Critique and Reply---Perspectives on Rawlsian Justice

In this blog, I will reply to some of the comments I got on my previous blog: Justice 1---Why I disagree with Rawls?

The first critique and reply is addressed at the general audience, while the second is more technical and abstract (euphemism for boring for most people), in that it tries to connect the problem with the problem of statistical inference.

I sincerely thank my two great friends for their input, because you make me to think harder on the question. I recently saw the following statement on a blog:

I love to argue one on one, and common beliefs are not important for friendship — instead I value honesty and passion.

I think it is fitting to put it here. I still cling to my belief, and really appreciate that you are there to challenge me.

I will address two critiques:

Critique 1 

So would you say the Rawls argument would be favorable by someone who is extremely risk adverse? If the axioms of rationality doesn't hold then your argument wouldn't hold. the stock example that you use has such small loss that it makes the rationality argument seem more reasonable than it really is. what if it is like this- stock A: 0 all the time, B: 90% chance of 100, 10% chance of -800. or even: A: 0 all the time, B: 10% chance of 900, 90% chance of -9. the axioms of rationality surely doesn't describe how we actually make decisions. But I think it isn't even necessarily the way that we SHOULD make decisions, because in this case there is reason to be extremely risk averse, and that because of the human beings that we are, equity could be an intrinsic good such that the huge disparity in outcome would discount the expectation that you take. but the point you made about ex-ante and ex-post is very illuminating for me.

Reply:

Von-Neunmann Framework does accommodate risk aversion. Indeed, it was developed to accommodate risk aversion when people try to analyze the decision making of gambling, when they find the concept of expected value incapable to deal with risk aversion. The stock example you give can be analyzed in such a framework. Depending on our parameters, we will get different prescriptions, but I think this is a strength, in that is shows this framework is rich enough to allow different degrees of risk aversion. Of course, some degrees of risk aversion are reasonable, others are not, which could be revealed by the decisions people make. 

Over the years, this framework has been examined with different further restrictions---for example, utility should be bounded so that we will not run into some sort of St. Petersburg Paradox.  This is an example where our intuition of risk aversion help us refine this framework, in this case putting a lower bound on risk aversion.

As for the axioms of rationality. If you look at them, they are very very primitive---so primitive that it is shocking when we find empirical evidence that people could violate such principles when we make decisions---we just could not even pass such primitive requirements of rationality. But as I commented, those evidence point to the irrationality of human beings, not the logical coherence of this framework. It is a perfect model for how decision should be made, though a crappy model for decisions are actually made.

Critique 2:

I was trying to argue that the veil of ignorance extends to the distribution with which one takes the expected value to get expected utility. Analogizing to Bayes, when you don't have an actual prior, then you should do minimaxity and I think minimaxity will lead to Rawls's conclusion

When you say "aggregate welfare ex post" do you mean maximize over \theta given the observed distribution of types in the world? Say that I am of type i*, but this is unknown to me, so I assume that i* follows the observed distribution of types in the world (e.g. just tally how many rich/poor people there are in the world). I choose \theta to maximize my expected utility. Is this what you mean by maximizing aggregate welfare ex post? But I think Rawls is considering the following situation which is slightly different: I am of type i* (again, I don't get to observe this), but this time there is a veil of ignorance so that I do not get to observe the distribution of types (pretend someone deleted data on how many rich/poor are in the world). I can't do expected utility maxmization in this case. Depending on whether data on rich/poor is available, this could lead to drastically different outcomes. Suppose that I am told most people are rich in the world, then given this observed distribution, I'd choose \theta to benefit rich people, since most likely that will benefit me. But if I need to make a decision without knowing the relative number of rich and poor, I'd make sure that everyone is somewhat well off under my decision rule.

Reply

Despite its resemblance to minimax (in fact Wikipedia attributed an application of minimax to Rawlsian idea), I will argue the resemblance is only superficial, and the logic does not carry through.

So I will formalize the problem of inference and justice, in such a way to make the structure parallel.

Inference:
We have a type $i|\alpha\sim F_\alpha$. That is $i$ is the unknown parameter, and its distribution comes from a family of distribution (priors) with parameter $\alpha$. But we do not know which prior it is, that is we do not know $\alpha$.

We are looking for a rule $\theta$ according to which we can do inference. Every time we act according to the rule, we incur some loss, and this is captured by the perfomance function $U(\cdot)$ (negative of loss). Since the performance of the rule also depends on $i$ itself, $U$ is a function of not only the rule $\theta$, but also the type $i$.

As remarked, $i$ is a random variable, how $\theta$ performs in expectation depends on $\alpha$, that is the number we are concerned about is
\[
E[U(\theta,i)|\alpha]
\]
We would like to maximize that number, but we do not know $\alpha$. So we choose the rule such that it will gives us the best result in its worst case scenario.  In essence we are applying the minimax principle to $\alpha$ the parameter that determines the distribution, not to $i$, the type that we are interested in.

I have taken some time to set up the problem of statistical inference slowly, because I do not need to do this for social choice again. We are facing the very same problem, maximizing the following
\[
E[U(\theta,i)|\alpha]
\]
We can apply the minimax principle to $\alpha$, but not to $i$. What Rawls argue is that, we need to apply minimax principle to the type $i$, to maximize the welfare of the worst of individual, not to $\alpha$ to maximize the general welfare in the worst kind of society. This, is in my views, unjustified. While I can acknowledge the logic minimax estimator in statistical inference, that logic does not justify Rawls argument, which I believe is flawed.

Where does my utilitarian principle lie? It still fits this framework and it has deeper connection to statistical inference than I thought. Since this is not the focus, I will be brief, but it suffices to say that a utilitarian rule is always admissible (in the sense of Bayesian statistical inference).

Can we still reach the optimal utilitarian rule under this extension of veil of ignorance? The answer is yes.

First, I state the obvious. If people has the right prior (they know $\alpha$, they should choose the rule according to utilitarian view, that is
\[
\theta^*=argmax_\theta\: E(U(i,\theta)|F_\alpha)
\]
Now we consider that they do not have the prior, they would like to be able to choose the same rule, but they cannot. but they observe that they do not have to choose "the rule" now. They can postpone choosing "the rule" after the veil is lifted. All they need to do is to choose a rule for choosing "the rule" after the veil is lifted. After the veil is lifted, they will observe $\alpha$. They stipulate that the rule chosen after the veil is lifted will be the same rule if they were to choose the rule now with the actual prior. In essence they stipulated that the rule that will be chose after the veil is lifted will be in accordance with the utilitarian principle. Put another way, they choose a family of (utilitarian) rules $\theta_\alpha$, and say they will implement the rule $\theta_{\alpha_0}$ when they observe $\alpha=\alpha_0$ after the lifting of the veil.

Finally, from my point of view, I am not in favor of extending the veil of ignorance towards the distribution of types as a thought experiment. For me Rawls was more concerned that our knowledge of our own relative position in the type distribution will bias us (rich do not want too much welfare state). Thus the veil of ignorance is to avoid bias between the relative well off and relative worse off within a society, not to avoid bias resulting from knowledge of differences across societies. I now actually feel I should argue this point more forcefully because it does have implications. If we think the veil of ignorance should extend over the distribution of types as well, then it will imply that all societies, should only have one just rule. But if we only allow the veil of ignorance over types, then we would allow rules to differ across societies. For example, in a society where everyone is already so rich that they live comfortably, there should be less redistribution; while in a society when only some live very comfortably and some live miserably, we might need to be more aggressive in redistribution.

Justice 1---Why I disagree with Rawls

As I mentioned in the previous blog, this is a series of blogs that I will discuss about issues related to justice. I dedicate this series of blog to my US history teacher, Mock Trial coach, and mentor when I was an exchange student. He challenged me to read widely, think deeply about important issues.  It was during a discussion with him, when I first invoked a Rawlsian argument, forced to defend it, and think hard about it. Today, however, I intend to tear it down.

Rawls' framework

Rawls had a powerful idea---the veil of ignorance. The idea is that if we debate policy now, our opinion will be influenced by our current positions and status---a rich person might favor small redistribution, an African American might favor Affirmative action, and an healthy person might fight against universal health care. Rawls' idea is that, let us return to the "original position", that is we do not know who we will be, whether we are black or white, rich or poor, healthy or frail. We decide on what kind of policy we will want:

"no one knows his place in society, his class position or social status, nor does anyone know his fortune in the distribution of natural assets and abilities, his intelligence, strength, and the like. I shall even assume that the parties do not know their conceptions of the good or their special psychological propensities. The principles of justice are chosen behind a veil of ignorance."

