Saturday, June 7, 2008

Individual volatility can be very different from average, or group, volatility

In Mark Thoma's June 5th post, "The Great Moderation and Household Income Volatility" he writes:

David Beckworth looks at a paper by Steven Davis and James Kahn that tries to solve a puzzle. If, as shown by the Great Moderation, aggregate income volatility is decreasing, how can individual household income volatility be increasing as many have claimed? Shouldn't the increased stability in GDP cause household income be more stable? Not necessarily

One of the fundamental reasons why this can easily happen, and has actually happened big time, is that large independent risks faced by many individuals and their families (called idiosyncratic risks), even very large and devastating ones, can average out for the statistics for the group, especially for a large group. And our economy consists of a very large group of workers, over 100 million. I'd like to explain this phenomenon more concretely and clearly by going through a hypothetical example:

Case A – All 100 million individual workers have a wage that's based on a separate coin flip for each with:

Heads: $10,000/year

Tails: $70,000/year

Case B – All 100 million workers get paid $40,000/year no matter what.

In case A, individual workers have massive income volatility. In case B individual workers have no income volatility, but in both cases the income volatility for the aggregate economy, the economy as a whole, will be essentially the same. It will be virtually zero in the first case, and exactly zero in the second case.

In case A, although individual workers can have massive volatility in their earnings, and face massive risk, and decrease in the quality of their and their family's lives, including perhaps the inability to pay for medical care, the aggregate average earnings in the economy are $40,000/year, with a standard deviation of just 0.3 cents per year!

The intuitive reason is, as you'd expect, that if you do as many an 100 million independent coin flips, the odds of getting anything more than a micro percentage over 50% being heads, or a micro percentage over 50% being tails, are infinitesimal. The odds are for all practical purposes zero. So the economy as a whole always has average income stably at $40,000, even though individual workers incomes vary massively over the years, and they face devastating risk to themselves and their families, and cannot plan well and efficiently long term.

The moral of the story: Individual volatility and aggregate volatility for the economy as a whole can be very different. Each individual can face massive risk and volatility, but in the economy as a whole, at the end of the day, the individuals who had good luck can average out the individuals who had bad luck and really suffered, so that the average looks ok and is always about the same. But as an individual you don't want to be exposed to these kinds of ups and downs, this kind of risk, and you certainly don't want your family to be exposed to it – that's real family valuing.