101ism, overtime pay edition

John Cochrane wrote a blog post criticizing the Obama administration's new rule extending overtime pay to low-paid salaried employees. Cochrane thinks about overtime in the context of an Econ 101 type model of labor supply and demand. I'm not going to defend the overtime rule, but I think Cochrane's analysis is an example of what I've been calling "101ism".

One red flag indicating that 101 models are being abused here is that Cochrane applies the same model in two different ways. First, he models overtime pay as a wage floor:

Then he alternatively models it as a negative labor demand shock:

Well, which is it? A wage floor, or a negative labor demand shock? The former makes wages go up, while the latter makes wages go down, so the answer is clearly important. If using the 101 model gives you two different, contradictory answers, it's a clue that you shouldn't be using the 101 model.

In fact, overtime rules are not quite like either wage floors or negative labor demand shocks. Overtime rules stipulate not a wage level, but a ratio between base wages and wages paid on hours worked per worker above a certain amount.

In the Econ 101 model of labor supply and demand, there's no distinction between the extensive and the intensive margin - hiring the same number of employees for fewer hours each is exactly the same as hiring fewer employees for the same number of hours each. But with overtime rules, those two are obviously not the same. For a given base wage, under overtime rules, hiring 100 workers for 40 hours each is cheaper than hiring 40 workers for 100 hours each, even though the total number of labor hours is the same. That breaks the 101 model.

With overtime rules, weird things can happen. First of all, base wages can fall while keeping employment the same, even if labor demand is elastic. Why? Because if companies fix the hours that their employees work, they can just set the base wage lower so that overall compensation stays the same, leading to the exact same equilibrium as before.

Overtime rules can also raise the level of employment. Suppose a firm is initially indifferent between A) hiring a very productive worker for 60 hours a week at $50 an hour, and B) hiring a very productive worker for 40 hours a week at $50 an hour, and hiring 2 less productive workers at 40 hours a week each for $25 an hour. Overtime rules immediately change that calculation, making option (B) cheaper. In general equilibrium, in a model with nonzero unemployment (because of reservation wages, or demand shortages, etc.), overtime rules should cut hours for productive workers and draw some less-productive workers into employment. In fact, this is exactly what Goldman Sachs expects to happen.

Now, to understand the true impact of overtime rules, we probably have to include more complicated stuff, like unobservable effort (what if people work longer but less hard?), laws regarding number of work hours, unobservable hours (since the new rule is for salaried employees), sticky wages, etc. But even if we want to think about the very most simple case, we can't use the basic 101 model, since the essence of overtime rules is to force firms to optimize over 2 different margins, and S-D graphs represent optimization over only 1 margin.

Using 101 models where they clearly don't apply is 101ism!