Under this framework, Rawls reached the conclusion that a just society will maximize the utility of its worst-off citizen (subject to preserving basic liberty, and equality of opportunity):

Social and economic inequalities are to be arranged so that they are to be of the greatest benefit of the least-advantaged members of society.

Rawls' Fallacy:

That I argue is wrong. Yes, we are behind the veil of ignorance, and we are unsure who we will be, but why do you assume we will design the rules so as to make our worst outcome as good as possible. Consider an analogy, when you pick stocks, you do not choose a stock that will give you the best return in the worst case scenario, you will consider the average return and the variation. For an extreme example, one asset will give you 0 return no matter what. Another asset will give you 100% return 90% of the time, but -0.1% return 10% of the time. It will be crazy to think one will just choose the first risk-free asset over the second asset.

Utilitarian Argument:

What should be the conclusion? I argue, it is utilitarian. Choosing the rule under the veil of ignorance is like making ex-ante optimization. I will show that this ex-ante maximization problem is equivalent to an ex-post aggregate utility maximization problem, thus justifying a utilitarian framework. If you see this, you can skip the next two paragraphs.

 Let me formalize this a bit, let $i$ be a random variable of the type of a person. Under the veil of ignorance, we do not observe our type. We choose the rule for the society $\theta$. After we choose the rule, the veil of ignorance is lifted, and we learn our types, and we get a utility depending on both our types and the rule we choose $U_i(\theta)$. The question is ex-ante, how will we choose the rule $\theta$? I think at this point, it is fairly obvious to economics student, what the answer is.  We need to decide on a decision rule and if we impose some axioms of rationality (discussed in appendix), like one can compare two rules under the veil of ignorance, we have only one way of choosing---the Von-Neumann Expected Utility Framework. In other words, we will choose the optimal $\theta$ so as to maximize
\[
\max_{\theta} E ~U(i,\theta)
\]
where the expectation is taken over $i$.

There are dual interpretations to the objective function shown above. It could be interpreted as ex-ante optimization with uncertainty over type, or it could be interpreted as maximizing average ex-post utility of people in the society. This dual interpretation means that an ex-ante expected utility maximization problem is equivalent to an ex-post aggregate utility maximization problem.  So if you accept the veil of ignorance and the rationality assumption, you have to accept that a just society maximized the aggregate welfare of all its people, weighting everyone equally, at least in principle.

Critiques:

I do have some criticisms/cautions.

The link from theory to practice is far from obvious. I briefly discuss three.

In reality, the rule we impose will influence the distribution of the type $i$ for later generations. For example, if rich and poor people have different birth rate, the distribution of types will change. Another channel is genetics, for intelligence and disease. I do not want to get into this, as a truthful discussion makes people uncomfortable. It suffices to say, the theory suggests an overly static framework.

It is impossible to assign utility value to different people in practice, thus, the ex-post maximization problem is ill-defined in practice. We have to assign the utility ex-post, but we are already out of the veil of ignorance, so our assignment could no longer be innocent.

Finally, let us not forget the political economy. People who make the rules ex-post are not angels, why could we trust them to design the rule optimally even if the model is perfect and they can get the utility function?

Of course, there is another possibility, after reaching the natural implication of the veil of ignorance (with the aid of assumptions), we might come to doubt this very assumption/framework to begin with?

Appendix:

Axioms of rationality that will lead to Von-Neunmann framework (from wikipedia)
I need to point out that it is true this framework has been attacked as a model for human decisions, (most prominently by prospect theory). But those attacks point to the irrationality of human beings, not the logical coherence of this framework. It is a perfect model for how decision should be made, though a crappy model for decisions are actually made.

Completeness assumes that an individual has well defined preferences and can always decide between any two alternatives.
Axiom (Completeness): For every A and B either or .


This means that the individual either prefers A to B, or is indifferent between A and B, or prefers B to A.


Transitivity assumes that, as an individual decides according to the completeness axiom, the individual also decides consistently.
Axiom (Transitivity): For every A, B and C with and we must have .


Independence also pertains to well-defined preferences and assumes that two gambles mixed with a third one maintain the same preference order as when the two are presented independently of the third one. The independence axiom is the most controversial one.
Axiom (Independence): Let A, B, and C be three lotteries with , and let ; then .


Continuity assumes that when there are three lotteries (A, B and C) and the individual prefers A to B and B to C, then there should be a possible combination of A and C in which the individual is then indifferent between this mix and the lottery B.
Axiom (Continuity): Let A, B and C be lotteries with ; then there exists a probability p such that B is equally good as
• .

What do you deserve?

I have been listening to Harvard Open Course on Justice. It has been an awesome experience, though from time to time I get deeply troubled by some of the responses students give. What troubles me most is in the class where Rawlsian idea of justice was debated.

One guy named Mike argued that the society should be based on meritocracy. To illustrate his point, he gave an example of college admission, where he argued forcefully that he worked hard, and put in effort, so he deserve to be admitted based on his merit alone.

To begin with, I must confess I embrace meritocracy, a topic for another day, but I am uncomfortable with the fact that he is so confident that his performance and his admission is due solely to his own merit (you need to watch the video or at least hear the conversation to see that conviction), and oblivious to the fact that he is fortunate to have many who helped him during the process.

His intrinsic assumption is that his excellence today, which secured him a place in Harvard, is all his doing, his merit and his effort. Let us put aside whether merit or talent is arbitrary in themselves, it is a mistake to think our performance or excellence is a deterministic function of our decisions, talents or other merits. Whenever I reflect upon my past, I am often amazed at how fragile this path has been, and how much uncertainty it involves---I was extremely lucky to meet numerous people, who were so kind to give me a helping hand when I need them, provide guidance when I am lost, and share their wisdom in discussions.  They never had to. My teachers in high school and professors in college never had to discuss ideas with me to foster my interest and kindle my curiosity, they never had to spend time writing an enthusiastic recommendation letter which were essential for my admission to Williams, and then to Harvard and Stanford. Without their enthusiasm, things would be very different.

I doubt if anyone has a different story. To say the very least, everyone in Harvard got in with at least a strong recommendation letter. Your recommender does not have to write such a good one. It takes time. Even if you are extremely talented, he still does not have to. It is a favor done for you. Don't take it for granted.

I think when people are given some favor, even for an arbitrary reason, they get used to it, and think somehow they deserve it. It is because of this, we feel entitled to everything we earn. But we don't. We owe a lot to those who helped us.  We are lucky to get those help.

This blog is about uncertainty, which shapes our world more profoundly than we typically recognize. It is via recognition of its role, can we understand our proper role, can we shred undue arrogance, can we fully appreciate our fortune that makes us who we are today.

My hope is from now on, I can write a series of blogs on several issues and dedicate them to the people who mostly influenced my thinking, and inspired my interest. Ten years later, I can look back at those blogs, I will not lose perspective of who have helped me along the way, will not falsely think that I deserve everything, and will be reminded of the responsibility I have because I owe so many people.

A Letter from UC Berkeley Professor

In response to some strike activity at US Berkeley, a Math Professor sent the following letter to his students. It is a powerful letter, and it is worth reading through. I feel his message is so important, that I am obliged to summarize his point for those who do not have time to read.

He offers to cover the sections for his students since two teaching assistant will be on strike, and he refuses to cancel his class. He then moves on to give his rationals----The world we live in is complicated, and we need to solve lots of difficult and complicated questions now and in the future. Students in UC Berkeley are immensely talented, and they should have the responsibility to tackle those questions in the future. Because of that, their education is extremely important for the future task:

And do not fall into the trap of thinking that you focusing on your education is a selfish thing. It’s not a selfish thing. It’s the most noble thing you could do.
Society is investing in you so that you can help solve the many challenges we are going to face in the coming decades, from profound technological challenges to helping people with the age old search for human happiness and meaning.

Learn well, it is not just a luxury, it is a responsibility.


Dear All,

As some of you may have heard, there is some strike activity taking place on campus tomorrow.

