Sunday, April 26, 2015

The Unit Root of the Matter: Is it Demand or Supply?

John Cochrane responds to my piece on why there is no evidence that the economy is self-correcting with an excellent blog post on unit roots. John's post raises two issues. The first is descriptive statistics. What is a parsimonious way to describe the time series properties of the unemployment rate? Here we agree. Unemployment is the sum of a persistent component and a transitory component.
The second is economics. How should we interpret the permanent component? I claim that the permanent component is caused by shifts from one equilibrium to another and that each of these equilibria is associated with a different permanent unemployment rate. I’ll call that the “demand side theory”. (More on the data here and here and my perspective on the theory here and here).

Modern macroeconomics interprets the permanent component as shifts in the natural rate of unemployment. I’ll call that the “supply side theory”. That theory is widely accepted and, in my view, wrong. As I predicted in the Financial Times back in 2009, "the next [great economic idea] to fall will be the natural rate hypothesis". 

Lets start with the statistics.

In the comments section, (always worth reading beyond the main post) John and I are in complete agreement that unemployment has two components. One is highly persistent, and well approximated by a random walk. The other is stationary.

Here is John

Hi Roger. We’re converging. Yes, there is an interesting low frequency component in unemployment, that might be modeled well in a short sample with a random walk (unit root = random walk plus stationary component). And unit root asymptotics might be a better approximation to finite sample distributions, plus warn of biases like the AR(1) coefficient.
A random walk, as its name suggests, has an equal chance of going up or down. A stationary variable always returns to a constant number. What about a series that is the sum of a random walk and a stationary component? The stationary bit is always pulling the unemployment rate back to something: but that something is not a number, it’s the random walk component. Unemployment is aiming at a moving target.

John has his own unit root tests. In John's words

"Look at the plot" and "think about the units"
I like that. Here is my “look at the plot” diagram seen through the lens of John’s comment that a unit root equals a “random walk plus stationary component”
John's Unit Root Test: "Look at the Plot":
The blue line is the unemployment rate since 1949, the grey shaded areas are the eleven post-war NBER recessions, and the red lines are the means of the unemployment rate for each of the eleven post-war expansions. Because unemployment has a “low frequency component”, the number the economy converges to is different after every recession. It is not a single number. It is a moving target.

So much for the statistics: What about the economics? 

The central question for policy makers and their academic advisors should be: Why is the target moving? 

My answer is that aggregate demand, driven by animal spirits, is pulling the economy from one inefficient equilibrium to another. My theoretical work explains how that idea is consistent with the rest of economic theory. 

The orthodox answer, one we have taught to graduate and undergraduate students alike for the past fifty years is that aggregate supply is shifting from one decade to the next, pushed by changing demographics, shifting tax policies and technological change.  

If permanent movements in the unemployment rate are caused by shifts in aggregate demand, as I believe, we can and should be reacting against these shifts by steering the economy back to the socially optimal unemployment rate. If instead, these movements are caused by shifts in aggregate supply, the moving target is the socially optimal unemployment rate.

John has not yet staked out a position. On this point he says…

I don't have a definite opinion. There is lots of interesting, new, and unexplored economics on that one. I'll read your paper!
Paul Krugman weighed in on this debate and he claims to agree with John about the statistics, although I’m not sure he read the comments section. 

John and I are in complete agreement: there is a permanent component in the unemployment rate. That component requires an explanation. Is it demand or is it supply? The answer to that question has huge implications for policy. 

Tired old 1950's theory would attribute the permanent component in unemployment to unavoidable natural rate shifts. Shiny new Neo-Paleo-Keynesian theory would attribute the permanent component to avoidable shifts in animal spirits. Which is it Paul: Demand or Supply?


  1. I appologize for the shameless self-promotion, but here is one possible explanation for the low-frequency movements.
    Why is Schumpeter and evolutionary economists in general so much ignored? :)

    1. Nothing wrong with self promotion. For those who want to read your paper, and can't be bothered to cut and paste (most people) here is a link to it. And for those of you wondering how I did that, here is a link to how to put a link in a comment. :)

    2. Thanks so much! For the record, in its original version I had cited your two 1988 papers to justify the inclusion of the interest rate as a control variable (though the main results were unaffected) but the referee was unsympathetic to the idea that the interest rate may influence the efficiency of matching. :(

  2. Total speculation, but there do appear to be a three major meta-stable states in the unemployment rate ... see this graph:

    unemployment rate

    Just under 8, just under 6 and around 4%. But maybe that is seeing a pattern where none exists ...

    1. Jason
      We can't interpret data except throug the lens of theory. As many of the comments on this blog, and others, point out: the data don't speak clearly enough to to decide the important questions on their own. Three meta stable states is plausible. But why? What is the economics?

  3. Large states queuing on on an eight year election period basis. You have to include Mexico, and we get the Southwest taking turns in dominating DC. California swaps with Texas mostly, but Mexico gets a foot in the door every so often.

  4. What if both supply and demand elements contribute to the permanent (ie "natural") unemployment rate?

    And what if both supply AND demand can be manipulated (by central banking, regulations, laws, nudges, and generical social manipulation)?

