion?
I've sketched a practical means for implementing Proportional Representation in Singapore. In doing so, I have implicitly argued that the basis for using such a system would improve representation and reduce the extent of disenfranchisement. That is to say, it would further the democratization of Singapore.
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Afternote: I'm also an advocate for Approval Voting, which can be said to properly measure "the mandate of the people". (Refer to this past post for details.) I would like to think of a way to integrate Approval Voting with Proportional Representation. Unfortunately, the two obvious ways of doing this (interpreting approvals as full votes and interpreting approvals as fractional votes) are less than satisfactory.
Monday, January 16, 2012
Improving the Verification of Credentials for Foreign Professionals
In view of the fact of endemic college application fraud in China and India (supported by a cottage industry of "Application Agencies"), it would not be surprising that application fraud from those countries would extend to the realm of work permit and Permanent Residency applications. In fact, it seems that the most distrustful of college applications from China turn out to be college professors who are themselves China nationals. (I put it down to it being likely that they have encountered the "Application Agencies" on their visits home.)
Perhaps higher verification standards should be used by the Singapore government for verifying the credentials of foreign professionals. The both applications for Permanent Residency and Employment Passes require documentary evidence of degrees and diplomas. This takes the form of originals which are viewed and returned. The high level of professionalism of the fraud industry would make it hard for ICA staff to detect fraud even with their training and experience.
Now, applications for postgraduate studies typically require original transcripts, either with the application or before an offer is made (scans are accepted as a preliminary in those cases). These transcripts are required to have been sent directly from the degree awarding institution to the assessing body at the applicant's own expense (typically less than SGD 20). This additional layer of security might reduce fraud. Or, it might turn out to be another iteration in the fraud arms race. Ultimately, I see a business opportunity for Chinese and Indian university registrars. (Which may end with fraud penetrating the university registrar, leading eventually to fraudulent grades, and finally a painful bursting of the fraud bubble.)
The future has always been bright for the street smart and amoral.
Perhaps higher verification standards should be used by the Singapore government for verifying the credentials of foreign professionals. The both applications for Permanent Residency and Employment Passes require documentary evidence of degrees and diplomas. This takes the form of originals which are viewed and returned. The high level of professionalism of the fraud industry would make it hard for ICA staff to detect fraud even with their training and experience.
Now, applications for postgraduate studies typically require original transcripts, either with the application or before an offer is made (scans are accepted as a preliminary in those cases). These transcripts are required to have been sent directly from the degree awarding institution to the assessing body at the applicant's own expense (typically less than SGD 20). This additional layer of security might reduce fraud. Or, it might turn out to be another iteration in the fraud arms race. Ultimately, I see a business opportunity for Chinese and Indian university registrars. (Which may end with fraud penetrating the university registrar, leading eventually to fraudulent grades, and finally a painful bursting of the fraud bubble.)
The future has always been bright for the street smart and amoral.
Sunday, January 15, 2012
Towards a Ministerial Salary Scheme Designed for Inclusive Growth
I would like to talk about developing KPIs that are robust to manipulation. Before beginning, I would like to apologize in advance that this article will be slightly technical. It has to be as KPIs have to be properly designed to be aligned with social objectives (such as "inclusive growth").
This alignment with social objectives has to be done with the maximizing behaviour of individual policy makers in mind. It is thus natural to begin with a discussion on how systems of KPIs are "gamed" by those who are the subject of measurement, since their pay-offs (salaries) are essentially (increasing) functions of the KPIs.
Following the discussion on how KPIs are manipulated, I will cover why KPI manipulation should be taken into account. Then, I will comment on the manipulability properties of the current salary scheme. Finally, principles by which robust KPIs may be designed will be discussed. In the annex, I will run through the process of creating a salary scheme aligned with the objective of encouraging "inclusive growth".
Preliminaries on KPI Manipulation
As a preliminary to what follows, it should be stated clearly that the process of manipulation of a system of KPIs is essentially one of performing optimization to maximize one's pay-off. (Here, the term optimization is used here in the sense of attempting to maximize some pay-off function over all possible decisions.) In practice, optimization is based on manipulating the (policy) levers that one has control over.
