dynamic consistency

What would a new macroeconomics look like?

pnrj critique of neoclassical economics, heuristics and biases, inequality, macroeconomics , , , , , , , , , , , , , ,

Dec 9 JDN 2458462

In previous posts I have extensively criticized the current paradigm of macroeconomics. But it’s always easier to tear the old edifice down than to build a better one in its place. So in this post I thought I’d try to be more constructive: What sort of new directions could macroeconomics take?

The most important change we need to make is to abandon the assumption of dynamic optimization. This will be a very hard sell, as most macroeconomists have become convinced that the Lucas Critique means we need to always base everything on the dynamic optimization of a single representative agent. I don’t think this was actually what Lucas meant (though maybe we should ask him; he’s still at Chicago), and I certainly don’t think it is what he should have meant. He had a legitimate point about the way macroeconomics was operating at that time: It was ignoring the feedback loops that occur when we start trying to change policies.

Goodhart’s Law is probably a better formulation: Once you make an indicator into a target, you make it less effective as an indicator. So while inflation does seem to be negatively correlated with unemployment, that doesn’t mean we should try to increase inflation to extreme levels in order to get rid of unemployment; sooner or later the economy is going to adapt and we’ll just have both inflation and unemployment at the same time. (Campbell’s Law provides a specific example that I wish more people in the US understood: Test scores would be a good measure of education if we didn’t use them to target educational resources.)

The reason we must get rid of dynamic optimization is quite simple: No one behaves that way.

It’s often computationally intractable even in our wildly oversimplified models that experts spend years working on—now you’re imagining that everyone does this constantly?

The most fundamental part of almost every DSGE model is the Euler equation; this equation comes directly from the dynamic optimization. It’s supposed to predict how people will choose to spend and save based upon their plans for an infinite sequence of future income and spending—and if this sounds utterly impossible, that’s because it is. Euler equations don’t fit the data at all, and even extreme attempts to save them by adding a proliferation of additional terms have failed. (It reminds me very much of the epicycles that astronomers used to add to the geocentric model of the universe to try to squeeze in weird results like Mars, before they had the heliocentric model.)

We should instead start over: How do people actually choose their spending? Well, first of all, it’s not completely rational. But it’s also not totally random. People spend on necessities before luxuries; they try to live within their means; they shop for bargains. There is a great deal of data from behavioral economics that could be brought to bear on understanding the actual heuristics people use in deciding how to spend and save. There have already been successful policy interventions using this knowledge, like Save More Tomorrow.

The best thing about this is that it should make our models simpler. We’re no longer asking each agent in the model to solve an impossible problem. However people actually make these decisions, we know it can be done, because it is being done. Most people don’t really think that hard, even when they probably should; so the heuristics really can’t be that complicated. My guess is that you can get a good fit—certainly better than an Euler equation—just by assuming that people set a target for how much they’re going to save (which is also probably pretty small for most people), and then spend the rest.

The second most important thing we need to add is inequality. Some people are much richer than others; this is a very important fact about economics that we need to understand. Yet it has taken the economics profession decades to figure this out, and even now I’m only aware of one class of macroeconomic models that seriously involves inequality, the Heterogeneous Agent New Keynesian (HANK) models which didn’t emerge until the last few years (the earliest publication I can find is 2016!). And these models are monsters; they are almost always computationally intractable and have a huge number of parameters to estimate.

Understanding inequality will require more parameters, that much is true. But if we abandon dynamic optimization, we won’t need as many as the HANK models have, and most of the new parameters are actually things we can observe, like the distribution of wages and years of schooling.

Observability of parameters is a big deal. Another problem with the way the Lucas Critique has been used is that we’ve been told we need to be using “deep structural parameters” like the temporal elasticity of substitution and the coefficient of relative risk aversion—but we have no idea what those actually are. We can’t observe them, and all of our attempts to measure them indirectly have yielded inconclusive or even inconsistent results. This is probably because these parameters are based on assumptions about human rationality that are simply not realistic. Most people probably don’t have a well-defined temporal elasticity of substitution, because their day-to-day decisions simply aren’t consistent enough over time for that to make sense. Sometimes they eat salad and exercise; sometimes they loaf on the couch and drink milkshakes. Likewise with risk aversion: many moons ago I wrote about how people will buy both insurance and lottery tickets, which no one with a consistent coefficient of relative risk aversion would ever do.

