Sunday, November 18, 2007

High-impact Education

The Economist ran a very enticing article on counterproductive regulations: it's really worth reading. Taken individually, most of the examples given have a small overall negative impact on the economy. Regulations protect individuals who do not have the time, money or motivation to engage in full counterparty oversight. In the service sector, regulations are usually in the form of competency assurance through relevant recognized education. For example, you cannot practice medicine in Quebec without being certified by the Collège des médecins du Québec, which prevents the majority of doctors having acquired their MDs outside Canada/US from practicing, regardless of work experience. I ask my surgeon prior to an operation: "How many times have you performed this operation before?". The CMQ asks "What was your GPA, adjusted for college notoriety?". Perhaps those regulators should only be given access to doctors that have the least experience. This policy has a greater overall economic impact than horse floaters in Texas, but the total effect remains small.

The bulk of the economic impact of service regulations is paid by consumers who indirectly cover the costs of unnecessary education forced upon their service providers. It would seem that our education system missed-out on the most important force driving post-industrialization growth: the division of labor. The ministry of education and university faculties seem to highly value graduates who could run the entire economy on their own: literature, history, economics, physics, biology, chemistry and advanced math. Perhaps they simply can't forecast what ratio of each profession will be needed, thus feel compelled to maximally hedge their position. By the time these students start doing real work, only a small fraction of what they learned is relevant; worse, the relevant notions were probably not concentrated at the very end, leading to poor retention, thus transferring training costs on their first employer — in things as simple as writing!

The sheer length of university programs combined with the lag between market needs and matching curricula seriously discounts the useful skills acquirable through post-secondary education. As technology pushes the division of labor further (and at a faster rate), school programs should become shorter. Though there is more total information that can be learned, teaching anything useful requires reducing the turn time between a new expertise emerging, updating the curriculum and getting a person through it. This implies teaching less material to a single student.

Due to the poor performance of our education system, the value of experience grossly outweighs that of education in all fields of work, leading to an increase in salaries over time. Otherwise, a graduate would start at the highest salary level during his first work day, then see his salary decrease as his knowledge becomes obsolete (and eventually, retraining would be required keep his salary positive!). Non-human capital behaves exactly in this way.

There are several other casualties of long mandatory education, other than increased retail costs. Though education is heavily subsidized, it is more expensive to study than it is to work: you are not paid 30K$ a year to study! Thus very capable students from a poorer background cannot afford to forgo work during the 4 to 8 years required to complete post-secondary education. Might such education last only one year, just about anyone could get a private loan to get by. Thus long education sustains class differences despite subsidies — even in France where education is free. The patience required to acquire a diploma is independent of the qualities required to work in most fields. Thus people that like "action" and respond particularly well to short term incentives, but can't stand the boredom and futility of post-secondary education, will drop out rather than pursue four more years of zero productivity.

The work life of an average post-secondary graduate is 35 years (25-60). Shaving off 3 years of education increases this period by 8.5%. Those extra years just happen to be when persons have little responsibility outside of work (no children) and peak intellectual capability, thus they can work harder and in a more productive way than in the years to follow. Additionally, the cost of changing fields, either due to personal preference or direct economic incentives, is significantly reduced. If you finish a four year program and realize that you don't like working in the field of choice, your options are limited to halfheartedly continuing your career, investing in another 4 years of schooling, or choosing a line of work requiring little education — all terrible outcomes.

To be fair, there are some upsides for employers in the current educational system which are worth mentioning. Class selection correlates well with cultural traits that employers look for: workers who perform well due to peer-pressure (from their families and friends). Hierarchy often develops based on the number of post-secondary years of schooling, which may be easier to accept for subordinates (less infighting and psychological harm). Having a post-secondary degree sets a minimum bound to the product of intelligence and perseverance possessed by the diploma holder. And finally, such a diploma proves that a person is capable of completing a very long uninteresting project.

What should we do about this? First, I would split out government sponsored research from the rest of the education system. Second, I would stop subsidizing specialized skills in all education. This means teaching only reading, writing, basic math, and social education (social education gives students recommendations on how to react to situations that frequently occur in one's life: for example using a condom during intercourse). All specialized education must not be subsidized in anyway. The market forces driving it would make it applicable, cheap and short. Government subsidies are most appropriate to support capital with very long amortization time for which the future need is indisputable. Incentives to have children are the best example of this. Subsidies are clearly counter productive in the last years of specialized education. Best of all, reducing the total cost of specialized education limits the damage that can be done by service regulators.

