Mulligan compares the small growth in employment in December to the large growth in sales and concludes that demand-side policies don't work.
First, let's address the problem with how Mulligan thinks about cycles. Retail sales increase in December and fall in January. Mine certainly do. I'm sure all of yours do too. Does this surprise anyone? No - and that's largely the point. This is an extremely predictable, well known clustering of purchases. It's a seasonal cycle because it comes at regular calendar intervals. Seasonal cycles are very predictable by definition. So yes, retail stores will need more staff on hand so you'll get a bump in employment (and a subsequent drop in January), but the increased income and the increased demand is already factored in by everyone. Entry-level workers know they can find work around Christmas easier. They will plan their demand accordingly. Firms know they will earn more in the Christmas season. They will plan accordingly. Consumption will be smoothed in relation to unsmooth, seasonally cyclical earnings. There is no story here. You can't compare a predictable seasonal cycle with an unpredictable business cycle.
Mulligan is also comparing apples and oranges. The price of a retail good sold in December is the sum total of the value added of lots of stages of the production process. Retail is just the final bit of value-added at the top. Now, there's going to be some seasonality in manufacturing as well, but not as much as you see in retail - its not like factories have to work significantly harder in late November and early December to meet holiday demand - they also have more of a chance to smooth production and therefore employment. So while the value you see in increased retail figures reflects an entire stream of value added, the employment change is going to be much smaller because the only shock you see there is in the retail sector. Again, why? Because people know this is coming. If you are a miner, a farmer, a manufacturer, or a wholesaler you will smooth your production in response to this shock as much as inventory costs allow you to. If you're a retailer you don't have much room for smoothing. But nobody is caught off guard by these seasonal fluctuations. Keynesian recovery occurs when income increases due to increases in demand. A Christmas retail spike is a predictable increase in demand in December relative to a level of demand in November. In other words, you can have total income (and thus employment) decrease at the same time that you preserve the predictable seasonal clustering of that total income.
This is not the first time Mulligan goofs this. Earlier he tried to point to summer youth employment shocks as proof that Keynesian demand concerns are baseless. When this came out, it was shocking to me that someone employed by the University of Chicago could get away with writing such drivel. This is the graph he presents:
What do we see here? A predictable seasonal spike because supply increases (students are out of work), and perhaps because some demand increases (lawns need to be mowed in the summer, construction picks up in the summer, vacation/resort/recreational businesses pick up in the summer). So a spike. No surprise. But the 2010 spike is sitting much lower than the spike from any earlier year. It's unfathomable to me that this didn't set off any alarm bells Mulligan. The lower employment doesn't tell you whether its Keynesian or not, of course. But this graphic shouts out "seasonal fluctuations occur even within business cycle fluctuations".
Mulligan also makes this mistake of confusing demand with consumption, which of course also weakens his example of December consumption as a critique of Keynesian stimulus.