Gravity and Darkness

As a trade economist, much of my recent work has involved what we call the "gravity equation" for bilateral trade (it also works for bilateral migration flows and FDI stocks). Originally (1960s) it was inspired by Newton's gravity equation.  Although it seemed to "work" pretty well, it was not respected within our field because models are supposed to be based on assumptions, not analogies. Thankfully, now there are very compelling derivations of bilateral trade equations that bear a strong resemblance to the gravity equation in physics.  

OK, that's the prologue.  The reason I'm actually writing today (other than the usual procrastination motive) is that I was reading my step-father's Physics World magazine and came across the following quote:

there is always a sort of war between those who tend to assume the absolute correctness of the laws of physics that are in use, even when this requires imagining previously unseen entities governed by those laws, and those who instead are inclined to imagine that new laws of physics must be discovered. The conservatives are more frequently right....[but sometimes] the "new laws" hypothesis turns out to be right... (Giovanni Amelino-Camelia, Physics World, July 2009)

The current incarnation of the "new entities" versus "new laws" debate revolves (so to speak) around the questions of dark matter and dark energy. The problem that dark matter solves has to do with the rotation of speed of stars as a function of the distance of the star to the center of the galaxy.

I love this figure because it is the type of figure I have done in my own work so I can almost feel like I understand it (which I don't of course, having only taken 1 semester of university physics and one "physics for poets" course about light). But anyway, the point is you have to postulate the existence of lots of invisible dark matter in order to fit the data using the existing laws.  Similarly (I guess) you have to postulate dark energy to explain why the universe is expanding at an accelerating rate.

The "new laws" types take another approach: they have a more general theory that reverts to standard Newton/Einstein gravity at the scale of the solar system but is capable of explaining the anomalies at the galactic scale. This article explains it all very well and I more or less understood it except the part about tensors. Vectors and scalars, fine. But what the heck's a tensor?

In another article in Physics World, I find the following intriguing idea.

Moffat and Brownstein, however, argue MOG [the theory of modified gravity] can provide a more natural explanation by removing the need to invoke mysterious dark matter. Essentially MOG adds extra terms to Einstein’s theory of gravitation — general relativity — that allow the gravitational constant G to vary across space and time.

So back to my day job: understanding trade. We already know that there is no gravitational constant for bilateral trade.  In addition to distance and country sizes, bilateral trade depends on large set of linkage indicators (shared languages, laws, currencies).  This question of new laws motivates me to revisit questions that came up in earlier work. Do commercial interactions between people decline in proportion to distance at all scales of observation (inside a country, inside a city, inside a building)?  Do the same gravity equation parameters that apply to high-trading country pairs also apply to low-trading country pairs?

Mystery Achievement: Ambition and Depression

President Obama is to give a speech to schoolchildren.  One of the passages  quoted in a Guardian article caught my attention.

He also references Harry Potter author, JK Rowling, and basketball legend Michael Jordan. "Some of the most successful people in the world are the ones who've had the most failures," he will say. "JK Rowling's first Harry Potter book was rejected 12 times before it was finally published. Michael Jordan was cut from his high school basketball team, and he lost hundreds of games and missed thousands of shots during his career. But he once said, 'I have failed over and over and over again in my life. And that is why I succeed.'"

The problem I have with this is that there are many aspiring authors and basketball players out there.  Most of them will never be published or play a single game in the NBA.  No matter how hard they work, if they keep trying, they will keep failing. 

That's not pessimism speaking; it's statistics.  

Obama is right that highly successful people often had to overcome numerous setbacks and even failures along the way.  But so did everyone who ended up not making it in their desired field.  How do you know who you are? How do you know when to quit?

The Economist recently had an article on the relationship between goals and depression. Recent research suggests

Mild depressive symptoms can therefore be seen as a natural part of dealing with failure in young adulthood. They set in when a goal is identified as unreachable and lead to a decline in motivation. In this period of low motivation, energy is saved and new goals can be found. If this mechanism does not function properly, though, severe depression can be the consequence.

So persistent pursuit of one's "dreams" may not be worth encouraging afterall. Of course no one ever got anything important done by giving up at the first obstacle. So we have to be good Bayesians. After enough failures, we give up.  Of course Harry Potter readers must be very happy that Rowling had such strong prior beliefs in her work. I wonder how she knew to persist.

 I can't resist closing with a favourite quote by Chrissie Hynde:

Mystery achievement, where's my sand beach?

I had my dreams like everybody else.

But they're out of reach. 

I said right out of reach.

something rotten in the state of Macro

Reading Krugman's NYT Magazine article (it's long but well worthwhile to get all the way through) I also thought back to discussions I had in grad school.  Didn't we talk about the idea that macroeconomics needs micro-foundations but not neoclassical ones? That seems to be the final message of Krugman (that salvation will come from behavioural finance).   Another idea I recall vaguely from our discussions is that static maximization--which we use all the time in our micro models--is a decent approximation because people go to the grocery store over and over so they have time to learn... But dynamic optimization over person's lifetime--such as cutting back on spending now so that one can save to pay back expected tax obligations in the future--cannot be instilled by repetition and experience. 

Noting that Krugman referred to Cochrane's claim that Keynesian ideas had been "proven false", I wanted to see what the proof was. Here is a link to his article on stimulus.

http://faculty.chicagobooth.edu/john.cochrane/research/Papers/fiscal2.htm

After reading Krugman and Cochrane, i felt baffled. These are not stupid people. Stupid people can't become full profs at Princeton and Chicago (can they?).

And yet.  Each of them writes as if the other person were a complete moron, incapable of absorbing basic facts and theory.

now i feel like i'm the moron... since i can't really untangle this mess of arguments.

here's one idea i had: Compared to the standards of empirical evidence used in labour economics, macro still depends to an astonishing extent on a priori beliefs.  Krugman dismisses modern macro because it's intuitively obvious to him that recessions aren't vacations and people just don't behave like Ricardian equivalence requires. Over and over in the article he dismisses their ideas not with statistical evidence but, well, with "dismissiveness."

  On the other side, Cochrane doesn't seem to be moved by empirical evidence either. Instead he wants to build up models based on budget constraints ("the money has to come from somewhere"), forward-thinking behaviour, and the notion that government cannot fool people repeatedly. He doesn't actually prove anything false with evidence. Instead, like Krugman's blog entry criticizing Cochrane, he mainly accuses the other side of adhering to "fallacies."

Imagine that in labour economics one side said that the (productivity) return to education was actually zero because it is all just Spence signalling. And the other side said the return was equal to the interest rate because that is what dynamic optimization requires. We'd laugh and say, "look it's an empirical issue. let's just estimate the damn return."

But that's not what either Krugman or Cochrane seem to want to do. Indeed Cochrane tells us the govt spending multiplier is zero.  And he refers to a blog entry by Mankiw. So i went to that entry and discovered that Mankiw says the best estimates of the multiplier put it at one or slightly over.  OK to me these numbers don't make sense because the keynesian theory says the multiplier depends on the amount of slack in the economy, right? but anyway, my point is that macroeconomics not only needs new micro-foundations but it also needs to become evidence-based.  but of course i know next to nothing about macroeconomics so you should have stopped reading this blog entry long ago...perhaps you did!