A tale of two asset pricing models

A while ago I talked about the fact that DSGE macro models haven't seen industry applications, and that this means people don't yet trust them to give a good conditional forecast of the effect of economic policy changes on macro variables. How about asset pricing models from the finance literature? How do these pass the market test?

There are basically three things you might use an asset pricing model for in the real world. The first is to measure risk. The second is to beat the market, if you believe that the model represents a long-term equilibrium from which assets will only deviate for a short time. The third is to arrive at a fair starting price when brokering deals between two parties.

There are two main classes of asset pricing models in the finance literature. The first class is equilibrium models. These are basically economic models that treat asset prices as solutions to consumers' utility maximization problem (and, sometimes, firms' profit maximization problem). The most famous of these is the CCAPM. Modern extensions of that include Bansal and Yaron's long-run risk model, Campbell and Cochrane's habit formation model, and various models based on "rare disasters." Though these days these models are usually pitched as solutions to time-series puzzles like the equity premium, excess volatility, and volatility clustering puzzles, they are models of risk and of the cross-section of expected returns. 

The second main class of models is factor models, such as the Fama-French 3-factor model, the Carhart 4-factor model, and various macroeconomic factor models. These models are based not on any behavioral assumptions like utility or profit maximization. They only require no-arbitrage conditions, and some assumptions about the structure of the market. Though they may be motivated by economics, they are not economic models, in the modern sense of the neoclassical, maximization-based econ that we are all used to. 

Factor models can end up looking a lot like equilibrium models - factor models give you factor betas and equilibrium models give you consumption betas and stuff like that. But the methods they use to derive the betas are much different, and the substance of the conclusions is almost always very different. 

I don't have a comprehensive data set of the finance industry, so don't regard my info as complete, but I've talked to a fairly large number of industry people, and they all say the same thing. Factor models are very common, even ubiquitous, in the industry. Equilibrium models are essentially never used by anybody.

The most obvious reason for this is that equilibrium models are harder to make. You have to make a bunch of assumptions, solve an optimization problem, then estimate the thing to see how well it works. With factor models you just skip the first two steps, slap down some factors, and estimate it. As you might expect, the ease of generating factor models leads to a lot of false positives in the academic literature. But in the finance industry, a lot of effort goes into exhaustive backtesting and robustness-checking of factor models, which cuts down massively on false positives (though overfitting is of course still a danger). You have companies that exist just to make, test, and sell factor models.

So is the disuse of equilibrium asset-pricing models just a function of the effort that goes into making them? Maybe. But you'd think that eventually, academics - who are more than willing to put in that effort, and who in fact make oodles of such models - would come up with a really good one that industry would adopt. It's no harder to use an equilibrium model than it is to use a factor model.

But they don't. No one I've talked to or heard about uses consumption betas of any kind, including ones based on habit formation or Epstein-Zin preferences. Despite decades of high-powered research, equilibrium models are not yet passing the market test. 

I assume that this is because when you test these things, factor models come out ahead. I hope that someone is using information criteria or some other defense against overfitting when these comparisons are made. If they are, then what it means is that the best factor models are more empirically successful than the best equilibrium models. Which in turn implies that equilibrium asset-pricing models are, basically, misspecified. 

Why would equilibrium models be misspecified? They might be focusing on fitting time-series facts and neglecting the cross-section. Or there might simply be something very wrong with the workhorse assumptions economists use to describe consumer behavior at the aggregate level - something so deep that modifications like Epstein-Zin or habit formation can't fix it. Tests of the basic consumption Euler equation make me suspect that that is the case. If economists find that wrong thing and fix it, it could reap big dividends not just for asset pricing models, but for macroeconomics as well.


Updates

Two caveats to this post! First of all, the story isn't over yet. New models are coming out all the time - for example, a commenter points me to this model from 2014, which is a hybrid of a typical factor model and a production-based theory of firm investment behavior. Looking over it, it looks pretty good. It also agrees with my prior that firm behavior is a lot more important and a lot easier to explain than consumer behavior. But the main point is that industry could start using equilibrium models - even consumption-based equilibrium models - at any time.

