Casey Mulligan seems to believe that because some groups (i.e. older workers) can increase their employment in a downturn, that the problem is one of supply and not demand. As I noted in my past exchange, a recession does not mean that some demographic groups will not be preferred to others. In the downturn there has been an increase in employment for college grads also.
There is nothing inconsistent with the idea that demand is a constraint on employment yet some individuals may be able to beat out others for the jobs that are available, either because they have more experience in the case of older workers or they have better skills in the case of college educated workers. This is very different from saying that if only all our workers had these advantages (being more experienced or college educated) that we would not have a problem of unemployment.
In fact, even among these groups unemployment has risen substantially in the downturn. If we snapped our fingers and suddenly our whole workforce had the experience of the over 55 population or the skills of a college graduate then we would see many more experienced and college educated workers unemployed. I don't see anything in Mulligan's story suggesting otherwise.
(As another example, Mulligan shows us that employment has increased in Texas. Is this a surprise? There has been a huge increase in oil and gas prices that has both increased demand in these industries and led to a substantial increase in the money flowing into the state for royalties. Also, Texas did not have as large a housing bubble as states like Nevada and California. Therefore, it suffered much less damage when the bubble burst.)
Finally, Mulligan insists that us Keynesian types have no evidence that lack of demand explains the downturn. Actually, there are a number of macroeconomic models that have been built up over the years based on evidence of firm and individual behavior. These do support the view that the downturn is attributable to a lack of demand. Also, there was a study (Feyrer and Sacerdote, 2011 and my comment) of the state by state effects of the stimulus that found multipliers that were very much consistent with the ones predicted by these macroeconomic models. So, we have the standard Keynesian theory, which is largely embedded in macroeconomic models based on years of data collection, that is now supported by a careful analysis of the impact of the stimulus.
That seems pretty good in the evidence department, what does Professor Mulligan have?
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