Having spoken briefly about manipulation, let us consider "growth". One might summarize all forms of economic and technological engineering as effort directed at two objectives that may be concurrent: (i) improving efficiency to reach the efficiency frontier (where it is possible for every aspect to be improved without making any aspect perform more poorly; "transitioning to a better indifference curve"), and (ii) making the trade-offs that maximize one's benefit. Of the two, only (i) may be thought of as true growth and happens to be the more challenging objective, while (ii) is the task of selecting, from economically efficient alternatives, the one most beneficial to oneself.
Now, we are concerned about policy makers trading something that benefits them less for something that benefits them more. In other words, KPI manipulation. When a policy maker does that to increase his own pay-off, winners and losers are created. In simple economic (game theoretic) analysis (which assumes self-interested behaviour), the pay-offs for those winners and losers do not matter to the policy maker, who is only interested in his own pay-off.
Why Bother?
We cannot be so naive as to assume that intelligent people will not optimize for their own benefit. This will happen, and our policy makers are, at the very least, not stupid. As such, incentives have to be set up such that the maximizing behaviour of policy makers are aligned with social objectives.
To be cynical about the present government, a peg to the salaries top earners generates the incentive to implement precisely two types of policies: (i) those that encourage higher salaries for top earners and (ii) those which trade the welfare of non-top earners for higher salaries at the top. The only defence against this behaviour would be "human goodness" or "the threat of non-election". Game theory and common sense would tell us that appeals to the former are nothing but cheap talk. This configuration of incentives is undesirable. Incentives should be in place to directly support "inclusive growth" (or whatever policy objective is articulated) rather than leaving the objective out of the incentive system (which makes sense to office holders only if it is there for public consumption and is not, in fact, the true objective).
The current and proposed ministerial salary systems are textbook examples of incentive systems which are not aligned with the stated policy objective ("inclusive growth"). Subsequently, I will do a cursory analysis of the current ministerial salary scheme, which I will abbreviate as MSS.
An Analysis of the Current Salary Scheme
One important observation that can be made about the MSS is that some aspects of the growth objective are weighed much more heavily than others. In the MSS case, the ratio of the weight given to the salaries of top earners to those of low-income workers is extreme. Without bonuses (which is based on GDP growth), this ratio is infinity (i.e.: the income of low-income workers do not matter at all). Thus, the underlying optimization problem might be framed (polemically) as such:
It should be recognized that this is a simple model designed to be polemical. However, it highlights the fact that when (intelligent) policy makers optimize for their own benefit, it can negatively affect general welfare unless their incentives are aligned with the general good.
Principles of Design for a KPI System/Salary Scheme
"Inclusive growth" is a policy objective of the "general welfare" type. The other being of the "narrow quantum leap" variety such as "putting an man on the moon by the end of the 1960s". The former entails spreading out resources and the latter entails focusing them. Presently, I'd like to make suggestions of the kind of ingredients that might go into KPIs/salary formulas for policy objectives of the "general welfare" variety.
To ensure that no one is left behind, it is important to ensure that the KPIs do not make it profitable to lower the welfare of one group in favour of another. For instance, with a KPI such as C1 [Factor A] + C2 [Factor B], and a technological/economic aspect that allows trading of 1 unit of [Factor A] for 2 units of [Factor B] using 1 unit of "policy effort", unless the coefficient C1 is close enough to 2 C2, trade offs will be made that lower one of the factors to its minimum level. (For this example, if C1 - 2C2 exceeds 1, [Factor A] will be increased and [Factor B] decreased; and if 2C2 - C1 exceeds 1, [Factor B] will be increased and [Factor A] decreased. Also, for the more mathematically inclined, this example clearly brings out how "linear" KPIs without feasibility conditions/veto criteria can be dangerous.)
Trade offs are the essential mechanism by which KPIs are manipulated. (I know of no others and would be keen to learn of others.) If the effort to make a trade off is worthwhile for the self-interested policy maker, the motivation to make that trade-off will exist. This principle has other serious implications in the public sector which I decline to touch on at this point.
Now, the converse to the aforementioned principle (which is also true), is that if the effort to make a trade off is not worthwhile for the self-interested policy maker, the motivation to make that trade-off will not exist. I believe that if growing the pie becomes the only practical means of increasing their rewards and remuneration, policy makers' efforts can be focused to that end and it will be possible to promote objectives like "inclusive growth".
As a rule of thumb, the more broad-based a KPI is, the more effort required to make gains due to trade-offs. Furthermore, a broad-based KPI is precisely what is needed to measure "inclusive growth". (The more mathematically inclined might think of using a function of the minimum of a set of subsidiary KPIs, or a function of the a set of the "order statistics" of subsidiary KPIs, which would require that all/most sub-KPIs rise in order for the parent KPI to rise.)