The second caveat is that the notion of what it means to "use" a model is a lot more subtle than I'm making it out to be. For example, you could find factors by data mining, then use an equilibrium model to convince yourself that the factors will be stable in the future (in fact, that's exactly how you might use the model I linked to above). To my knowledge this kind of use is very rare so far, and I've heard stories of people in industry trying and failing to do just this. But if people do start doing it, it won't look like people ditching factor models for equilibrium models. It will look like people using equilibrium models to check their factor models. Another way you could use equilibrium models is to search for new ideas for factors. But since the set of available macro variables is too limited, it's highly likely that data-mining will find the factors long before equilibrium modelers do.

The forsaken

Sorry, folks, one more sentimental, overwrought, non-economics-related post. I promise I'll try my best not to turn this from an econ blog into a sentimental, sappy blog about nationalism and culture and stuff like that. But anyway, I just had to do a follow-up to my last post.

In my last post, I wrote about what I see as the fundamental core of the United States as a nation - the concept of equality. Ta-Nehisi Coates, in a much longer, more personal, and better-written essay than mine, expresses a very different vision of what America is all about. I encourage you to read his piece from start to finish (don't skim).

Here are just a couple small excerpts (again, you should read the whole piece):

To be black in the Baltimore of my youth was to be naked before the elements of the world, before all the guns, fists, knives, crack, rape, and disease. The law did not protect us. And now, in your time, the law has become an excuse for stopping and frisking you, which is to say, for furthering the assault on your body. But a society that protects some people through a safety net of schools, government-backed home loans, and ancestral wealth but can only protect you with the club of criminal justice has either failed at enforcing its good intentions or has succeeded at something much darker... 

Before I could escape [the ghetto], I had to survive, and this could only mean a clash with the streets, by which I mean not just physical blocks, nor simply the people packed into them, but the array of lethal puzzles and strange perils which seem to rise up from the asphalt itself. The streets transform every ordinary day into a series of trick questions, and every incorrect answer risks a beat-down, a shooting, or a pregnancy. No one survives unscathed. When I was your age, fully one-third of my brain was concerned with who I was walking to school with, our precise number, the manner of our walk, the number of times I smiled, who or what I smiled at, who offered a pound and who did not—all of which is to say that I practiced the culture of the streets, a culture concerned chiefly with securing the body...

This America that Coates sees is very real. How can his America be the same America that I believe in so strongly?

Let me try to explain. I am not as eloquent as Coates, so I'll use my typical plain-spoken, spluttering style, with visual aids.

Because I grew up Jewish, my parents made me read about the Holocaust at a very young age. I read the testimonials, I saw the pictures. It really freaked me out. I was scared. I remember walking down the street with my dad at the age of 7, and asking him: "Is there anyone like the Nazis around today?" He said "Well, the Soviet Union is a little like the Nazis." That scared me. "What if the Soviet Union comes to get us?", I asked. And his answer was: "We have the most powerful military in the world. And we have tens of thousands of nuclear weapons. There's no way they can get us."

And that was it. Suddenly I felt safe from those cosmic threats, those vast and distant hosts of evil. I had the ultimate backup.

I had this on my side:

I may be too weak to defend myself against an army of bad guys, but behind me stands what you see in the picture above. That is a picture of America coming to protect the weak and forsaken. That is a picture of the ultimate backup.

What about black Americans? Do they have that same backup? Well, they used to, at least once in a while. In the Civil War they did. And in the Civil Rights era they did. Check out this:

That's what I'm talkin' about!! That is the 101st Airborne Division - the same guys from D-Day! - protecting some black kids from assholes who want to stop them from going to school. And the guy who ordered them to do it was the same guy from D-Day - Dwight D. Eisenhower! And how about when the assholes tried to stop the black kids from going to school? This!

Damn straight! 'MURICA!!

But here's the thing - this only happens once in a while. Most of the time, large chunks of black America - not the whole thing, not all African-Americans, but vast swathes - are either left to rot in the anarchy Coates describes, or actively oppressed by police, courts, and prisons.

Don't believe me? What's this, then?

WHAT THE F******************* IS THAT S***?!!!

Or this?!!!

These are peaceful protesters being menaced by militarized police!! These are not racist individuals making personal choices to be mean to black people! This is an institutional, organized, official act of government oppression of a peaceful American populace! Where's the 101st Airborne when you need them???!!