    Even if we discard the demand-driven permanent unemployment part of the explanation, how can we passively accept the current "social optimality"? maybe we can do something to modify society and modify that rate, to get a better equilibrium rate, from a neo-positive point of view at the very least.

    Unless we strongly believe that the whole of society is built of perma-maximizers of intertemporal stocastic utility functions agents that is :-) But i thought that model had been discarded a long time ago.

    In layman terms, if we believe society is making some kind of social mistake, we can and should fix it even if we only believe in supply-driven permanent unemployment.

    If then we add the little "detail" of at least some part of the permanent unemployment rate explained by demand elements.. then the need for some action is crystal clear.

    1. Luciom
      Yes, you are right to suggest that there are both demand and supply at work here. But to act, we must decide which components are demand and which are supply. My (theory based) rule is to assume swings in the PE ratio are primarily inefficient swings in demand induced by animal spirits.

  5. Perhaps this is a story about the long and short run? Keynes surely did not rule out that economies are exposed to all sorts of so-called "exogenous" and other shocks that result in continuous regime changes and Marxian style disequilibrating tendencies inherent in capitalism - secular stagnation seems to be a new word for a lot of that). However the immediate problem to be addressed in recessions is inadequate demand caused by deflationary psychology (animal spirits) which needs to be dealt with through demand management policy. So in short, while I do not want to preempt Krugman's answer, the supply and demand side both matter, but the demand side needs to be addressed first.

    I agree with you that 1950s theory is unhelpful in providing any real insight, but people fall back on that because economic theory went from bad to irrelevant after it. But still, dusting off these gadgets after every crisis is not the way to go and was almost certainly the kind of stuff Keynes was referring to when he said:

    "(Classical Theory), being based on so flimsy a foundation, it is subject to sudden and violent changes. The practice of calmness and immobility, of certainty and security, suddenly breaks down. New fears and hopes will, without warning, take charge of human conduct. The forces of disillusion may suddenly impose a new conventional basis of valuation. All these pretty, polite techniques, made for a well-panelled Board Room and a nicely regulated market, are liable to collapse. At all times the vague panic fears and equally vague and unreasoned hopes are not really lulled, and lie but a little way below the surface (Keynes 1937, p. 215).

    It is time to work more like an historian. Events like 2008 were caused by the interaction of a large number of events, some of which were building up during the Great Moderation, or even earlier. Good analysis starts from the bottom up and should look at all of them. The model, if there is one, comes at the end: it does not dictate analysis at the beginning.

    1. Your emeritus colleague Axel Leijonhufud was apparently even more damning:

      You say,

      "My theoretical work explains how that idea is consistent with the rest of economic theory. "

      That should not be the basis of valuation. Unless you can prove that the micro-foundations are on sound ontological and epistemological territory. They are not. You might be a natural exponent of Manchesterstrum , but the adoption Darwinian Victorian foundations (in contrast to, for example those of the European Enlightenment) as the basis of explaining an interactive social system a national economy), are arbitrary and/or reflect power relations. Ahistorical devices like NAIRU stay around because the mainstream of the discipline has been totally stripped of any philosophical and historical content and the aggressive efforts of Sargent et al to sideline the General Theory et al to revive pre - Great Depression economics. (I know Sargent did some "history", but that stuff is a non-starter to an historian.) Victorian and Walrasian constructs are basically incompatible with the General Theory (and to many with the objectives of civilised society in the Twenty First Century):

      "Perhaps the reader feels that this general, philosophical disquisition on the behaviour of mankind is somewhat remote from the economic theory under discussion. But I think not. Tho this is how we behave in the market place, the theory we devise in the study of how we behave in the market place should not itself submit to market-place idols. I accuse the classical economic theory of being itself one of these pretty, polite techniques which tries to deal with the present by abstracting from the fact that we know very little about the future (Keynes 1937:, p 215)."

    2. I would not condem all of neoclassical economic theory. Auction theory, for example, has been helpful in selling rights to the electromagnetic spectrum and Shapley's work on matching is widely used to allocate kidneys. Theory does develop: it just doesn't always happen in a linear fashion.

  6. I don't think you need animal spirits in a demand side model. The usual constraint on sending is lack of money. It seems to be more about dead presidents.

  7. It seems to me that the statistics that you choose to summarize the data -- average unemployment between recessions -- strongly conditions your interpretation here.

    When I look at that data, it seems to me to show two principal random variables: the duration of the recovery and the size of the unemployment spike at the next recession. The behavior of the unemployment curve between recessions seems rather general, and perhaps "universal", given those two controlling variables. The mean unemployment of the recovery period appears to me to be a secondary quantity, which would be greater in each period if the following recession were advanced, and lower if the following recession were retarded.

    If one were to accept that interpretation of the data, then -- it seems to me -- the modeling focus would shift from "what are those new "equilibria", and why are they bouncing around?" to "what determines the duration of the recovery, given the initial unemployment spike, and why does the recovery trajectory of unemployment look sort of like a one-parameter family of functions, parametrized by spike size?"


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