Conclusion
I hope the forgoing discussion was useful and helped stimulate thought on how to design KPIs or a salary scheme to achieve policy objectives. We have discussed how the ability to make trade-offs allows policy makers to optimize their KPIs without growing the economic pie (or the per-capita economic pie) and how this can be dangerous. It has been suggested that if these trade-offs are no longer easy to make, it would be more profitable for policy makers to work on "increasing the general welfare" (as a chief means for increasing their pay-offs).
I would like to close with a suggestion of a Ministerial Salary Scheme that I believe is more compatible with "inclusive growth" than the existing and proposed ones. I will describe the development of that scheme and what motivates the various components of it. I hope that the principles outlined in this article will eventually be used in the development of an improved (and more rigorous) salary scheme. (The reader should be warned that math will be encountered.)
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Annex: A Proposed Ministerial Salary Scheme Designed for Inclusive Growth
Note that this does not consider MP allowances, which are (rightly) paid over and above ministerial salaries. The salary scheme will be based on a benchmark salary paid to a junior minister, with senior grades getting (arbitrary) multiples of that salary. This benchmark will move in response to changes in economic conditions and the economic performance of Singapore. Let us denote the benchmark salary for the year Y, as SY.
Suppose a target salary is computed using a scheme like that suggested by former NMP Siew Kum Hong and call it C2012 (where the 2012 refers to the year of the original benchmark and "C" is for consumption). For those who have not read Siew Kum Hong opinion piece, S2012 is the price of a basket of goods and services that amounts to a decent standard of living for someone of a minister's social standing. Now let CY be cost of the same basket of goods in year Y.
I would suggest that a minister's salary be partially inflation adjusted to make it robust to market changes. (This would be one perk of office, and is entirely arbitrary.) Suppose that (arbitrarily) that amounts to one third of the original basket of goods. The rest should move with the wage levels of Singaporeans.
Define the income at the α fractile (highest income among the lowest earning 100α % of working Singapore citizens.) in year Y is Iα,Y, and determine Kα such that 2/3 C2012 = Kα Iα,Y.
So we find that S2012 = C2012 = (1/3) C2012 + Kα Iα,2012 for all values of α, and we can benchmark ministerial salaries as
Suppose α were drawn from the set A = {0.05, 0.06, 0.07, ..., 0.99}. I start from the 5% level to avoid pathological low-income cases (such as refusal to work) and end at the 99% level. Now for any set of positive weights w0.05, w0.06, w0.07, ..., w0.99 corresponding to the elements of the set A such that they sum to 1 (Sum[α in A] wα = 1), the following holds: C2012 = (1/3) C2012 + Sum[α in A] wα Kα Iα,2012. This leads to a fairly broad based benchmark:
Unemployment can be incorporated in this framework by including unemployed people in the income distribution. However, care should be taken to not build in the incentive for policy makers to introduce policies that introduce disincentives for home making and other economically valuable but unpaid work. This would require a lot more work to flesh out, so this will be left as an idea.
The final modification might appear a little complicated, but the idea is simple. We would like broad income growth and not income growth focused on the "easiest" part of the income distribution. Thus, we should consider the fractiles which have had the lowest growth since the benchmark year. Since A has 95 elements (95 possible values of α), we could perhaps consider 60 elements every year.
Let G(Y) be the set {Iα,Y/Iα,2012 : α in A} and let B(Y) be the set {α in A : Iα,Y/Iα,2012 is one of the bottom 60 elements of G(Y)}. Let the normalizing constant for the weights used, MY := 1 / (Sum[α in B(Y)] wα). (This ensures that MY Sum[α in B(Y)] wα = 1.)
Now, we arrive at the salary benchmark:
I hope this portion has been informative and interesting. I must emphasize that this is just an example of how to apply the ideas in the forgoing article. However, I hope that such ideas might be used to develop a salary benchmark in a more rigorous fashion.
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Afternote 1: A final element of this scheme would be conditions for when a re-benchmarking can be called for. My sense is that it would be sensible for this to be done after each election. Also, I feel that the President's pay should be entirely inflation adjusted.
Afternote 2: It does strike me that a 1% rise in part of pay for a 1% overall rise in income seems stingy. However, it is arguable that while government policies are able to torpedo incomes, the dominant cause of rising incomes are drive and intelligent action on the part of individuals. To postulate a further bonus for income growth does not make much sense.
