Monday, June 8, 2015

Maximum entropy and the 'natural rate' of unemployment

I mentioned in this post that maximum entropy in the MINIMAC model gives us a pretty simple mechanism to generate a 'natural rate' of unemployment. Not a perfect model, but pretty good:

You'd imagine policy to kick in if the unemployment rate got to high (stimulus) or too low (tight money to reign in inflation), which would shape the distribution ... and there's the finite number of measurements ...

But it's a heck of simple model! Large number of consumption periods (D >> 1) + finite supply of labor (constraint L) = natural rate (L' < L). Just use this diagram (from here)


  1. How do you define unemployment?

    1. The specific definition doesn't matter given the fidelity of the model, but I was using the FRED series UNRATE:

    2. I brought up the question for three reasons. First, because there is a relation between the natural rate of unemployment and the number of time periods of consumption. Second, because the definition of the unemployment rate is partly political and ideological. Third, because there is something peculiar about current unemployment numbers.

      The term, "unemployment", came into use around 1890 to refer to large scale involuntary unemployment such as that caused by factory layoffs. As its usage evolved, the question of voluntary vs. involuntary unemployment arose. How voluntary is the unemployment of a skilled laborer who refrains from taking less skilled work while waiting for a more appropriate job to open up? The question of voluntary vs. involuntary unemployment is still significant. There are economists who regard all unemployment as voluntary. Krugman mocks that view, saying that in that case we should call the Great Depression the Great Vacation. ;) The headline measure, U-3, requires that a person have looked for a job during the past 4 weeks to be considered unemployed. That means that unemployment under that definition is generally more involuntary than if the person had only to have looked for a job during the past year.

      IIUC, since the information transfer approach is not concerned with human motivations, a broad measure of unemployment that includes both involuntary and voluntary unemployment might be better, such as U-6, which is still greater than 10%, I believe. Or perhaps even 1 minus the labor participation rate, which would yield around 40%.

      The U-3 standard definition, which was adopted under Reagan, has come under attack from the political left as blaming the victim by giving too much responsibility to the unemployed worker for being unemployed. Interestingly, it has also come under fire from the political right in the wake of the recent financial crisis and recession. In part that is to lay blame on Obama, but in part it has to do with the fact that, unlike in previous recoveries, several millions of people who became unemployed are no longer considered part of the work force. In fact, the drop in the unemployment rate, at least up to 2012, was almost entirely not the result of unemployed people finding work, but of unemployed people leaving the work force, at least officially. It hardly indicates a recovery. Quite the opposite. That is why people across the political spectrum began to focus on the labor force participation rate.

      Anyway, it seems to me to make a significant difference whether we say that the unemployment rate is around 5% (U-3), 10% (U-6). 40% (I minus the labor force participation rate), or 25% (1 minus a modified participation rate that tends to exclude students and retirees).

      See, for instance, and .

    3. Oops! I see I had the wrong idea about the participation rate. It does not represent employment. :(

      The question about the participation rate is whether the labor force is defined correctly.

    4. Hi Bill,

      You are right -- the proper way to do it here would be to look at all possible people (total population) and the total number of people with jobs. This would actually come out wrong because the real model would have to take into account people can't work in the US when they're under 16, and many people retire in their 60s. However these would be real deviations from the model -- they are factors that exist, but are not part of the maximum entropy model as constructed. Thus there should be a deviation from the maximum entropy solution!

    5. Thanks. :) Sorry about my confusion about the participation rate. :(

      One thing that has bugged me about public economic discourse since the financial crisis is how people talk about ratios. Usually they focus on the numerator, assuming that the denominator is constant, or nearly so. (Maybe it's a foreground/background phenomenon.) So if the unemployment rate in a depression falls, that seems to be a good thing, and it would be if the labor force remained constant, but may not be if the labor force falls. Similarly, people who wanted the government debt to GDP ratio to fall focused on reducing the debt, instead of thinking about increasing the GDP.


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