Sunday, November 11, 2007

Formal Fair Trade

In a previous post, I mentioned that the fair value of an asset involved in a two party trade can be calculated as the multiplicative average of each party's valuation of the asset, but I did not justify why. An alternate simpler solution would be to settle at the additive average. Various other functions could be proposed, as long as the settling price is between the two parties' valuations. In our current financial system, just about any settling function can be used since the gap between selling valuations and buying valuations is very low for frequently traded assets.

Though the pricing mechanisms at auctions of unique assets (like a painting) don't quite match those of regular liquid markets (like shares), it's worth discussing how auctions settle, since these are infrequent trades for which the gap between the selling and bidding prices is large. The seller at an auction specifies the starting price; below this amount the seller prefers to keep the item for himself (he would buy it from someone else at that price if he did not own it already). The buyers bid (in the extreme case, an incremental dollar at a time) until there is only a single bid remaining; that person has bought the item at the valuation of the second highest bidder, which is likely lower than his own valuation. A more efficient way of doing exactly the same thing, but without going through an endless number of bids, is for the seller to give the item to a temporary trust and set a public reserve value (which matches the seller's valuation). Buyers can then send their bids privately to the trust. Once the auction's bidding has closed, the trust sells the item to the buyer with the highest bid at the second highest bid price, and returns the proceeds to the seller.

When there is only one bidder participating in an auction, the settling price will be the valuation of the seller. When there are multiple bidders in an auction, the settling price will be that of the second highest bidder, which is located randomly between the seller's and highest bidder's valuations. Isn't there a way of splitting the benefits of the trade more fairly between the seller and the buyers?

Lets create a fictitious stock market on which a single share is traded between two people. At noon on the first day of every month, our two protagonists have the opportunity to trade the share; the market is otherwise closed, which means the two people are clearly Frenchmen. Only one of the two persons can own the share at a time (since there is only one share). From the point of view of both persons, the value of the share changes on a day to day basis due to new information, but there is no reason to either calculate or reveal this value between trading days, since trading is not possible. Both persons thus spend all non-trading days at the beach having a good time, during which they don't worry about the value of this share at all. On the morning of the first day of each month, both persons calculate the current value of the share and secretly enter it in the trading system. If the person who owns the share values it less then the person who does not own it, a trade occurs at a settling price calculated by the trading system. What is the fair settling value? Keep in mind that during a month many things may have changed and the two valuations can be significantly different, so the choice of using a multiplicative or additive average makes a big difference in the settling price.

During the month, both persons receive benefits ("dividends" in a broad sense) from the assets they own, might the assets be some money and the one share, or simply more money. So the first Frenchman gets his benefits by claiming he is the most powerful man on the beach (attracting women who like powerful illiquid men), and the second Frenchmen gets his from claiming that he is the richest man on the beach (attracting women who like rich liquid men). These are the only "dividends" that they get from holding the assets. Note that the benefits are entirely consumed by the time the month ends, thus they will not have any impact on the current value of the share: the current value is only based on future benefits. The return on investment captured through these "dividends" during the month is usually not the same for both persons, but it is fair since they chose which assets they wanted to own at the start.

Before the trade takes place, both persons evaluate the current value of the share based on future expected benefits. The one that held the share during the month can calculate his total return on investment during that month by summing the "dividends" received with the difference between the valuation he gave the share at the beginning of the month and its current value (as measured by him only, since he does not know what the other Frenchmen thinks the share is worth yet). This total return on investment is fair, since it is entirely controlled by the guy who owns the share.

When the share ownership changes at the end of the month, the trade allows both Frenchmen to statistically receive more future benefits then would have been possible otherwise, as long as their forecasts of benefits are accurate. In this case, they must each estimate how many other people of the two categories mentioned above they will meet over time at the beach, to maximize the number of hookups. When the share is traded, both men are very happy because they are suddenly better off. The trade commits quickly and the benefits are positive, which gives us a very high return on investment during the time that the transaction was being performed. A fair settling price for the trade would give both Frenchmen the same return on investment over the period of time that both the share and money were tied up in the trading system, however short a time this might be. This requires using a multiplicative average.

