VSL is BS?

Gabriel wants to talk about SVL or “statistical value of life” (aka VSL). Where would we be without acronyms.

First, why should we have such a thing? Isn’t putting money value on human life too icky to contemplate? If we have such a value, wouldn’t it suggest Bill Gates could buy our lives? Would it be condoning slavery?

Answers: because we have to, yes but someone’s got to do it, no and really no. Simply put: there’s no way to know how much money to spend on life preserving/extending goods and services if we don’t have a sense of how much its worth to us to preserve that life. “Life is priceless” is a nice sentiment, but taking it literally, and via a sufficiently snarky reductio ad absurdum, this refrain would suggest we spend infinite resources making sure people don’t get the slightest owies. See how absurdum that reductio would be?

Anyway, how much I spend on air bags for my bicycle or how much time I spend indoors instead of braving the mean streets of Davis ((Bikers don’t think they need to follow road rules.)) reflects the value I give to my life. If I value my life more, I’ll spend more time in bed. Usually, I don’t spend all my time in bed so I can’t have an infinite value for my life. If I value my life less, I’ll spend more time sky-diving. Because I’m not spending all my time jumping out of perfectly good airplanes, the value I give to my life can’t be zero. Somewhere between zero and infinity, then, you’ll find the value of my life. The things between zero and infinity are called numbers and that’s all economists are doing when they assign a money value to life; they’re assigning a number to that subjective value we all have in our heads anyway.

There’s a couple of things we’d expect to be true about that number:

  1. It shouldn’t vary too much between different types of people
  2. To the extent it does vary, it should do so primarily because of the underlying difference in risk preferences of individuals
  3. It shouldn’t vary too much by age except in the last moments of life
  4. It should be big in any case. It would be really disappointing (and unbelievable) if economists said lives were worth pocket change (even, or especially, for the infirm) .

With my limited imagination, I can think of two ways to put a dollar value on a human life. The first is to use lifetime income or the slight variant, the income yet to be earned. In other words, just add up pay checks. This breaks a bunch of the rules listed above, but mostly it violates #2 and #3.

Another way to come up with a dollar figure is to look at how much money people spend on safety equipment (willingness to pay) or how much extra money they earn doing dangerous jobs (compensating differentials) relative to mortality rates. The fancy folks down the hall that specialize in Public economics call this the value of a statistical life (emphasis on the “statistical”).

There’s lots of estimates of this value, but most put it between $4m and $9m ((see Viscusi and Aldy. They find safety is a normal good, unions are associated with higher hazard pay and VSL declines with age.)). This method does an OK job not breaking any of the above rules. Take for example the estimates showing a 10% increase in income leads to a 5% increase in VSL. This may seem disturbing at first, but assuming I’ve done my marginal effects calculations right, this values Americans at the poverty line at $2.5m or so ((and Bill Gates at $1.5B, but he may be slightly out of sample)).

What do egalitarians care about?

I dunno, but if its “capabilities” or equality of opportunity then tracking income inequality between various income percentiles is the wrong measure to concern themselves with.

Income is a flow. Its tenuous. Its dynamic. It does not determine the size of your budget set; it does not determine your capabilities or opportunities.

If you doubt this, talk to Dell about the new computer I just bought on credit ((I know, I know… Cash flows are very irregular for grad students and I got a good price on the computer with zero interest)). Talk to the Bank where I took out my student loans.

If you care about the size of budget sets, then you care about lifetime income (and access to the credit market, but I don’t think this is a problem in the U.S.). This is because if someone has earning potential (let’s say they’re a college student or they’re just starting their career) then lenders will loan them money, even if they have low income today, because the lenders know their earnings, and thus their ability to pay the lenders back, will increase over their lifetime.

Is current income at least a good measure for lifetime income? Nope. Early in careers, there’s little correlation between current earnings and total lifetime earnings ((see this paper for a nice discussion of the issues involved in measuring lifetime income. They use some really, very cool Swedish data to estimate the relationship between current income and lifetime income.)). This picture shows the ratio between current and permanent income (annualized):

So, why do egalitarians seems to care so much about (current) income inequality dynamics?

Explaining behavior

After observing that lots and lots of genes can interact to determine a particular phenotype, Razib asks some good questions about Social Science:

I’ve been thinking about this when it comes social phenomena. Much of the verbal treatment presupposes a few large effect explanatory variables; but what if that’s not correct? What if most social phenomena are contingent upon thousands of small effect predictors? How are you going to talk about this? And since we don’t know the “gene” unit of social phenomena where do you even start? Of course quantitative social scientists focus on phenomena which do have independent variables of big effect; but most of the action might not be low hanging fruit, but rather dispersed in the canopy.

I’ll just observe that underlying any gene explanation, even ones that have many, many causal genes, is genetic theory (“One explanation to rule them all”) itself. When social scientists are trying to describe a particular behavior (e.g. why Davis undergrads go to The Graduate on Friday nights) then they may have to go after a multitude of explanations. If they’re trying to describe a type of behavior (e.g. demand for alcoholic beverages), this may not be the case.

