The revelation of who opened accounts on the Ashley Madison site for adulterers got the attention of curiousity seekers and suspicious spouses. Josh Barro and Justin Wolfers had a different impulse. They wondered whether a surge in marital trouble resulting from the Ashley Madison hack could hurt the economy — or even, surprisingly, make it grow faster.

Josh:

The Ashley Madison hack, which appears to have exposed personal information about millions of users of the website for married people looking to have affairs, is likely to cause trouble in lots of marriages. Could that add up to trouble in the American economy?

My instinct is that, economically, the impact of the Ashley Madison hack could look a lot like a hurricane. It is likely to unexpectedly destroy a lot of capital people invested time and money in creating – except, instead of buildings and infrastructure, this capital would consist of valuable human relationships.

Divorce is costly, not just emotionally but financially. If you have to save up to pay a lawyer and rent a studio apartment, won’t you eat out less and put off buying a new car? Could this be felt at the level of the macroeconomy — a divorce drag? How many divorces do you have to precipitate to tip the economy into recession?

Justin:

Lemme try to do some back-of-the-envelope math. And warning, most of my guesses will be wrong, but hopefully they’re good enough to get the order of magnitude right.

News media reports say there were 32 million accounts, but that doesn’t mean 32 million American members. Ashley Madison originated in Canada, and many of the accounts could be duplicates or dummies. The site didn’t even require verification of sign-up emails; one user signed up as “This email address is being protected from spambots. You need JavaScript enabled to view it.,” and I very much doubt that was actually the former British prime minister.

Let’s guess that 10 million accounts are real and from the United States, and nearly all are men. That still seems high, actually, as there are only 65 million married men in the United States, so that would put 15 percent of them on Ashley Madison.

But let’s run with the number for a worst-case scenario, and let’s say that half of them were dumb enough to use easily identifiable email addresses or can be identified through credit card information. That brings us to 5 million marriages at risk. And let’s say that half of all spouses actually check the files to see if their partner is there (that seems incredibly high to me but perhaps that is plausible once the data become easily accessible). Then we are down to 2.5 million marriages, and let’s say that half of them can’t work their way through it, then we have 1.25 million divorces. Let’s say that a third of these folks would eventually have been caught cheating anyway or would have divorced for other reasons. So we have around 800,000 extra divorces.

O.K., so in terms of divorce statistics, that’s a big jump. We normally get a bit more than one million divorces each year, so that would be around an 80 percent jump. The more likely pattern is that the effect would be spread over several years — partly because it takes couples a while to decide, it takes them a while to get around to it, and state law imposes separation requirements that can be several years long.

So a very aggressive estimate of the destruction from this hack would give us an extra 200,000 divorces over each of the next four years, and so the divorce rate is 20 percent higher for each of the next four years. That’s definitely noticeable, but not unheard-of.

So what’s the macroeconomic impact? Here’s where I’m truly making numbers up.

Divorce is actually pretty simple in lots of cases — you just fill in the forms. (There’s an argument that paralegals should be able to do this work.) Let’s say that each divorce leads to $5,000 in extra spending on lawyers. That would mean an extra $1 billion in extra spending on lawyers per year, for each of the next four years. Value-added in the legal service industry was $225 billion in 2013, so the impact on the legal services industry as a whole turns out to be pretty small — a spike of about 0.4 percent higher demand for the next four years. Of course the impact on family lawyers will be much more concentrated, but still, this isn’t huge.

For the economy as a whole, you have to decide whether the extra spending on divorce lawyers is extra spending, or whether it comes partly from cutting back on other things. Even if it all comes with no offsetting spending in other categories, then $1 billion in legal fees pales in comparison to a $17 trillion economy. G.D.P. would be higher by 0.006 percent for a few years – too small an effect to measure.

I suspect the bigger economic issue is what these divorces would do for new household formation. If all these newly single people formed new households, then household formation will be 200,000 higher each year for the next four years, and that would fuel demand for construction. But that seems too big: In the United States, folks who have been divorced start by moving in with friends or family, and then very often move in quickly with new partners. A lot of this is musical chairs not leading to demand for an extra home.

A reasonable guess might be that annual household formation would be 100,000 higher for the next four years (the other half quickly repartner), but 50,000 lower for the subsequent four years (as some of the extra divorced folks continue to repartner). I’m not quite sure how to convert this into G.D.P.-equivalents, but it seems relatively small compared to household formation rates.

Let’s assume each new household involves construction of a $200,000 home or apartment, which is roughly the median home price. (Estimates vary.) That’s $20 billion in extra home construction each year for four years. That’s big enough to matter, enough to raise G.D.P. by 0.12 percent in the first year. But while G.D.P. would remain higher for the next three years, G.D.P. growth would not be. And some of this effect would be temporary.

