Winner of the New Statesman SPERI Prize in Political Economy 2016

Saturday 19 April 2014

Misunderstanding macroeconomic models

The first half of this post is meant for non-economists, but it ends with a couple of points on OLG modelling

I recently wrote a post on the Eggertsson and Mehrotra paper on secular stagnation, because I thought the paper was interesting. A much more critical post from Unlearning Economics (UE) has just appeared in Pieria. UE says it “helps to illustrate the troubles faced by contemporary macroeconomics”. One of UE’s complaints seems to reflect a misunderstanding, often shared by non-economists, about what much academic macromodelling is designed to do.

UE objects to the fact that the model assumes that the amount the young can borrow (the degree of leverage) is exogenous, which means that there is no attempt to explain where this constraint on the borrowing of the young comes from. UE also complains that the model contains no banks, and no investment in physical capital. In other words, the model is much too simple. It is a natural enough idea: to explain what might be currently going on, you need a more complex model that includes everything that could be important.

There is certainly a place for this kind of more elaborate model. Christiano, Eichenbaum and Trabandt in this paper want to argue that a model based on New Keynesian theory can track what has happened over the last ten years. Their model has 40 equations. If I was trying to do a similar exercise, I would want to augment the standard New Keynesian framework with at least the following: nominal wage stickiness as well as price stickiness, a financial sector that endogenised both the cost and rationing of credit, a model of consumption which allowed for credit constraints and precautionary saving, a housing market, a model of the labour market that combined matching with rationing (as here), and something that allowed recessions to have long lasting (hysteretic) impacts on labour supply and technical progress. However large models like this will involve many macroeconomic ‘mechanisms’, and it will generally be unclear which mechanisms are important at driving particular results or explaining particular facts. We do not want to treat the elaborate model as a black box, but instead we want to understand its properties.

To understand complex models, we need much simpler models. (I once - in this paper - called the process of relating complex models to simpler models ‘theoretical deconstruction’.) In fact it is often sensible to start with the simpler model. For example, a particular issue with secular stagnation is to show how the natural real interest rate can be negative for decades rather than years (i.e. beyond the Keynesian short term)? What mechanism can do this? As I explained in my post, neither a standard representative agent model nor a standard two period overlapping generations model (OLG model, where the two generations are those earning and those retired) will give you that result. What Eggertsson and Mehrotra show is that a very simple three period OLG model (which adds a young generation that borrows) where borrowing by the young is constrained (they would like to borrow more but cannot) can provide just that mechanism.

That is a key point of the paper. The paper is not designed to explain where borrowing constraints come from: there is now a big literature on that. Thankfully the authors do not feel compelled to microfound these constraints. Instead the paper simply offers and explores a mechanism whereby an increase in these borrowing constraints could move the natural interest rate into negative territory, and for it to stay there. Having established that result, it is for subsequent work (which the authors intend to do) to see if that mechanism survives complicating the model, by for example adding investment.

Suppose the endeavour is successful, and a more complex but realistic model is able to provide an account of secular stagnation that includes other important mechanisms and which is based on a realistic set of parameter values. That would be a success, but those not familiar with all the work would ask: why does this model allow real interest rates to be negative when the standard models we know do not. The reply would be that the three period OLG structure was critical, and to see why have a look at the original, simple model.

Now you might say the authors should wait until they have built the more realistic model before creating what could turn out to be a research path that might fail to achieve its goal. That would be quite wrong, because the more debate there is within the academic community when ideas are at their early stages the better. I want to give an example of this, but here I will go into territory that will probably only interest macroeconomists.

It might be the case, for example, that the authors intuition that their results will survive introducing other assets like physical capital can be shown to be wrong very quickly. Indeed, Nick Rowe has already made such a claim, arguing that the presence of land as an asset ensures a positive real interest rate. If Nick was right this could be enough to kill the research programme, without any more time being wasted. Whether he is right is another matter: this paper by Rhee may be relevant in that respect.

Here I just want to add a final thought. Within an OLG framework, it may not be necessary to establish the existence of a steady state with negative real interest rates. The typical period in an OLG model lasts two or more decades. So if the dynamics of such a model involved some overshooting, it might be possible to generate prolonged periods (in years) of negative interest rates even if the steady state real interest rate was positive. To be honest I’m not sure what might give rise to overshooting of this kind, but that may just reflect my inadequate imagination.  


