I didn’t know you at all. But when you spoke of The Dream, I understood that I must have seen you before. I understood that the lifelong feeling I had that I was standing on the outer circumference of what was a large snow globe, an observatory, filled with sponge cakes and Christmas was in fact, not just my own isolated illusion. We are all standing around the edges, pressing our faces against the glass; maybe if we are close enough, we can see what The Dream is all about. Maybe I can be a part of it.

The globe is round, and I can see you watching The Dream too, through the glass, on the other side of the globe.

There is a whole world between you and me, but I can see you.




For all our notoriety about being unemotional, unsocial, and unfeeling, economists have a preoccupation with issues of human happiness, at least from a theoretical point of view. One of the things we obsess over is something that we haven’t quite solved, which is the concept of fairness.

Recently, issues of fairness came up in the form of the sport that I love, where the debate is over prize money: should men and women get equal prize purses when there are less women competing? Since this is exactly the kind of thing I do for a living, this kind of philosophical question is going to drag me into dangerously nerdy territory.

The problem of the pie

Distributional issues involve trying to split two different ‘pies’: either I’m trying to divide up the costs of things between various people, or I’m trying to divide up wealth.  It is essentially the same thing; let’s focus on the cost allocation question in the simple example of postal services, good old fashioned letters you write with your hands. It becomes complicated when:

  • There are different kinds of costs. Some costs exist even if nobody sent any letters and are fixed (the rent on the storage buildings), and some are costs based on the sender/recipient (the gas for the trucks that need to drive out to the postal locations) and some are based on the number of letters (the number of workers at the postal processing centre).
  • Every letter costs something different. Some people are sending letters from London, to London, and others are sending them from the Shetlands to Fattiehead (I looked that one up, it DOES EXIST, lol – it was probably the least offensive English town name on the list of weird English town names). The cost for the storage buildings is the same for both letters but the truck that drives from the Shetlands to Fattiehead, the cost is much greater.

The question appears when you decide how to set the prices, because the costs need to be recovered from people who are sending letters. There are two extremes:

  • Everyone for themselves. One way to do it is if everyone pays the amount to send the letter that it costs the post office to send it.  That means services provided in central London are dirt cheap, and ones in the Shetlands are very expensive.  In a related example, if the cost of goods is reflected in the cost of shipping it wherever it needs to go, this explains why costs of food are several times higher in remote parts of Canada, where the price reflects the actual cost of getting food to those remote locations.
  • Smear the cost equally. Another solution is to charge everyone the same thing, regardless of if they are sending a letter from the Shetlands or central London. This means that letter senders in London are subsidizing service in other parts of the UK by covering more than their share of costs.
  • Some kind of compromise. Maybe the charges are done by zones; the same base charge for everyone, but ones that are north of central England pay a fixed higher charge. There are a variety of ways to design a system of postage stamp prices which would be somewhere between totally uniform prices and totally unique prices.

The problem has problems

There are major questions which need to be answered in designing a good way to cut the pie.

What about the different needs of different people? London has a significnatly higher level of income per capital than more remote parts of the country. Maybe access to electricity, internet, and postal services is poorer outside of Southeast England and these services are needed in order to encourage development. Should a concern for need mean that those who have lower costs shoulder a larger share of the burden?

What’s going cause the least interference? Economists are super concerned about ‘distortion’, and try to minimize the ways in which any cost or tax policy deviates from what would naturally happen in a market. This means that there is a certain pressure to maintain a cost structure that reflects what costs users of the system are actually incurring. According to the Ramsey rule for optimal commodity taxes, the most efficient way to design a tax system would be to impose the highest level of tax on things that people really need (milk and bread), and the lowest on things that are optional (luxury vehicles). (This is sometimes considered super unfair and will be discussed later). If the postage cost is the same across the country, then this may encourage more people in remote places to use post (increasing the cost to the system) and cause those in low cost areas to look for other ways of getting letters delivered (lowering the amount of subsidizing users). The gap in available funds to cover the cost is caused by the way the pricing encourages people to behave in ways they otherwise wouldn’t.

What’s efficient? Efficiency is considered in the sense of who would make the best use of a reduction in postage cost. Maybe the businesses in London are larger and more important for overall productivity than remote firms. Making the productive firms subsidize the cost means they have less available funds for other investments.  Also, maybe the postage system doesn’t *want* to encourage people to set up shops in the Shetlands, since that would be expensive, and keeping the price of business down in London would encourage more people to locate their businesses in the same place. Efficiency and distortion are often related concepts.

