How much should we give?

Nov 4 JDN 2458427

How much should we give of ourselves to others?

I’ve previously struggled with this basic question when it comes to donating money; I have written multiple posts on it now, some philosophical, some empirical, and some purely mathematical.

But the question is broader than this: We don’t simply give money. We also give effort. We also give emotion. Above all, we also give time. How much should we be volunteering? How many protest marches should we join? How many Senators should we call?

It’s easy to convince yourself that you aren’t doing enough. You can always point to some hour when you weren’t doing anything particularly important, and think about all the millions of lives that hang in the balance on issues like poverty and climate change, and then feel a wave of guilt for spending that hour watching Netflix or playing video games instead of doing one more march. This, however, is clearly unhealthy: You won’t actually make yourself into a more effective activist, you’ll just destroy yourself psychologically and become no use to anybody.

I previously argued for a sort of Kantian notion that we should commit to giving our fair share, defined as the amount we would have to give if everyone gave that amount. This is quite appealing, and if I can indeed get anyone to donate 1% of their income as a result, I will be quite glad. (If I can get 100 people to do so, that’s better than I could ever have done myself—a good example of highly cost-effective slacktivism.)

Lately I have come to believe that this is probably inadequate. We know that not everyone will take this advice, which means that by construction it won’t be good enough to actually solve global problems.

This means I must make a slightly greater demand: Define your fair share as the amount you would have to give if everyone among people who are likely to give gave that amount.

Unfortunately, this question is considerably harder. It may not even have a unique answer. The number of people willing to give an amount n is obviously dependent upon the amount x itself, and we are nowhere close to knowing what that function n(x) looks like.

So let me instead put some mathematical constraints on it, by choosing an elasticity. Instead of an elasticity of demand or elasticity of supply, we could call this an elasticity of contribution.

Presumably the elasticity is negative: The more you ask of people, the fewer people you’ll get to contribute.

Suppose that the elasticity is something like -0.5, where contribution is relatively inelastic. This means that if you increase the amount you ask for by 2%, you’ll only decrease the number of contributors by 1%. In that case, you should be like Peter Singer and ask for everything. At that point, you’re basically counting on Bill Gates to save us, because nobody else is giving anything. The total amount contributed n(x) * x is increasing in x.

On the other hand, suppose that elasticity is something like 2, where contribution is relatively elastic. This means that if you increase the amount you ask for by 2%, you will decrease the number of contributors by 4%. In that case, you should ask for very little. You’re asking everyone in the world to give 1% of their income, as I did earlier. The total amount contributed n(x) * x is now decreasing in x.

But there is also a third option: What if the elasticity is exactly -1, unit elastic? Then if you increase the amount you ask for by 2%, you’ll decrease the number of contributors by 2%. Then it doesn’t matter how much you ask for: The total amount contributed n(x) * x is constant.

Of course, there’s no guarantee that the elasticity is constant over all possible choices of x—indeed, it would be quite surprising if it were. A quite likely scenario is that contribution is inelastic for small amounts, then passes through a regime where it is nearly unit elastic, and finally it becomes elastic as you start asking for really large amounts of money.

The simplest way to model that is to just assume that n(x) is linear in x, something like n = N – k x.

There is a parameter N that sets the maximum number of people who will ever donate, and a parameter k that sets how rapidly the number of contributors drops off as the amount asked for increases.

The first-order condition for maximizing n(x) * x is then quite simple: x = N/(2k)

This actually turns out to be the precisely the point at which the elasticity of contribution is -1.

The total amount you can get under that condition is N2/(4k)

Of course, I have no idea what N and k are in real life, so this isn’t terribly helpful. But what I really want to know is whether we should be asking for more money from each person, or asking for less money and trying to get more people on board.

In real life we can sometimes do both: Ask each person to give more than they are presently giving, whatever they are presently giving. (Just be sure to run your slogans by a diverse committee, so you don’t end up with “I’ve upped my standards. Now, up yours!”) But since we’re trying to find a benchmark level to demand of ourselves, let’s ignore that for now.

About 25% of American adults volunteer some of their time, averaging 140 hours of volunteer work per year. This is about 1.6% of all the hours in a year, or 2.4% of all waking hours. Total monetary contributions in the US reached $400 billion for the first time this year; this is about 2.0% of GDP. So the balance between volunteer hours and donations is actually pretty even. It would probably be better to tilt it a bit more toward donations, but it’s really not bad. About 60% of US households made some sort of charitable contribution, though only half of these received the charitable tax deduction.

This suggests to me that the quantity of people who give is probably about as high as it’s going to get—and therefore we need to start talking more about the amount of money. We may be in the inelastic regime, where the way to increase total contributions is to demand more from each individual.