To illustrate this, assume that the Frenchman who owns the share values it at 1$, and the other one values it at 4$. Over a given short period of time, if they don't trade, they are both getting 0% ROI, because the share continues to be worth 1$ for the first guy, and the 4$ continues to be worth 4$ to the second guy (trivially). This makes them both miserable, since they are looking for ways to maximize their ROI. By trading, they can both improve their net worth. For the trade to be fair, both should benefit from the same ROI during the very short time that it takes for the trade to complete. Thus the settling price should be 2$. The first guy turned a low value share into twice the amount of money that he though it was worth. The second guy turned a low value toonee (2$) into a high value share, worth twice the amount disbursed. The ROI of this transaction is matched at 2:1.

It is possible to extend this trading system to multiple sellers and buyers. All sellers submit their minimum price secretly to a trust, and all buyers submit their maximum price in the same way. When bidding closes, the trust repeatedly matches the lowest selling price with the highest buying price, until matches are no longer possible (the lowest remaining ask price is higher than the highest remaining bid price). All trades are then settled at the multiplicative average of the closest matched sell/buy order (because identical assets should have a single market price at a given time, all assets are traded at a price matching the closest matched sell/buy order). This allows market participants to place a sell order at 0$, and (usually) not get 0$ for their share. The whole process does not maximize the number of trades, but it globally maximizes asset valuations, while giving the price setting seller/buyer pair the highest ROI possible. An alternate pricing method would be to settle each matched sell/buy pair at the multiplicative average of their prices, regardless of other simultaneous matched pairs.

An example greatly clarifies the multi-party trades of the above paragraph. Say there are four participants in a market where two identical shares are traded. Person A holds a share that he values at 2$, person B wants to purchase a share for 3$, person C holds a share that he values at 7$, and person D wants to purchase a share for 8$. Solution one would be for A&B to trade at 2.45$ and C&D to trade at 7.48$, and solution two would be for A&D to trade at 4$. Solution one makes the world 2$ richer (0.45+0.55+0.48+0.52), and solution two makes the world 6$ richer (2+0+0+6). Solution two is obviously better. In a trading system where sell/buy orders are not placed concurrently, if person A posts his ask price first and person B is (randomly) faster than D in bidding, he will force the market to match A&B and C&D, which is globally sub-optimal.

Like any market, such a system works poorly when there are few traders on either the buying or selling side. This allows multiple consecutive auctions to be conducted to do a "price sweep", detecting the value of the highest or lowest price. Such price fixing is unavoidable in situations of monopoly or oligopoly (might they be on the seller's or buyer's side), or in illiquid markets.

Friday, November 9, 2007

Humans are a strain on GDP growth

In a previous post, I drew graphs which showed that an investment's "yield average" and "yield variance" are positively correlated. In plain English, this means that a high risk investment will have a better return on investment than low risk investments, even after fully accounting for the risks of delinquency and default. Why does this occur in practice?

There are two opposing forces which influence the "appetite for risk". From an individual's micro-economic perspective, losing all of his money creates more harm to him than the good that would result in doubling his bank roll. That's why it does not make any sense to go to the casino and wager all your assets on black at roulette (even if the green slots were removed, making the wager completely fair). The reason for this is that our appreciation of various products is not proportional to the price of the acquired good or service.

To illustrate this point, lets compare apples and oranges. An apple is worth 5$ of "pleasure" to me, and an orange is worth 9$ of pleasure (I obviously prefer oranges to apples). If the price of oranges is above 9$ and the price of apples is above 5$, I will buy neither. Say I have 16$ to spend, and the price of apples is 4$ and the price of oranges is 8$, I will definitely buy something. What will I buy? 16$ buys me 4 apples, which gives me 20$ of pleasure (I net 4$ of pleasure if I buy apples). 16$ buys me 2 oranges, which gives me 18$ of pleasure (I net 2$ of pleasure if I buy oranges). So despite the fact that I prefer oranges to apples on a 1:1 basis, at some price points I will buy apples rather than oranges.

