Showing posts with label Incentives. Show all posts
Showing posts with label Incentives. Show all posts
Wednesday, October 17, 2012
Gaming the System? When You Have a Policy Based What You Think is an Ingenious Quantitative Formula, Please Think it Through
Remarks on policy making with quantitative metrics and real incentives on my new website. A lot of analysis is needed on the behavioural incentives at work before committing to a policy. Examples include a gamed public tender in the Netherlands, housing grants and subsidized rental rates.
Sunday, August 26, 2012
On "Incentive Compatibility" in High-Frequency Trading
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.
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.
Monday, July 2, 2012
Adverse Incentives in Universities and the Impact on our National Competency Build Up
Today, I was at lunch with an older gentleman. Older in the sense of, was-sent-off-to-NS-in-a-3-tonner and ate-food-cooked-by-fellow-NSFs. He mentioned that he took an AI course at NUS Computer Science and had an extremely negative experience where lecturers did not care about students and were unable to express ideas well. He contrasted this with the good treatment he received at NUS's Institute of Systems Science (a centre for professional learning) where the instructors "want you to succeed".
He surmised that the failings of the former were due to the overriding importance placed on publishing, and that teaching was seen as a chore to be quickly finished so one might get back to doing things that affect their KPIs.
Now, in the course of that interaction, he came across as a knowledgeable and experienced IT professional with a very balanced personality, so I am inclined towards the view that he arrived at his position on his AI lecturer(s) at NUS Computer Science in a fair and balanced manner.
It is thus disturbing that professionals seeking to extend their skill sets can come away with little or nothing after a few days away from work and having their employers pay a pretty penny (a neat double whammy). This is not to say that all university instructors for professional development courses are unable to help their students extend their knowledge and skills. The point is that we should be seeking guarantees for a minimum service level for professional development. Otherwise, any initiatives with the objective of "raising productivity" through professional education will inherit the lack of a "minimum service level".
The incentives in universities that place little value on teaching are well known. Unfortunately, they are tremendously damaging. The question that tax payers should be asking themselves is what exactly they are funding. If the role of Singapore's universities is to break new ground in the physical sciences, medicine, technology and social sciences, can we say we are succeeding? If the role of Singapore's universities is to impart knowledge and skills to students prior to their entry to the workforce, are we succeeding? On both counts, we are not very successful.
One of the most cynical views I have come across is that a small number of exceptional individuals around the world appear to be justifying the contemplative life for many others. There is some truth to it. Some people do love to learn, but are not as keen on the grind of breaking new ground. These people tend to love to teach, but there is no suitable incentive scheme that enables them to build a rewarding career (those few new "teaching schemes" considered).
The trouble with adjusting the incentive framework for university faculty is that it will put us out of joint with international practice, possibly making Singapore an unattractive place to be a faculty member unless one does not want to ever work at a university outside of Singapore.
However, without effective incentives, we have to rely on the "milk of human goodness: to generate good professional development results, and history has shown us that said milk is not exactly reliable.
It is necessary to take a "calibrated" approach to incentives in university faculty. Ground breaking research is great to have, but unless we are in a technological arms race, it has the lowest priority among the three major roles of university faculty which are, highest priority first, (i) imparting knowledge and skills effectively, (ii) inspiring students, and (iii) doing high quality research.
He surmised that the failings of the former were due to the overriding importance placed on publishing, and that teaching was seen as a chore to be quickly finished so one might get back to doing things that affect their KPIs.
Now, in the course of that interaction, he came across as a knowledgeable and experienced IT professional with a very balanced personality, so I am inclined towards the view that he arrived at his position on his AI lecturer(s) at NUS Computer Science in a fair and balanced manner.
It is thus disturbing that professionals seeking to extend their skill sets can come away with little or nothing after a few days away from work and having their employers pay a pretty penny (a neat double whammy). This is not to say that all university instructors for professional development courses are unable to help their students extend their knowledge and skills. The point is that we should be seeking guarantees for a minimum service level for professional development. Otherwise, any initiatives with the objective of "raising productivity" through professional education will inherit the lack of a "minimum service level".