So if we are interested in deep structural parameters, we need to base those parameters on behavioral experiments so that we can understand actual human behavior. And frankly I don’t think we need deep structural parameters; I think this is a form of greedy reductionism, where we assume that the way to understand something is always to look at smaller pieces. Sometimes the whole is more than the sum of its parts. Economists obviously feel a lot of envy for physics; but they don’t seem to understand that aerodynamics would never have (ahem) gotten off the ground if we had first waited for an exact quantum mechanical solution of the oxygen atom (which we still don’t have, by the way). Macroeconomics may not actually need “microfoundations” in the strong sense that most economists intend; it needs to be consistent with small-scale behavior, but it doesn’t need to be derived from small-scale behavior.

This means that the new paradigm in macroeconomics does not need to be computationally intractable. Using heuristics instead of dynamic optimization and worrying less about microfoundations will make the models simpler; adding inequality need not make them so much more complicated.

What is the price of time?

pnrj critique of neoclassical economics, heuristics and biases , , , , , , , , , , , , , , ,

JDN 2457562

If they were asked outright, “What is the price of time?” most people would find that it sounds nonsensical, like I’ve asked you “What is the diameter of calculus?” or “What is the electric charge of justice?” (It’s interesting that we generally try to assign meaning to such nonsensical questions, and they often seem strangely profound when we do; a good deal of what passes for “profound wisdom” is really better explained as this sort of reaction to nonsense. Deepak Chopra, for instance.)

But there is actually a quite sensible economic meaning of this question, and answering it turns out to have many important implications for how we should run our countries and how we should live our lives.

What we are really asking for is temporal discounting; we want to know how much more money today is worth compared to tomorrow, and how much more money tomorrow is worth compared to two days from now.

If you say that they are exactly the same, your discount rate (your “price of time”) is zero; if that is indeed how you feel, may I please borrow your entire net wealth at 0% interest for the next thirty years? If you like we can even inflation-index the interest rate so it always produces a real interest rate of zero, thus protecting you from potential inflation risk.
What? You don’t like my deal? You say you need that money sooner? Then your discount rate is not zero. Similarly, it can’t be negative; if you actually valued money tomorrow more than money today, you’d gladly give me my loan.

Money today is worth more to you than money tomorrow—the only question is how much more.

There’s a very simple theorem which says that as long as your temporal discounting doesn’t change over time, so it is dynamically consistent, it must have a very specific form. I don’t normally use math this advanced in my blog, but this one is so elegant I couldn’t resist. I’ll encase it in blockquotes so you can skim over it if you must.

The value of $1 today relative to… today is of course 1; f(0) = 1.

If you are dynamically consistent, at any time t you should discount tomorrow relative to today the same as you discounted today relative to yesterday, so for all t, f(t+1)/f(t) = f(t)/f(t-1)
Thus, f(t+1)/f(t) is independent of t, and therefore equal to some constant, which we can call r:

f(t+1)/f(t) = r, which implies f(t+1) = r f(t).

Starting at f(0) = 1, we have:

f(0) = 1, f(1) = r, f(2) = r^2

We can prove that this pattern continues to hold by mathematical induction.

Suppose the following is true for some integer k; we already know it works for k = 1:

f(k) = r^k

Let t = k:

f(k+1) = r f(k)

Therefore:

f(k+1) = r^(k+1)

Which by induction proves that for all integers n:

f(n) = r^n

The name of the variable doesn’t matter. Therefore:

f(t) = r^t

Whether you agree with me that this is beautiful, or you have no idea what I just said, the take-away is the same: If your discount rate is consistent over time, it must be exponential. There must be some constant number 0 < r < 1 such that each successive time period is worth r times as much as the previous. (You can also generalize this to the case of continuous time, where instead of r^t you get e^(-r t). This requires even more advanced math, so I’ll spare you.)

Most neoclassical economists would stop right there. But there are two very big problems with this argument:

(1) It doesn’t tell us the value r should actually be, only that it should be a constant.