I want to let you know that I will not be striking, which means that I will be, so-to-speak, crossing a picket line. Moreover, I know that two of your GSIs have decided to strike, but because I happen to be free in the afternoon when they teach, and because I enjoy teaching smaller classes from time to time and I haven’t had a chance to in a while, I’ll be covering those sections. If you were planning to see me at office hours tomorrow afternoon, then feel free to come to one of the sections I’ll be covering. I will be in Stephens 230c from 2:10 to 4pm, Cory Hall 285 from 4:10pm to 5pm, and Evans Hall 6 from 5:10pm-6pm.

The reason for me taking this decision is extremely simple: We have 7 class days left until the end of the course. Despite the fact that we've made good time and are likely to finish the syllabus with a few lectures in hand for review, class hours are valuable and your education is too important to just cancel a class if we don’t have to. Whatever the alleged injustices are that are being protested about tomorrow, it is clear that you are not responsible for those things, whatever they are, and I do not think you should be denied an education because of someone else’s fight that you are not responsible for. I say this with no disrespect whatsoever to the two GSIs who have decided to strike. Societies where people stand up for what they believe in are generally better than societies where people do not, sometimes dramatically so. Further, I cannot discount the possibility that I may be in the wrong on this and they may be right. I have certainly been on the wrong side of political judgements before and I’m sure I will be again. However from a practical point of view I’ve made my decision and you should all turn up to class and discussion tomorrow as normal.



Beyond practical matters, I think it’s also worth reflecting a little on the broader relationship between politics and your education, and I think I have some important things to share on this topic that may be helpful to you.

I do this with some trepidation. Normally I try to avoid talking about politics with my students and also my professional colleagues because people have a wide variety of views, sometimes held with great conviction and feeling. If I was to get into a political disagreement with one of you or one of my colleagues, it might get in the way of or distract us from the central mission we have of working together to give you a great education.



However sometimes political events reach into our lives without our invitation or control, and we have no choice but to engage with each other about politics. Many times in history it has done so with far more violence and disruption than a strike, and it is wise to be psychologically prepared for this fact.

If I’ve learned one thing about politics since I was your age, it is this: Politics, like most things in life worth thinking about, including mathematics, is very big, very complicated, and very interconnected. I’ve lived and worked in four countries on four continents, all with societies set up differently both politically and socially. I’ve discovered that there is no unique or obviously best way of setting up society. For every decision and judgement you reach, there are people who benefit and people who lose out. It’s the same with the way I teach my classes. I know that for every decision I make about how to teach you there are some of you who benefit and there are others who would do better if I did things differently. There is no way of getting around that. Every judgement you make in life is a question of balancing different interests and ideals. Reasonable good people can disagree on political questions like whether to strike or not, and they can disagree about far more contentious topics also.

All this may sound like speaking in platitudes. However it is a point worth making to all of you because you are so young. One of the nice things about being young is that your thinking can be very clear and your mind not so cluttered up with memories and experiences. This clarity can give you a lot of conviction, but it can also lead you astray because you might not yet appreciate just how complicated the world is. As you get older you tend to accumulate life experiences to learn from, and this is the source of wisdom, but the trouble is that the lessons we glean from life do not all point in the same direction. Sometimes it is hard to tease the correct learning from the experiences life throws at us.

So what are we to do with the fact that when we are young we lack a lot of the perspective we need to make definitive judgements about what is right, but that as we get older our judgements tend to be informed by our experiences, and these experiences guide us in contradictory ways, both between different people and within the same person?

I don’t know.

However one thing I do know is that you are not going to be able to avoid making these kinds of judgements, just as I cannot avoid making a judgment about whether to strike or not. Like it or not, I have to make a political choice, and I have to talk to you about it. For me, the choice not to strike is quite easy, but for you the kinds of judgements and choices you are going to face in your lives are going to be far from easy; they are going to be of a complexity and importance that will rival that faced by any previous generation. To an extent that you may not yet appreciate, the world is changing incredibly quickly. In just a decade, since I was your age, the internet and telecommunications has truly transformed the way we live, not just in rich countries but around the world. When I was an undergraduate, if I wanted to check my email I went to a little room in the basement to use a computer, and if I wanted to learn something I went to a library. The kinds of breakthroughs we are seeing in biotechnology remind me of the way people were talking about electricity in 1900. Of course I don’t know - nobody knows - but my guess is that biotechnology in the 21st century could be similarly transformative to the way the full power of electricity only hit prime-time in the 20th century. The recent controversy about the NSA has shown that the role of information technology on society can be, or at least might become, double edged. There is climate change, another controversial and difficult topic, the exact impact of which we do not yet know. These are just a few of the challenges we can see, and we should remember that history has a habit of throwing curve balls at each generation that nobody saw coming. And among all this tumult, our search for common human peace and happiness on some level becomes more difficult, though no less important. A previous generation dodged the bullet of nuclear armageddon when things looked bleak, but for your generation the bullets are coming thicker and faster than ever before. The potential all of you in your generation are going to have for both good and harm is tremendous.

I suspect many of you have heard sentiments along these lines before. However I also suspect that many of you will think something in response along the lines of `I know all that, but these things are for someone else to figure out, not me.’

That is a mistake.

One of the things you can lose track of when you attend a top tier university like Berkeley is just how exceptional and amazing you really are. I’m blown away every time I talk to you. The way you ask penetrating questions, the way you improved so much between midterm 1 and 2, the way you challenge me to be a better teacher, it just knocks my socks off. You really are amazing. I’ve taught students all over the world, and I’ve never seen a group of students so talented. I’m not just talking about some of you. I’m talking about all of you. It’s a privilege to be your professor. Sadly, however, I know many of you don’t feel that way. The difficulty you all face is that as you look around at all your fellow students, it’s easy to have your eye drawn by people doing better than you. Or rather, I should say people who look like they’re doing better than you. In reality the true extent of how much people are learning can be difficult to measure. Sometimes failures and adversity are better preparations for long term success than effortless progress.

Why am I telling you all this?

I’m telling you this because you all need to know that there is not some great pool of amazing people in some other place who are going to shape the way our species navigates the coming decades. The simple fact is that, like it or not, technology is going to change the way we live in the future, and you’re going to have to solve some very hard problems, as well as figure out how best to use new technology for good, while at the same time facing human dangers that have haunted humanity throughout history.

Part of the work of your generation is going to be technological, using scientific ideas to serve the interests of society, and part of the work is going to be fundamentally human, tied inexorably with qualities of the human condition - human emotion - that dominate the whole of history. These things are not separate, but are inexorably linked, and you are in a better place to understand that connection than me.

I can’t tell you what your particular role should be in the new realities of the 21st century. It’s up to you to decide if you want to make the focus of your life technological, focused on new innovations to drive society forward, or essentially human, focused on the age-old struggles of trying to get along, work together, and find happiness, or some combination of the two.

However I can tell you this:

Whatever you decide to do with your life, it’s going to be really, really complicated.

Science and technology is complicated. History and politics is complicated. People are complicated. Figuring out how to be happy, and do simple things like take care of our kids and maintain friendships and relationships, is complicated.

In order for you to navigate the increasing complexity of the 21st century you need a world-class education, and thankfully you have an opportunity to get one. I don’t just mean the education you get in class, but I mean the education you get in everything you do, every book you read, every conversation you have, every thought you think.

You need to optimize your life for learning.

You need to live and breath your education.

You need to be *obsessed* with your education.

Do not fall into the trap of thinking that because you are surrounded by so many dazzlingly smart fellow students that means you’re no good. Nothing could be further from the truth.

And do not fall into the trap of thinking that you focusing on your education is a selfish thing. It’s not a selfish thing. It’s the most noble thing you could do.

Society is investing in you so that you can help solve the many challenges we are going to face in the coming decades, from profound technological challenges to helping people with the age old search for human happiness and meaning.

That is why I am not canceling class tomorrow. Your education is really really important, not just to you, but in a far broader and wider reaching way than I think any of you have yet to fully appreciate.

Admission Bias?

Update: I realized there is a coding error in my previous version, and I have corrected it. The result now is not as dramatic, but I think it is still striking. I mistakenly plotted the conditional (on wealth) probability of admission, when we are interested in what is the implied percentage of student population based on wealth. I apologize for my mistake.

Motivation:

A friend of mine emailed me a note she wrote on Harvard's admission status. The main finding is that the admitted students tend to come disproportionately from wealthy families, suggesting that, despite the bind-need policy, there is still a selection bias towards the rich. For example, the author found:

About 150 students come from family with less than \$20,000 income, that is about 2.2\% in Harvard’s 6,700 undergraduate population. In the whole country, there are about 20% of families with household income below \$20,000 (Census, 2012)..... 40\% of Harvard graduates presumably come from families with annual income higher than [200,000]. But in the US, only 4.5\% families make more than \$200,000. 40\% of Harvard’s students come from the top 4.5\% of America’s family income spectrum.