What is politically palatable? UK postal provider Royal Mail actually does have a Universal Service Obligation to serve everyone and charge an equal rate. This is done for both political and fairness reasons, which are often intertwined.  It is hard for a policy to publicly justify charging or taxing different groups differently, and society may have an innate concern for fairness and the protection of minority/vulnerable groups. This may mean that society is willing to forego a certain amount of efficiency or undergo a level of distortion to achieve a fairness aim, although the concepts of fairness, efficiency, and distortion don’t necessarily have to be at odds. For example, even though Ramsey would suggest the best way to tax goods is to tax basic necessities higher than optional luxury goods, it may be hard to sell such a policy to a group of poverty-sensitive voters.

What’s easy? In another example, electricity grids, and the generators that flow electricity through these grids, are often owned by two or more different sets of people. In order to determine how much to charge a generator for the use of its grid, the grid operator would need to know where power is being introduced/drawn out of the grid, in what levels, at what locations, the cost of the grid, and all of this would need to be measured in real time. The different cost that one generator imposes depends on every other user. Also, this would need to be *predicted*, as they are probably paying a price now and we don’t know where the power is actually going. The measurement of this is no small feat of mathematics and engineering, and it takes more money and effort to figure out how much to charge users than simply adding up the total and dividing by everyone. At the end of the day, after the debates about fairness, efficiency, etc, the real deciding factor is often which way is the cheapest way to figure out how to cut the pie.

What to actually do?

Out of the three ways to divide costs (everyone for themselves, smear the costs equally, or compromise), one seems to be more immune to public scrutiny than the other two, which is to just promise equal costs.  Is this absolutely the fairest, most efficient system based on the different needs of the people? Probably not in all cases, but it does not open the pie-cutting process itself up to scrutiny. For example, if everyone were to pay a different cost of postage based on a different cost of delivery, trying to identify everyone’s costs will be difficult; what about the always changing price of transport? What happens if two neighbours in a remote town decide to send letters on the same day? Does the price get halved? The pricing structure would need some kind of a system for justifying differences in pricing in order to avoid accusations of arbitrariness and unfairness.

Out of all the ways to allocate costs, there are winners and there are losers, and if the losers know they are losing, they may cry foul. While its  potentially better to think about what’s an efficient, non-distortive way to split costs, sometimes the easiest thing to do is to give an equal share to everyone unless there’s an extremely compelling reason to do something differently. It better be damn compelling. All the competing factors play may have legitimate arguments in favour of one way of cost splitting over another, but we live in a world where political palatability and doing something convenient/feasible tends to win out over other kinds of reasoning. Want to have a sports tournament? Pay gender divisions equal prizes. Don’t want to do that? Be prepared to show everyone the math you have done. Don’t have any math? See the first suggestion.

The biggest lesson you can probably draw from this is that economists spend a lot of time trying not to upset people that we allegedly have no feelings about.

This is the second part of my thinking.  Is it related to the first? Do I completely contradict myself?  Probably. If my experience with my parents tells me anything, that’s what happens when you get old. 

A few things have happened in the last few weeks which have made me thinking about the ways in which we communicate with each other.

The first involved meeting K’s parents last month, where we shared no languages in common. They were very nice, but we will never really know what the other is thinking unless Google Glass invents a subtitle function. It was so different because as an English speaker, I am so accustomed to people accommodating my language requirements that I am not often presented with cases where this can’t happen. It does become taken for granted. On a side note, I think this subtitles thing could be a wicked function, Google.

The second was at work. One of the partners at my firm looks kind of like my mom, and I think if my mom had more money growing up or was born ten years later, she may have ended up with the same kind of life – Beijing University, Oxford educated, the works. We were in the kitchen during free fruit Wednesday and she was talking about the challenges of trying to get her daughter to speak Mandarin in a house were she is the only speaker (her husband is English I think), and despite her best efforts, it was difficult to teach a language to a child when she doesn’t have the opportunity to constantly hear it being used in context. I pointed out, that even as that child, in a household with two native Mandarin speakers, I’d lost a lot of my potential ability to speak in that language the second I went to an English speaking school.