It's not just black people who get this treatment these days, of course - I saw the same scene at anti-Iraq War protests in 2003. But for a lot of black Americans, this is their only contact with the police, with the armed might of America, except for getting arrested and thrown in hellish prisons.

We lock up millions of people in this nation - far more even than authoritarian nations like China and Russia. It's our own Gulag Archipelago. In these prisons most inmates are raped and beaten. All of them are forced to do slave labor. After they are released, they can never vote in American elections again. And they have extreme trouble ever finding jobs again. They are, in short, tortured, enslaved, and then reduced to permanent second-class citizens.

Black Americans are far more vulnerable to this bullshit than other Americans. Racial profiling means they are far more likely to get arrested (and are killed by police at much higher rates). Racist sentencing means they are far more likely to be given prison terms, and longer ones. And the militarized response of police to protests in Ferguson and Baltimore makes it clear to black communities that America is not on their side - that the police are not simply trying to protect poor black communities from a few bad apples, but simply trying to suppress and contain poor black communities and keep them cordoned off from the rest of America. 

This is exactly what Coates talks about in his essay. It's real. It's true. You can see it on YouTube.

For white Americans, there is at least the idea that this is temporary, that America will correct these abuses, right the wrongs, and return to the correct path. For Asian or Hispanic Americans, there is probably less certainty (remember those internment camps?), but still an overall feeling of positivity. But when black Americans look back on American history, what do they see? Centuries of racial enslavement. Another century of lynchings, segregation, and KKK terrorism. And essentially zero lag between the end of segregation and the beginning of the prison gulags.

For me, growing up, America represented the ultimate backup, the ultimate protector. Many black Americans - not all, of course, but many - feel utterly forsaken by that protector. They are lost, abandoned in a violent, frightening world, with no backup, no sheltering presence, no cavalry to ride to the rescue when the chips are down. Maybe just cavalry to ride over your face.

To me this unacceptable. Unacceptable! Those are our people - our countrymen! America should be the protector of the weak, not the oppressor - and when the weak are Americans themselves, the imperative is a million times stronger! No American should ever feel forsaken by the powers that be. No American should ever feel that the system is against him or her.

To me the plight of American black people is not about justice. It's not about righting the wrongs of history. It's about giving black Americans the certainty that America is a country that is always - ALWAYS - on their side, that will always fight for them, not against them. It's about backup. 

I'm a nationalist. I firmly believe that the fundamental essence of America is the belief in human equality and freedom, and that this essence will continue to win out over the darker tendencies that afflict our nation and all nations. But this essence is not a magical force that rights all wrongs while we sit on our couches and scarf Doritos and Mountain Dew. My relatives weren't in the D-Day picture above, but they were in the overall effort, flying planes or fighting in Asia or doing cryptography. The army of backup doesn't exist unless a bunch of us join up and volunteer. 

And to our credit, lots of us are joining up and volunteering. The protests after the killing of Eric Garner were enormous. But we need more than protesters - we need police departments, judges, and legislators to use their power to stop the madness. Stop the police militarization, stop the racial profiling, stop the racist sentencing, and stop mass incarceration.

If we can save France from Hitler, if we can save China from the Japanese Empire, if we can save Europe from the Soviet Union, we can save our own people from our own system.  

The words that changed the world

(Warning: This post does not contain economics, and does contain nationalism.)

The 4th of July isn't the anniversary of the Constitution, it's the anniversary of the Declaration of Independence. The Constitution set up our government, and Americans tend to revere it as the immortal symbol and spirit of our country, much as Japanese people traditionally saw the Emperor. But in many ways, the Declaration of Independence is the more important document. By declaring when it's OK for a populace to abolish their government and form a new one, the Declaration necessarily appeals to powers that are higher than any Constitution, king, or emperor. The powers it appeals to are 1) People power, 2) God, and 3) moral ideals.

The ideals of the Declaration are many, but the basic ones are laid out in the second sentence:

We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness.

This is the sentence everyone can quote, and with good reason. This sentence is the core idea of the United States as a nation-state.