The incentives in universities that place little value on teaching are well known. Unfortunately, they are tremendously damaging. The question that tax payers should be asking themselves is what exactly they are funding. If the role of Singapore's universities is to break new ground in the physical sciences, medicine, technology and social sciences, can we say we are succeeding? If the role of Singapore's universities is to impart knowledge and skills to students prior to their entry to the workforce, are we succeeding? On both counts, we are not very successful.
One of the most cynical views I have come across is that a small number of exceptional individuals around the world appear to be justifying the contemplative life for many others. There is some truth to it. Some people do love to learn, but are not as keen on the grind of breaking new ground. These people tend to love to teach, but there is no suitable incentive scheme that enables them to build a rewarding career (those few new "teaching schemes" considered).
The trouble with adjusting the incentive framework for university faculty is that it will put us out of joint with international practice, possibly making Singapore an unattractive place to be a faculty member unless one does not want to ever work at a university outside of Singapore.
However, without effective incentives, we have to rely on the "milk of human goodness: to generate good professional development results, and history has shown us that said milk is not exactly reliable.
It is necessary to take a "calibrated" approach to incentives in university faculty. Ground breaking research is great to have, but unless we are in a technological arms race, it has the lowest priority among the three major roles of university faculty which are, highest priority first, (i) imparting knowledge and skills effectively, (ii) inspiring students, and (iii) doing high quality research.
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.
Saturday, February 11, 2012
How to Pay People
In the midst of the recent alleged scandals in politics, and the reminders of past (almost literally) hushed scandals, the issue of pay may now seem passé, but I'd like to share a short article on behavioral responses to incentive schemes.
In a way, it tangentially supports a past contention that KPIs, if they are used, should be cognitively complicated to game. Yet, there is also support for "I think he/she did well" type of bonus schemes. (For those, reports should be published justifying the bonuses awarded.) Anyway, on to the main event.
How to Pay People
by Dan Ariely
Most of the time, when you hire people you don't want to specify exactly what they do and how much they would get paid -- you don't want to say if you do X you will get this much, and if you do Y you will get that much. That type of contract is what we call a complete contract. Creating one is basically impossible, especially with higher-level jobs. If you try to do it, you cause "crowding out." People focus on everything you've included and exclude everything else. What's left out of the contract tends to drop out of their motivation as well. You are taking away from their judgment and goodwill and teaching them to be like rats in a maze.
It's like the difference between asking someone to help you change a tire and offering them $5 to do it. The moment you introduce money, you change how the person views the exchange. They say, "Oh, this is work. I don't work for $5, give me $150 and we can talk." When I was at MIT, they told us we had to teach 112 points per year. They a complex formula for how many students and how many hours and so on would translate to teaching points. Basically, MIT was conditioning me to put the least effort into getting the most points. This became the game. I was quite good at it. And I taught very little.
It happens with all kinds of compensation. A consulting company once told me that if you stayed until 8 in the five, you could order food and use the car service to get home. So what happens? A ton of people are there at 8. Nobody's there at 8:05. It's the same with pay: If you're hiring the right people, you don't want to include anything too specific in the contract. You want people to buy into the objectives of the company. Be specific about those, and then trustpeople to quickly understand how they can help maximize the objectives at each point in time. People actually know to a high degree which actions are good for the company and which are not -- regardless of what you pay them for.
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.)
----
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.
----
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.)
----
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.
----
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.
Monday, October 31, 2011
On Pay For Performance
Ministerial salaries in Singapore are a bit on the high side. In a just world where everything fit, that fact would imply that Singapore is prospering (check: more or less) and the people are extremely pleased with government services, the business environment, their standard of living and the direction the country is taking. On the latter count(s), it would take tremendous sampling bias to check those off today. Thus, there appears to be a remuneration mismatch which I will attempt to delve into.
