Second-order effects

Ask what happens next, and who is on the other side of the trade.

In 1969 the city of Stuttgart tried to fix a traffic problem by adding a stretch of road. Congestion got worse. They closed the new stretch, and traffic improved. Nothing else changed, no driver behaved oddly, and nobody had made an error in the survey.

The rule

Ask what happens next. Then ask it again.

The first consequence of anything is the one everybody can see, which means it is already in the price, already in the plan, and already in the argument. The second one is where the information is, and reaching it does not take cleverness. It takes asking a question you had no particular reason to stop asking.

A road that makes everybody slower

Below is a network with two routes. Each one has a leg that jams up when it is busy and a leg that always takes 45 minutes. A new road connects the middle of one route to the middle of the other. It is free, it is instant, and it is optional.

Every driver's trip

80 min

Without the new road

65 min

The road costs each driver

+15 min

Every driver is 15 minutes slower than before the road was built, and no single one of them can fix it by changing route. That is 1,000 hours a day, thrown away by adding a road that is free and instant.

Cars trying to cross4,000The new road is open

Slide the traffic up through three thousand cars. Below that number the new road does exactly what a new road should. Above it, the same road makes every single driver slower, and no driver can fix it by changing route.

Worked example

Why nobody can escape it

With 4,000 cars and no shortcut, drivers split evenly. Each route carries 2,000 cars, so the congested leg costs 20 minutes and the fixed leg costs 45. Everybody takes 65 minutes.

Open the shortcut and follow one driver's reasoning.

The shortcut route skips both 45 minute legs. It uses the congested leg at the start and the congested leg at the end, which is faster than sitting in a fixed 45 minutes as long as the roads are not saturated. So take it.
Every driver reasons the same way. Now all 4,000 are on the first congested leg and all 4,000 are on the last one. Each costs 40 minutes. The trip is 80.
Nobody can improve by switching. Leaving the shortcut for a long route means one congested leg carrying all 4,000 cars, at 40 minutes, plus a fixed 45. That is 85, which is worse than 80. So nobody moves.

Every driver made the right choice for themselves at every moment, and all of them ended up fifteen minutes worse off. That is a thousand hours a day, given away by adding a road that costs nothing to use.

The reason the first-order analysis missed it is that it asked what the new road does to one driver holding everyone else fixed. Everyone else was not fixed.

Named for Dietrich Braess, who published it in 1968. The Stuttgart closure and a similar episode on 42nd Street in New York in 1990 are both documented in the transport literature. The figures above are computed by the model on this page, which is unit tested, including a check that no driver on the shortcut can improve by leaving it.

ConventionAn arrangement where nobody can improve by changing their own move alone is a Nash equilibrium. What the road shows is that an equilibrium can be worse for everybody than an arrangement they could all have agreed to, and that no amount of individual good sense gets them there. This is the same shape as the prisoner's dilemma and the same shape as a bank run, which is why it is worth having a name for.

Three places the second effect hides

The other side of the trade. Every buyer has a seller, every borrower has a lender, and every winner in a market has somebody who took the losing side. If a move looks free, find out who is paying for it, because somebody is.
The reaction of everybody else. A strategy that works because few people use it stops working when many do. A tax on one thing moves activity to the untaxed thing next to it. A rule that binds one channel pushes the flow into whichever channel the rule did not name.
The change in what people expect. A bailout resolves this crisis and changes what everybody believes about the next one. A one-time bonus becomes the baseline against which next year is judged. The precedent outlives the event.

What breaks

Naming an effect is not sizing it. The second-order effect is often real and much smaller than the first. Safer cars do make people drive faster, and road deaths have still collapsed. People who learn this habit tend to overshoot into arguing that every intervention cancels itself out, which is a worse error than not knowing about second-order effects at all.

Chains get speculative fast. The first consequence is usually solid, the second is usually worth taking seriously, and by the fourth you are writing a plot rather than an analysis. If your argument needs five links, the honest summary is that you do not know.

It is not an argument against acting.Doing nothing has second-order effects too, and they are less visible because nobody has to announce them. The question is always which set of consequences you prefer, and comparing a policy's side effects against an imagined clean alternative is not a comparison.

What to do with this

Two questions, asked in order. And then what happens? Then, once you have an answer, and then what happens? again. Stop at two or three. Most of the value is in the first repetition, which is the one almost nobody does.

And when a decision affects a lot of people at once, check whether your reasoning held everyone else still. That is the specific mistake in the road, in the crowded trade, in the strategy that stops working when it gets popular, and in most confident predictions about how a market will respond.

Test yourself

01Cars get much safer: better brakes, better tires, anti-lock systems. What is the second-order effect, and what does the evidence say about it?

People drive faster and closer, because the perceived risk of doing so has fallen. The safety improvement partly gets spent on speed rather than banked as fewer crashes.

The honest version is that this offsets some of the gain and nowhere near all of it. Road deaths per mile driven have fallen enormously over decades, so the first-order effect clearly won. The second-order effect is real, it is smaller than the first, and people who know about it often overcorrect into claiming safety measures do nothing. Naming an effect is not the same as sizing it.

02A company announces layoffs and its share price rises. Walk through why, and then walk through what happens over three years.

First order: costs fall, so expected profit rises, so the price rises. That is the effect priced within the hour.

Second order: the people who leave first are the ones with the best outside options, which is the opposite of the ones you wanted to lose. Everyone who stays updates their view on how safe the job is, so the next best offer they receive gets a fairer hearing. Institutional knowledge walks out with no handover.

Third order: whether any of it mattered depends entirely on whether the cuts were to a bloated cost base or to the capacity that produced the revenue, and you find out about two years later. The share price move on the day contains none of this information.

03Why does 'and then what happens?' work better than trying to be clever about consequences?

Because the trap is stopping, not thinking badly. The first consequence is the one everybody sees and the one already in the price. Asking the question one more time is a mechanical move that requires no cleverness, and it is where the information that other people do not have tends to live. Two rounds is usually enough. Beyond three you are writing fiction.

A tutor that knows this lesson. It asks before it explains, and it will not tell you what to do with your own money.

Educational material, not investment or policy advice. Figures are cited where they come from a filing or a statistical series, and labelled as illustrative where they do not.