The problem with this is that indifference to facilitating income growth might be encouraged on the part of office holders. It this makes sense is to add loss aversion into the mix (c.f.: prospect theory, which led to a Nobel Prize in Economics), where drops in income at the reference fractiles are penalized more heavily than increases are rewarded.
Afternote 3: It is entirely possible to use a similar mechanism to allow salaries to rise to match that of top earners if national income growth targets are met. (Naturally, I refer to stretch goals.) The functional form of such a benchmark, RY ("R" for reward), might look like the following:
Afternote 4: It is appears that the idea of designing KPIs to make effortful manipulation non-profitable has not been mentioned in the academic literature. I would like to pre-emptively coin the term "friction" for it.
This alignment with social objectives has to be done with the maximizing behaviour of individual policy makers in mind. It is thus natural to begin with a discussion on how systems of KPIs are "gamed" by those who are the subject of measurement, since their pay-offs (salaries) are essentially (increasing) functions of the KPIs.
Following the discussion on how KPIs are manipulated, I will cover why KPI manipulation should be taken into account. Then, I will comment on the manipulability properties of the current salary scheme. Finally, principles by which robust KPIs may be designed will be discussed. In the annex, I will run through the process of creating a salary scheme aligned with the objective of encouraging "inclusive growth".
Preliminaries on KPI Manipulation
As a preliminary to what follows, it should be stated clearly that the process of manipulation of a system of KPIs is essentially one of performing optimization to maximize one's pay-off. (Here, the term optimization is used here in the sense of attempting to maximize some pay-off function over all possible decisions.) In practice, optimization is based on manipulating the (policy) levers that one has control over.
Having spoken briefly about manipulation, let us consider "growth". One might summarize all forms of economic and technological engineering as effort directed at two objectives that may be concurrent: (i) improving efficiency to reach the efficiency frontier (where it is possible for every aspect to be improved without making any aspect perform more poorly; "transitioning to a better indifference curve"), and (ii) making the trade-offs that maximize one's benefit. Of the two, only (i) may be thought of as true growth and happens to be the more challenging objective, while (ii) is the task of selecting, from economically efficient alternatives, the one most beneficial to oneself.
Now, we are concerned about policy makers trading something that benefits them less for something that benefits them more. In other words, KPI manipulation. When a policy maker does that to increase his own pay-off, winners and losers are created. In simple economic (game theoretic) analysis (which assumes self-interested behaviour), the pay-offs for those winners and losers do not matter to the policy maker, who is only interested in his own pay-off.
Why Bother?
We cannot be so naive as to assume that intelligent people will not optimize for their own benefit. This will happen, and our policy makers are, at the very least, not stupid. As such, incentives have to be set up such that the maximizing behaviour of policy makers are aligned with social objectives.
To be cynical about the present government, a peg to the salaries top earners generates the incentive to implement precisely two types of policies: (i) those that encourage higher salaries for top earners and (ii) those which trade the welfare of non-top earners for higher salaries at the top. The only defence against this behaviour would be "human goodness" or "the threat of non-election". Game theory and common sense would tell us that appeals to the former are nothing but cheap talk. This configuration of incentives is undesirable. Incentives should be in place to directly support "inclusive growth" (or whatever policy objective is articulated) rather than leaving the objective out of the incentive system (which makes sense to office holders only if it is there for public consumption and is not, in fact, the true objective).
The current and proposed ministerial salary systems are textbook examples of incentive systems which are not aligned with the stated policy objective ("inclusive growth"). Subsequently, I will do a cursory analysis of the current ministerial salary scheme, which I will abbreviate as MSS.
An Analysis of the Current Salary Scheme
One important observation that can be made about the MSS is that some aspects of the growth objective are weighed much more heavily than others. In the MSS case, the ratio of the weight given to the salaries of top earners to those of low-income workers is extreme. Without bonuses (which is based on GDP growth), this ratio is infinity (i.e.: the income of low-income workers do not matter at all). Thus, the underlying optimization problem might be framed (polemically) as such:
- maximize Expected Salaries
over: Feasible Economic Policies
subject to: Probability[Re-election with Comfortable Majority] ≥ 1-δ
- maximize 0.6 Expected Median Salary of Top 1000 Earners (EMS)
over: non-negative EMS and Expected Median Salary of Singapore Citizens (EMSSC)
where: α EMS + β EMSSC ≤ γ (Efficiency frontier type Constraint)
subject to: EMSSC ≥ λ ("Re-election Constraint")
It should be recognized that this is a simple model designed to be polemical. However, it highlights the fact that when (intelligent) policy makers optimize for their own benefit, it can negatively affect general welfare unless their incentives are aligned with the general good.
