A puzzle and my critique

Foreword: I started the blog with the intention to write only two paragraphs with the title "A puzzle or not". Fortunately for me, and unfortunately for the reluctant readers, many related ideas came to me when I wrote this, and before I know it, this blog contains a hodgepodge of ideas.

In Economics, there are often "puzzles". These puzzles refer to the  situations that the observed behavior deviates from the optimal one. For example, the famous equity premium puzzle refers to the fact that "mysteriously" people are under-investing in equity, given the high equity premium. There are numerous such puzzles in game theory, when numerous experiments confirmed that people are not behaving optimally on average.

Are these puzzles?

Many economists say "yes". Their argument is this, while we do not expect complete individual rationality  there is no reason to expect people's behavior to systematically deviate from the optimal. In other words, people's deviation from the optimal should cancel each out! Since many earlier famous economists are trained in Physics, they might even draw an analogy with Physics (I am not aware if anyone did indeed draw such an analogy, but I imagine some would), when there is a voltage difference, the electrons will on average predictably flow in one direction, even individual electron might deviate from the predicted flow. More philosophically, local disorder does not preclude global order. This is indeed such a powerful idea, upon which many sciences, physical or social rest upon. I personally am obsessed with this idea, and I think if I can only remember one idea, this will be the one. Nevertheless, this idea has its bounds.

While local disorder does not preclude global order, it does not GUARANTEE global order either. While we do not expect people's behavior to systematically deviate from the optimal, we do not have any reason to expect that the average behavior will converge either! Then what is this average behavior then? Let me first divert you to a story the mighty Richard Feynman told:


Nobody was permitted to see the Emperor of China, and the question was, What is the length
of the Emperor of China’s nose? To find out, you go all over the country asking people what
they think the length of the Emperor of China’s nose is, and you average it. And that would
be very “accurate” because you averaged so many people. But it’s no way to find anything out;
when you have a very wide range of people who contribute without looking carefully at it, you
don’t improve your knowledge of the situation by averaging.

That's the point! When we are confronted with a very complicated economic decision (it does not have to be really complicated, it could be as simple as a game of flipping coins), many of us the laypeople are confused and have no idea what is optimal. When the welfare consequences are not that high, we basically just choose one action that looks right to us, and there is no guarantee what looks right to us will average out to be optimal. Yeah, you are right, we have some sense of what could be optimal and what could not. But even in the story of the nose length, the people have some sense. They know 100 inch is unlikely, neither is 0.005 inch.  It will be obvious to people that some options are bad, but that's it.

Why I bother to write this blog? For one thing, I like to test out my ideas on the internet and see if there are loopholes or counter-arguments obvious to other readers. But I actually think this is an important idea (no claim of originality here, as Feynman definitely saw this): semi-optimization (eliminating obviously bad choices) or bounded rationality will not lead us to optimal behavior on average. This calls into question lots of the work we do in Economics. When we run regression to estimate parameters like elasticity, many of the implicit assumption is that the average behavior we observe is optimal. This assumption actually does not need to hold, and when that's the case, the fancy regression some people do might be of the same quality as the estimation of the emperor's nose length.

One challenge facing social scientists is causality. For example, when we try to estimate the marginal value of education, we worry about omitted variable bias. We worry that one's education level might be correlated with the person's innate ability, which might again correlate with his earnings. Thus what some people do is to construct a model where the person choose the level of education optimally based on his innate ability. From that model, they design some statistical inference procedure. If only the average behavior is optimal.

Causality is indeed a huge challenge confronting social scientists. However, there are other challenges. The fact that the objects social scientists study (us!) do not fully optimize is a serious challenge. If we do not optimize at all, it is easy to deal with. If we fully optimize, it is slightly more complicated, but handleable. But semi-optimization is tough to deal with. We need to keep in mind people look to social science to guide their optimization--we might choose whether we want to continue education based on economists' estimates of marginal value of education, and it will be pretty funny to know that the very estimates economists come up with is based on the assumption that people have on average optimized.

What is the right attitude to do science? It is often tempting to make some assumptions so that things are tractable. If those are innocuous assumptions, then go ahead, and I think it is great! However, when those assumptions might invalidate the results we get, I would suggest caution. We do not do science because we want to be able to say something about it, but because we want to say something right! I do not mean, however, that we should stop, we might still benefit from a model with dubious assumption as that model might act as a benchmark. Nevertheless, we need to be aware of the model's limit. To act or implement policy assuming the model is correct is a "pretense of knowledge".  Austrian school distrust econometrics, for a reason---so many things could go wrong. Mainstream economists dislike them, and I think part of the reason is that they will not be able to do much with the data under the Austrian critique.  While I believe we could still do thoughtful empirical work, I have to admit the market is flooded with mindless regressions with no value what so ever!