While I do agree certain selection criterion like so called leadership, and versatility are unfair to the poor, I think we need to dig deeper into the selection process and data to get a better sense. This phenomonon, could be the result of fair admission process with no bias towards the poor. What do I mean by this?

Theoretical Framework:

Let me illustrate with a model.

Let $Y_i$ be the relevant performance of an individual for admission process. We have
\[
Y_i=\beta_x X_i+\beta_z Z_i+e_i
\]
where $X_i$ is talent, $Z_i$ is work ethics, and $e_i$ is pure luck.
Now we consider the family wealth of that student $T_i$:
\[
T_i=\alpha_x X'_i+\epsilon'_i
\]
where $X'_i$ is the talent of the parents, and $\epsilon$ is all the other factors. We would expect there to be a inter-generational correlation of talents. We could decompose $X_i$ into the inherited part ($E(X_i|X'_i)$) and the innovation part $\xi'_i$. For simplicity, however, we will decompose in the following way:
\[
X_i=E(X_i|T_i)+\xi_i=\delta T_i+\xi_i
\]
This means that talent is not independent of family wealth simply because
1) talent has positive inter-generational correlation;
2) higher talent means higher wealth level in expectation.
Now we can write the performance in the following way
\[
Y_i=\beta T_i+e'_i
\]
Note that $\beta=\beta_x\cdot \delta$, and $e'_i=\beta_z Z_i+e_i+\xi_i$.

A calibration and result

Let us do some calibration. We will scale $e'_i$ so that $\beta=1$. We let $e'_i\sim N(0,3)$ and $T_i\sim N(0,1)$.

Technical fuss: I know wealth does not come from Normal distribution, but consider a function acting on wealth to make the output normally distributed. For example, log-normal distribution is considered to be a good approximation for the distribution of wealth, so instead of saying $T_i$ is wealth, we could say $T_i$ models the log of wealth, which then becomes normally distributed. If you work through the argument, you will find none of these matters.

So the rest is a Bayesian exercise. Conditional on observing getting admitted to Harvard $Y_i>cutoff$, what is the conditional distribution of $T_i$? I calculated the cutoff and did the corresponding calculation, (no worry, I will show you the code and how I calculate the cutoff in the end for transparency). Here is what I find.

The conditional distribution is highly skewed to the right---that is conditional on admission through this fair process, we would expect most of the students come from rich families. Here is the distribution:

The above plot is the percentage of students admitted as a function of income. On the y-axis, it is the percentage of admitted student with respect to total college student population---to find the population percentage among admits, you need to multiply the number by 1000. Note that unconditional $T_i$ comes from $N(0,1)$. Notice the lack of admission in the lower income group until 1 standard deviation below mean.

Another graph. What is the probability of admission in each income group?

As you can see, as the family income goes up, the chance of getting admitted is monotonically increasing. According to our model, this correlation is not causal (family wealth does not cause better performance), and is a result of the centrality of talent.

Ok, let me give you a number in the end. What will the predicted percentage of students coming from the top 4.5% of income distribution? 49.4238%

Discussion

What is the point? The point is not that the education system is fair. The point is we need to be more careful in our diagnosis. Let me give some far-fetched general comments, not validated by the work I did in this blog. The problem might very well lie in the inequality in elementary education and secondary education, and if that is the case, targeting higher education admission process is unlikely to be effective. Efforts like affirmative action aiming to change the result, without addressing the root of the problem, is not only doomed to fail but also likely to create new problems.

I am of the minority view that in empirical work, we need to think harder about the structure of the problem. As those tiny details matter for policy. We need to know the industry we are talking about, understand its structure, and use data to give as precise a picture of the industry. We could gain a lot from reduced-form estimation, but in some applications, without forcing us to be clear the data generating process and the structure, and link them with data, the policy implication could be very limited.

Robustness Check and Technical addendum:

How I choose the parameters for the random variables? Well, I did some exercise finding a reasonable range for the parameters. As it turned out, they tell similar stories. so I choose the parameters that is simple for expository purposes.  I hate blackbox, and I will disclose the workings, which lead to a different set of parameters (slightly more complicated), and show you that the result is basically the same.

So for the first equation

\[
Y_i=\beta_x X_i+\beta_z Z_i+e_i
\],
I let $\beta$'s to be 1 and all variables come from iid $N(0,4)$. That is talent accounts only 1/3 of the performance. (I am using variance 4 to reduce fractions later in calculations)

then for family wealth,
\[
T_i=\alpha_x X'_i+\alpha_\epsilon \epsilon'_i
\]
I let $\alpha$'s to be $\frac{1}{\sqrt{2}}$, and both random variables come from $N(0,4)$. That is talent accounts for only half of the variation in wealth.
Finally, for inherited talent, I assume the correlation is only 1/2.
\[
X'_i=\frac{1}{\sqrt{2}} X_i+\frac{1}{\sqrt{2}}\xi_i
\]
The weird scaling is to make sure that the variance of talent is steady over generation.
If you work through the algebra, you will find the following regression function:
\[
X_i=\frac{1}{2} T_i+\frac{\sqrt{3}}{2}\epsilon'_i
\]
substituting in, we have
\[
Y_i=\frac{1}{2}T_i+\frac{\sqrt{3}}{2}\epsilon'_i+Z_i+e_i
\]
We can pack the last three terms as one error with variance 11, and $\frac{1}{2}T_i$ as scaled wealth $\sim N(0,1)$. In essence we have
\[
Y_i=\tilde{T}_i+\sqrt{11}\tilde{\epsilon}_i
\]
where both random variables are iid standard normal.
 What will the predicted percentage of students coming from the top 4.5% of income distribution be? 22.56%.
Feel free to try different numbers.

Appendix:

 So to make this transparent, I will show you what I did.

How to calculate cutoff? The number of students enrolled in Harvard is 6700, which means 6700/4 students each year. In US about 25 m students enroll in colleges each year. Of course there are other great universities, like Princeton, Williams (yes!), Yale, Stanford. So let me be generous, and say Harvard get the top 0.1%. So with this we can find the 99.9 quantile in terms of Y, which is about 6.18. The rest is coding it up (I used Mathematica):
In[49]:= cutoff = Quantile[NormalDistribution[0, 2], 1 - 10^(-3)];

In[50]:= N[cutoff]

Out[50]= 6.18046

In[51]:= F[x_] := 
 NIntegrate[
  PDF[NormalDistribution[0, 1], x] PDF[NormalDistribution[0, Sqrt[3]],
     y - x], {y, cutoff, +\[Infinity]}]

In[52]:= Plot[F[x], {x, 0, 5}]

In[43]:= wealth = Quantile[NormalDistribution[], 0.955]

Out[43]= 1.6954

In[54]:= ratio = NIntegrate[F[x], {x, wealth, +\[Infinity]}]/0.001

Cleaning the Wound

I had a bike crash yesterday. Something dirty got under my skin. Fearing pain, I only did a superficial wash and applied some antibiotics.

Unfortunately, this morning, I discovered that the site is swollen with pus coming out---a clear sign of ongoing infection. I had to cut open the wound and thoroughly clean it with a scrub. It was quite painful.

I knew I could not just bury those things away. I need to clean it eventually, and it gonna be more painful if I do it later. But I was too much of a wimp to cut it open and clean it yesterday. I am not even sure if I cleaned it thoroughly enough today.

Research

If I have to pick one single most important thing I have learned in college, it will be an easy choice. It is not an answer to any question. It is a question that I learnt to ask: "Who cares?"  or "So what?" I am grateful for being instilled that no-nonsense ideal.

This has since defined my attitudes toward research. As Ed Leamer nicely put, we need to think if that research has any value beyond "mere mathematical amusement".

An epidemic in China

Two pieces of news from Forbes first.
China's Zoomlion Tangles With Feisty Newspaper Over Fraud Claims

Arrested Reporter in Zoomlion Case Admits To Taking Bribes And Inaccurate Reporting
Underlying these two pieces of news is the real big challenge for Chinese Economic development---loose accounting standard and dishonest accounting practices. It is a epidemic haunting China's business community.  The tax system is partly to blame together with the loose enforcement, which makes a prisoners' dilemma---no one can afford to be honest.

