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Friday, February 20, 2015

Further Comments On The Apparent Limitations Of OLG Models

This article is a short response to the article Sam and Janet go to College, by Professor Roger Farmer. The original impetus for that article was to respond to comments I made earlier. I have looked at the papers he suggested, and I am still circling back to roughly where I was earlier with regards to overlapping generations (OLG) models. I still have not found any OLG models which meet my fairly strong criteria for what constitutes a useful economic model for analysing fiscal policy. I explain those criteria here, as I did not want to spam his website with a 1000 word comment. Since the literature is huge, and I do not have access to an academic library, that does not mean such models do not exist. I am simply unaware of them. But they are certainly well hidden from the public domain. Moreover, I have my doubts about the analytical tractability of such models.

I want to keep my comments here tightly focussed, as this could easily degenerate into a much wider debate about Dynamic Stochastic General Equilibrium (DGSE) models.

I seek to avoid the debate about "debt burdens"; the problem is that a "debt burden" is not a very well defined concept. Instead, I will just look at a more limited, yet interested problem: could an OLG model tell us anything useful about how the economy will evolve as the "baby boom" generation moves into retirement (under current policy settings, or under alternative settings)? If a model offer a description of this evolution, which is of crucial importance for fiscal dynamics, I am hard pressed to see how the model can offer insights to even more abstract problems.

Professor Farmer helpfully lists some articles to read, as well as some books. Since I currently have a backlog of things to read, I only looked at the articles. I have read other DSGE textbooks, and each one only covers OLG models where households live for 2 or 3 periods. I explain elsewhere why I reject the usefulness of such models, with their very long time increments.

Blanchard Paper

Olivier Blanchard's Debt, Deficits and Infinite Horizons (1984) is described in that article as:
Olivier Blanchard, the research director of the IMF, developed an elegant version of the OLG model in which people have long lives, but they die each period with some probability.
I have already sketched out a longer discussion of this paper. I would not describe this article as being an OLG model, as all households are akin to J.R.R. Tolkien's elves: they do not die of old age, but they can die for other reasons (accidents, orcs). Mathematically, all living households have the same finite expected life span. Even with the addition of declining incomes, this does not fit the longevity profile of a real world population; in particular the issues associated with the "baby boom" generation.

Since I am not interested in the fate of individual model households, rather the aggregate economy, this model looks to me just like the Ramsey models used by central banks, but with a modified consumption function. Once we close the model with a central bank reaction function, it looks to me like the effect of fiscal policy will be the same as in the Ramsey model away from the zero bound: nothing. This raises a lot of issues that are a distraction relative to the topic of this article.

This is an interesting paper, but I would be hard pressed to see why this model would be any easier to fit to the demographic profile of the baby boom generation than the Ramsey model. But since I would not consider this a true OLG model, it does not contradict my earlier statements about them.

Kehoe and Levine [1985]

I only glanced at the paper Comparative Statics and Perfect Foresight in Infinite Horizon Economies, by Timothy J. Kehoe and David K. Levine (Econometrica, 1985). The OLG portion of the paper had households that were only within the model for two periods. Whatever merits this paper has, it does not address my concerns about long time increments.

Auerbach, Gokhale and Kotlikoff

The paper Generational Accounts: A Meaningful Alternative to Deficit Accounting, by Auerbach, Gokhale and Kotlikoff, develops a detailed breakdown of net spending over time, including different scenarios. Their objective is to demonstrate whether different generations are being treated fairly relative to each other.

I will not address their logic, other than to say that I find it highly questionable. I will instead whether their work constitutes an "economic model". I would characterise their work as "an accounting framework", and not a model. There is no attempt to model variables such as inflation and unemployment. These are critical for the determination of the fiscal balance, and are dependent upon fiscal policy choices.

In other word, the trajectory of the economy is exogenous to the accounting framework. I imagine that this exercise could be extended by "dynamic scoring", but without an actual model, how do we do the "scoring"?

The CBO does this sort of accounting framework, and they were famously worried about U.S. Treasury debt disappearing a few years back. This might not have happened if they used an actual economy model which includes feedback effects between different sectors.

More generally, I have seen other OLG models with a fine-grained time increment (for example, annual) applied to things like retirement savings. These were closer to true economic models, with optimising households trading assets with each other. However, these models were only able to simulate some portion of the economy (for example, financial markets), and all of the interesting economic variables were largely exogenous.

Lacking a means of calculating those exogenous variables means that these accounting exercises are only of limited usefulness to policymakers. All they can do is reproduce the effects of the exogenously determined variables, and we have no way of determining whether those exogenous variables are internally consistent with policy settings. 