Decision

First let me quote from The Art of Choosing,

the more choice you have, the greater the number of appealing options, no matter how discriminating your tastes...So you'll have to make some sacrifices, and each of these carries a psychological cost. Your enjoyment of the chosen will be diminished by your regret over what you had to give up. In fact, the sum total of the regret over all the "lost" options may end up being greater than your joy over your chosen options, leaving you less satisfied than you would have been if you had had less choice to begin with.

I read the book when I felt I could not deal with all the tough choices anymore, I chose to study the very process of choosing. As it turns out, theory enlightens but does not solve everything. In the end, I had to face the tough problem head-on.

It was tough. Actually no. It was tormenting. Lots of people made it very hard, but I do not mean it in a bad way---I loved those people and really wish I could hang out with them in the next five years. I care about the feelings of lots of people--scoff at as you may, but that is part of my upbringing.

 In the words o Harry Triandis, they are "primarily motivated by the norms of, and duties imposed by, those collectives" and "are willing to give priority to the goals of these collectives over their personal goals," emphasizing above all else "their connectedness to members of these collectives"...it's believed that individuals can be happy only when the needs of the group as a whole are met.

The above quote from The Art of Choosing serves to illustrate the very different mode of thinking that those brought up in the Western world is unfamiliar with. I am not trying to explain my decisions, I just wish to say because of my mindset, it is just tougher.

Chuan, Nick and Jenny, I really wish to join you all for the greater Williams community in Bay area, I am sorry I cannot. Jessy, Kelly and all the other friends I have or I have made in Stanford, how I wish to be able to hang out with you during the next five years. I am really sorry. Fate is relentless---I won't get it all. I hope it will somehow bring us back together sometime in the future.

I wish to say no more about the decision. I wish to explain it no more. However I made the decision is no longer important. The important thing is that I will live with it for the rest of my life. I will not regret. I will do my best.

I am really exhausted. I long for a cup of nicely marked caffe machiatto.

Let the data speak!

I am against the trend that we let data, and only data to speak for themselves. But I do have some thoughts on what they should speak. Namely, questions!

Asking the right question is an important, important skill. What is a good question? It is relevant, and we have a good attack! In statistical science, the second point means we have the right data! If we only have like 10 data points and you wish to estimate the parameters for a super-complicated models involving 10 parameters, I wish you good luck.

When I took Econometrics, I was cynical. I am unhappy with linear models. As far as I see, the relation we try to estimate could be quite non-linear.  However, there is a point, that I just begin to see. For a long time, (still in many areas today), data are scarce. It will be unrealistic to do a highly structural estimation, and it makes perfect sense for us to restrict us to linear models. At least, we recover correlations. The caveat many miss is that, once the model is ill-specified, the coefficients we get might not be interpretable, or requires more thinking, and quantifiers.

If I indeed get lots of observations for each possible vector of independent variable, I could impose no structure  I could simply estimate the mean of y_i for each possible vector of independent variable, and here we go.  I am not saying that's the right way to do it, but it will be ok.

A related talk I heard last semester is on spatial statistics. It talks about estimating earthquake frequency. The talk discusses how fine the grid should be. The solution is let the data decide! If you happen to have lots of observations, you can have finer grids...duh.

My view is that there is no physical probability! The world is deterministic. (For example, the coin flip is not random! At Persi can toss it however he wants) There is only belief. Lots of things we observe in life are just very complicated, and obtaining enough data to recover the deterministic relation becomes a bad bad question (because it is impossible). What is our job? We try our best to collect data, and based on the available data, we try to come up with the right question! The questions involves the model with the parameters to be estimated. The complexity of the model should match the data. What we could not be incorporated, we take them as "noise". It is our discretion to decide what is noise (the log term, or quadratic term, or that variable). This is where reasoning comes in. From research in the corresponding fields, we get a sense of what might be important and what might be negligible, and we make our assumptions accordingly. Data and assumptions are complementary not substitutable!

We are in the era of big data. There is no deny. But instead of being lazy and striving to make as few assumptions as we could, the availability of new data grants us the opportunity to ask questions that could not be asked before! Ask yourself not, what I can leave the data to do, ask yourself, what can I do with the data!