I happen to know some accountants in China and what they told me is shocking beyond the kind of news you will see. I will quote anonymously what one accountant told me.

"Accounting is a stressful job. I hesitated a lot before taking another accounting job after I retired. It is just you have to make up the books when you do the job, otherwise, no one will hire you. The trouble is the accounts will be kept for ten more years, and I do not want to be haunted by the possibility of getting arrested five years down the road....audition is not the way to go either. You are too naive. Audition is super lucrative, but that does not come from its legal pay. You are certain to find problems in the books you audit, and you need to look the other way. That is where the money comes from. Also, why would anyone ask you to audit when they know you will find the problem and they can hire others to give their book a nod? That stupid certificate, is a stamp of approval, worth so much money. You can lease it out to others and earn a good profit without doing anything. Of course, that is when everything goes well."

He added, "do you understand? You are probably too young to understand".

Actually, it is not such a complicated explanation. You hear that a lot when it comes to the explanation for financial crisis. The incentive for rating agencies.

I think there are a small number of problems that account for most of our troubles. Sometimes we do not know how to solve them. Sometimes, we understand how to solve them very well, but the political system will not allow us to solve them.

Chinese Romanticism or stupidity

China has undergone gigantic changes in recent years, especially in economic areas. The market economy reform has disrupted the old system, leaving many disgruntled. Many complaints about the current outcomes are unfair for three reasons. 1) The current outcomes compared to the old unsustainable outcomes 2)The comparison ignores the gains and focuses on the losses alone 3) The comparison is made with the rest of the world, partially imagined by the Chinese to justify their complaints.


I will give some examples to illustrate how ridiculous such perceptions can get.


Education. People in China have so much complaints about their education. They think it sucks. The American education, on the other hand, rocks. American high school kids are stress-free, they do not have to work hard, they still get into good colleges and earn good money. That is how a Chinese people think. Our school teaches Maths and Science that is useless. American never need to learn that, and they are fine. So our school system is so outdated. Mea culpa. I once thought so as well. Indeed even after I came to US and realize that the US education system is far worse than the ideal I imagined it to be, I still held a bias against my hometown education (though I was never aware of it). I was shocked when I read in NYT the other day that Shanghai public secondary schools topped the world charts in the 2009 PISA (Program for International Student Assessment). When I told this to my parents, their response is "really? that is weird!"


Health care. Chinese people think they have the most expensive health care. They feel doctors earn too much. Look at Americans, their health care is much more affordable and the poor do not have to worry about not being able to go to the hospital. Nothing could be farther from the truth. I am not sure how they would react if I tell them that it cost me \$364 to get a chest X-ray, which cost a bit above 100 RMB (\$20). It is revealing to observe that when Chinese students in US go back for vacation, they rush to the dentist to get their wisdom teeth out, regardless they are impacted or not.



Housing prices. People complain about housing prices. yes, no doubt the housing prices are high. But it is unfair comparison. Americans pay property tax, but there is no property tax in China. So when you compare property prices, you have to add in the present value of all future tax payment. Also, you cannot compare Shanghai to Philadelphia. NYC is probably the only legit comparison. Many so called cities in US are nothing but small towns in China in terms of population. The demand for housing is simply no comparison. Also there is enormous difference in infrastructure. Cities in China means unparalleled public school system, convenient public transportation, better health care, and safety. The cities in US tend to have lots of problems like crime-ridden slums, inner city schools. With the only exception of NYC, the public transportation is no comparison. Even for NYC, their public transportation is outdated when compared to most cities in China.


Automobile ownership. China does tax automobile ownership a lot---this is done via expensive motor registration. The right to register is auctioned off in places like Shanghai in limited quantity, and people just bid up the prices. In Shanghai at least, that right to register could be more expensive than the car itself. I actually applaud this. I think in cities in China, the sheer number of automobiles create huge negative externalities in terms of pollution and congestion. This externatlity is best internalized via taxation, not only in car ownership and oil tax. In US, car ownership in cities is usually taxed in another form---the difficulty to find a parking place. It is so prohibitive that some people think twice before driving to cities. This tax is prevalent---even in the tiny "city" of Seattle, you will need to drive around for quite a while to get a roadside parking place. Finally it is funny to note that while a shanghainese will complain that the government do so little to alleviate the congestion problem and the pollution problem and complain that it is so expensive for him to buy another car.

You Shall Not Crucify Mankind on [the] cross of Ignorance and Arrogance

There is no typo in the title, it is when ignorance and arrogance cross that I am referring to. That crossing is not "a cross of gold", by all means.

When I came to US, it was a humbling experience. Everyone seemed to know so much and display so much confidence when they discuss various things. I on the other hand, never felt confident enough to discuss anything. Then I realized that they do not know more than I do. The question becomes:Why don't you shut the f*** up and listen? the answer is, because we think we know it all.

As a student of economics, I think I still fail to understand so many issues---the meaning of an empirical test, the consequences of monetary policy,  the function of exchange rate, or the effect of health insurance. But I understand these issues more than the lay people. However, it is troubling to observe that the lay people have much more confidence in their interpretation/opinions of these issues.

The sad truth is that we human beings are not "noble in reason" or "infinite in faculty". We are far from being "like a god" "in apprehension". Our brain however, tend to think we are as perfect as Hamlet sees. Because we are like a god in apprehension, then we should have a consistent story. As a result, our brain constructs a consistent story based on limited information we have, by downplaying contradicting information. When we obtain new information, our brain confirms our original story if the new information is consistent, but tend to rationalize/distort/ignore the new information if it is not. After all, how can a god's judgement be false. It must be that the new information is wrong! This phenomenon is extensively documented in the "confirmation bias" in psychology. Things get worse from here. Our brains take in irrelevant information. For example when we evaluate a person's competence, we take into factor such as if he looks good. In an embarrassing study, researchers found that asking people rate people by looking at their picture, and these meaningless ratings predict election result very well (from local elections). Indeed, that is why newspapers like to include irrelevant information to stir up our emotion. Look at those shocking pictures! Are those pictures powerful because they convey much information or because they stir up strong feelings, that is sure to get entangled with your reasoning?

Indeed, what a crappy piece of work is a man!

So some anecdotes. I have some American guy tells me how I am wrong about what it is like living in China. But I have lived in China for more than 18 years! And he barely spent one year in China. wow!

I know you all have strong opinions, on lots of things. But you seriously do not know them all. How much do you seriously understand what health insurance is about when economics as a profession think they only scratched the surface? How could you think you are a competent judge of the territorial disputes between  China and the Philippines, by just reading a NYT article?

Fellow human beings, be humble. Admit you do not know it all. do not have so much faith in your story. Listen to those who might know more.

Real Explanations for Chinese Trade Surplus---Finale

So I have discussed three explanations I have for Chinese Trade Surplus. There are more of them. I do not wish to write about them all, as it gets tedious for the readers. Nevertheless, I think there are some lessons to be learnt.

The first lesson is do not trust economists religiously. First look at the following diagram. It is the IMF forecasts of Chinese Current Account Surplus vs the actual data. What is striking but not surprising from this diagram is how they systematically got it wrong. Impressive record.

When economists manage to keep such a lousy record, you know they are missing something important. They simply do not understand.

The inability or reluctance to contextualize data is a fatal trend among researchers in general. We ask RA to collect data and we never bother to waste another minute on the data other than running some damn regression to find some spurious relations to publish. We sometimes do not even know what is a canonical data point is like. In this case, it never occurred to us that given such an anomaly, we probably need to understand the country a little bit better. No.

This is a sure recipe for disaster. We never recognize or admit our mistakes (even with a lousy record as shown in the graph) until a disaster takes place and force us to rethink. This is true of Asian financial crisis, the 2007 financial crisis. We can only ex post rationalize, and head towards the next mistake.

The industry of publication no longer cares about truth. We are no longer interested in a simple story linked to the context of a country. Country idiosyncrasies do not matter. They are error term. However, once in a while, we are sure to get a real big error term. We want fancy statistical methods carried out on a huge data set. Thus many of us spend hours to construct dataset without ever thinking or looking at the data. We use all kinds of fancy names, pooled data, panel techniques, cluster analysis, instrumental variables and GMM. This is a complete farce.

Real Explanations for Chinese Trade Surplus 3

In the previous two posts, I discussed two explanations for Chinese trade surplus. I now continue to offer another one.

