Greg Mankiw considers Casey Mulligan's summer employment effect to be a challenge for Keynesian economists to explain. Now, I am not an economist; however, I think this represents a lapse in numeracy, not economic theory
Let's discuss orders of magnitude. Mulligan describes a summer employment effect -- employment among the 16-19 year old cohort rises relative to the 20-24 year old cohort from May to June -- representing an increase in the supply of labor accompanying an increase in the demand for that labor that purportedly contradicts the Keynesian view that aggregate demand in a recession is controlling unemployment. Here is the graph:
How big is this bump? Going back to the data, we get 4.1 million 16-19 year olds employed vs 12 million 20-24 year olds in May of 2010, for a ratio of 0.34. For June 2010, these numbers at 4.9, 12.6 and 0.39 respectively. So about ~ 800,000 kids become newly employed. At $10/hour for 500 hours (for the summer, both of which are probable overestimates), that represents $4 billion dollars of economic activity.
The US economy is about $15 trillion dollars. That $4 billion dollars represents about 0.03% (no, really, 0.0003) of the US economy, and about 0.5% (no, really, 0.005) of the ARRA stimulus.
There is no theory in economics that predicts anything to 1%. Maybe they can get you the number of pennies you'd get for change of a dollar. Maybe.
This is a bit like a physicist saying that the Lamb shift represents a serious challenge to theoretical physics even before the development of quantum mechanics.
I think this another aspect of a problem with economics that Matthew Yglesias describes as "doing work that superficially resembles physics and therefore counts as science-like". I wish they would pay more attention to how physicists work, not just how our interminable papers look. Yes, there appears to be an effect, but it is at most a 1% effect. Supply and demand appears to work at the order of magnitude level. Now show me Real Business Cycle theory or new Keynesian economics or whatever getting stuff right to 10%, then we can talk about this.
And though I am not an economist, I have a feeling that this represents 16-19 year olds getting jobs at the mall, Denny's and the movie theater so that they can have money to go to the mall, Denny's and the movie theater. It seems like it could occur largely independent of aggregate demand in the economy.