Saturday, February 21, 2015

Expectations

Great Expectations. Wikimedia commons.

One of the ways in which I tend to diverge from 'mainstream' economics is in my treatment of expectations, broadly construed. I've talked about this before (see also here and here), and I was reminded of it by commenter LAL recently.

Menzie Chinn states the mainstream view succinctly in the first half of this sentence:
In point of fact, in modern macroeconomics where expectations of the future are central, the most important variables are often not observable.
Emphasis in the original. Chinn is defending the approach of using unobservable quantities in reference to a commenter Tom, and continues: 
So when one hears a criticism like that leveled by Tom, realize that taking such a criticism to its logical conclusion means that almost no macroeconomic discussion can proceed. Everything will have to have appended to it the adjective “estimated”.

This represents one branch of opposition to expectations: market expectations are unobservable, so should be left out of economic theory. Chinn's defense is that expectations can be estimated from other variables (e.g. the TIPS spread as a measure of inflation) -- and I agree. I have no objection to the use of unobservable theoretical constructs in theories. As a physicist, I have no problem using the quantum mechanical wavefunctions (unobservable) in calculations. The properties of the wavefunction (like its phase and amplitude) can be estimated through measurements, like the probability density of electrons striking a screen in the two-slit experiment.

My issue with expectations are different and two-fold ...

Arbitrariness: While there is a Schrodinger equation to define the unobservable wavefunction, there is no universally accepted constraints on what expectations are allowed to be. As long as one can come up with a plausible sounding argument ... what Noah Smith refers to as judgment calls ... any model of human beliefs is allowed into the model.

One can incorporate the latest theory from the study of human behavior in microeconomic settings, which is interesting. But more typically, it seems that macroeconomists just make up plausible sounding assumptions, put them in the theory and see what happens. There is nothing wrong with this as long as you make a connection to empirical data. If you don't, you could end up with a chameleon model [pdf]. As Pfleiderer defines them:
A model becomes a chameleon when it is built on assumptions with dubious connections to the real world but nevertheless has conclusions that are uncritically (or not critically enough) applied to understanding our economy.
I go a bit further than Pfleiderer and say that these problematic assumptions are almost entirely ad hoc assumptions about expectations. I once made a joke about the arbitrariness of models of expectations (calling them bad ad hoc).

Rational expectations (agents have the expectations produced by the model -- i.e. model-consistent expectations) are one way to deal with the arbitrariness, but just shifts the arbitrariness from the expectations to an arbitrariness in the model. Again, this is fine if you then test the model with empirical data.

Arbitrariness can always be solved with a dose of empirical success.

Centrality: This is where I am one of Nick Rowe's so-called people of the concrete steppes. This is also where I think macroeconomics is actually wrong and it can be shown with a couple of simple thought experiments.

First thought experiment: what happens to your theory if the market doesn't believe your theory? Look at market monetarism, for example. If markets didn't believe the theory, then it's a bunch of nonsense. Equation (3) at this link would be entirely determined by the undefined systematic error term. NGDP forecasts would be independent of central bank targets. Essentially, the whole framework falls down. Now it is possible this is how the real world works -- the only functioning economies are those that believe correct or approximately correct theories of markets. But I believe markets naturally arise without the economic agents even knowing what economics is.

Second thought experiment: let's assume there exists a fundamental theory of macroeconomics -- a macroeconomic theory of everything. Call this T0. Let's say, according to T0, fiscal policy has no effect on NGDP or inflation (e.g. monetary offset is the mechanism). Now let's say we live in a world that doesn't know T0, but rather has a 'Keynesian' theory TK in its collective head where fiscal policy has a positive multiplier; fiscal expansion (government spending) leads to increased NGDP and higher inflation.