UPDATE: I wrote this as a comment below, but I thought it fit better up here:
“I think his critique confuses a couple of things. First of all, there are several levels of abstraction even in the hard sciences. Chemists don’t reduce everything they study into sub-atomic behaviors and certainly biologist and geneticists don’t. Even if everything can be reduced, sometimes the emergent behaviors are so complex we, with our feeble minds, have to strip some of the complexity away. In other words, chemist *could* talk about sub-atomic behaviors of their chemicals — which represent billions of interactions between billions of sub-atomic particles — but they don’t, mostly because they, being human, aren’t suited for it.

The other thing he seems confused by, and this may be related to the first confusion, is the nature of social science. We’re not about predicting particular behaviors. We’re about predicting types of behaviors. Sometimes you hear a critique of economics suggesting we’re bad at predicting business cycles and so we don’t know much about business cycles. This is clearly false, we know a bunch about business cycles just as chemist know a bunch about specific chemical reactions. Do chemist not know chemistry because they can’t predict the velocity of a particular molecule during a reaction? Do they not know chemistry because they can’t predict the exact timing when a particular reaction will take place between two molecules (or if it will happen at all)? These questions are funny because we wouldn’t even suggest chemists should know these particular things.

I guess I’m saying social science is about general patterns of social interaction. This upsets people who want us to be seers.”

The power of corporations

Recently I ran regressions of wages and labor force composition on the density of Walmarts in States. Walmart — the largest private employer in the U.S. with sales of over $350B or about 3% of GDP — has had zero effect on wages and labor force composition in aggregate. This was much to my disappointment because zero results don’t get published.

This (non-)result suggests that the largest corporation on the planet has little effect on the macro economy. How does one square this fact with the narrative of the omnipotently evil multinational corporation? Does it make sense to compare GDPs to sales (or profits) of corporations? If not, what is a good way to compare the power of corporations to the power of nations?

Abortion and adoption

(Wow, never noticed how similar those word are…)

This graph is cool ((In the “wow, look at the pretty data” sense not the “wow, isn’t abortion cool” sense. See this.))

Abortion and adoption

In 1968 abortion was legalized in the U.K. Adoption rates declined dramatically, but children taken into State custody remained at about the same rate. The authors of the article suggest this is one more chink in the armor of the abortion caused lower crime hypothesis. In the Levitt story, unwanted children — who are future criminals (obviously) — stopped being born after abortion was legalized, i.e. if a woman didn’t want a kid, she’d get an abortion instead of having the kid and raising it to be a criminal. However, adopted babies are, if nothing, the definition of wanted children so if abortion reduced adoptions significantly, its safe to say there weren’t that many “unwanted” kids being born before the legalization of abortion. Adoption and abortion are substitutes.

The best ((ibid)) part of this new thesis is that because of mass substitution from adoption to abortion, the adoption infrastructure suffered. This means for the marginal unwanted baby, it was harder for her mother to get an adoption and thus more likely for that baby to be raised in a bad, criminal creating, home. Creating marginally more restrictive abortion laws ((e.g. roe v. wade?)) would generate more crime.

Another explanation for the constant number of State interventions, though, is that fixed-budget child welfare bureaucrats started taking less marginal children away from their parents. In other words, in absolute terms, less unwanted kids, even accounting for adoptions, were being born, but more kids were being taken from their homes than would have been otherwise. The bureaucrats have to justify their budgets.

The above is a discussion of the supply side factors, but what about demand? Are “unwanted” children being underproduced?

(h/t SM,CI & SS… Andrew Gelman has a good discussion of testing long term mechanisms via short term effects. I call this, “testing the other implications of a theory.”)

How to easily reject the rantings of a dumb blogger

Ok, ok. I admit my last post on the children and happiness issue didn’t, in the end, add much to the debate. Economists that have studied the issue have found negative (and small) effects of children on happiness and they’ve done so without including controls for squishily measured variables ((But the analysis is still valid in general!)).

But I’m still skeptical. Until I see a good mechanism to explain this result, I’ll remain so. Here’s an old post by Dan Gilmore that addresses why my intuition might be mistaken:

First, when something makes us happy we are willing to pay a lot for it, which is why the worst Belgian chocolate is more expensive than the best Belgian tofu. But that process can work in reverse: when we pay a lot for something, we assume it makes us happy, which is why we swear to the wonders of bottled water and Armani socks. The compulsion to care for our children was long ago written into our DNA, so we toil and sweat, lose sleep and hair, play nurse, housekeeper, chauffeur and cook, and we do all that because nature just won’t have it any other way. Given the high price we pay, it isn’t surprising that we rationalize those costs and conclude that our children must be repaying us with happiness.

Second, if the Red Sox and the Yankees were scoreless until Manny Ramirez hit a grand slam in the bottom of the ninth, you can be sure that Boston fans would remember it as the best game of the season. Memories are dominated by their most powerful—and not their most typical—instances. Just as a glorious game-winning homer can erase our memory of 8 1/2 dull innings, the sublime moment when our 3-year-old looks up from the mess she is making with her mashed potatoes and says, “I wub you, Daddy,” can erase eight hours of no, not yet, not now and stop asking. Children may not make us happy very often, but when they do, that happiness is both transcendent and amnesic.