Principles of Design for a KPI System/Salary Scheme
"Inclusive growth" is a policy objective of the "general welfare" type. The other being of the "narrow quantum leap" variety such as "putting an man on the moon by the end of the 1960s". The former entails spreading out resources and the latter entails focusing them. Presently, I'd like to make suggestions of the kind of ingredients that might go into KPIs/salary formulas for policy objectives of the "general welfare" variety.
To ensure that no one is left behind, it is important to ensure that the KPIs do not make it profitable to lower the welfare of one group in favour of another. For instance, with a KPI such as C1 [Factor A] + C2 [Factor B], and a technological/economic aspect that allows trading of 1 unit of [Factor A] for 2 units of [Factor B] using 1 unit of "policy effort", unless the coefficient C1 is close enough to 2 C2, trade offs will be made that lower one of the factors to its minimum level. (For this example, if C1 - 2C2 exceeds 1, [Factor A] will be increased and [Factor B] decreased; and if 2C2 - C1 exceeds 1, [Factor B] will be increased and [Factor A] decreased. Also, for the more mathematically inclined, this example clearly brings out how "linear" KPIs without feasibility conditions/veto criteria can be dangerous.)
Trade offs are the essential mechanism by which KPIs are manipulated. (I know of no others and would be keen to learn of others.) If the effort to make a trade off is worthwhile for the self-interested policy maker, the motivation to make that trade-off will exist. This principle has other serious implications in the public sector which I decline to touch on at this point.
Now, the converse to the aforementioned principle (which is also true), is that if the effort to make a trade off is not worthwhile for the self-interested policy maker, the motivation to make that trade-off will not exist. I believe that if growing the pie becomes the only practical means of increasing their rewards and remuneration, policy makers' efforts can be focused to that end and it will be possible to promote objectives like "inclusive growth".
As a rule of thumb, the more broad-based a KPI is, the more effort required to make gains due to trade-offs. Furthermore, a broad-based KPI is precisely what is needed to measure "inclusive growth". (The more mathematically inclined might think of using a function of the minimum of a set of subsidiary KPIs, or a function of the a set of the "order statistics" of subsidiary KPIs, which would require that all/most sub-KPIs rise in order for the parent KPI to rise.)
Conclusion
I hope the forgoing discussion was useful and helped stimulate thought on how to design KPIs or a salary scheme to achieve policy objectives. We have discussed how the ability to make trade-offs allows policy makers to optimize their KPIs without growing the economic pie (or the per-capita economic pie) and how this can be dangerous. It has been suggested that if these trade-offs are no longer easy to make, it would be more profitable for policy makers to work on "increasing the general welfare" (as a chief means for increasing their pay-offs).
I would like to close with a suggestion of a Ministerial Salary Scheme that I believe is more compatible with "inclusive growth" than the existing and proposed ones. I will describe the development of that scheme and what motivates the various components of it. I hope that the principles outlined in this article will eventually be used in the development of an improved (and more rigorous) salary scheme. (The reader should be warned that math will be encountered.)
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Annex: A Proposed Ministerial Salary Scheme Designed for Inclusive Growth
Note that this does not consider MP allowances, which are (rightly) paid over and above ministerial salaries. The salary scheme will be based on a benchmark salary paid to a junior minister, with senior grades getting (arbitrary) multiples of that salary. This benchmark will move in response to changes in economic conditions and the economic performance of Singapore. Let us denote the benchmark salary for the year Y, as SY.
Suppose a target salary is computed using a scheme like that suggested by former NMP Siew Kum Hong and call it C2012 (where the 2012 refers to the year of the original benchmark and "C" is for consumption). For those who have not read Siew Kum Hong opinion piece, S2012 is the price of a basket of goods and services that amounts to a decent standard of living for someone of a minister's social standing. Now let CY be cost of the same basket of goods in year Y.
I would suggest that a minister's salary be partially inflation adjusted to make it robust to market changes. (This would be one perk of office, and is entirely arbitrary.) Suppose that (arbitrarily) that amounts to one third of the original basket of goods. The rest should move with the wage levels of Singaporeans.
