Thursday, March 22, 2018

Effective information in complex models of the economy

Feedbacks in the economy (section)

Let me first say this is a great post from Sri Thiruvadanthai, and I largely agree with its recommendation to aim towards a resilient economic system rather than a stable one. And I would also agree that the idea that a single interest rate can stabilize the system (partially) pictured above from Sri's blog post is at best idealistic (at worst foolhardy) — if we viewed this system as a blueprint for a mathematical model. A mathematical model this complex is likely intractable as well, above and beyond using a single interest rate to stabilize it.

However, when I saw the diagram another diagram from Erik Hoel appeared in my head; I've placed Sri's diagram alongside Erik's:


Now it's true that Erik is talking about simple Markov chain models, but that might be interpreted as the limiting case of the information contained in asset prices, credit markets, economic activity, and benchmark rates [1]. In the limiting case, the "effective information" in this model for forming a causal explanation is basically zero. Another way to put it is that given enough feedbacks and connections between observables, your model becomes too complex to be useful to explain anything.

Now Erik's paper motivates so-called causal emergence: just as there are local minima of effective information, there are local maxima and we can think of the separation between these local maxima being related to scales in the theory. We understand chemistry at the atomic scale, but we understand biology at the cellular scale. Erik's conjecture is that this is a general property of causal descriptions of the universe from quarks to quantitative easing.

Now I understand this is just my opinion, but this is why I don't think a lot of "this is how the banking system actually works" will help us understand macroeconomics. Effective information and causal emergence is always at the forefront of my mind when I see descriptions like this (click to expand):


Such a model might well capture the details of the system, but might yield no insight as to how it actually works. Knowing what every neuron does could capture the phenomena of a brain system, but it probably won't yield answers to questions about consciousness or even how humans recognize objects in images [2].

And since the "emergent" but approximate descriptions with higher effective information at the higher scale don't have a 1-to-1 relationship with the model at the lower scale (they cannot because that 1-to-1 relationship could be used to translate one to the other implying that the effective information of the models at the two scales would be equal), there is no reason to expect the models to behave in ways interpretable in terms of the lower scale sub-units.

And now I come back to Sri's contention that changes to a single interest rate is unlikely to stabilize the system diagrammed above — especially if we think of interest rates in terms of the causal model above where we make some loose associate between raising interest rates and tightening monetary policy and damping economic activity.

I make the rather contrarian assertion in my blog post about monetary policy in the 80s that the increase in interest rates and "decisive action" from the Volcker Fed may well have mitigated the first 80s recession, but then the same stance caused the second. This is of course makes no sense on the surface (raising rates are both good and bad for the economy), but the feedbacks and strong coupling in Sri's diagram mean the system is probably so complex as to obliterate an obvious 1-to-1 relationship between the discount rate and economic activity.

However, it might have an effective description thought the causal emergence of politics and "Wall Street opinion". Volcker's "decisive action" in raising interest rates/targeting monetary aggregates was considered "good" because the government (Fed) was "doing something". The recessionary pressure ebbed, and the first recession faded. In the same way, quantitative easing might well have had "symbolic" effect in stopping the panic involved in the 2008 financial crisis. Volcker's and Bernanke's "decisive actions" might well have no sensible interpretation in terms of the underlying complex model at the lower scale. But at the macro scale, they may have helped.

That's also how Volcker doing almost exactly the same thing again about a year later could cause a recession. Instead of being seen as "decisive action", the second surge in the discount rate was seen as the shock to future prices it was intended to be. In the underlying model, firms laid off workers and unemployment rose dramatically.

There's no single interest rate that stabilizes Sri's system, but one interest rate could be used as a focus for business sentiment and a complex signal of information.

Now there is a danger lurking in this kind of analysis because it leaves you vulnerable to "just so" stories at the higher scale, especially if you try an interpret things in terms of the complex underlying model. That's why models at the higher scale need to be constructed and compared to data. While we have physics models of protons, neutrons, and electrons, and use them to model atoms, we don't then say that chemistry involves complex interactions of atoms and use that to produce "just so" stories. We find empirical regularities in chemistry which have their own degrees of freedom like concentration and acidity. In some cases we can make direct connection between atoms and chemical processes, but other chemical processes are so complex that they're intractable in terms of atoms.