Now what happens in this thought experiment when a large stimulus package like the ARRA is announced?
Does inflation rise to the level predicted by TK, i.e. the expected value, and stay there? No. That would contradict T0.  
Does inflation only rise initially according to TK, but then fall back to a value governed by T0? In this option, expectations cause market volatility, but have no impact on the long run.
So expectations can only have a limited impact under the assumptions made in the thought experiment: T0 exists and is unknown, TK is wrong. So how does one escape from this problem? By ignoring the premise of the thought experiment:

  1. Macroeconomics (or the market) is always right (T0 is known): there is no possibility of two theories T0 and TK. Markets cannot believe incorrect theories like TK. Only T0 and T0 expectations exist. This means you cannot know what the correct expectations are until you know T0 -- i.e. it assumes you already know the fundamental theory if you include expectations in your model.
  2. Rational expectations (assume TK is right): expectations must be model consistent, i.e. you can only have TK expectations in theory TK and T0 expectations in theory T0. This is a weakening of option 1 where more theories than just T0 are allowed. This is sensible, but since you can build models that do anything, expectations can do anything. Additionally, there is no way to argue against any particular model except empirically.
  3. Expectations are central (T0 is pure expectations, therefore TK = T0): there is no possibility of two theories TK and T0. If TK is the dominant theory, then expectations are TK and in fact the fundamental economic theory of everything is TK. T0 is then whatever the market believes, regardless of anything that is not expectations in your theory (such as measurements of the money supply). Concrete steps (like printing currency) are unnecessary. I've referred to this as model-independent expectations in the past. This implies that all you need to do is convince markets that Keynesianism is right to make Keynesianism right. Or you could convince markets that monetarism is right, which would make monetarism right. There is no reason to believe any particular theory so you can't logically suggest monetarism over Keynesianism, you can only put it forward as political preference.
  4. Markets are always right and expectations are central (T0 is known and T0 is pure expectations): this is the combination of 1 and 3 and is the method of e.g. market monetarism [1]. This not only assumes you are right, but additionally that everyone knows you are right. It effectively disallows the possibility in 3 that markets could be convinced of a different economic theory. However, like 3, it also does not require concrete steps.

These are all excellent options if you are extremely confident you are correct and don't care about comparing your model to empirical data. 

Overall, I'd sum up my problem with the centrality of expectations with a question to Scott Sumner: what happens to your theory if markets don't believe market monetarism? In a sense, this question cannot be addressed by market monetarism. The "market" piece presumes markets believe the theory (i.e. market expectations are consistent with market monetarism, i.e. assuming rational expectations in market monetarism ... I called this circular reasoning before, but charitably, this could be taken that market monetarism is the only self-consistent theory of expectations as I mention in a comment at that link).

I personally like to hold on to some skepticism of theory and believe that comparing to empirical data is a necessity. Therefore, while I consider expectations to have real effects in economies, I do not think e.g expectations set by a central bank can hold inflation on a 2% path indefinitely. In particular, economies that try will eventually fail. I am uncertain if the information transfer model is T0, so there is a possibility I will be wrong. And the only thing that happens if the market were to believe the information transfer model is that there would be a minor reduction in excess volatility.



Update 7/18/2015:

[1] In a later post, I realized Sumner's view of market monetarism is actually closer to option 3 above. I think (but am not sure) Nick Rowe's view is closer to 4 still, though.

12 comments:

  1. Do you have an opinion of Keynes's treatment of expectations in chapter 12 in is General theory? And how those expectation of the future influences the present, as Keynes writes in chapter 11?

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    1. In chapter 12, Keynes wrote: " ... there is the instability due to the characteristic of human nature that a large proportion of our positive activities depend on spontaneous optimism rather than on a mathematical expectation, whether moral or hedonistic or economic." -- it's part of the bit on 'animal spirits'.

      In a sense this probably comes closest to the idea I've presented that most of the time, there is economic growth, but a dose of coordinated pessimism can cause economies to experience strong shocks:

      http://informationtransfereconomics.blogspot.com/2014/10/coordination-costs-money-causes.html

      But I admit I have a hard time understanding Keynes in the original. Overall, Keynes conclusions tend to be supported by the information equilibrium view ... but that is dependent on the state of the economy. Basically, a low inflation economy is a Keynesian one and a high inflation economy is more like a monetarist economy.