I will once again start with a story. Imagine you are the firm of one multi-national. You have one branch in country A and one branch in country B. You discovered that you have to pay lots of taxes on profits in country B, but you can evade taxes in country A due to its loose taxation enforcement, poor auditing system, and favorable tax conditions. You also know that there is gigantic intra-firm trade---some things are made in country A and sold to country B and vice versa. What can you do to maximize profit.

This is strategy 101. When you sell things made in country A to the branch in country B, you simply price them a lot higher, so that when branch in country B resell it, it does not seem to make any profit. You will do the opposite for things made in country B. In this way, you have transferred your profits to country A.

I hypothesized this in my sophomore year, and after sending out an email describing hypothesis, I learnt this strategy is not new at all, it is called "Transfer Pricing". Yesterday while working in HBS, I learnt that it is a hot topic in strategy.

Let me make this more lucrative. You happen to think that the currency in country A gonna appreciate against the currency of country B. wow, such a good deal. Thus transfer pricing takes place and it looks as if country A is having a gigantic trade surplus.

Back to China. It is quite self-explanatory how to apply this theory to China. Nike shoes are produced at cost of about $1, and is sold around $60 say. There is plenty of room to transfer profits.

Another aspect of this is the mere expectation that Yuan will appreciate make this transfer pricing more attractive. However, what many people did not realize is that some of the trade surplus might be exactly due to such practices---in other words, such practice is self-reinforcing due to opacity. What you see in trade surplus is not real (due to the reasons I explained in previous two posts), and you expect Yuan to appreciate, so you engage in transfer pricing, enlarging the trade surplus, amplifiying the "false trade surplus".

Real Explanations for Chinese Trade Surplus 2

In the previous blog, Real Explanations for Chinese Trade Surplus 1, I discussed "Suppressed Import Hypothesis". In this entry, I will discuss "Fickle Citizen Hypothesis".

Imagine there is one very rich person in country A. He is capable of making tons of things through his own labor. Each year he exports so much to another country B. He makes a handsome profit out of it. There is no doubt that you suspect this young man is causing a potential trade surplus of country A. Absolutely, you are right. That is what we see in data. However, data are damned by fickle accounting standards. What if I suddenly tell you that young fellow has been revealed to be a citizen of country B instead? Then what he sells to country B is no longer exports (As Rachel correctly points out, from a GDP perspective it is still exports, but not from a GNP perspective. See the technical addendum for a discussion and justification)! If that is the only trade taking place, there is no trade surplus at all! This story shows how sensitive our Current Account (CA) deficits (you can think of this as trade deficit, properly defined) number are to citizenship definition.

Back to China. Many of the super wealthy are thinking of migrating out (for lots of reasons, sometimes for better education opportunities for their kids, which is linked to the story I told in the previous blog, but many times because what they earned is semi-legal via corruption).  If this takes place, and there is indeed evidence it is beginning to take place, we could witness a big capital flow that will wipe out all the trade surplus accumulated in previous years. By that time, not only will appreciation pressure on
RMB disappear, but also there might be depreciation pressure.




Technical Addendum:
I have been sloppy about trade surplus and CA surplus. For one thing I wish not to introduce too much technicalities, and for another, I think CA account is the proper definition of trade account. Trade account, too narrowly defines what is trade. In some sense, CA surplus is the trade surplus with respect to GNP, but trade account is trade surplus with respect to GDP. GNP, in my opinion is a more appropriate measure, but in most cases, there is little difference between GDP and GNP.
In general it is the large CA surplus that is disturbing. If country A earn huge trade surplus, but that is balanced out in its equally gigantic payments on foreign investment, it is no big deal, it is just a very different trade structure in that country B exports its capital service.

In China's case, most people ascribe the CA surplus to trade surplus. What this blog aims to illustrate is that such a large trade surplus is not incompatible with a balanced CA account, if proper adjustment is made. The important piece here is not net factor payment, however, it is rather capital account, namely cash transfers, which will take place when citizenship changes. Capital account has been completely out of discussion since it is generally unimportant, but what I argue here is it is illuminating to consider this channel in China's case.

Real Explanations for Chinese Trade Surplus 1

By real, I mean the real side, not the monetary/currency side. Of course, I am playing the pun that what politicians and economists in DC says aren't real.

Suppose there is a country A. Its people want to import a good from country B. However that has not been possible due to all kinds of reasons. Nevertheless, it expects that it will soon be able to import that good. If the expected import of that good is large enough, we will not be surprised to witness a gigantic trade surplus for country A now. This is my "Suppressed Import Hypothesis".

Back to China. What is the suppressed import I have in mind? Education. The number of students coming from China to US (or abroad more generally) for high school and undergraduates have been growing exponentially. I have not yet looked up official data, but anecdotal evidence is striking enough. For UC Berkeley, it started with single digit, and within 2 years, it reached 3 digits. NowI think the number is about 400. I heard similar stories in other state universities. I am talking about undergraduates here, who for the most part, pay every single cent. That is a gigantic number. This trend is a new phenomenon, and it should partly explain the current account surplus of China in previous year. There are lots of other reasons I will discuss in later blogs, but I think this is one story that is missing from the scene.

I simply need to share this----College Admission

Writing (or ridiculing, depending on your persepective) about american college admission system was on my agenda. Now, I probably won't because there is a better article.
http://www.newrepublic.com/article/114848/college-admissions-criteria-american-vs-british

About Models

I did not intend to write this, but I felt I need to after reading a comment to my post.

There are two kinds of models. One kind of model is to make a point, or formalize an insight. The other kind of model is used to model the reality closely, and they are intended to be brought to empirical tests.

The first kind of model are designed to be as simple as possible, but not simpler. The second kind is designed to be as realistic as possible. We calibrate the parameters, and estimate the distributions if there is stochastic elements. Each parameter or variable has a direct implications---none of which is true for the first model.

I probably will only discuss and present the first kind of model in my blogs (I tend to prefer them in research as well). So what to make of my model? There are some basic take-aways, and that is why I wrote the model down. There are also many conclusions specific to the model assumptions, do not pay attention to them. They are not likely to be robust.  The general rule is that do not be religious of the numbers I generate, and they depend on model assumptions heavily. Nevertheless, I try to present robust qualitative results.

There are tons of criticisms that I could leash out against normal distribution. But I will use them anyway. It is unlikely it gonna change the basic idea, and it is convenient.


I will end with a semi-relevant anecdote. In class one day, professor Helpman decided to present a general model of multiple goods. There is one "theoretic" guy in class and he asked:" Why don't we make the model more realistic and generalize to a continuum of goods?" Not a super impressive question. With finite numbers of molecules in the universe (yes, a large number),  "continuum" is is not more realistic than "general N".

The Dirty Secrets of Achievement

Nowadays people are obsessed with achievements. What school we get in, what jobs we get, how much money we get, and how famous we are.

Every time some famous or achieved person talks, there will be disciples eagerly listening to words of wisdom and religiously put them into use.

Let us be skeptical. I have written about prosecutor's fallacy in my post Official Nonsense. In essence, while the probability of success conditioning on a good strategy/talent is high, the probability of good strategy/talent conditioning on success might not be high. In other words, we could not infer that much from success. What they did might not get you anywhere.

Let me do a calibration. Suppose there are four strategies: a,b, c, d. You can also think there are four talent groups. Each individual in the group will produce a random outcome following a normal distribution. The mean (average level) and standard deviation (dispersion) will be different for each groups.For group A, it is N(3,1), B---N(2,2), C---N(1,3), D---N(0,4). In other words, in expectation, group A is the best, not just in terms of average outcome, but also in terms of risks. Group A has the lowest risks. From a mean-variance analysis point of view, group A dominates the other groups. No question. However, when we do the simulation, and we wish to calculate, among those in 90, 95 and 99 percentiles, how much of them come from each group. Here are my results.
        90           95         99
  A  0.0025         0         0
  B  0.0525         0         0
  C  0.1050         0         0
  D  0.8400    1.0000    1.0000

The results are striking! Most of the successful people come from group D! and all of the super-successful come from group D!

This simulation uses 1000 people in each group.