Concluding Remarks

Leaving aside the question of whether the Blanchard model is an OLG model, I still have not seen an OLG model framework that could be applied to the following problem.
  • Time increments no longer than a year.
  • Simulation of the age profile and longevity of the baby boom generation.
  • Private and public pensions.
  • Tax rates are set by policy makers and hence the fiscal balance is endogenous. 
  • Unemployment and inflation rates determined within the model (although one might assume inflation is always at the inflation target).
  • Capital stock determined within the model.
Additionally, it would be nice to handle:
  • private sector financial assets;
  • different savings profiles based on wealth cohort;
  • external sector, including the effect of the large holdings of U.S. financial assets by foreigners. 
This is obviously a fairly impressive wish list. I doubt that a model could get a very accurate fit. But we will need to capture these effects in order to at least understand what the trade-offs are for fiscal policy choices.

And this is not an impossible task, as long as we drop the strange insistence upon model-consistent rational expectations. A stock-flow consistent modelling framework could be adapted to this problem; all that needs to be done is to dis-aggregate the household sector into annual cohorts. (As an aside, it's a project which I am slowly working on.)

(c) Brian Romanchuk 2015


  1. It depends what you are expecting a model to do really. Some models might be designed to help make some quantitative assessments about real economies, but most are just there to help set out lines of reasoning when discussing particular issues. Most of the OLG stuff I've seen fits into that latter category.

    Why do we use such models? Just to make things clearer. We often make general statements in economics like: "If X happens, then Y will happen". The problem with this is that there are so many complicating factors, that if I hear someone say this, I don't know what they are assuming and what they are ignoring. We might spend hours arguing about it before I end up saying something like "Oh, you were assuming monetary policy holds the nominal interest rate constant. Well in that case, I can see why you think that, but in my view, something else is the real cause there". For example.

    So what a model does, hopefully, is set out the basis for making such a point. What is assumed and what is ignored. We can then judge whether that might translate into something that happens in the real world. Which is the difficult bit. But to make it useful we have to be able to see how the results flow from the assumptions. Which means it needs to be very simple. Adding bits to models can rapidly lead to it becoming very hard to see why they respond as they do.

    In these terms, I have learned a lot from looking at looking OLG models. I also find it hard to see how to have a useful discussion about "debt burdens" without using models like that for the reason I gave above - the risk of talking at cross-purposes. I am also very interested in what has happened in economies like the UK, where household debt ratios have risen enormously over a fifty year period and the relationship between this, property prices, generational wealth distribution and spending patterns. OLG models are very helpful in thinking about this, but the more complicated they are (and adding generations does make it more complicated) the harder it is to see what is going on.

    Another thing that has interested me is that most OLG models behave essentially the same as typical for SFC models and for essentially the same reason. Personally, I don't think models have to be micro-founded or use model consistent expectations to be useful, but some people do. My point has been that it doesn't really matter. Even if you adopt these things, and hopefully therefore have something more acceptable to the orthodox, many of the standard results of SFC models still apply. I'm just looking for common ground. If someone needs to see the argument set out in micro-founded terms - fine, here it is. In fact, from when I first started looking a SFC models, I always had in my mind that there was some kind of OLG idea underlying it.

    Lastly, I share your wariness about the shortness of the period and the lumpiness of the generations. This is necessary to have models where we can easily see what is going on, but we need to be careful that it is not misleading us. Will the conclusions still stack up, if we look at shorter periods and multiple generations? But this is always the case with models. To make it simple, we have to leave stuff out and maybe that stuff matters. I believe there is quite a lot that we can take away from a two generation model and say that something similar would happen in a more complicated version, but certainly not all.

    1. Obviously, they help people in thinking about problems. But I object to the tone that one has "proved" something by looking at an OLG model, which is what has been insinuated within the "debt burden" debate.

      The more I think about it, the problem with that "debate" is that it makes it look like you can arbitrarily set the debt level, and see the effect. In the real world, unless you are defaulting on your debt, the pre-existing stock of debt reflects previous decisions that cannot be undone. All you can do is look at different policies, and see their effects, going forward.

      The simplicity of the OLG framework, with the fairy tales about orchards that produce 100 apples per generation, has abstracted out the policy decisions we actually face, at least with respect to fiscal policy.

      Hence my ongoing series of complaining articles....

    2. Well I share you irritation here with those that think that what the OLG models show is that we should try to run surpluses now for the sake of future generations. I don't think they actually show that when examined properly.

      And I also don't like the suggestion that models "prove" any real world result. They don't, but that limitation is true of any type of model.


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