  1. Apologies for the long comment, but I would like to offer a few thoughts on this paper in particular and the broader discussion regarding the need for microfoundations and usefulness of ad hoc assumptions.

    Starting from the end, I am fully in agreement with you that we should be comfortable with the idea that we don't need microfoundations for every single aspect of our models, especially if the particular mechanisms we want to analyse exist and have been "microfounded" elsewhere. I see nothing wrong with that in principle. The Devil, however, is in the detail. If this were a model of how negative interest rates can come about following some unspecified financial shock, I see no reason why we would need them; indeed, avoiding a more cumbersome modelling strategy greatly facilitates the exposition of the model and adds clarity.

    Seeing as it has been presented as a model of "secular stagnation", which in my understanding would be a long-run equilibrium with a negative natural interest rate, then I am much less in favour of abstracting from the origins of this constraint. The negative rates arise in the model because agents have no income source in the last period of their lives and there is a single investment vehicle: lending to the currently young. Because there is a limit on how much agents can lend and they are desperate to smooth consumption, they accept negative rates - gladly! So if you're trying to tell a story about a long-term equilibrium in which borrowers want to pay high rates of interest and savers are so desperate to save they accept negative rates, I want to see a more detailed mechanism outlining it. Indeed, if one considers the existence of an alternative savings vehicle, earning zero interest, the second period agents would indeed avoid paying the negative rates.

    The land criticism isn't particularly useful, what drives the results in this model is the need to store the endowment or production generated during the agents' middle age into old age. If you could save in the form of land, then we'd sidestep the issue, but there is nothing particularly interesting about land that would yield different results. The only asset you can own is loans to the young, so land matters only to the extent that it provides an alternative savings vehicle.

    Finally, one must be careful when extrapolating results from models: negative interest rates can exist in this model and indeed have economic value. It is far less clear what real world implications should be drawn from it given the mechanism driving the results in the model. Personally, I think it captures the idea of how asset market frictions can affect output (via temporary shocks to D). I find it less persuasive as a model of economies being at an equilibrium with permanently lower output (D is permanently lower even though everyone could be made better off).

    The idea that this represents the "troubles" faced by contemporary macroeconomics is quite perplexing to me. Models as clear as this one can be easily deconstructed and analysed, and the only genuinely interesting ideas to argue over are those we can not just prove wrong or provide counterfactuals for, but those we can actually understand.

    1. I'm not so concerned about the fact that the constraint is on gross borrowing by the young. You need that in this model because log utility implies the supply of loans is independent of the interest rate. If the amount of saving by the middle aged was positively related to the interest rate, you could maybe avoid that assumption.

      My concern on robustness is the existence of alternative assets for the middle aged. If you allow for capital, government debt and land, is it really the case that there is still an unmet desire for assets such that interest rates are forced below zero? I suspect you may need to restrict the demand for capital by firms in some way. However investment has been low, at least in the West, so maybe this is not so unreasonable.

    2. I agree that you need it in the model, and I don't disagree with its use in principle to talk about how the way asset market frictions can lead to much larger fluctuations in output than a competitive model would predict. So it is true that you "need" it in the model to get that result. To move on from that and talk about permanent changes in the debt limit so that the economy moves to a new steady-state with permanently lower output requires a stronger story, i.e., microfoundations, for us to really pay attention to the mechanism.

      Speaking of which, because of how this mechanism generates negative rates, it is not clear that it is a good story about a similar outcome (negative natural rates) in the real world. Firstly, because negative rates in the model can exist and make sense (though not in reality - the repo rate has nothing to do with the interest rate in this model); secondly, because as you mention, other saving vehicles would mean that negative rates would be *much* harder to generate.

  2. In your opinion, is the actual mechanism that Eggertsson and Mehrotra use in the model for getting the negative natural rate a realistic one?

    Specifically (as I mentioned in my comment on your previous post), the causal mechanism involves a high interest rate reducing the amount lenders will lend, because they reference a debt limit gross of interest. If they were to reference a net debt limit, there would be no such effect (in fact you get the opposite effect in the long run - use equation (4) to cancel out D and D(t-1) in equation (11) and treat B as the debt limit).

    In a three period OLG model, where each time period represents a few decades, compounded interest on debt would indeed represent a substantial amount of the exposure, but in reality very few debts are compounded over that kind of period and the difference of a few percentage points in the interest rate has a minimal impact on exposures.