Let us be robust, what about only 100 people in each group? Here is the result:

        90           95         99

A            0         0         0

B    0.0250         0         0

C    0.1000         0         0

D    0.8750    1.0000    1.0000

The moral of the study is NOT that people who are successful took the inferior path. This simulation only cautions against inferring too much from outcomes. The reason I used different means for each group is to demonstrate that, given enough risks, you could expect people to stand out even if they are not the type of people who would normally succeed. It is the triumph of risks in ex post observation against expectation. 

Basically the take-away is : worship is unnecessary, and above all, do not worship yourself.

I have attached the Matlab code I used in case curious readers wanna play with different specifications. It is quite robust.

rng(1)

a=normrnd(3,1,100,1);

b=normrnd(2,2,100,1);

c=normrnd(1,3,100,1);

d=normrnd(0,16,100,1);

complete=[a;b;c;d];

achievement90=quantile(complete,0.9);

achievement95=quantile(complete,0.95);

achievement99=quantile(complete,0.99);

m=[a';b';c';d'];

summary=[mean((m>achievement90),2)/0.4,mean((m>achievement95),2)/0.2,mean((m>achievement99)/0.04,2)]

a=normrnd(3,1,1000,1);

b=normrnd(2,2,1000,1);

c=normrnd(1,3,1000,1);

d=normrnd(0,16,1000,1);

complete=[a;b;c;d];

achievement90=quantile(complete,0.9);

achievement95=quantile(complete,0.95);

achievement99=quantile(complete,0.99);

m=[a';b';c';d'];

summary=[mean((m>achievement90),2)/0.4,mean((m>achievement95),2)/0.2,mean((m>achievement99)/0.04,2)]

about grad school

so an update on grad school.

So far so good, despite the fact that I got sick twice already.  I am extremely happy with where I am, with whom I am. It is easy to say this since the winter has not yet come, but we all know that "The winter is coming. It gonna be long".

I really like the people. I actually now enjoy going to my office, because I get to see some people I enjoy working with.  I actually wish I could collaborate with them in some future work. Great thing about Cambridge is that I just have more friends to hang out with here, and that actually makes a much larger difference than I anticipated.

I like the program. It is super flexible which is a big plus for me and I am only taking classes I am interested in. Fabulous class so far---I hope I can still say this after my first Matlab exercise. I had the great fortune of having Daniel as my TF. For one thing it is great that I can actually get to meet him regularly, for another, he is just so good at teaching, which is rare among grad students.

I really enjoy being a grad student. Yeah, I get paid very little--compared to the outside jobs. (This is answer to a question posed by some people how can academia pay so little without worrying it does not attract people). I feel I am learning interesting things everyday, and I get insights very often. I constantly have ideas, some are crappy, some are great. Among the great ones, I often find them already published. But there are survivors, and I look forward to working on them after I am done with coursework.

There is a lot I wish to write about, but I am a little behind on work due to my untimely and frequent sickness. But here is a list of things I am hoping to write about:
1. myopic tracking and incentive distortion.
2. internal consistency and rational expectation---when necessary?
3.  incentivized dogmatism
4. emperics is king.

Some ranting against technology

This is not going to be a very coherent argument as I still have fever. I will revise this soon.
So there is the trend to tech things up---the most extreme being "no child left untableted". I am personally against that. For one thing there is no evidence that the marginal benefit of introducing technology justifies the cost---which consists for government expenditure, (which in turn includes staffing cost) and deadweight loss associated with taxation needed for such expenditures. To be honest, I doubt if there is any marginal benefit for kids introduced with all these fancy stuff.
I am a reluctant technology user---by reluctant I mean, I feel I have taken up say smartphones because it is a better option for me, given that everyone else is using them. However, my overall satisfaction has fallen dramatically. I would be much better off were smartphones not introduced at all.
By imposing technology on kids so early on, we are only reinforcing this effect.

Ultimately, I wish to retire the use of smartphones, then emails, like Donal Knuth.

On microfoundation

There are two ways we can model the whole macroeconomy. We can model the aggregates directly, like aggregate consumption, price, and so forth. Alternatively, we could build from the bottom up, we start from people's decision making---solving their optimization problem, and then model their interaction, and finally the whole market. The second approach is a multi-layered approach in that in each layer you specify the rule, you study each layer separately, from the bottom up, and using the result you solved for in the previous layer as input. The idea of micro-founded economics is illustrated in the following diagram.

An Illustration of Microfoundation

A digression for the super serious: what the above diagram illustrates is a more hierarchical model where different groups of individuals make decisions sequentially. In reality, and in literature, different groups often make decisions simultaneously, and yet taking into account what other group will be doing (and other group will take into account of what that group is doing as well in an infinite loop) (for those who know game theory, we are looking at Nash Equilibrium). 

So an obvious observation is that the second approach is so complicated. After all, why bother to study from the bottom up if all you are interested is the top level? Indeed, economists have taken the first approach for a long time, until comes along the famous Lucas Critique:

"Given that the structure of an econometric model consists of optimal decision rules of economic agents, and that optimal decision rules vary systematically with changes in the structure of series relevant to the decision maker, it follows that any change in policy will systematically alter the structure of econometric models."

What in essence Lucas Critique says is that, when we model the top layer and decide to engineer some policy to bring out better outcomes, we have changed the environment the individuals face---and that change will pass through all those layers into the top layer---which means that our old model of the top layer becomes invalid. The most famous illustration is the Philipps Curve.

So we have turned to the second approach, with lots of added effort. The extra effort does not mean we are golden. Quite the contrary. The problem is when we model each layer, it will be highly imprecise. All those imprecision adds up and amplify each other, and when we get to the top, it is nothing like the the real world---that is how we get highly unrealistic models that very few has faith in. The standard approach in economics is that calibrate our model----find parameters (the very first inputs) to match our data.  Because of the problem I mentioned, to fit the macro data, our estimates of the parameters would be non-sensible in the micro level.  Not surprisingly, micro-level and macro-level data often give us highly different estimates.

Another Digression for the super-serious: Imprecision is a bad word choice as it suggests a mere error term that would be dealt with in statistical analysis. Instead, I mean the deviations of structures from the reality. For example, imposing homothetic utility does not just generate random errors. Another point is that, we can always tweak our models so that it will fit micro-level and macro-level data. But are we just telling stories so that the data will fit, or are we actually making the first several layers more precise? In some sense, the purpose deviates from the true spirit of micro-foundation, to spinning a story that resembles micro-foundation.

An example to illustrate. When I was young, I like to play with ship models. I liked those fancy ones where you build from very tiny parts. Those require very careful work, but I was clumsy. When I put together those little pieces in a less than perfect manner, I could no longer fit that giant chunk into the frame of the ship. I used brute force, squeezing here and there until it fits, more or less. But when I looked back at those little parts, it is so distorted now. Several parts were displaced, some parts fell off, and it was just a mess. I think that is very similar to the mess economists are dealing with.
While my modeling experience could be improved via better craftsmanship, the modeling experience of economists are in some sense hopeless----To mathematically model these layers, things get so complicated. To make things tractable, we have to make numerous simplifying assumptions, not all of which are innocuous. Further more, by imposing those assumptions, we limit the type of questions we could ask as well.

So which approach is better? I do not think there is a definitive answer yet, but I want to contribute my two cents. The critique against the first is that it is not robust to policy changes, but it could be fine in the absence of policy change/paradigm shift. The second approach is aimed to address this inadequacy. But it fails the job---the changes in policy/environment pass through the model highly distorted due to the imprecisions added at each layer.

Admittedly, if we take the first approach, we can be a scientist, but we can never be an engineer---the very attempt of engineering would destroy our model. However, could we ever aspire to be an engineer in those fields? There are always things we do not model, and those things might be irrelevant in the previous world, but matter a lot in an engineered world. If you think you can fine-tune the economy with DSGE, you are guilty of the pretense of knowledge.  As a conclusion, I want to be provocative and say that  mathematical thinking and careful judgements+intuition are not substitutes, and they as a whole make up rigorous thinking (though some arrogant people tend to view mathematical thinking is necessary and sufficient for rigor).


