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Monday, April 14, 2014

Stuff Happens - Or Why I Am Not A Fan Of Overlapping Generations Models

One could correctly summarise Newtonian physics as: stuff happens. However, this formulation tells us a lot less about the world around us than his three laws of motion. And my view is that overlapping generations models are uncomfortably close to the "stuff happens" end of the spectrum.


This paper from Gauti Eggertsson and Neil Mehrotra has generated a fair amount of commentary around the economics blogosphere. Nick Edmonds, at Reflections on Monetary Economics, re-derived the results using a stock-flow consistent model. His article was in response to the critique of the paper by "Unlearning Economics" - How Not To Do Macroeconomics. "Unlearning Economics" stated that he would prefer seeing a stock-flow consistent model, and so Nick Edmonds obliged by putting the results into such a framework.

I like reading Nick Edmonds' articles, as he knows a lot more about stock-flow consistent models than I do. But it appears that we do not agree about the usefulness of overlapping generations models. That could just be the result of having different analytical objectives; I have a fairly narrow set of things that I am interested in modelling.

I currently knee deep in looking at fiscal policy within the DSGE framework. As the Eggertsson and Mehrotra article is too tangential for what I am working on right now, I did not go through the entire paper in detail. If I were to write about it, I hope I would end up with something similar to what Nick Edmonds wrote.* Instead, I want to make a more general point about "overlapping generations" models here.

Two Wings Of DSGE Macro


I am not a fan of Dynamic Stochastic General Equilibrium (DSGE) models. One complication in discussing them is the fact that there are two classes of DSGE models used within macroeconomics.**
  1. Business Cycle Macro Models These are the models with a Representative Household which plans  its consumption from the present until times goes to infinity. These models have generated a lot of controversy on the internet in recent years. These are the models I am interested in, and the ones that I think are mathematically dubious.
  2. Overlapping Generations Models. These may look similar to the other models, but they are based on the planning problems for households with finite (and possibly random) lifespans. The consumption and savings plans between cohorts interact. I am not very interested in these models, for reasons I discuss below. Their saving grace is that the mathematical framework used appears correct.
Note that it is difficult to generalise about these models. The academic community is churning these models out continuously as the result of the publish-or-perish environment.

Overlapping generations models analyse spending patterns over individuals' lifetimes with some limited realism, unlike the ludicrous infinitely long-lived Representative Household of business cycle macro. However, in order to model these savings plans, the models abstract out of existence the economic cycle. This is done to make the models mathematically tractable. (Stochastic - the "S" in "DSGE" - is just the mathematical term for random; it was derived from a Greek root.) "Unlearning Economics" pointed out the problems that arise when you eliminate the economy from within what is alleged to be an economic model in his discussion of the Eggertsson and Mehrotra paper.

I believe that mainstream economists would strenuously object to my sharp distinction between the two classes of models. Both classes of models are driven by similar microeconomic assumptions. However, only the business cycle macro models attempt to describe business cycle fluctuations.*** The business cycle models also include some macro accounting identities. (My feeling is that there are specified incorrectly, but that is a subject for other articles.)

A Question Of Time


Even if we accept the lack of a cycle within an overlapping generation model, the models are entirely unfalsifiable. If we look at the model of Eggertsson and Mehrotra, there are three generations (young, workers, retirees). The model describes how cash will flow amongst those age cohorts based on the assumption that the households want to smooth their lifetime consumption.

But we see an obvious problem if we wanted to fit this model to an economy. This is a discrete-time model where the time step represents about 30 years.****

If we set 2014 as t=0, the previous time steps were 1984 (t=-1) and then 1954 (t=-2). An examination of economic history tells us that a lot happened over that period; the world was extremely different at each of those points in time. Since there is almost no relationship of the state of the world between time points, there is no useful way of characterising the dynamics for the state transitions from time t to time t+1.

The only use of such a model is to see how conditions would change now based on parameters changing. For example, if the rate of interest goes up, what happens as a result of the change in consumption plans? Economists are familiar with this style of analysis; for decades economic debate largely consisted of drawing two lines on a chalkboard and arguing about the angles at which to draw the lines (or what would happen if you shift one line). The switch to overlapping generations models puts a thin veneer of mathematics over the graphical exercise. Even though the models are effectively only about the present, they appear to incorporate time dynamics (the "D" is DSGE).

Unfortunately, a clever mathematician with too much time on his or her hands can create a slightly different overlapping generations model which generates a completely different outcome, even if the "behavioural parameters" used are the same. Since the overlapping generations models cannot be empirically tested  (we would need many centuries of economic data), there is no way of determining which model is "correct".  In other words, we are stuck at "stuff happens".

Although the mathematics behind the business cycle DSGE models is questionable, at least central banks can use them to create linearisations that can be fitted to quarterly or monthly economic data. Those fitted models can then be used to generate falsifiable predictions. Given the low quality of the predictions, this does not give us much, but at least it looks more sophisticated than a couple of lines on a chalkboard.