(2) No actual human being thinks of time this way.

There is still ongoing research as to exactly how real human beings discount time, but one thing is quite clear from the experiments: It certainly isn’t exponential.

From about 2000 to 2010, the consensus among cognitive economists was that humans discount time hyperbolically; that is, our discount function looks like this:

f(t) = 1/(1 + r t)

In the 1990s there were a couple of experiments supporting hyperbolic discounting. There is even some theoretical work trying to show that this is actually optimal, given a certain kind of uncertainty about the future, and the argument for exponential discounting relies upon certainty we don’t actually have. Hyperbolic discounting could also result if we were reasoning as though we are given a simple interest rate, rather than a compound interest rate.

But even that doesn’t really seem like humans think, now does it? It’s already weird enough for someone to say “Should I take out this loan at 5%? Well, my discount rate is 7%, so yes.” But I can at least imagine that happening when people are comparing two different interest rates (“Should I pay down my student loans, or my credit cards?”). But I can’t imagine anyone thinking, “Should I take out this loan at 5% APR which I’d need to repay after 5 years? Well, let’s check my discount function, 1/(1+0.05 (5)) = 0.8, multiplied by 1.05^5 = 1.28, the product of which is 1.02, greater than 1, so no, I shouldn’t.” That isn’t how human brains function.

Moreover, recent experiments have shown that people often don’t seem to behave according to what hyperbolic discounting would predict.

Therefore I am very much in the other camp of cognitive economists, who say that we don’t have a well-defined discount function. It’s not exponential, it’s not hyperbolic, it’s not “quasi-hyperbolic” (yes that is a thing); we just don’t have one. We reason about time by simple heuristics. You can’t make a coherent function out of it because human beings… don’t always reason coherently.

Some economists seem to have an incredible amount of trouble accepting that; here we have one from the University of Chicago arguing that hyperbolic discounting can’t possibly exist, because then people could be Dutch-booked out of all their money; but this amounts to saying that human behavior cannot ever be irrational, lest all our money magically disappear. Yes, we know hyperbolic discounting (and heuristics) allow for Dutch-booking; that’s why they’re irrational. If you really want to know the formal assumption this paper makes that is wrong, it assumes that we have complete markets—and yes, complete markets essentially force you to be perfectly rational or die, because the slightest inconsistency in your reasoning results in someone convincing you to bet all your money on a sure loss. Why was it that we wanted complete markets, again? (Oh, yes, the fanciful Arrow-Debreu model, the magical fairy land where everyone is perfectly rational and all markets are complete and we all have perfect information and the same amount of wealth and skills and the same preferences, where everything automatically achieves a perfect equilibrium.)

There was a very good experiment on this, showing that rather than discount hyperbolically, behavior is better explained by a heuristic that people judge which of two options is better by a weighted sum of the absolute distance in time plus the relative distance in time. Now that sounds like something human beings might actually do. “$100 today or $110 tomorrow? That’s only 1 day away, but it’s also twice as long. I’m not waiting.” “$100 next year, or $110 in a year and a day? It’s only 1 day apart, and it’s only slightly longer, so I’ll wait.”

That might not actually be the precise heuristic we use, but it at least seems like one that people could use.

John Duffy, whom I hope to work with at UCI starting this fall, has been working on another experiment to test a different heuristic, based on the work of Daniel Kahneman, saying essentially that we have a fast, impulsive, System 1 reasoning layer and a slow, deliberative, System 2 reasoning layer; the result is that our judgments combine both “hand to mouth” where our System 1 essentially tries to get everything immediately and spend whatever we can get our hands on, and a more rational assessment by System 2 that might actually resemble an exponential discount rate. In the 5-minute judgment, System 1’s voice is overwhelming; but if we’re already planning a year out, System 1 doesn’t even care anymore and System 2 can take over. This model also has the nice feature of explaining why people with better self-control seem to behave more like they use exponential discounting,[PDF link] and why people do on occasion reason more or less exponentially, while I have literally never heard anyone try to reason hyperbolically, only economic theorists trying to use hyperbolic models to explain behavior.

