By Karl Smith
There are a lot of reasons why this graph,
should be very weak evidence that stimulus doesn’t work. Many of them are hashed out by my liberal friends everyday. However, I think I may be able to explain the issue in a way that makes more sense to my conservative friends.
To begin, lets understand that this graph – which shows unemployment higher than predicted – is undoubtedly evidence against the proposition that stimulus worked. There is no way that I know of to logically get around this fact.
The easiest way to see this is to imagine what one would have thought if the unemployment rate tracked exactly along the curve that Romer and Bernstein laid out. First, off it would have been strong evidence that Romer and Bernstein were working with an ungodly good model of the economy. Predicting the future is hard for any discipline.
No one doubts that the weather runs by the laws of thermodynamics but anyone who could dead-on predict the number of hurricanes every 3-months seven years into the future would be a modeling genius.
So, if Romer and Bernstein had got it dead-on we would think that their model was incredibly good and since their incredibly good model tells us that stimulus worked that’s strong evidence that it worked.
If that’s true, then it must be the case that observing the opposite condition is evidence against both their model and stimulus. This is Bayesian Conservation of Probability. X cannot increase the probability of Y, unless not-X increases the probability of not-Y.
So we know failure of the Romer and Bernstein prediction increases the probability that stimulus does not work. The question is by how much does it increase the probability. The answer should be almost nothing.
Why? Well, the short mathematical answer is because it was overwhelmingly likely to be the case that Romer and Bernstein were wrong whether stimulus worked or not. That they missed should be surprising to no one.
I don’t know if anyone has named the Law of Conservation of Surprise, but it extends naturally from the Conservation of Probability. If it would have been extremely surprising that for Romer and Bernstein to nail the right answer then it must be unsurprising for them to miss.
Here is an analogy – and the original motivation for this post – that might help clarify.
Suppose I asked Casey Mulligan whether or not raising the minimum wage to $12 an hour would create or destroy jobs. If I may be so bold I will assume that he would say that it would destroy jobs. Fine.
Now, I say, tell me both what the path of Non-Farm Payrolls will be over the next 7 years and tell me also what they will be if Obama raises the minimum wage to $12 an hour.
Now, suppose Mulligan made his prediction, the Obama administration raised the minimum wage and he was dead-on right about the path of Non-Farm Payrolls. That would be crazy evidence in favor of the proposition that raising the minimum wage to $12 destroys jobs.
However, suppose he was wrong. Suppose the path of the Non-Farm payrolls was actually higher than his baseline. Would that be strong evidence that raising the minimum wage does not destroy jobs?
For me it would be practically no evidence at all.
Because I already believe that Mulligan will mis-forecast the path. I don’t think he or anyone else has access to a model that good
So, his missing on this question would not be very strong evidence and would not be a reason for folks to go around saying – look the minimum wage doesn’t hurt employment growth after all.