In this opinion piece, I will discuss the basis of ministerial remuneration and pay for performance. I will talk about the inadequacy of using GDP growth as an indicator and show, by example, how one may easily develop better indicators. My intent is to contribute to the discourse on how we may more precisely reward good performance on the part of our ministers and provide incentives for good policy making.
The Basis for Remuneration
The nation's leadership must be properly remunerated for the time they put in to policy making and for the associated burden of responsibility. Remuneration for this base-load of effort would be partially covered by the non-variable component of their salaries. In addition to this, the nation's leadership should also be rewarded (or punished) for facilitating good (or poor) social, economic, security or foreign relations outcomes. This position is very much in line with what the ruling PAP government has argued in explaining the justifications behind their salaries. While I agree with the idea of pay for performance, I feel it has not been properly implemented.
On Performance Evaluation
What is good performance for government and how can it be evaluated? Presently, GDP growth is used as an indicator that determines a significant portion of ministers’ (and senior civil servants’) bonuses. By and large, it is agreeable that this is insufficient to cover the gamut of areas where government has a significant impact.
In addition to the above, a significant portion of ministerial bonuses is confidential and known only to the Prime Minister and the minister in question. We shall assume that the Prime Minister is privy to the efforts that each minister puts in and is qualified to judge the quality and effectiveness of the initiatives put in place by each minister. Behind this appears to be the assumption that the body politic is not qualified to properly judge these and their input could have a distorting effect on rewarding the deserving and punishing the blundering. This is only partially correct.
Before elaborating on why, let me enumerate on the major components of performance: (i) the standard of living of the body politic, (ii) the delivery and effectiveness of government services, (iii) the state of the business environment, (iv) economic and geopolitical security, (v) the direction of the country and (vi) the effort put in by individual ministers.
I believe that it would also be agreeable that while the body politic are able to evaluate (i) thru (iii), they are not equipped with the information and knowledge to evaluate (iv) thru (vi). Conversely, the Prime Minster is far less qualified than the body politic to evaluate (i) and (ii). The Prime Minister may also be less qualified than the average business owner to evaluate many aspects of (iii).
While we might conclude that the Prime Minister and selected advisors should be the ones to evaluate (iv) thru (vi), and to some extent, (iii), we might also conclude that there are gaps in the evaluation of (i) thru (iii). Furthermore, it is (i), (ii) and aspects of (iii) that the body politic care most about and are most qualified to evaluate. As it is impractical to award ministerial bonuses by referendum, proxy indicators must be used to measure these effects that arise indirectly from the actions of our ministers. These proxy indicators must also be formulated such that the body politic would agree that they measure the aforementioned elements of performance.
On GDP Growth as an Indicator
GDP growth has little relation to (iv) thru (vi), it is also only weakly correlated with (i) and (iii). However, it would appear that GDP growth is, in some sense, being used as a catch-all to evaluate the changes in standards of living, the state of the business environment and even the quality of government services. Supporting the truth of this hunch is the fact that a substantial portion of ministerial (and civil service) bonuses depend on the level of GDP growth. If this does, in fact, reflect reality, then there is a problem.
I would like to, first, justify the inadequacy of GDP growth as an indicator by quickly explaining why GDP is only weakly correlated with (i). There can be many economic outcomes (states) in which GDP growth can be high but large segments of the population experience decreasing standards of living. It is the existence of these outcomes and the likelihood of their occurrence (we have been experiencing these outcomes in recent years) that justifies the contention that GDP is only weakly correlated with (i).
(Note: A more precise mathematical statement on the inadequacy of GDP growth as an indicator could be made along the above lines. In addition, except for effects arising from the regulation of businesses and promotion of competition, it is difficult to relate GDP growth to (ii). Also, it would take more effort and business /economic reasoning to explain why GDP growth is ineffective as an indicator for (iii).)
