Calculated Risk has identified a howler in Intrade's futures contract on whether or not we'll have a depression. Intrade, of course, is the site where you can bet on all kinds of events, from sports to politics to economics. The informal definition of a depression seems to be a decline in GDP of 10 percent or more. Intrade's site indicates that traders believe there is a 56 percent chance of depression this year.

How will the Intrade rulemakers decide if there is a depression?

This contract will settle (expire) at 100 ($10.00) if quarterly GDP figures show the US economy has gone into a depression in 2009.

The contract will settle (expire) at 0 ($0.00) if quarterly GDP figures DO NOT show the US economy has gone into a depression in 2009.

For expiry purposes a depression is defined as a cumulative decline in GDP of more than 10.0% over four consecutive quarters. This is calculated by adding together the published (annualized) Real GDP figures (as detailed below). If these annualised figures add up to more than -10.0% over four consecutive quarters then the contract will expire at 100.

Example 1:

In Q1 the Final Real GDP figure is -3.5%
In Q2 the Final Real GDP figure is -2.5%
In Q3 the Final Real GDP figure is -2.0%
In Q4 the Final Real GDP figure is -2.3%

The sum of these figures is -10.3% so the contract will be expired at 100.
...
Negative quarters in the preceding year will count towards the total GDP decline for expiration purposes. For example, if the total decline in GDP from Q3 2008 to Q2 2009 exceeds 10.0% then the contract will expire at 100.

Yikes! As CR points out, the quarterly GDP figures are annualized. That is to say, they express a quarter's change in GDP as if the trend continued for a whole year. The actual GDP shrinkage in the first quarter in Example 1 isn't 3.5 percent. It's really less than 1 percent. The actual annual GDP shrinkage in Example 1 would be something around 2.6 percent, not 10.3 percent. No wonder betters are placing 56 percent odds on a winning contract. According to the above example, the Intrade "depression" contract will pay off even if there is only a moderately severe recession.

This language, also in Intrade's description -- "For expiry purposes a depression is defined as a cumulative decline in GDP of more than 10.0% over four consecutive quarters" -- is the proper way to phrase it and conflicts with the examples. Lawsuits?

UPDATE: Others noted the problem in the Intrade contract before Calculated Risk, among them James Kwak of RGE Monitor and Baseline Scenario.