Mulligan's present post is a response to a post from Dean Baker of the Center for Economic and Policy Research, which takes a different tack:
There is a simple way to try to test this story. We can look at patterns in wage growth since the downturn. If Mulligan's story is right then we might expect to see the wages of older workers rise less rapidly than for younger workers. (These are nominal wages.) The idea is that the desperate older workers are willing to take big pay cuts to keep or get a job, while the young whipersnappers (sic) would rather lounge around on the couch watching TV.
Baker follows this up with a chart that plots wage growth over 2007-2011 by age group. It turns out that elderly individuals have had higher measured wage growth than non-elderly individuals.
As with any simple test, the simplicity might mask other interesting effects. To see one possible labor-supply-side effect behind this chart, suppose that the only thing that happened on account of the recession is a halving of housing prices.
Such a shock would disproportionately affect the moderately-well-off who own houses more than not-so-well-off who do not. Faced with a sharp decline in household wealth, elderly with wealth tied up in housing would stick with their jobs for longer than before (Mulligan's supply story). Because their income is higher than the not-so-well off group, this effect makes it look like incomes of elderly have gone up when we compare the income of the 2007 elderly to the income of the 2011 elderly. But, I just told a story about supply, not demand.
With the right data, one can test for this story. Just produce a bar chart like Baker's bar chart but just using data on individuals who do not own houses (and wouldn't necessarily have the same impetus to stay in the labor market into their golden years). It isn't a clean test -- some elderly had retirement portfolios decline in value -- but it is a rather simple test.