Proposing a Better Indicator
More effective indicators can be easily developed. As an exercise, consider using real household income growth to build one. We will use a weighted sum of average real household income growth of various segments of the population. For example: 0.5 times the average growth of the lower 50% plus 0.5 times that of the upper 50%. Extending that logic, consider measuring at finer granularities such as 10% segments of households or even 1% segments. For weights, we adopt the "democratic option" of equal weight being given to each individual regardless of income level, which is consistent with our electoral system. Let us call this indicator "Aggregate Real Household Income Growth" (ARHIG) and suppose that ten equally weighted 10% segments are used.
This indicator is consistent with findings in behavioral psychology where percentage growth is what matters and not absolute growth. In addition, prospect theory, which has been empirically verified in a wide range of activities involving expressions of preference, informs us that losses loom larger than gains, which suggests that percentage income contraction should be weighed more heavily than growth. Naturally, the difference in weight between growth and contraction should be determined by a proper survey.
Clearly, ARHIG and similar indicators correlates far better with standard of living. In fact, one could reasonably argue for a causal relation. Furthermore, income growth at all levels may be a better measure of the quality of the business environment as it measures the benefits derived by all elements of the economic hierarchy. I have not thought about this in sufficiently detail and thus can only make a conjecture. On top of all this, ARHIG is eminently easy to explain to the body politic.
As the this section indicates, it is possible to build indicators that are more relevant to ministerial remuneration. I believe in this short section, I have convincingly argued that the ARHIG that we have sketched out is superior to GDP growth as an indicator for standard of living. Competent government economists should have proposed something like this at several points, and if it was, I wonder why it was rejected each time.
Admittedly, we have worked on an indicator for the aspect of performance that is easiest to measure. With more work, one could describe an indicator for (ii) and (iii), though my sense is that a survey of sorts would be needed, necessitating a (secret) sampling process.
Summing Up
In this unexpectedly long opinion piece, we have discussed the basis of remuneration and the measurement of the various aspects of performance. I have explained why GDP growth is a poor indicator for improvements in the general standard of living. To show that it is not difficult to build more relevant measures, "Aggregate Real Household Income Growth" (ARHIG) was presented as a simple indicator that more directly measures improvements in the general standard of living. The fact that such indicators are not used do not square with the fact that many Ivy League and Oxbridge educated economists are working in government ministries. Without good indicators, "pay for performance" does not mean anything. Thus, the failure to use better indicators should be explained. In so far as the ruling party is correct that rewarding good performance is a vital ingredient for good government, the lack of good indicators of performance is harmful and is a problem that should be addressed with haste.
In this opinion piece, I will discuss the basis of ministerial remuneration and pay for performance. I will talk about the inadequacy of using GDP growth as an indicator and show, by example, how one may easily develop better indicators. My intent is to contribute to the discourse on how we may more precisely reward good performance on the part of our ministers and provide incentives for good policy making.
The Basis for Remuneration
The nation's leadership must be properly remunerated for the time they put in to policy making and for the associated burden of responsibility. Remuneration for this base-load of effort would be partially covered by the non-variable component of their salaries. In addition to this, the nation's leadership should also be rewarded (or punished) for facilitating good (or poor) social, economic, security or foreign relations outcomes. This position is very much in line with what the ruling PAP government has argued in explaining the justifications behind their salaries. While I agree with the idea of pay for performance, I feel it has not been properly implemented.
On Performance Evaluation
What is good performance for government and how can it be evaluated? Presently, GDP growth is used as an indicator that determines a significant portion of ministers’ (and senior civil servants’) bonuses. By and large, it is agreeable that this is insufficient to cover the gamut of areas where government has a significant impact.
In addition to the above, a significant portion of ministerial bonuses is confidential and known only to the Prime Minister and the minister in question. We shall assume that the Prime Minister is privy to the efforts that each minister puts in and is qualified to judge the quality and effectiveness of the initiatives put in place by each minister. Behind this appears to be the assumption that the body politic is not qualified to properly judge these and their input could have a distorting effect on rewarding the deserving and punishing the blundering. This is only partially correct.
