Against Day Fines

Today, more than 30 European and Latin American countries levy penalties using an income-graduated, or “day fine,” model. Under this system, people who break the law pay a fine equivalent to a percentage of their income, rather than a flat fee. … “can be thus seen to be more equal and effective than a system where the amount of fine is fixed.” … American lawmakers have failed to take the idea of income-adjusted fines seriously. (More)

Yes, making crime fines proportional to income can achieve a more progressive taxation. Even so, “day fines” make us worse off compared to using more direct forms of progressive taxation. To see this, consider the case of speeding and other rushed driving offenses.

When people are driving, they trade the risk of an accident against saving time. For example, in their rush to get places, drivers can choose to not take as much time looking for pedestrians before making a right turn, or checking that a lane is empty before changing lanes. And they might drive faster; the rate of fatal accidents per mile seems to go as the cube of driving speed in the city, and rises even faster in rural areas.

Of course if they were just at risk of hurting themselves, we might not care how they made their trade-offs. But most car accidents also involve other cars. So we want a way to encourage drivers to take the harm that their accident might inflict on other drivers into account. Speeding fines, and accident liability, help us to induce such concern. (B.t.w., with vouchers and well-set accident liability, we wouldn’t need speeding fines.)

All else equal, drivers with twice the wages tend to put twice the dollar value on both saving an other minute of driving, and also on preventing another small chance of their own death. So if the dollar amounts of their speeding tickets and liability given an accident were also twice as large, then the dollar amounts on both sides of their tradeoff would all be twice as large. Thus in the same circumstances they would make the same choices to trade time versus the chance of an accident. So in the same car on the same road etc., they’d drive the same speed, and take the same time to check before turning or changing lanes.

However, having two drivers, one with twice the wage of the other, each take the same amount of time to use the same technology to prevent the same amount of harm to others is not efficient. That’s wasteful, just like having a high-wage donor work the line at a soup kitchen, instead of working at their high-wage job a bit more to pay a low-wage worker to work that soup kitchen line. In the driving case, we can keep the car accident rate the same and make both drivers better off, if we have the lower wage person drive more carefully, the higher wage person drive less carefully, and have the high wage person pay the lower some cash.

For example, the median US wage is now ~$16/hr, and workers tend to value commuting time at about half of their wage rate. So imagine that drivers A and B value each their driving time at $9/hr and $18/hr respectively, which is one and two pennies per four seconds. In this case both A and B can be better off, while the total accident rate stays the same, if B gains 1.0 pennies by putting in 2 fewer seconds, A loses 0.5 pennies by putting in 2 more seconds, and B pays A 0.75 pennies.

In general, we use traffic fines and accident liability to buy the time of drivers’ to prevent more accidents. Day-fines proportional to income buy the same amount of time from all drivers in similar circumstances. But we can be better off if we instead buy more time from drivers with lower wages, and less time from drivers with higher wages. And roughly the right amount of time is induced from each via fines and liability that do not vary with income.

You might complain that ordinary constant fines, that do not vary with income, do not include a cash transfer from high to low wage drivers. But that critique only makes sense if we currently had day-fines, and I was proposing to switch to constant fines. In fact constant fines are our status quo, which I’m proposing that we keep. I don’t see we should need transfers to reject an inefficient change and keep things the same.

Note that a similar argument also says it is inefficient to give the same jail time sentence to high and low wage convicts. Jail is the least efficient of all known forms of punishment, and equal duration sentences just makes this worse. We should instead delegate punishment choices to vouchers.

For the math-literate, here’s a simple math model. Consider a driver who drives at speed si, values their life at Vi, causes accidents at rate r(si), faces average speeding fines Ti(si), and faces liability from a fatal accident of Fi. The cost they seek to cut might be written Ci = Vi/si + Ti(si) + r(si)(Vi + Fi). (Note that fine Ti(si) has the same effect as r(si)*Fi.)

Ignoring enforcement costs, the social harm from each driver might be written Si = Vi/si + r(si)(Vi + A), where A is the average over Vi, assuming random accident victims. So we can induce drivers to set si to minimize this social harm by setting each Fi = A. (Setting Ti(si) = r(si)A also works.) This choice also (nearly) minimizes Sumi Si under the constraints that each i will pick si to min Ci, and that we must use transfers to ensure each driver expects to be no worse with our choice than in some arbitrary initial Fi setup.

Note that we could have used any function vi(si) instead of Vi/si here.

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