The main value of language, and why it is so hard to create a desire to save small ones, is that the value doesn’t come from knowing it, but from the sharing of it between two people who are already at a minimum level of fluency. For example, me and K:

language venn diagram 1

And only those located at intersections are maintained.  It becomes a critical mass effect where over the course of many years (and especially with the internet), it’s not that the common piece of the intersection is shrinking in terms of language options, it is just that more and more people are adding their own language circles to the mix, which is reducing the number of languages that can be considered universally shared.

language venn diagram 2

When a two parent family where each parent is from different language cultures then decides to raise children, the effect is probably amplified since communication happens at the intersection (as in the case with the partner at work). The next generation then has an over-exposure to the intersection of the diagram and not enough at the edges. Not to say it is impossible, but since fluency is something that requires a lot of constant exposure, it would most likely come from the language that parents are most frequently using for communication themselves. Maybe fluency at the fringe languages  requires a Herculean effort to expose children to mother tongues.

When I was a kid I never understood why my parents used to make me go back to China for the summers. Besides being a relief from babysitting, it was a great opportunity for them to expose me to the language that I came from, without having to battle the constant influx of English language influences that I would face at Canadian summer camp. I used to hate it, but now I am grateful for their concerted effort not to give up on me. At several points in my childhood they also cancelled cable and started exclusively streaming Chinese shows off the internet, which also used to annoy me because it wasn’t MTV.  I’ve lost a lot of the ability to speak now, but sometimes, I listen to a show or something in Mandarin and it feels like being in the house again. I wonder if I will be strong enough to have the same kind of commitment to teaching anyone else Mandarin that my parents had with me, especially if I’m alone in that regard.

I’m not sure what the future will hold, but maybe it will look something like my dinner table last night. There was sweet potato noodles (japchae, I know, it is Korean, but I love it), sitting next to a baguette and about six different types of cured Spanish sausages. None of it was consistent, but we will each bring what we like to the table, meeting at the intersection, and figure out our lives as we go.

Mathematicians like to take the fun out of everything, according to non-mathematicians. I like think more of this as a fun-replacement, with a new language of fun that most people hate. This may be because the only thing I got for Christmas from Santa were math books. For example, K bought me this book, Things to do and make in the fourth dimension, which takes all sorts of mundane topics, like knots, and bubbles, and adds a fun-jection of math.

The Secretary Problem goes something like this: you are interviewing potential candidates for a secretary position, and there are twenty lined up outside the office waiting for their turn.  The interview is done one at a time.  We live in an archaic world where email communication is not possible, so your only chance to provide feedback to the candidates is to give them a yes or no at the end of their interview. We also live in a seller’s market, in the sense that once you say no, a candidate becomes so angry that he/she will storm off with a permanent grudge, never to return again. So you better be sure your ‘no’ is justified. You are also afraid that if you say yes to a candidate, there may have been someone further down the queue, who may have been better suited for the job.

This has (well, I think) a more direct application in the romance market. It also been called the Marriage Problem, which makes sense in a world where people date sequentially (assuming you aren’t dating multiple people simultaneously), and also that once you break up with someone, they will never come back. Once you marry someone, you are committed to them forever. That means you stop dating. You are also afraid of this:


. . . .

So obviously, math came in and found the least romantic way to optimally find happiness by avoiding the situation above, but also the one where you date 20 people, reject all of them out of risk averse-ness and end up alone forever. Not that being alone is some horrible life sentence anyways! Who decided that? Ugh. The point is, based on an assumed distribution the quality of your potential mates (I forget which one, probably normal?), the optimal strategy would be to take your entire useful dating life (let’s assume, you are planning on dating from when you are 18 to when you are 33), play the field without committing to anyone for the first 1/3 of that period (date until you are 23 sans commitment), and then choose the first person who comes along after this period which is better than anyone you observed previously. Obviously, there are risks, but without any foresight, this is theoretically the optimal way to maximize your chances of finding the best partner.