Third, although most of us think of heroin as a source of human misery, shooting heroin doesn’t actually make people feel miserable. It makes them feel really, really good—so good, in fact, that it crowds out every other source of pleasure. Family, friends, work, play, food, sex—none can compete with the narcotic experience; hence all fall by the wayside. The analogy to children is all too clear. Even if their company were an unremitting pleasure, the fact that they require so much company means that other sources of pleasure will all but disappear. Movies, theater, parties, travel—those are just a few of the English nouns that parents of young children quickly forget how to pronounce. We believe our children are our greatest joy, and we’re absolutely right. When you have one joy, it’s bound to be the greatest.

Gee, maybe day to day, minute by minute experienced happiness isn’t the only thing people care about?

How to easily reject results from Happiness research

Will Wilkinson is giddy over happiness research these days. One of the results he cited the other day was controlling for everything, kids make people less happy.

Here’s why that’s complete bullocks, as they say. Let’s say you have a survey that asks people whether or not they have kids (K) and asks people to rate on a scale from 1-10 their satisfaction with their marriage (M*) and on the same scale ask their overall happiness (H). Of course these survey instruments are more sophisticated then that, but the point is you have two types of questions, ones with a lot of measurement error (and actually is just a proxy) and one that has little or no measurement error.

Now, people can report whether or not they have kids with tremendous accuracy and precision. We’re great “kid counting” instruments. We’re lousy at measuring our own satisfaction (M), though. We’re inaccurate at measuring our satisfaction because its not clear what scale we should be using. We’re answering “satisfied – 8” on the wrong 1-10 scale when we should be answering “satisfied – 132” on the negative 17 to infinity scale.

Compounding the problem is that having kids probably changes our measurement of our own satisfaction with marriage. By this, I don’t mean that there’s necessarily a correlation between true satisfaction and having kids. I mean our measurement of satisfaction is correlated with having kids.

We’re also not precise instruments of satisfaction measurement. We would answer “132” on the correct satisfaction scale but we can’t really differentiate between a 132 or a 133. In fact, we probably have a whole range of satisfaction scores that we wouldn’t be able to differentiate between.

So what? Well, the problem is that this means the satisfaction with marriage score we get from surveys is a proxy for a true measure of satisfaction and it is correlated with having kids. Proxies correlated with other regressors introduce biases that make it more likely to find kids make us less happy in general even though in reality this isn’t true.

UPDATE: I think my post as previously written was confusing where proxy/measurement error comes into play. The original study regressed overall happiness on having kids and some other subjective, poorly measured variables (like happiness in marriage). There are two problems with the measurement of those subjective variables. The first is that the measure itself may be correlated with having kids. People with kids may believe kids makes marriages more happy. The second problem is standard measurement error (i.e. lack of precision and accuracy). I’ve rewritten a little in hopes of improving clarity.

UPDATE 2: Take 2. I replaced “happiness in marriage” with “marriage satisfaction” so as not to confuse that with overall happiness. YouNotSneaky! is so much better at this…

The math below the fold proves these point.

Continue reading “How to easily reject results from Happiness research”

What’s so special about zero?

Mark Thoma asks what went wrong with the risk models during the most recent crisis. He has a good discussion of structural vs. reduced form models. In practice, people use the later models because the former are pretty bad. We don’t know, in general, the causal mechanism between any two variables.

With reduced form models, measuring the correlation between two variables allows us to predict how changes in one variable will change the other variable. Because we know gold prices are inversely correlated with GDP, we can predict that in a recession gold prices will go up.

The problem with reduced form models is that we don’t understand what’s causing the correlation and that causal relationship might change over time. Maybe, in the past, gold prices happen to go up because demand for gold tooth fillings goes up in recessions as people switch their diets to cheaper, sugary foods. But in this recession corn prices, and thus corn syrup, has become much more expensive, sugary foods aren’t cheaper and thus gold prices don’t go up. (WARNING: I completely made up this example.)

In any case, you see my point. Correlation’s not causation and all that.

But that’s not I want to talk about. What I want to question is why do we think the risk models failed? The risk models don’t guarantee against negative shocks, they make them less likely. We happened to hit a state of the economy where lots of returns where zero. This doesn’t mean the models didn’t anticipate zero returns. Because it was an unlikely, but not impossible, event, its likely the models had this set of events priced in.

Would we ask this question if returns were unusually low, but not zero? Probably not. What’s so special about zero returns that realizing them means our models are broken?

I almost titled this post, “Life has a measure zero.”


This segment of the latest science bloggingheads contains an interesting definition of science. In short: theory (a collection of hypotheses) suggests places to look for data and then data, once found, doesn’t falsify but it increases or decreases confidence in particular theories.

Under this view, Ottaviano/Peri’s result decreased the confidence in a production economy where immigrants and natives are perfect substitutes. Borjas’ response, not rejecting the hypothesis of perfect substitutes, doesn’t really repair confidence in his theory. To repair confidence, he would have to demonstrate that implications of his model, that differ from the implications of the “complementarity” model, are true.

UPDATE: he goes back to this issue later in the show. The whole thing is worth watching actually.