Before elaborating on why, let me enumerate on the major components of performance: (i) the standard of living of the body politic, (ii) the delivery and effectiveness of government services, (iii) the state of the business environment, (iv) economic and geopolitical security, (v) the direction of the country and (vi) the effort put in by individual ministers.
I believe that it would also be agreeable that while the body politic are able to evaluate (i) thru (iii), they are not equipped with the information and knowledge to evaluate (iv) thru (vi). Conversely, the Prime Minster is far less qualified than the body politic to evaluate (i) and (ii). The Prime Minister may also be less qualified than the average business owner to evaluate many aspects of (iii).
While we might conclude that the Prime Minister and selected advisors should be the ones to evaluate (iv) thru (vi), and to some extent, (iii), we might also conclude that there are gaps in the evaluation of (i) thru (iii). Furthermore, it is (i), (ii) and aspects of (iii) that the body politic care most about and are most qualified to evaluate. As it is impractical to award ministerial bonuses by referendum, proxy indicators must be used to measure these effects that arise indirectly from the actions of our ministers. These proxy indicators must also be formulated such that the body politic would agree that they measure the aforementioned elements of performance.
On GDP Growth as an Indicator
GDP growth has little relation to (iv) thru (vi), it is also only weakly correlated with (i) and (iii). However, it would appear that GDP growth is, in some sense, being used as a catch-all to evaluate the changes in standards of living, the state of the business environment and even the quality of government services. Supporting the truth of this hunch is the fact that a substantial portion of ministerial (and civil service) bonuses depend on the level of GDP growth. If this does, in fact, reflect reality, then there is a problem.
I would like to, first, justify the inadequacy of GDP growth as an indicator by quickly explaining why GDP is only weakly correlated with (i). There can be many economic outcomes (states) in which GDP growth can be high but large segments of the population experience decreasing standards of living. It is the existence of these outcomes and the likelihood of their occurrence (we have been experiencing these outcomes in recent years) that justifies the contention that GDP is only weakly correlated with (i).
(Note: A more precise mathematical statement on the inadequacy of GDP growth as an indicator could be made along the above lines. In addition, except for effects arising from the regulation of businesses and promotion of competition, it is difficult to relate GDP growth to (ii). Also, it would take more effort and business /economic reasoning to explain why GDP growth is ineffective as an indicator for (iii).)
Proposing a Better Indicator
More effective indicators can be easily developed. As an exercise, consider using real household income growth to build one. We will use a weighted sum of average real household income growth of various segments of the population. For example: 0.5 times the average growth of the lower 50% plus 0.5 times that of the upper 50%. Extending that logic, consider measuring at finer granularities such as 10% segments of households or even 1% segments. For weights, we adopt the "democratic option" of equal weight being given to each individual regardless of income level, which is consistent with our electoral system. Let us call this indicator "Aggregate Real Household Income Growth" (ARHIG) and suppose that ten equally weighted 10% segments are used.
This indicator is consistent with findings in behavioral psychology where percentage growth is what matters and not absolute growth. In addition, prospect theory, which has been empirically verified in a wide range of activities involving expressions of preference, informs us that losses loom larger than gains, which suggests that percentage income contraction should be weighed more heavily than growth. Naturally, the difference in weight between growth and contraction should be determined by a proper survey.
Clearly, ARHIG and similar indicators correlates far better with standard of living. In fact, one could reasonably argue for a causal relation. Furthermore, income growth at all levels may be a better measure of the quality of the business environment as it measures the benefits derived by all elements of the economic hierarchy. I have not thought about this in sufficiently detail and thus can only make a conjecture. On top of all this, ARHIG is eminently easy to explain to the body politic.