      Keynes seems to develop a specific model of expectations that can influence economies in the short run, very similar to how I view them in the second thought experiment above. Keynes famously said "in the long run, we're all dead", which expressed his view that, sure, pessimistic expectations won't keep an economy down forever, but can for an extended period of time. Hence the need for demand management.

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  2. I'm probably in the rational expectations camp, and one of the nicest things is that when I specify a stochastic process sigma_t, I am by convention eliminating a whole lot of processes. For instance the expectation over the distribution must at least exist, and conditions for being able to find an optimal path must hold. (see for instance the Feller criteria in Stokey and Lucas)

    The use of expectations in the model is to show how agents can use expectations to formulate plans...ultimately information efficiency is just trying to replace maximizing expectations of utility functions as a criterion for equilibrium. Since the necessary optimal condition is now about integration of log variables: that seems less restrictive..so I'm seeing more possible models...hence more arbitrariness...

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    1. Hi LAL -- you said:

      "... ultimately information efficiency is just trying to replace maximizing expectations of utility functions as a criterion for equilibrium."

      Information equilibrium is not the same as just changing the criterion for equilbrium. For systems of agents with utility functions, you end up with (given various conditions) an Arrow-Debreu equilibrium. There may be thousands of these equilibria.

      In one world, android phones dominate the market, while in another, iPhones do. Then there's the case where microsoft windows dominates laptop OS market and where OS X does. That creates four worlds that are four separate Arrow-Debreu equilibria (iPhones and OS X, iPhones and Windows, Android and Windows, and Android and OS X). The information transfer model/information equilibrium model assumes those equilibria to be equally likely and gives the result for NGDP that averages over those possibilities. As you add more and more choices, you end up with an enormous number of possible equilibria, making the maximum entropy (information equilibrium) solution the most likely possibility.

      http://informationtransfereconomics.blogspot.com/2014/06/towards-arrow-debreu-mckenzie_27.html

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    2. I think I wrote the second half of my above comment before fully absorbing some of your other responses to my comments, I am seeing now how there is probably a more complicated relationship between information equilibrium and arrow-debreu style equilibrium than I was understanding...I had in mind that I was trying to generalize I think Chris Sims approach where he has agents optimizing under information control constraints:

      (http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.201.3711&rep=rep1&type=pdf)

      when you say the most likely possibility, you mean for NGDP? and to whom is it most likely (we the empirical observes or the agents)?

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    3. That is an interesting paper, and probably one of the ones that comes closest to the way I am using information theory. I will probably have more to say about it later. My first take is that it seems like with rational inattention Sims is addressing a problem created by the use of rational expectations in the first place! If you didn't assume that expectations controlled market outcomes and then invent rational expectations to make that assumption tractable ... you wouldn't have to then invent rational inattention to say that people frequently make decisions as if they didn't know macro models or market prices :)

      In a sense, you could take the model I am advocating here as starting from the assumption of rational inattention.

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  3. This comment has been removed by the author.

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  4. This is interesting but I have a different perspective. Expectations do exist but they exist at the micro level and are not currently accessible at the macro level.


    Macroeconomics involves discussion of various concepts which do not ‘exist’ except at the micro level. For example, assets, jobs, sales. What ‘exists’ at the macro level is mostly just those elements recorded at the micro level and then summarised to the macro level. For example, GDP ‘exists’ because we record various transactions and then add them up. Imagine an economy several hundred years ago. The concept of GDP might have existed but the processes and technologies to calculate GDP might not have existed or might have existed only in a very basic form. You might argue that GDP exists only in a very basic form even today. Nevertheless, it’s all we have.

    A few macro concepts do exist at the macro level. For example, currencies, interest rates, tax rates. However, these are exceptions.