Yes, They Are Totally Unrealistic Models


As a final point, the assumption that households plan out their consumption for the rest of their lives appears incorrect. I have just launched a personal finance section of my web site, and my sense of the situation is that I will not be able to assume that readers will have spent any time doing such a planning exercise. Such people do exist, but they seem to represent a small target audience. More importantly, the baby boomers are walking into a retirement crisis that would be impossible to generate within a model in which households smooth their lifetime consumption levels.

In conclusion, these defects mean that I do not expect to spend much of my time looking at overlapping generations models.

Footnotes:

* This is good, since I was mis-identified as the author of his article on Twitter. That helped my reputation, so thanks!

** To make life even more complicated, people do financial asset pricing models within a DSGE framework. I would not view these as macro models; they are microeconomic models at best. My profession opinion is that they represent a rather silly approach to pricing financial instruments, but academics like them because it gives them another avenue to publish papers.

*** Well, "Real Business Cycle" models do not have a recognisable business cycle that occurs within them, but I view those models as being an elaborate practical joke being played on economics graduate students.

**** There are overlapping generations models with finer time scales, such as one year. But these models appeared to me to be even further from being able to model an economy.

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(c) Brian Romanchuk 2014

4 comments:

  1. Some people make the point that Macro-economics is simply the sum of Micro-economics. If so, the next need is to create a model of the Micro-economic reality. OLG models seem to me to be a valid step in that direction.

    In a comment on Nick Edmonds' post, I suggested that the three sector model could be meaningfully improved by expanding it into a four sector model. My logic was that the three sector model did not have a smooth transition between sector breakpoints; a failing that could be corrected by adding one additional sector.

    Now, whether Micro-economics should be modeled by OLG logic, DSGE logic, or some other logic, it seems to me like the real issue is the extent to which Macro-economics can be linked to Micro-economics. I welcome post which explore methods of modeling, no matter what their ultimate utility to the bigger Micro-Macro Economics discussion.

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    1. My complaint with the microfoundations approach is that the macroeconomic elements are not incorporated properly. For example, the "intertemporal governmental budget constraint" is either trivial or wrong. And it represents the only macro identity that is incorporated into most DSGE business cycle models; everything else is micro.

      Returning to your point about exploring macro from different ways is a good one. Overlapping generations models are a way of looking at the economy, and may be helpful for a lot of people. But I named my blog "Bond Economics" for a reason - I am interested in business cycle macro.

      OLG models are interesting, but they can only tell use things about household behaviour, with the rest of the economy assumed out of existence. There is some attempt to get something resembling economic fluctuations in the original paper, but with time points 30 years apart, it is still effectively a static analysis. Although one could write down a more interesting OLG model with a business cycle, the model would be impossible to solve.

      And since the long run is a series of short runs, it is a lot easier to understand what is happening. To me, "secular stagnation" is easily explained; the fact that mainstream economists have long debates about it tells me their modelling framework does not fit reality too well.


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  2. Brian,

    Some fair points there.

    I think OLG models can be useful as toy models to think about the relationships between wealth and income, but it is hard to translate them from theoretical models into practical ones. The main problem is the time period one you describe. To see what is going on, you really need a simple two or three period model, but then the real length of the time periods bears no relation to the time periods you want to look at.

    I actually started playing around with OLG ideas, before I even knew that there was any literature on them. Because of my SFC focus, I place a lot of store on national balance sheets and the way these affect and are affected by current spending decisions. Residential property, mortgages and pensions constitute a significant part of household balance sheets and I think that lifecycle behaviour plays an part in shaping these.

    You will know that a standard SFC household savings function will take the form of an incremental adjustment towards a steady state stock-flow ratio. I wanted to understand what might be driving the parameters in such a function and so I started looking at lifecycle savings patterns. That's not to say that I think everyone behaves like that - I think it's complex; but it's an important part of what is going on.

    I also think that OLG is important because introducing the idea that today's consumers are not the same people as tomorrow's consumers overturns many of the standard mainstream results, including things like Ricardian Equivalence.

    But, it is probably true that I've gone a bit overboard writing about OLG recently and have perhaps given the impression that I believe in micro-founded macro-modelling based on OLG. I don't. I find it useful to think about theoretical issues, but I can't as yet see a way to base empirical models on it. I have played around with OLG structures with realistic time frames with a view to trying to parameterise them, but it doesn't seem very promising. However, I am thinking that consideration of typical lifecycle savings patterns will help shape the functional form and parameters that I might choose to use in a more conventional SFC model.

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    1. I can see the direction you are going in. My concern was that I was citing your article when I explained why I am unhappy with OLG models in general. Your suggested usages make more sense to me than attempting to explain secular stagnation with an OLG model.

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