When you think about it, it's pretty incredible that people - especially people in the 18th century - would put a moral statement as their reason for founding a new nation. This sentence makes it clear that the United States was created as fundamentally not just a group of people and the plot of land they live on. It was a nation created to advance a set of moral ideals.

Of the ideals in that sentence, the most dramatic, the most memorable, and the most astonishingly radical is "all men are created equal". I feel like if the idea of the United States of America were stripped down to its very essence, these are the five words that would remain.

What the heck does "all men are created equal" even mean? Does it mean that they're equal in some measurable characteristic, like height? Obviously not. In fact, "equal" obviously doesn't mean - can't mean - anything that can be proven or disproven with facts. The founders could not possibly be using the words "self-evident truth" to mean "measurable fact", so they must be using them to mean something else. "All men are created equal" must be a prescriptive statement - a statement of opinion, a codified expression of emotion.

It's a statement about how society ought to treat people. It says, basically, that society shouldn't treat people differently based on the conditions of their birth. There's really nothing else it could mean.

"All men are created equal"! What an astounding thing to say! What an astounding thing for a bunch of slaveholders to say! And what an astounding thing to base a country on! Centuries later people from other countries still boggled and balked at it. It's a statement that turns almost everything about traditional human society on its head.

Now, lots of people make sweeping moral statements that they or their descendants completely ignore. But this one has proven to be astonishingly powerful down through the centuries. Again and again "all men are created equal" is something Americans have proven willing to fight for. We fought the Civil War to enforce the ideal of "all men are created equal" (no, slavery was not the only reason the Union fought, but it was really what the conflict was all about). George Washington knew from Day 1 that this was going to happen. In 1797 he told a guest that "I can clearly foresee that nothing but the rooting out of slavery can perpetuate the existence of our union, by consolidating it in a common bond of principal (sic)."

The rest of American history involves a long list of episodes in which people fought for the principle of "all men are created equal". It wasn't too long before it became obvious that "men" meant women as well - the women's rights and feminist movements clearly spring from the idea that "all [people] are created equal". Civil rights was another battle, and just recently, the triumph of gay marriage was another. The fight against police racism is an ongoing example. The U.S. is not always the first to implement policies that confer greater equality (though we're usually one of the first), but I can't think of another country where the cause of equality arouses as much popular feeling.

The American ideal of "freedom" has traditionally been conflated with this ideal of "equality" - in fact, some early drafts of the Declaration said "all men are born equally free." The idea is that a society that treats people differently due to their circumstances of birth is not a free society. Later, Communism adopted the language of "equality", using the term to mean something very different (and leading to interminable high-school debates over "equality of opportunity vs. equality of outcome"). But the notion of "equality" as "freedom from social discrimination based on the circumstances of birth" lives on, and now that Communism is effectively dead, the word "equality" is starting to make a comeback - e.g. in the marriage equality movement.

In fact, I don't think it's a stretch to say that every distinctly American ideal springs from "all men are created equal". Democracy, the rule of law, human rights and civil liberties - these all follow from that one animating idea. If "all men are created equal", they all deserve to have a voice in government, they all deserve equal treatment under the law, and they all deserve the same rights and protections. Even capitalism itself relies partly on the notion that everyone should have an equal chance to participate in the economy - that there should be no hereditary rentier class pulling the levers.

The American idea of "all men are created equal" is a radical ideology of incredible power, and it has influenced other nations tremendously. It inspired the French Revolution. It inspired the thinking of the Meiji Restoration reformers. It reshaped much of Europe and Asia after the World Wars, inspiring people there to remake their societies in America's image.

This is why I'm a nationalist at heart. I'm not a jingoist who thinks America always does the right thing. I'm not a blood-and-soil nationalist who thinks of America as a race plus a plot of land. I believe in those five words - "all men are created equal". It's an ambiguous statement, an emotional statement, a religious statement. It's also one of the most powerful and transformative and positive ideas the world has ever known.

That's why we should celebrate July 4th. When our founders wrote those five words, everything changed. Once you say "all men are created equal," once you throw down that gauntlet, you can never take it back. As long as America exists - and even if it dies - "all men are created equal" is here to stay, animating the hearts and minds of billions. In terms of human history, there was Before July 4th, 1776, and there was After July 4th, 1776. I'm damn glad I live in the After.