    Expectations exist at the micro level but we do not record them in the same way that we record sales transactions. Expectations emerge in plans. However, businesses like to keep their plans secret and consumers don’t record their plans at all. This means that expectations can’t ‘exist’ at the macro level.

    Consider a kettle manufacturing business. At the start of each period, the business has to decide how many kettles to supply to the market. How should it do this?

    Some people already know they will demand a kettle at this point. However, they don’t tell anyone and they know only their own demand. Also, some will change their minds before demanding a kettle. Worse, some people who will demand a kettle do not yet realise they will demand a kettle. They will only realise that they will demand a kettle when they drop their existing kettle on the kitchen floor and break it. Worse still, most people will decide which brand and model of kettle to demand only a few minutes before they demand a kettle.

    The kettle business needs to decide how many kettles to supply when no-one anywhere in the economy knows the demand for kettles. It must base its decisions on its own forecasts.

    Expectations are just forecasts and plans made under uncertainty. They are intelligent guesses.

    This gives macroeconomists a problem. If expectations are important but not accessible at the macro level then what should they do? I’d suggest that there are three alternatives.

    First, make up some generic theories / nonsense about representative agents and rational expectations and assume that they can replace observation and measurement.

    Second, find a way of understanding the macro-economy without using expectations and take the risk that is still useful.

    Third, find a way of recording expectations at the micro level and then summarising this information to the macro level. That’s why you see surveys of procurement manager sentiment. Increases in procurement activity are one if the first visible signs of positive business expectations. However, procurement surveys are very basic tools.

    As far as I can see, mainstream economists use option 1, you use option 2 and I’d prefer a more sophisticated version of option 3 if it ever becomes feasible!

    Making decisions under uncertainty is risky, so businesses look for ways to minimise the risk associated with such decisions, including revamping their business models.

    In Star Trek, the existence of replicators avoids the need for expectations. When Captain Picard demands tea the replicator supplies tea. Presumably, the replicator has a recipe for tea somewhere so the recipe provider must have had a generic expectation that someone somewhere sometime might ask for tea. However, the captain expects tea to be supplied immediately on demand. No uncertainty is involved unless the replicator breaks down.

    To some extent, iTunes and similar electronic stores are the beginning of a move to an economy where expectations play a reduced role.

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    1. Your assessment about the options 1, 2 and 3 is pretty much correct, except I'd put 2 as putting forward ideas that must be true regardless of microfoundations and seeing they are useful.

      I'd completely agree that detailed micro level data (option 3) would be best.

      I imagine Engineering has some model of human behavior in order to know how much energy needs to be available at any given time for Earl Grey -- however, it does seem as if the actual way they solved the problem is to have so much energy available, most conceivable replicator needs represent a tiny perturbation. In a couple of episodes, I had heard of replicator credits, though :)

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    2. OK. I hadn’t heard of replicator credits. I guess they would be required if insufficient energy was available to power the replicator to meet the expected requirements of the entire crew. I always assumed that they had an energy source which was much larger than was required for all practical purposes so the supply of energy was no longer a supply constraint. You can tell I’m not a physicist!

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  5. Have you seen this?

    http://www.nature.com/news/physicists-make-weather-forecasts-for-economies-1.16963

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    1. Thanks for the link Jamie -- I hadn't seen that. The paper is interesting. I have some skepticism ... for one, the difference between the laminar flow and the turbulent flow regions are primarily along the x-direction (i.e. in the direction of their invented variable "fitness"). That is to say they invented a variable and it describes the difference between economies -- a process similar to "indices of economic freedom" that various think-tanks put forward.

      That said, what is interesting is how they constructed their fitness variable variable. I believe it is kind of a principal component analysis of a bipartite graph that essentially measures 'complexity' by counting the number of distinguishable exports. That is especially interesting to me because that could mean "fitness" is related to a variable I call γ ... e.g. here:

      http://informationtransfereconomics.blogspot.com/2014/09/the-economic-combinatorial-problem.html

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