There are some potential caveats to why the direct transposition of the Secretary Problem onto the Marriage problem doesn’t make sense, so don’t run off and breakup with your person just yet:

  • Unlike interviews, your observations of eligible candidates can occur while you are still in a relationship. Well, take from this what you want, but I mean in the sense that while you are with someone, you are observing people around them, and are free to make passive evaluations on whether or not they would be a good partner without anyone being the wiser. This should mean that your search time goes down, since you are collecting information on what’s out there all the time.
  • Unlike interviews, your pool is changing. Sometimes, rapidly so. In the interviews, your pool of 20 candidates is captive, sitting there and waiting for you to make decisions. In romance, I’m going to assume that as you get older, and making a very simplifying assumption that you are looking for someone around your age (ahem), you are going to find that this pool is shrinking from death/marriage and commitment to people who are not you. I feel like once I hit 23 (which is ridiculous), the number of weddings popping up on Facebook started to blow up my newsfeed. Do these people know about the optimization? Did they all meet the best person right after their evaluation window ended? That means that you may have to spend more time searching before you find someone suitable.
  • Unlike interviews, you can observe what other people are doing and apply their experiences to your own search. Based on those previously mentioned weddings, your friends, what your family is telling you, you probably have a lot of research done for you on what a happy relationship looks like. You also have a lot of information on what a crazy relationship looks like.  You will probably use this in some way to better your understanding of what you are looking for, which makes your search time go down.
  • Your secretaries are interviewing their own secretaries. They may be applying the exact same type of optimization simultaneously, which makes the whole problem kind of a problem within a problem within a yeah . . .

Which one of these competing forces will win? I’m not sure, but I think that the last two are key.  I more than anyone would love a well-reasoned approach to all my living sources of happiness, but who really knows what they are doing?

And in great timing, at work today we were talking about how to calculate option values correctly, and what it means for something to have an option. An example came up about prime number theory. I’m not sure what this means, since I can only be bothered to do a basic Google which tells me nothing, but from what I gather it can be one of two things:

1) There are an infinite number of prime numbers. The proof for this goes something like, if there were a finite number of primes, and the last one was n, then you could multiply all of the prime numbers up to n by each other, add one, and have created a new number that is indivisible by any of the prime numbers you just used.

2) Large numbers are really hard to factor, even for computers, because there is no way to do it elegantly.

Nobody really thought there would be any use for prime numbers, except basically people who like to do math for fun. Math hobbyists. The eventual value of primes was uncovered after it was discovered that they could be incredibly useful for encryption, and voila. The option value of playing with numbers.



This was originally going to be an individual post about dying languages, but I think I’m going to split it into two.  

While wandering around the British Museum back in January, I was looking through the bookstore and came across an edition of the Romance of the Three Kingdoms. InEnglish. Immediately enthused at the prospect of maybe being able to finally understand the story that my parents had been telling me about for decades, I texted my dad with the news, only to have him respond that:

  1. translations are awful, especially for something as classic as this.
  2. maybe I would be interested in something more modern instead?
  3. A link to the 1987 make of the “Dream of Red Chamber” on youtube.
  4. A link to some show about Chinese pageant contestants, which he assumed I would actually watch.

I’ve been thinking a lot about languages lately. Words without equivalents in other languages. Languages which have their own unique interpretation of the world. The idea that there are endangered languages in the world, languages that are being lost as users switch to more mainstream languages, a process which is being accelerated by globalisation.

There are a lot of similarities between endangered languages and biodiversity, but the main one is that they are being lost, and while in order for them to be preserved, there needs to be a certain level of public salience and commitment to keeping them alive. But how? I recall in biology class, it is still incredibly challenging to convince people to value biodiversity when there isn’t a strong economic value attached to its preservation. Biologists and economists have to get creative in understanding ways to convince a sometimes reluctant public to champion a cause which is sometimes quite costly and without clear, immediate, material rewards.

Biodiversity has been valued in several ways to make it more understandable for non-biologists, and some of these arguments might apply to language diversity.

Direct economic activity: pretty obvious, in the sense that biodiversity can be consumed (through products, consumption, medicine, etc). I’m not sure what the language analogy would be in this sense.

Spiritual/cultural/aesthetic value: in the sense that beautiful landscapes inspired countless poems and lots of general utility. Homes next to beautiful natural landscapes are valued at higher prices than otherwise equivalent homes. This has probably the most direct application to language diversity, in the sense that each language brings a beautiful unique interpretation of the world with it, and the inherent existence of these languages brings people happiness.

Recreation/tourism: biodiversity brings in revenue through tourism. I think I recall some sort of a segment from Anthony Bourdain’s No Reservations in which hordes of American tourists travelled to a remote village somewhere in southeast Asia to listen to a traditional song performance, so clearly concept has some equivalent applications.

Education/research: biodiversity is valuable in that its existence allows researchers and institutions to learn more about the natural world. This seems like a bit of a circular argument; if biodiversity didn’t exist, then there would be no need to learn about it. At the same time, language preservation being justified by allowing people to learn about languages is also a bit of a weak argument.