Our goal is to increase the total contribution to poverty eradication by about 1% of GDP in both the US and Europe. So if 60% of people give, and currently total contributions are about 2.0% of GDP, this means that the average contribution is about 3.3% of the contributor’s gross income. Therefore I should tell them to donate 4.3%, right? Not quite; some of them might drop out entirely, and the rest will have to give more to compensate.
Without knowing the exact form of the function n(x), I can’t say precisely what the optimal value is. But it is most likely somewhat larger than 4.3%; 5% would be a nice round number in the right general range. This would raise contributions in the US to 2.6% of GDP, or about $500 billion. That’s a 20% increase over the current level, which is large, but feasible.

Accomplishing a similar increase in Europe would then give us a total of $200 billion per year in additional funds to fight global poverty; this might not quite be enough to end world hunger (depending on which estimate you use), but it would definitely have a large impact.

I asked you before to give 1%. I am afraid I must now ask for more. Set a target of 5%. You don’t have to reach it this year; you can gradually increase your donations each year for several years (I call this “Save More Lives Tomorrow”, after Thaler’s highly successful program “Save More Tomorrow”). This is in some sense more than your fair share; I’m relying on the assumption that half the population won’t actually give anything. But ultimately this isn’t about what’s fair to us. It’s about solving global problems.

Happy Capybara Day! Or the power of culture

JDN 2457131 EDT 14:33.

Did you celebrate Capybara Day yesterday? You didn’t? Why not? We weren’t able to find any actual capybaras this year, but maybe next year we’ll be able to plan better and find a capybara at a zoo; unfortunately the nearest zoo with a capybara appears to be in Maryland. But where would we be without a capybara to consult annually on the stock market?

Right now you are probably rather confused, perhaps wondering if I’ve gone completely insane. This is because Capybara Day is a holiday of my own invention, one which only a handful of people have even heard about.

But if you think we’d never have a holiday so bizarre, think again: For all I did was make some slight modifications to Groundhog Day. Instead of consulting a groundhog about the weather every February 2, I proposed that we consult a capybara about the stock market every April 17. And if you think you have some reason why groundhogs are better at predicting the weather (perhaps because they at least have some vague notion of what weather is) than capybaras are at predicting the stock market (since they have no concept of money or numbers), think about this: Capybara Day could produce extremely accurate predictions, provided only that people actually believed it. The prophecy of rising or falling stock prices could very easily become self-fulfilling. If it were a cultural habit of ours to consult capybaras about the stock market, capybaras would become good predictors of the stock market.

That might seem a bit far-fetched, but think about this: Why is there a January Effect? (To be fair, some researchers argue that there isn’t, and the apparent correlation between higher stock prices and the month of January is simply an illusion, perhaps the result of data overfitting.)

But I think it probably is real, and moreover has some very obvious reasons behind it. In this I’m in agreement with Richard Thaler, a founder of cognitive economics who wrote about such anomalies in the 1980s. December is a time when two very culturally-important events occur: The end of the year, during which many contracts end, profits are assessed, and tax liabilities are determined; and Christmas, the greatest surge of consumer spending and consumer debt.

The first effect means that corporations are very likely to liquidate assets—particularly assets that are running at a loss—in order to minimize their tax liabilities for the year, which will drive down prices. The second effect means that consumers are in search of financing for extravagant gift purchases, and those who don’t run up credit cards may instead sell off stocks. This is if anything a more rational way of dealing with the credit constraint, since interest rates on credit cards are typically far in excess of stock returns. But this surge of selling due to credit constraints further depresses prices.

In January, things return to normal; assets are repurchased, debt is repaid. This brings prices back up to where they were, which results in a higher than normal return for January.

Neoclassical economists are loath to admit that such a seasonal effect could exist, because it violates their concept of how markets work—and to be fair, the January Effect is actually weak enough to be somewhat ambiguous. But actually it doesn’t take much deviation from neoclassical models to explain the effect: Tax policies and credit constraints are basically enough to do it, so you don’t even need to go that far into understanding human behavior. It’s perfectly rational to behave this way given the distortions that are created by taxes and credit limits, and the arbitrage opportunity is one that you can only take advantage of if you have large amounts of credit and aren’t worried about minimizing your tax liabilities. It’s important to remember just how strong the assumptions of models like CAPM truly are; in addition to the usual infinite identical psychopaths, CAPM assumes there are no taxes, no transaction costs, and unlimited access to credit. I’d say it’s amazing that it works at all, but actually, it doesn’t—check out this graph of risk versus return and tell me if you think CAPM is actually giving us any information at all about how stock markets behave. It frankly looks like you could have drawn a random line through a scatter plot and gotten just as good a fit. Knowing how strong its assumptions are, we would not expect CAPM to work—and sure enough, it doesn’t.