Another theory is that discounting is “subadditive”, that is, if you break up a long time interval into many short intervals, people will discount it more, because it feels longer that way. Imagine a century. Now imagine a year, another year, another year, all the way up to 100 years. Now imagine a day, another day, another day, all the way up to 365 days for the first year, and then 365 days for the second year, and that on and on up to 100 years. It feels longer, doesn’t it? It is of course exactly the same. This can account for some weird anomalies in choice behavior, but I’m not convinced it’s as good as the two-system model.

Another theory is that we simply have a “present bias”, which we treat as a sort of fixed cost that we incur regardless of what the payments are. I like this because it is so supremely simple, but there’s something very fishy about it, because in this experiment it was just fixed at $4, and that can’t be right. It must be fixed at some proportion of the rewards, or something like that; or else we would always exhibit near-perfect exponential discounting for large amounts of money, which is more expensive to test (quite directly), but still seems rather unlikely.

Why is this important? This post is getting long, so I’ll save it for future posts, but in short, the ways that we value future costs and benefits, both as we actually do, and as we ought to, have far-reaching implications for everything from inflation to saving to environmental sustainability.

Moral responsibility does not inherit across generations

pnrj cognitive science, core principles, ethics, public policy, Uncategorized , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , ,

JDN 2457548

In last week’s post I made a sharp distinction between believing in human progress and believing that colonialism was justified. To make this argument, I relied upon a moral assumption that seems to me perfectly obvious, and probably would to most ethicists as well: Moral responsibility does not inherit across generations, and people are only responsible for their individual actions.

But is in fact this principle is not uncontroversial in many circles. When I read utterly nonsensical arguments like this one from the aptly-named Race Baitr saying that White people have no role to play in the liberation of Black people apparently because our blood is somehow tainted by the crimes our ancestors, it becomes apparent to me that this principle is not obvious to everyone, and therefore is worth defending. Indeed, many applications of the concept of “White Privilege” seem to ignore this principle, speaking as though racism is not something one does or participates in, but something that one is simply by being born with less melanin. Here’s a Salon interview specifically rejecting the proposition that racism is something one does:

For white people, their identities rest on the idea of racism as about good or bad people, about moral or immoral singular acts, and if we’re good, moral people we can’t be racist – we don’t engage in those acts. This is one of the most effective adaptations of racism over time—that we can think of racism as only something that individuals either are or are not “doing.”

If racism isn’t something one does, then what in the world is it? It’s all well and good to talk about systems and social institutions, but ultimately systems and social institutions are made of human behaviors. If you think most White people aren’t doing enough to combat racism (which sounds about right to me!), say that—don’t make some bizarre accusation that simply by existing we are inherently racist. (Also: We? I’m only 75% White, so am I only 75% inherently racist?) And please, stop redefining the word “racism” to mean something other than what everyone uses it to mean; “White people are snakes” is in fact a racist sentiment (and yes, one I’ve actually heard–indeed, here is the late Muhammad Ali comparing all White people to rattlesnakes, and Huffington Post fawning over him for it).

Racism is clearly more common and typically worse when performed by White people against Black people—but contrary to the claims of some social justice activists the White perpetrator and Black victim are not part of the definition of racism. Similarly, sexism is more common and more severe committed by men against women, but that doesn’t mean that “men are pigs” is not a sexist statement (and don’t tell me you haven’t heard that one). I don’t have a good word for bigotry by gay people against straight people (“heterophobia”?) but it clearly does happen on occasion, and similarly cannot be defined out of existence.

I wouldn’t care so much that you make this distinction between “racism” and “racial prejudice”, except that it’s not the normal usage of the word “racism” and therefore confuses people, and also this redefinition clearly is meant to serve a political purpose that is quite insidious, namely making excuses for the most extreme and hateful prejudice as long as it’s committed by people of the appropriate color. If “White people are snakes” is not racism, then the word has no meaning.

Not all discussions of “White Privilege” are like this, of course; this article from Occupy Wall Street actually does a fairly good job of making “White Privilege” into a sensible concept, albeit still not a terribly useful one in my opinion. I think the useful concept is oppression—the problem here is not how we are treating White people, but how we are treating everyone else. “What privilege gives you is the freedom to be who you are.”? Shouldn’t everyone have that?

