Speeding Fines That Vary With Income: Absolute vs. Relative Risk Aversion and Public Policy

Where there are posted restrictions, most European countries take speeding very seriously and levy hefty fines. The latest case in point is a 37 year-old Swedish man who was clocked at 180 miles per hour on a motorway between Bern and Lausanne in Switzerland.

Unfortunately for this driver of a new Mercedes-Benz SLS AMG, Switzerland doesn’t have fixed fines for speeding. Instead they use a formula similar to that in Finland where the fine is calculated based on the vehicle’s speed and the driver’s income. Back in 2002, Nokia executive Anssi Vanjoki had to pay a fine of \$103,600 for going 47 mph in a 31 mph zone.

A student in my Law, Economics, and Organization seminar mentioned the article quoted above last week when I was explaining the difference between the twin concepts of absolute and relative risk aversion.

In economics, risk is not so much about what most people call risk as it is about gambles over income. In other words, risk preferences are defined over income or wealth. See here for an excellent discussion starting on page 64 in chapter 6 of David Friedman’s Law’s Order. So why would Switzerland and Finland have speeding fines that vary with income?

Absolute Versus Relative Risk Aversion

Two measures of risk in economics are absolute risk aversion — one’s risk preferences over absolute amounts of money (e.g., a gamble involving a 50-percent chance of losing \$200 and a 50-percent chance of winning \$500) — and relative risk aversion — one’s risk preferences over proportions of one’s wealth or income (e.g., a gamble involving a 50-percent chance of losing 0.2 percent of one’s annual income and a 50-percent chance of winning 0.5 percent of one’s annual income).

Analytically, the two concepts are closely related. Letting w denote income or wealth, A(w) denote absolute risk aversion, and R(w) denote relative risk aversion, both as a function of income and wealth, we have that R(w) = w·A(w).

It is generally the case that people getting less absolutely risk averse as they get wealthier. In other words, as w increases, A(w) decreases.

When A(w) decreases as income increases, we talk of decreasing absolute risk aversion. If it is the case that people are decreasingly absolutely risk averse — that is, if a gamble over a specific dollar amount is increasingly attractive as someone gets wealthier — then this means that wealthier individuals are more likely to be risk-seeking. In other words, wealthier individuals will be more likely to drive too fast, since for them, a \$250 speeding fine represents a smaller (absolute) risk.

To curb this type of behavior, it makes sense that policy makers might want to tie speeding fines to the driver’s income or wealth, as in the article above.

Under a vast number of circumstances, even if absolute risk aversion A(w) decreases as w increases, relative risk aversion R(w) will increase as w increases. This means that when speeding fines are proportions of a driver’s income (e.g., you pay 5 percent of your income if you are caught speeding) rather than absolute dollar amounts (e.g., you pay \$250 if you are caught speeding).

More importantly, this also suggests that courts could — and, if you take the distinction between absolute and relative risk aversion seriously, should — impose damages proportional to the defendant’s income rather than fixed damages when deciding how much a defendant should compensate a plaintiff for a loss or injury.

(HT: Dylan Flye.)