Option value: just having something there is a value in itself, whether or not it provides any immediate benefit.  For example, there may be a cure for a disease or a new antibiotic that isn’t yet discovered in a rainforest, and having it around is a value in that this may one day be discovered and provide a direct economic benefit at a later date. Also, not sure how this applies to language preservation. It would imply that there is something hidden in a language that may become valuable in the future, which I’m having a hard time picturing.

Existence value: Just the act of being around is enough to provide some value, even without the possibility of a future direct benefit.  People are willing to donate funds to keeping the Amazon alive, whether or not they have any intentions of visiting or benefiting from its existence directly. I think this is the most applicable to language preservation; when I hear people communicating in a language I don’t understand, it’s kind of magical to just experience the unfamiliar combination of sounds and tones, and to know that these are being used to convey abstract ideas.  I imagine that this sense of magic is how people felt about wireless communication years ago.

It’s hard to come up with concrete arguments for why people should make a concerted effort to preserve the world’s smaller languages; rationalising the preservation of biodiversity is hard enough for conservationists to do, and many of their reasons don’t seem to apply.

I think I’m going to focus next week on my own personal understanding of why languages are dying, and why I think that I need to keep my own alive. It probably has nothing to do with a poorly translated version of a Chinese classic, but my parents will be happy nonetheless.

Happy belated Valentine’s Day! It’s time to think about love. Math love.

While Scarlet O’Hara was brazenly optimistic in proclaiming tomorrow a new day, the reality is that she was just being naive – no day exists in a vacuum.  It’s unlikely that Rhett would feel differently about Miss Scarlett a day after walking out on their marriage. It’s also probably likely that the mood you were in when you went to bed will affect how you start your day eight hours later, especially if you were in a really sour one. But as the day goes on, you are likely to be affected by little bumps in the road, little surprises throughout the day that you weren’t expecting (either a welcome or negative).

This is an especially tough problem for statisticians and macroeconomists to figure out, for all macroeconomic indicators, such as unemployment, inflation or GDP.  Today’s unemployment rate is a function of yesterday’s.  Yesterday’s rate is affected by the day before that, and so on. It becomes one of those picture in a picture in a picture headaches that you’ve probably seen before.


I’ve recently been thinking about this issue, but in the context of love. What happens if you meet someone amazing and wonderful, and he or she is perfect, but the beginning of the relationship itself is rather tumultuous? Can you make things peaceful despite a crazy start?  Can something that starts crazy, not implode? I think that maybe it’s going to be fine.  Actually, I know it’s going to be more than fine.

Let’s say this is the function of how you feel about someone in month t. But this is also a function of how you felt about them for the last 12 consecutive months. In each month you also introduce the new shock – a major life event, money problems, babies, etc.

love var

So t=1.  It’s the beginning, there are no past values to tell you how to feel about someone. The craziness of the beginning manifests itself in the error term. But the next month, you know that your relationship is also a function of the first month, which includes with it, the first period shock. This shows up again and again, month after month, influencing the relationship every month for the first year. Furthermore, you know that one year from how, your relationship is a function of the state it was in for each of the twelve months prior, which are all affected by that one first period shock. It’s one big chain reaction.

The stability depends on whether the entire relationship is covariance stationary. It’s a bit of math that boils down to whether you can solve for the zeros in an equation where you are trying to solve for L values. If it is, then over time, over enough time, even a big shock in the beginning will be absorbed by the inherent stability of the system and become smoothed over time.  If it isn’t then, the system isn’t stable, and any small disruptions, will cause the relationship to spiral wildly out of control.

The covariance stationary single-variable relationship will be fine, as long as you can ride out the initial crash landing.  Anything that isn’t, is already doomed. So in a way, there’s really no point in wondering whether a relationship can survive an initial big shock, or what you can do – it’s already been pre-determined. For Miss Scarlett, there’s nothing she can do to bring Rhett back. For the rest of us, it may be a relief to know that as time goes on, a system that is inherently resilient, will be able to weather the occasional big storm.

On an interesting sidenote, I’m not the only one who’s been thinking about applying econometric models to relationships – there’s been work on determining whether this can be used to estimate, in a two variable case, whether two countries will stabilise a chilly relationship or spiral into nuclear war.  In reality, using vector autoregressions to figure out whether or not nuclear escalation is likely, even when looking at ex post examples, is actually pretty tricky. Read about it here.