Almost all the so-called “benefits” or “perks” associated with “privilege” are actually forgone harms—they are not good things done to you, but bad things not done to you. “But benefitting from racist systems doesn’t mean that everything is magically easy for us. It just means that as hard as things are, they could always be worse.” No, that is not what the word “benefit” means. The word “benefit” means you would be worse off without it—and in most cases that simply isn’t true. Many White people obviously think that it is true—which is probably a big reason why so many White people fight so hard to defend racism, you know; you’ve convinced them it is in their self-interest. But, with rare exceptions, it is not; most racial discrimination has literally zero long-run benefit. It’s just bad. Maybe if we helped people appreciate that more, they would be less resistant to fighting racism!

The only features of “privilege” that really make sense as benefits are those that occur in a state of competition—like being more likely to be hired for a job or get a loan—but one of the most important insights of economics is that competition is nonzero-sum, and fairer competition ultimately means a more efficient economy and thus more prosperity for everyone.

But okay, let’s set that aside and talk about this core question of what sort of responsibility we bear for the acts of our ancestors. Many White people clearly do feel deep shame about what their ancestors (or people the same color as their ancestors!) did hundreds of years ago. The psychological reactance to that shame may actually be what makes so many White people deny that racism even exists (or exists anymore)—though a majority of Americans of all races do believe that racism is still widespread.

We also apply some sense of moral responsibility applied to whole races quite frequently. We speak of a policy “benefiting White people” or “harming Black people” and quickly elide the distinction between harming specific people who are Black, and somehow harming “Black people” as a group. The former happens all the time—the latter is utterly nonsensical. Similarly, we speak of a “debt owed by White people to Black people” (which might actually make sense in the very narrow sense of economic reparations, because people do inherit money! They probably shouldn’t, that is literally feudalist, but in the existing system they in fact do), which makes about as much sense as a debt owed by tall people to short people. As Walter Michaels pointed out in The Trouble with Diversity (which I highly recommend), because of this bizarre sense of responsibility we are often in the habit of “apologizing for something you didn’t do to people to whom you didn’t do it (indeed to whom it wasn’t done)”. It is my responsibility to condemn colonialism (which I indeed do), to fight to ensure that it never happens again; it is not my responsibility to apologize for colonialism.

This makes some sense in evolutionary terms; it’s part of the all-encompassing tribal paradigm, wherein human beings come to identify themselves with groups and treat those groups as the meaningful moral agents. It’s much easier to maintain the cohesion of a tribe against the slings and arrows (sometimes quite literal) of outrageous fortune if everyone believes that the tribe is one moral agent worthy of ultimate concern.

This concept of racial responsibility is clearly deeply ingrained in human minds, for it appears in some of our oldest texts, including the Bible: “You shall not bow down to them or worship them; for I, the Lord your God, am a jealous God, punishing the children for the sin of the parents to the third and fourth generation of those who hate me,” (Exodus 20:5)

Why is inheritance of moral responsibility across generations nonsensical? Any number of reasons, take your pick. The economist in me leaps to “Ancestry cannot be incentivized.” There’s no point in holding people responsible for things they can’t control, because in doing so you will not in any way alter behavior. The Stanford Encyclopedia of Philosophy article on moral responsibility takes it as so obvious that people are only responsible for actions they themselves did that they don’t even bother to mention it as an assumption. (Their big question is how to reconcile moral responsibility with determinism, which turns out to be not all that difficult.)

An interesting counter-argument might be that descent can be incentivized: You could use rewards and punishments applied to future generations to motivate current actions. But this is actually one of the ways that incentives clearly depart from moral responsibilities; you could incentivize me to do something by threatening to murder 1,000 children in China if I don’t, but even if it was in fact something I ought to do, it wouldn’t be those children’s fault if I didn’t do it. They wouldn’t deserve punishment for my inaction—I might, and you certainly would for using such a cruel incentive.

Moreover, there’s a problem with dynamic consistency here: Once the action is already done, what’s the sense in carrying out the punishment? This is why a moral theory of punishment can’t merely be based on deterrence—the fact that you could deter a bad action by some other less-bad action doesn’t make the less-bad action necessarily a deserved punishment, particularly if it is applied to someone who wasn’t responsible for the action you sought to deter. In any case, people aren’t thinking that we should threaten to punish future generations if people are racist today; they are feeling guilty that their ancestors were racist generations ago. That doesn’t make any sense even on this deterrence theory.