After Note: Micro-foundation is the mainstream in macroeconomics, or any branch of economics these days. I thought about this for a long time, but never wrote much about it. This blog came out of a discussion I had with a friend, and I feel I need to write it down to invite further discussion.

an interesting comment

I saw an especially interesting comment today on facebook. Let me quote it in full.

i wish i could say this only applied to bowdoin:
What does Bowdoin not teach? Intellectual modesty. Self-restraint. Hard work. Virtue. Self-criticism. Moderation. A broad framework of intellectual history. Survey courses.English composition. A course on Edmund Spenser. A course primarily on the American Founders. A course on the American Revolution. The history of Western civilization from classical times to the present. A course on the Christian philosophical tradition. Public speaking. Tolerance towards dissenting views. The predicates of critical thinking. A coherent body of knowledge. How to distinguish importance from triviality. Wisdom. Culture.

btw, here's some of what they do teach: Queer Gardens, Beyond Pocahontas: Native American Stereotypes; Sexual Life of Colonialism; Modern Western Prostitutes.
Explores how the garden in Western literature and art serves as a space for desire. Pays special attention to the link between gardens and transgression. Also considers how gardens become eccentric spaces and call into question distinctions between nature and culture. Examines the work of gay and lesbian gardeners and traces how marginal identities find expression in specific garden spaces. Reconsiders one of the founding myths of Western culture: the idea of a lost Eden. Authors and gardeners may include Marvell, Lanyer, Pope, Seward, Dickinson, Burnett, Carroll, Sackville-West, Nichols, Jarman, and Pollan.

Are we ready for knowledge?

Knowledge is a huge burden. Without it, we act on default. When we know about the consequences of default however, it is impossible to continue act on default without debating over alternative actions, which inevitably involve moral judgement and clashes over value systems.

Let me give a concrete examples. Studies have shown that when girls and boys are educated in the same class for maths and science, girls learn worse than when they are taught separately. However, boys learn better in a co-ed system. The problem is shall we bring them apart? Some would say yes, arguing it is unacceptable that allow boys do well at the expense of girls' suffering. Well, that is one argument, but this argument uses the reference of boys and girls studying separately. However, if our reference is co-ed, and we consider the alternative, we might ask, is it ethical to let boys do worse so as to make girls learn better?
When we know nothing, choice does not carry a moral consequence. Ignorance is amoral, not immoral. However, when we know what each option would entail, it is just tough. Anyone who tries to make an overly simplistic picture for his own agenda, is a demagogue at best, most likely a dangerous man, and a devil at worst.
As a future researcher, I could just focus on positive analysis, and leave normative analysis to others. However, I have to constantly remind myself, that we live in a dangerous world, and positive analysis could easily abused to benefit an ambitious and evil group.

official nonsense

The background is that I went to the Boston RMV to apply for a learner's permit. I had to go through the driver's manual. Unfortunately, there is some statistical non-sense in the manual that annoys me greatly.

In order to convince drivers to wear safetybelt all the time, they say "Most motor vehicle crashes happen within 25 miles of home. In fact eight out of every ten accidents occur when drivers are going 40 mph or less".  The problem of this sentence is that it is irrelevant and misleading. This is what is called a prosecutor's fallacy (http://en.wikipedia.org/wiki/Prosecutor's_fallacy). The idea is the the probability of event A given B could be very different from the probability of event B given A.  Whether we want to wear a seatbelt is dependent on the probability of having an accident conditional on we are only driving within 25 miles of home.  If that is too low to justify the cost of putting on a seatbelt, a rational person might decide not to. However, we are not interested in the probability of being within 25 miles of home given an accident happen. Reductio ad absurdum, Imagine a world where everyone drives within 25 miles of home. Even if the accident rate is negligible (less than the accident rate of air plane), we can still claim that most (actually in this case, all) motor vehicle crashes happen within 25 miles of home.

I completely understand that the intention of RMV is good--to convince people to wear safety belt. But good intention does not justify ignorance/stupidity or outright misleading. (I myself have lots against the compulsory seat belt wearing thing, as I think it makes the road less safe, but that is a topic for another day)

Prosecutor's fallacy is rampant, to my dismay. Let me digress and point out how prevalent it is. The Phi Beta Kappa society, which claims itself to be an elite society, points out that "Since inception, 17 U.S. Presidents, 38 U.S. Supreme Court Justices, and 136 Nobel Laureates have been inducted members." seems likes a high percentage for a lay person? Not really? I have an even better number. All  of US presidents, US Supreme Court Justics, and Nobel Prize winners are human beings!!! So the right thing to consider is what is the probability of doing great things given a PBK membership? Probably pathetically low. My fellow PBKs, I do not think you have any reason to register any pride with this society. 

Back to RMV. When I entered RMV at 11:51. I got a slip saying that the estimated waiting time is 14 min. I thought to myself, great!!! Then I was called when it was past 13:00. I doubt if takes super advanced statistics to get a slightly more accurate estimates. 

Why I hate dogs

I hate dogs.

I like to bike and many times when I bike pass some house, there will be a dog barking fiercely at me, sometimes even chase me, as if I am about to invade their house.

From the intelligence of a human being, I am so unlikely to be an invader, by just biking past a house. But for the intelligence of a dog, what do you expect? Perhaps, I should not hate them, but I am annoyed.

Some politicians like to call this country a threat and that country a threat when those countries are peacefully minding their own business, just like me. Perhaps, even more ridiculous, a dog won't even bark at an ant walking past its house.

paranoid, or?

No pressure, my friend

I like to be pressure-free. Neither do I like to pressure myself, nor do I like to get pressure from others.

Friends. I have always believed in the Chinese saying that the friendship between noble people should be as bland as water 君子之交淡如水。It means that when we make friends, we should not expect anything from friends, and we should not make friends feel pressured to do anything because of us.  I am always hesitant to ask favors from friends, especially close friends---being close friends, I fear they will tend to feel the pressure to agree, and that makes me feel upset. I really hope one day people around me, will always tell me honestly, whenever they feel inconvenient to do something I asked for.

People now like to show "support" for friends. For me, I think it is quite unnecessary. We are friends because we share similar interests, but we do not have identical interests. When I am doing something I am interested in but you are not, why should you feel obliged to show support? Friendship, I feel, should be based on common interests and goals, not on reciprocity. One of my friends told me after my thesis defense that when he arrived, he knew he would not understand anything, and said those things are about friendship. I replied that is exactly the reason why I was reluctant to tell him the time and place of my defense. I feel guilty for creating pressure on you, my friend.  I showed up to your history thesis defense not because you are my friend, but because I am genuinely intrigued by your paper.

Friendship should be simple. No burden. Simple joy.

Why I gave up martial art

I used to be a student of martial art, a fervent one. During my worst days, that was my only companion--it was only during those hours when I practice martial art that I could focus and not distracted by painful thoughts. I seriously thought I would take it as a life-long pursuit.

But I gave it up in college. Williams is not to be blamed. It is true we do not have such a professional martial art club, but I gave it up more because I wanted to.

My first encounter with Martial Art is Tai Chi, an ancient form of Chinese martial art.  The first day we did not learn forms, but about the philosophies. I remember very clearly what the master said: " The purpose of martial art is not violence, but is to stop violence. We learnt that our biggest enemy is never others people, but ourselves, our inner urge toward violence and brutality, and to master martial art, we need to master the art to curb such aggression. （克己） This is not an idealistic romantic tenet of some ancient Chinese philosophers, but a very wise idea---you can be very strong, as strong as you can, but if you cannot curb your urge to violence and aggression, soon it will backfire when you upset enough people and/or strong enough people. We will turn old and weak, and none of us can stay on the top, aggression and violence will turn back toward us if we do not curb them in the first place. Respect (礼）and benevolence (任）are always stressed. As these guide the previous principle, which literally means hold back yourself from you should not do. Even in Japan, the tenet of Bushido includes respect and benevolence, but they over-stressed loyalty and honor, and when being loyal to the wrong thing, and taking honor in the wrong thing, things get bad. What happened in WWII is only a sick and disgusting deviation from the true spirit, not the orthodox martial art philosophy. In the movie Yip Man, Yip Man said rightly: " You Japanese invaders are unworthy of martial art".

That is all good and beautiful. Later I realized however, mastering martial art will not help stop violence. In this age, violence never takes the form of bare-fist fight between individuals, but are staged by countries, organizations, and using deadly weapons that easily out-power the most skillful martial artist. In the movie Yip Man, Yip Man felt the same futility when he saw Japanese invaders did horrible things, and killed people but he could do nothing though he is the best martial artist of the time. What is more, I realized I began to develop knee problems from martial art practice. The purpose of martial art is to protect others from violence, and not only is that impossible, but also, instead of protecting ourselves, we are hurting ourselves. That was the last straw.

In this world, when the media continuously distort the truth, we do not even know what is right and what is wrong, then what is the use of power?