Return on investment is usually measured in dollars invested against dollars paid back (put dollars in, then wait some amount of time and get dollars out). When consumer goods are purchased in retail sales, the return on investment must be measured as dollars in, then wait some amount of time (usually very short), and get pleasure out. For a transaction to be completed, the selling party has to own an asset which he values less than the buying party. As long as the price of the transaction is between the two valuations, both parties will gain from the trade. The fair price for the trade is the multiplicative middle. If a seller and buyer simultaneously value an item at 1$ and 4$ respectively, then the fair trade value would be 2$, so that each person gets a return on investment of 2:1 on the transaction; in practice there are multiple sellers and buyers of a given item, and the market price is set to the multiplicative average between the two closest prices, which are always very close in any liquid market.

At first glance, markets do not seem to obey the rule of trading at the multiplicative average of the valuations. Take water as an example: if I can't buy water on a daily basis, I will die. So the value of water is very high for me (at least 25$ dollars a day), much more than the 1$ I pay for a 2L bottle of water (good for 1 day's worth of water consumption). The ROI that I am getting on water is 2500% a day (10^508 % a year). So why isn't the price of water 24.997$ for a 2L bottle (at this rate, the yearly ROI is 5%)? If there was only one person that owned all the water in the world, he could set the price at 24.997$ and I would grudgingly buy it. But this person would probably not be respecting the fair price of trade stated in the previous paragraph. That's because an individual highly values 2L of water per day, but he has very little use of the 10^19 other litres of fresh water available on Earth. Thus water for him is worth very close to 0$ per litre. The multiplicative average of 0$ and 25$ is darn close to zero (the 1$ cost comes mostly from packaging, publicity, distribution and retailing; it is fair, so don't write a letter to your MP complaining about the "Big Water" lobby).

The average person has an extremely good return on investment in buying water and basic foods (these are cheap and keep you alive!). In decreasing order of priority, most people would then buy clothing and housing, better tasting food, transportation, and luxury goods. The return on investment for consumer spending is called utility. The utility of an extra dollar of income is always lower or equal to the utility of the last dollar spent (this means that you don't wait for your salary to have reached 30K$ a year before you start buying food!). The function is thus decreasing (or flat) by definition.

The utility function that I use for myself has three steps: the first 10K$ covers my essential living needs (pleasure ROI > 100%), the next 20K$ covers my discretionary living needs (pleasure ROI > 25%), and I have yet to find a use for the 30K$ and above money, so I barely care about it at all (pleasure ROI 0+%). Say I stumble upon a winning lottery ticket tomorrow morning, and I suddenly receive 10M$. I'm lazy, so I decide to never work again, and I have 50 years left to live. How do I invest the money? I can't afford to be short of pleasure at either 100% or 25% interest rates, which means that I pretty much have to guarantee an income of 30K$ a year for 50 years. So I will set aside 1.5M$ in AAA government bonds (their effective yield after inflation and taxes in Canada is 0%!). And since my utility function is flat for the rest of my money, I'll invest the 8.5M$ remaining in the highest average yield and highest variance instrument that I can find. I'm using an extreme example to illustrate how a non-flat utility function necessarily leads to a "balanced" portfolio requiring different investment instruments which bear different variance and average yield. To balance your portfolio, you must choose investments with risks and yields that maximize the dollar value of pleasure that you will consume in your life. Note that at 100% ROI, being short of essential living pleasure at any time is horribly expensive.

That's force number one: the utility function of humans is not flat. Might we have a flat utility function (if happiness was linearly proportional to income), variance would not affect our investment decisions at all. Everyone would invest in the highest average yield assets, which means the riskiest investments. This would greatly increase GDP output.

Force number two is in the opposite direction: it encourages us to take risks. In a financial system that only allows collateralized loans, the worst that can happen to you is that you lose everything (all your assets). That is not so bad in occidental countries, since the state guarantees about 20K$ a year of cash and services, which supplies us with the first 10K$ of essential living needs (it prevents us from dying of thirst, or otherwise loaning ourselves essential living needs at a usurious rate of 100% a year!).