There’s another problem with trying to inherit moral responsibility: People have lots of ancestors. Some of my ancestors were most likely rapists and murderers; most were ordinary folk; a few may have been great heroes—and this is true of just about anyone anywhere. We all have bad ancestors, great ancestors, and, mostly, pretty good ancestors. 75% of my ancestors are European, but 25% are Native American; so if I am to apologize for colonialism, should I be apologizing to myself? (Only 75%, perhaps?) If you go back enough generations, literally everyone is related—and you may only have to go back about 4,000 years. That’s historical time.

Of course, we wouldn’t be different colors in the first place if there weren’t some differences in ancestry, but there is a huge amount of gene flow between different human populations. The US is a particularly mixed place; because most Black Americans are quite genetically mixed, it is about as likely that any randomly-selected Black person in the US is descended from a slaveowner as it is that any randomly-selected White person is. (Especially since there were a large number of Black slaveowners in Africa and even some in the United States.) What moral significance does this have? Basically none! That’s the whole point; your ancestors don’t define who you are.

If these facts do have any moral significance, it is to undermine the sense most people seem to have that there are well-defined groups called “races” that exist in reality, to which culture responds. No; races were created by culture. I’ve said this before, but it bears repeating: The “races” we hold most dear in the US, White and Black, are in fact the most nonsensical. “Asian” and “Native American” at least almost make sense as categories, though Chippewa are more closely related to Ainu than Ainu are to Papuans. “Latino” isn’t utterly incoherent, though it includes as much Aztec as it does Iberian. But “White” is a club one can join or be kicked out of, while “Black” is the majority of genetic diversity.

Sex is a real thing—while there are intermediate cases of course, broadly speaking humans, like most metazoa, are sexually dimorphic and come in “male” and “female” varieties. So sexism took a real phenomenon and applied cultural dynamics to it; but that’s not what happened with racism. Insofar as there was a real phenomenon, it was extremely superficial—quite literally skin deep. In that respect, race is more like class—a categorization that is itself the result of social institutions.

To be clear: Does the fact that we don’t inherit moral responsibility from our ancestors absolve us from doing anything to rectify the inequities of racism? Absolutely not. Not only is there plenty of present discrimination going on we should be fighting, there are also inherited inequities due to the way that assets and skills are passed on from one generation to the next. If my grandfather stole a painting from your grandfather and both our grandfathers are dead but I am now hanging that painting in my den, I don’t owe you an apology—but I damn well owe you a painting.

The further we become from the past discrimination the harder it gets to make reparations, but all hope is not lost; we still have the option of trying to reset everyone’s status to the same at birth and maintaining equality of opportunity from there. Of course we’ll never achieve total equality of opportunity—but we can get much closer than we presently are.

We could start by establishing an extremely high estate tax—on the order of 99%—because no one has a right to be born rich. Free public education is another good way of equalizing the distribution of “human capital” that would otherwise be concentrated in particular families, and expanding it to higher education would make it that much better. It even makes sense, at least in the short run, to establish some affirmative action policies that are race-conscious and sex-conscious, because there are so many biases in the opposite direction that sometimes you must fight bias with bias.

Actually what I think we should do in hiring, for example, is assemble a pool of applicants based on demographic quotas to ensure a representative sample, and then anonymize the applications and assess them on merit. This way we do ensure representation and reduce bias, but don’t ever end up hiring anyone other than the most qualified candidate. But nowhere should we think that this is something that White men “owe” to women or Black people; it’s something that people should do in order to correct the biases that otherwise exist in our society. Similarly with regard to sexism: Women exhibit just as much unconscious bias against other women as men do. This is not “men” hurting “women”—this is a set of unconscious biases found in almost everywhere and social structures almost everywhere that systematically discriminate against people because they are women.

Perhaps by understanding that this is not about which “team” you’re on (which tribe you’re in), but what policy we should have, we can finally make these biases disappear, or at least fade so small that they are negligible.