Define the income at the α fractile (highest income among the lowest earning 100α % of working Singapore citizens.) in year Y is Iα,Y, and determine Kα such that 2/3 C2012 = Kα Iα,Y.
So we find that S2012 = C2012 = (1/3) C2012 + Kα Iα,2012 for all values of α, and we can benchmark ministerial salaries as
- SY = (1/3) CY + Kα Iα,Y
Suppose α were drawn from the set A = {0.05, 0.06, 0.07, ..., 0.99}. I start from the 5% level to avoid pathological low-income cases (such as refusal to work) and end at the 99% level. Now for any set of positive weights w0.05, w0.06, w0.07, ..., w0.99 corresponding to the elements of the set A such that they sum to 1 (Sum[α in A] wα = 1), the following holds: C2012 = (1/3) C2012 + Sum[α in A] wα Kα Iα,2012. This leads to a fairly broad based benchmark:
- SY = (1/3) CY + Sum[α in A] wα Kα Iα,Y.
Unemployment can be incorporated in this framework by including unemployed people in the income distribution. However, care should be taken to not build in the incentive for policy makers to introduce policies that introduce disincentives for home making and other economically valuable but unpaid work. This would require a lot more work to flesh out, so this will be left as an idea.
The final modification might appear a little complicated, but the idea is simple. We would like broad income growth and not income growth focused on the "easiest" part of the income distribution. Thus, we should consider the fractiles which have had the lowest growth since the benchmark year. Since A has 95 elements (95 possible values of α), we could perhaps consider 60 elements every year.
Let G(Y) be the set {Iα,Y/Iα,2012 : α in A} and let B(Y) be the set {α in A : Iα,Y/Iα,2012 is one of the bottom 60 elements of G(Y)}. Let the normalizing constant for the weights used, MY := 1 / (Sum[α in B(Y)] wα). (This ensures that MY Sum[α in B(Y)] wα = 1.)
Now, we arrive at the salary benchmark:
- SY = (1/3) CY + MY Sum[α in B(Y)] wα Kα Iα,Y.
- Determine a benchmark standard of living, an associated basket of goods and services and its price in the benchmark year.
- Split the benchmark salary into an inflation adjusted component (perk!) and a market adjusted component which depends on the incomes of Singaporean workers.
- Made the benchmark depend on multiple income fractile points to account for the standards of living of a broad range of Singaporeans.
- Set the weights associated with each salary benchmark to promote the reduction of income inequality, while ensuring that the weights are not "badly skewed". (Note: In effect, this is a weighted average of all the salary benchmarks of item 2.)
- Decided to use only a sub-set of the elements of A to compute the weighted average. The elements used relate to the income levels which have grown the least since the benchmark year. This promotes the raising of all income levels, and punishes ministers (with stagnating wages) for stagnating wages of their constituents.
I hope this portion has been informative and interesting. I must emphasize that this is just an example of how to apply the ideas in the forgoing article. However, I hope that such ideas might be used to develop a salary benchmark in a more rigorous fashion.
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Afternote 1: A final element of this scheme would be conditions for when a re-benchmarking can be called for. My sense is that it would be sensible for this to be done after each election. Also, I feel that the President's pay should be entirely inflation adjusted.
Afternote 2: It does strike me that a 1% rise in part of pay for a 1% overall rise in income seems stingy. However, it is arguable that while government policies are able to torpedo incomes, the dominant cause of rising incomes are drive and intelligent action on the part of individuals. To postulate a further bonus for income growth does not make much sense.
The problem with this is that indifference to facilitating income growth might be encouraged on the part of office holders. It this makes sense is to add loss aversion into the mix (c.f.: prospect theory, which led to a Nobel Prize in Economics), where drops in income at the reference fractiles are penalized more heavily than increases are rewarded.
Afternote 3: It is entirely possible to use a similar mechanism to allow salaries to rise to match that of top earners if national income growth targets are met. (Naturally, I refer to stretch goals.) The functional form of such a benchmark, RY ("R" for reward), might look like the following:
- RY = SY + (ITarget,Y - SY) f(GY, GTarget )
- GY = {MY Sum[α in B(Y)] wα Kα (Iα,Y / Iα,2012) } - 1
Afternote 4: It is appears that the idea of designing KPIs to make effortful manipulation non-profitable has not been mentioned in the academic literature. I would like to pre-emptively coin the term "friction" for it.
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