This also doesn't mean the lower scale model isn't useful. Sometimes the insight comes from the lower scale model. Sometimes you need to understand parts of it to do some financial engineering (such as Sri's contention to focus on making the system more resilient — solutions might come in terms of specific kinds of transactions or for particular assets). The "shadow banking system" comes to mind here; looking at the details might point out a particular danger. But the macro model might not need to know the details and interpreting the financial crisis in terms of a run on the shadow banking system with a Diamond-Dybvig model will have more effective information for macro policy than the details of collateralized debt obligations.


Footnotes:

[1] We can think of the nodes in that network themselves made up of more complex models as in another paper from Erik:



[2] There are similar contentions with machine learning where a system might be able to recognize any picture of a dog, but we won't really understand why at the level of nodes.

5 comments:

  1. I'm curious as to what you think about just trying to make wages more flexible, for example, perhaps by fiat?

    ReplyDelete
    Replies
    1. In truth, I am not sure what the effect would be. Wages are entwined with measures of "status" (which also plays into considerations of whether a UBI or job guarantee would be optimal in the choice between the two). That is to say I think it would depend more strongly on social factors rather than economic ones -- and even if implemented as policy, wages might continue be rigid due to social factors. There aren't a lot of impasses right now to making wages flexible -- far fewer private sector unions than 50 years ago, and it's technologically much easier to implement. It might well be that wages are nominally rigid now because of those social factors (those social factors could just be status quo bias and custom).

      Delete
  2. Thanks for pointing me to this post. There is enough material here for a book - both in what you have written and in questions arising – so I will make only a few points.

    Sri’s blog no longer exists so I cannot see his post. However, his diagram looks a bit like a standard cause and effect loop diagram. In any large system there can be multiple relevant causes and effects, and combinations of these, that influence behaviour – some positive, some negative, some both. There can be chains of causes and effects, and networks, and feedback loops. Resilience requires us to understand and anticipate all sorts of unusual causes and effects.

    Jason: “A mathematical model this complex is likely intractable”

    Exactly. Mathematics alone will not help us solve problems in open systems with complex interacting causes and effects. So, what should we do?

    For example, capitalism causes many technological advances which, in turn, cause better living standards. However, capitalism has also caused social inequalities and the destruction of the environment.

    If we imagine ourselves as aliens watching this objectively, what we would see is that most people focus on specific parts of a loop diagram to simplify the problem. That includes economists. That leads to a phenomenon that I call “proof by ignoring things”. Some people focus on the improved living standards; others see mainly the inequalities; others see mainly the environmental impacts. Everyone ignores something.

    If we react to intractable mathematical models by simplifying the models just so they are tractable, we are also using proof by ignoring things. For example, why is it ok to focus on models of minor fluctuations in inflation, while ignoring, say, the destruction of the environment? The solution to one minor adverse effect may make another major systemic effect worse!

    Another problem is that some causes and effects change over time or are unpredictable. It is so long since the last world-wide pandemic that most people forgot about the possibility. However, the pandemic and our responses are probably the most important macro events of 2020. Another problem is that some causes and effects happen only once. For example, women joining the workforce. Another problem is that some effects require unusual combinations of causes. These are all examples of why Keynes questioned our ability to predict the future reliably.

    Ideas and beliefs can also be significant causes and effects. That includes the beliefs of policymakers, the public and economists. It is also true, as you indicated regarding Volcker, that two instances of the same policy action may produce different effects. Policymakers often revisit their most effective policies with unintended results.

    Multiple causes and effects have implications for modellers too. Suppose that you developed a model that predicted a stock-market crash next week and suppose that people believed your model. They would change their behaviour to sell their shares this week to avoid the effects of the crash. That might cause the market to crash this week, which would invalidate your prediction. Indeed, it could be argued that your prediction caused the crash, as there would be no evidence that a crash would have occurred at all without your prediction.

    There is an open question of how we should try to understand and manage complex human systems with multiple interacting causes and effects. In the meantime, an open-minded pluralist approach, and a dose of humility, seem best to me. However, mainstream economics lacks either attribute.

    As I have said before, in this situation, we should treat all formal predictions and policymaking as analogous to experiments in natural science, complete with expected results and a comparison with actual results. However, this process would destroy the reputation of many academic economists, so they are unlikely to agree. We do not need more mathematics to do this. Just discipline and ethics.

    ReplyDelete

Comments are welcome. Please see the Moderation and comment policy.

Also, try to avoid the use of dollar signs as they interfere with my setup of mathjax. I left it set up that way because I think this is funny for an economics blog. You can use € or £ instead.