Better yet, in a financial system that gives us loans without collateral, the worst that can happen to you is still that you lose everything (all your assets), because bankruptcy prevents your total net worth from going too far in the negatives (it is actually based on cash flow, not on net worth, but the result is very similar). Yet borrowing without collateral allows you to leverage your investments, reaping much larger rewards than would be achievable might you only be allowed to invest your hard earned assets. How does this make any sense?!? Why would someone loan you money to invest (either on the markets or in your own pleasure) that you may not payback? Obviously you are getting a better yield than the loaning party offered you, otherwise you would not have accepted the loan. Why shouldn't they invest the money themselves directly instead? For one thing, they can't benefit from your pleasure. So if the lender has a ROI of 5% on his pleasure, and you have an ROI of 10% on yours, by all means he should lend you his money. The same applies to traditional investments also (stocks especially). When the bank loans you at 6%, and you invest in the stock market and get 10%, you are either more risk tolerant or smarter than your banker (probably both!). You and your banker are getting a good deal out of the loan.

So the social safety net and bankruptcy laws encourage us to take risks on the one hand (increasing GDP growth), and our utility function for consumer spending pushes us to hedge our portfolio, rather than betting everything on the statistically fastest horse (decreasing GDP growth). William Poundstone should have read this paragraph before going ballistic on Kelly's criterion.

La conclusion de l'histoire: if humans had a flat utility function (or if the social safety net was 30K$ a year and everyone's utility function matched mine), the average yield of all investments would be exactly matched with GDP growth, making the previous post's graphs one dimensional, and making the deflation problem's solution trivial. Lady GDP puts it this way: "Humans: can't live with them, can't live without them!"

Before all you socio-communists reading this blog suggest dishing out 30K$ a year in social safety nets to increase the appetite for risky investments (thus GDP), keep in mind that the utility function that I use for myself is not universal. Most people actually know what to do with their 30K+ income tranche: that's how Porsche stays in business. Those that don't care about the 30K+ income tranche won't put any effort in producing this income. I'm a workaholic exception, so the pleasure of working and investing money brings my ROI above 30K$ from 0% to 0+%, which makes a huge difference. If I was the only human alive, I would produce 2000 Kg of bananas a year, even though I only consume 1000 Kg, just for the fun of producing more bananas. Thankfully, I live on a planet inhabited by lazy monkeys.

Wednesday, November 7, 2007

True Charity

I don't give money to beggars for several reasons. For one, it does not use my time or their time efficiently at all. They produce nothing and I work 15 seconds less that day in an effort to avoid them.

I'm all for charity, but beggars in Montreal make over 25$/hour; I would prefer giving money to the poor single mothers who make 8$/hour. Just based on this simple fact, it makes no sense to give beggars more money than they currently receive.

Just because they are there in front of you and it is easy to give them your coins does not mean that you are doing the most good (though sometimes giving directly can be more efficient because you save various fixed costs that organized charities must pay, taking a cut out of donations). But giving directly allows you to feel good immediately and often, by helping people right in front of you at a low cost in terms of money and effort (alternately, it may allow you to avoid feeling bad because you declined to be charitable). Helping people in your "heightened field of sympathy" gives you much more satisfaction than giving to people you only know through statistics read in the media.

Giving to a charity in a yearly fashion is much more efficient in helping people (per dollar spent), but you don't feel "fuzzy inside" 50 times longer because you gave 100$ in one lump sum, rather than 50 times 2$. This subject is well covered by a very good article in Slate: http://www.slate.com/id/2034/ .

Moreover, I prefer teaching a man to fish over handing him a fish. In today's world, that means giving to charities that do research over those that provide palliative care. Unfortunately, this gives me very little of that "fuzzy feeling", but it is what does the most good to the most people.

To be fair, charity is a form a "feel good" product that does give something back (good emotions) to the person that donates. Thus giving small amounts many times to causes that are dear to our hearts makes economic sense. Perhaps charity should be taxable, as the charitable soul is actually paid back fully in kind.

Also to be fair, beggars probably facilitate the process of giving, as giving money without regular solicitation would make charity prohibitively expensive for most. A good parallel is that of saving (for yourself!): prior to owning a house and making capital payments, most people can't save any money at all! Perhaps beggars could collect money for organized charities, legally taking a 33% cut for their services. A squeegee with a cause... that would be much better!