As the this section indicates, it is possible to build indicators that are more relevant to ministerial remuneration. I believe in this short section, I have convincingly argued that the ARHIG that we have sketched out is superior to GDP growth as an indicator for standard of living. Competent government economists should have proposed something like this at several points, and if it was, I wonder why it was rejected each time.
Admittedly, we have worked on an indicator for the aspect of performance that is easiest to measure. With more work, one could describe an indicator for (ii) and (iii), though my sense is that a survey of sorts would be needed, necessitating a (secret) sampling process.
Summing Up
In this unexpectedly long opinion piece, we have discussed the basis of remuneration and the measurement of the various aspects of performance. I have explained why GDP growth is a poor indicator for improvements in the general standard of living. To show that it is not difficult to build more relevant measures, "Aggregate Real Household Income Growth" (ARHIG) was presented as a simple indicator that more directly measures improvements in the general standard of living. The fact that such indicators are not used do not square with the fact that many Ivy League and Oxbridge educated economists are working in government ministries. Without good indicators, "pay for performance" does not mean anything. Thus, the failure to use better indicators should be explained. In so far as the ruling party is correct that rewarding good performance is a vital ingredient for good government, the lack of good indicators of performance is harmful and is a problem that should be addressed with haste.
----
Afternote: I've computed ARHIG for 2001 thru 2010 using data from SingStat, though it is annoying to reproduce them on a blog. (So I shall be lazy and not do so.)
There is one interesting tidbit though, real household income growth over 10 years has generally not been too shabby except for the lowest earning 10% of households. They experience a -6.55% contraction in real household income. (The 11-20% decile has 10%, the 41-50% and 51-60% have about 23%, and the 91-100% have 34.85%.)
However noting that SingStat's income data excludes government transfers, such as WorkFare, we see that measures are being taken to close the gap. In fact, a quick look at the Workfare Income Supplement numbers reveals that that WorkFare would result in real household income growth over 10 years for the lowest 10% of households of around 5% to 8%.
On the flip side, these (few) numbers do not provide a clear picture as only households with at least one working member are counted. Ideally, unemployed households should also be accounted for.
Afternote 2: This article was also published on New Asia Republic.
Tuesday, May 3, 2011
Immigration, Optimizing KPIs and Honesty
Allow me to pretend I understand human nature: where the outcome is defined in purely financial terms, one is best off by being a rational maximizer. Suppose the main actor's pay is determined by some KPI, we shall call G, in a monotone fashion. (G rises, pay rises.)
Clearly, it is optimal for the actor to maximize G in so far as resources allow. If G can be pumped up by pushing a strategy that suffocates other actors, so be it. That is rational maximization.
Suppose we have an elementary economic model.
- G(p) = K (M - p) p
A(p) = L p^{-a}
where a > 0. So G is the objective of the main player who controls p and A is the objective of the other actors who have no control over p.
G is a logistic model for GDP growth, and A denotes average wage where total wage is a concave monomial.
G is maximized at half absolute capacity (crush load), and since M is a rather large number, A(M/2) is tiny. Note that the main actor has no incentive to ensure that A(p) is a respectable number.
Now, the model is an obvious snipe at the immigrant labour policy. It is obvious that more immigrant labour means more GDP growth. But the lack of consideration of the average wage is (note: another snipe coming) symptomatic of a failure of all the PPE (Politics-Philosophy-Economics) graduates with excellent A level results to understand basic economics or making the assumption that the rest of the country does not understand.
Social Choice balances GDP growth and quality of life. The GDP growth KPI, in the parlance of economics, cannot implement the balance of GDP growth and quality of life. It would take very good men to resist the allure of optimizing their bonus KPIs at the expense of matters important to others. While it is possible to have a cabinet of such good men, let us protect the country. Let us legislate incentive compatibility into remuneration of our executive and our legislature. There is no negative impact of the on the good men who will direct their efforts in this direction anyway. Moreover, legislating this would be the honest thing to do, especially for a PPE graduate.
Subscribe to:
Posts (Atom)
Posts