My sense in all of this: I’ve almost surely overstated the number of divorces that will follow from Ashley Madison, and I’ve likely overstated how much extra construction this will lead to. If you think that this extra spending has multiplier effects, that could boost the macroeconomic impact. But if you asked me for a bottom line, I think that the net effect will be less than 0.1 percent — basically impossible to see in our noisy macroeconomic data.

Josh:

Wait. What you’re looking at here is a small but positive effect on the economy if the divorce rate rises?

That strikes me as implausible. Divorce may create demand for more housing, but it doesn’t make people more productive. It probably makes them less productive, because it’s distracting and unpleasant and often acrimonious.

If divorcing couples spend more on housing and lawyers but their income stays flat or goes down, they’ll have to cut back their consumption of something else. This is the main economic effect I was assuming you would see — people buying fewer new cars and going on fewer vacations and eating out less.

Saying extra divorces grow the economy is like saying paying people to dig holes and fill them up grows the economy — it can only be true if there is a serious demand gap, and new spending doesn’t do anything to crowd out other spending, which may have been true in 2009 but isn’t true today.

Also, even if you’re right, it takes time to add new housing units. There might be enough slack in the construction industry right now to simply increase the pace of housing construction by enough nationally, but not in every market. In some places, higher demand for housing will simply manifest as higher rents and prices.

That is, all the divorcing couples out there looking for studio apartments will drive up rents and make it harder for millennials to move out of their parents’ basements – adding another aspect of economic drag.

Justin:

You are right, my numbers come from thinking only about the demand side effects, and they are positive. But your argument that all this extra spending will crowd out other spending comes from thinking about people meeting their budget constraints period by period. But of course people can (and most likely will) borrow.

Think of an analogy. When someone wins a $1 million lottery, we don’t expect them to increase their spending by a $1 million that year. Instead, we expect them to raise their spending by $50,000 per year, for each of the next 20 or so years.

Divorce is a bit like losing the lottery – a one-time windfall loss instead of a gain. Or alternatively, think of it as a consumer durable — a long-run investment in a better life. We don’t typically expect people who buy a house or other durables to pay it all off overnight. Just because you spent $200,000 more on housing this year doesn’t mean you’ll spend $200,000 less on other stuff this year. Instead, you’ll borrow and pay it off slowly.

Likewise, the extra investments that divorce requires are all long-run investments that people will most likely “pay off” slowly over time. So I don’t think that the effect on buying fewer cars will be that large.

Josh:

That long-run approach is valid so long as people are liquid — that is, they can borrow or draw down assets to finance the cost of a divorce without significantly changing their other spending patterns. That’s true for some people; it’s not true for others. Some people have no choice but to respond to a negative one-time income shock by spending less. Relatedly, divorce can be a reason people file for bankruptcy.

But set aside these income shock effects. Relationships are valuable human capital, right? Shouldn’t an event that suddenly and unexpectedly destroys a chunk of them look a lot like a natural disaster that destroys a lot of real estate? The loss of capital ordinarily leads to a loss of output.

Justin:

Now we’re talking about the supply side of the economy. If relationships are productive — we are better on the job when married than when single — then the analogy with human capital is a good one. And destroying any form of capital lowers G.D.P.

But it’s not clear that marital relationships really are human capital in the economic sense. It’s not enough to show that people enjoyed being married or liked their spouses (before the Ashley Madison discovery). To have an effect on G.D.P., the marriage would have to have been increasing their productivity.

There is academic research on the “marriage earnings premium,” finding that married men are paid a few percent more than unmarried men, arguably supporting the idea that marriage is a productive form of capital. But the same literature finds a “marriage penalty” for married women versus unmarried women. I’m not sure I find this persuasive evidence that relationships are in fact economically productive. It might just be that high-earning men are more attractive spouses.

There are also longer-run effects to consider, but they’re a generation away. The Ashley Madison hack might mean that more kids grow up without married parents. In most cases, we might think that a loving and intact marriage is better for kids than divorce. But in reality, many of these families face a different trade-off, between mom and dad staying together in an unhappy and perhaps conflict-ridden marriage, versus getting divorced and possibly repartnering. It’s quite unclear what’s best for the kids in these situations.

But more important, you are right: The big costs here are real, it’s just that most of them aren’t measured in our economic statistics. They’re broken homes and broken hearts. Just as a natural disaster is terrible though not necessarily a major macroeconomic event, the Ashley Madison leak may be terrible for many families, though not a macroeconomic event.

Josh:

Well, I guess that’s a bit of comfort.