Of course, that leaves the question of why our tax policy would be structured in this way—why make the year end on December 31 instead of some other date? And for that, you need to go back through hundreds of years of history, the Gregorian calendar, which in turn was influenced by Christianity, and before that the Julian calendar—in other words, culture.

Culture is one of the most powerful forces that influences human behavior—and also one of the strangest and least-understood. Economic theory is basically silent on the matter of culture. Typically it is ignored entirely, assumed to be irrelevant against the economic incentives that are the true drivers of human action. (There’s a peculiar emotion many neoclassical economists express that I can best describe as self-righteous cynicism, the attitude that we alone—i.e., economists—understand that human beings are not the noble and altruistic creatures many imagine us to be, nor beings of art and culture, but simply cold, calculating machines whose true motives are reducible to profit incentives—and all who think otherwise are being foolish and naïve; true enlightenment is understanding that human beings are infinite identical psychopaths. This is the attitude epitomized by the economist who once sent me an email with “altruism” written in scare quotes.)

Occasionally culture will be invoked as an external (in jargon, exogenous) force, to explain some aspect of human behavior that is otherwise so totally irrational that even invoking nonsensical preferences won’t make it go away. When a suicide bomber blows himself up in a crowd of people, it’s really pretty hard to explain that in terms of rational profit incentives—though I have seen it tried. (It could be self-interest at a larger scale, like families or nations—but then, isn’t that just the tribal paradigm I’ve been arguing for all along?)

But culture doesn’t just motivate us to do extreme or wildly irrational things. It motivates us all the time, often in quite beneficial ways; we wait in line, hold doors for people walking behind us, tip waiters who serve us, and vote in elections, not because anyone pressures us directly to do so (unlike say Australia we do not have compulsory voting) but because it’s what we feel we ought to do. There is a sense of altruism—and altruism provides the ultimate justification for why it is right to do these things—but the primary motivator in most cases is culture—that’s what people do, and are expected to do, around here.

Indeed, even when there is a direct incentive against behaving a certain way—like criminal penalties against theft—the probability of actually suffering a direct penalty is generally so low that it really can’t be our primary motivation. Instead, the reason we don’t cheat and steal is that we think we shouldn’t, and a major part of why we think we shouldn’t is that we have cultural norms against it.

We can actually observe differences in cultural norms across countries in the laboratory. In this 2008 study by Massimo Castro (PDF) comparing British and Italian people playing an economic game called the public goods game in which you can pay a cost yourself to benefit the group as a whole, it was found not only that people were less willing to benefit groups of foreigners than groups of compatriots, British people were overall more generous than Italian people. This 2010 study by Gachter et. al. (actually Joshua Greene talked about it last week) compared how people play the game in various cities, they found three basic patterns: In Western European and American cities such as Zurich, Copenhagen and Boston, cooperation started out high and remained high throughout; people were just cooperative in general. In Asian cities such as Chengdu and Seoul, cooperation started out low, but if people were punished for not cooperating, cooperation would improve over time, eventually reaching about the same place as in the highly cooperative cities. And in Mediterranean cities such as Istanbul, Athens, and Riyadh, cooperation started low and stayed low—even when people could be punished for not cooperating, nobody actually punished them. (These patterns are broadly consistent with the World Bank corruption ratings of these regions, by the way; Western Europe shows very low corruption, while Asia and the Mediterranean show high corruption. Of course this isn’t all that’s going on—and Asia isn’t much less corrupt than the Middle East, while this experiment might make you think so.)

Interestingly, these cultural patterns showed Melbourne as behaving more like an Asian city than a Western European one—perhaps being in the Pacific has worn off on Australia more than they realize.

This is very preliminary, cutting-edge research I’m talking about, so be careful about drawing too many conclusions. But in general we’ve begun to find some fairly clear cultural differences in economic behavior across different societies. While this would not be at all surprising to a sociologist or anthropologist, it’s the sort of thing that economists have insisted for years is impossible.

This is the frontier of cognitive economics, in my opinion. We know that culture is a very powerful motivator of our behavior, and it is time for us to understand how it works—and then, how it can be changed. We know that culture can be changed—cultural norms do change over time, sometimes remarkably rapidly; but we have only a faint notion of how or why they change. Changing culture has the power to do things that simply changing policy cannot, however; policy requires enforcement, and when the enforcement is removed the behavior will often disappear. But if a cultural norm can be imparted, it could sustain itself for a thousand years without any government action at all.