    I find it hard to relate this aspect to what might be happening in the real world.

  3. Thanks for the link to the Rhee paper.

    I would restate Rhee's point: a sufficient condition for dynamic efficiency is if there exists *one type of* land whose rents as a share of income do not vanish in the limit. Recreation land? (I'm at a friend's cottage on the shore of Lake Huron!)

    Exploring the land question seems to me a more useful research program.

  4. My problem is not so much that the model is simplified - I even explicitly eschewed the common rants about utility maximisation etc. My problem is that by making D exogenous, EM essentially assume what they want to prove. I mean, it's implicit in the model that the young spend more than other generations and are financed entirely, so if you reduce their borrowing constraint the yeah, spending is going to fall. And these assumptions are made necessary by the fact that EM don't even include investment in their model, so it's actually impossible for them to study secular stagnation in any realistic sense.

    This is the real problem I have with macro. I expect you can probably get anything. into an OLG model with the right assumptions and number of agents. Maybe if I make old agents' utility functions convex, middle-aged agents save more, which says something about retirement plans and social security - I don't know. It just seems the model is incredibly narrow and set up in such a way that it's obviously going to give the 'intuitive' results EM set out to achieve.

    I appreciate the model is a starting point and in principle I actually see no problem with that. However, will the next one EM produce actually move us closer to having a reliable model of the economy, or will it just be another way to tell a story within economists' preferred framework? I've yet to see anything in macro which moves beyond the latter.

    1. Correction: "...and are financed entirely *by borrowing*, so if you..."

    2. I really do not see the problem here. The preferred frameworks say real interest rates have to be positive, so secular stagnation cannot happen. What the authors do is show one way it could happen. That is interesting, no? It is certainly not staying within preferred frameworks.

      You are right to eschew the normal heterodox 'rants', because they do not apply to this model! The only utility maximisation is just their to motivate saving for retirement, and because of log utility its a constant savings rate! Otherwise its just about 'accounting relations and flows of funds', which is the kind of model you say you like.

      So I'm tempted to ask, if this paper had been written by heterodox economists, how would it have been different?

    3. "..if this paper had been written by heterodox economists, how would it have been different?"

      It's interesting you should ask that. Wondering about that question prompted me to try to put it into heterodox terms:

      Maybe others would have done it differently.

    4. "The preferred frameworks say real interest rates have to be positive, so secular stagnation cannot happen. What the authors do is show one way it could happen. That is interesting, no?"

      I'm not sure about the definition of 'secular stagnation' as simply the natural RoI falling below zero: to me, that seems like a symptom rather than a cause. As I said above, EM only show 'secular stagnation' could happen by making its consequences all but implicit in the assumptions of the model. The model can give us no insight into the process of how or why secular stagnation might occur, because there are none of the key drivers of secular stagnation in the real world (bubbles, investment).

      It seems to me the model is purely of theoretical interest: all EM have proven is that you can set up an OLG model in such a way, with such assumptions, that the natural rate of interest can go below zero. I said on twitter that maybe this is just the way economists have conversations, which I suppose is OK, but if I actually wanted to understand secular stagnation I would look elsewhere.

      "It is certainly not staying within preferred frameworks."

      When I say 'preferred framework', I am not referring to specific type of OLG model (say, 2 gens). I'm referring to the whole framework: OLG modelling in general, microfoundations, optimisation etc.

      "So I'm tempted to ask, if this paper had been written by heterodox economists, how would it have been different?"

      This kind of paper wouldn't have been written by heterodox economists, that's the point! Whereas mainstream macro seems to go down the route of 'tell a story to highlight observation x' - hence producing an unholy amount of models, none of which seem to be any closer to 'the' true model - heterodox models are about trying to find a general model of the economy, one in which 'secular stagnation' would be a standard occurrence given certain conditions/parameter values.

      Let me give you an example: Andrew Kliman, the Marxist economist, has written a book called The Failure of Capitalist production. In it he argues that the rate of profit has fallen persistently since the 1970s, and that financialisation has occurred as a consequence of 'normal' investment not being profitable. Sound familiar? (FWIW he wrote this well before Summers made his speech).

      The best thing is that, while Kliman's framework isn't 'microfounded' and doesn't make precise predictions, there are no special assumptions required to explain secular stagnation: it flows naturally out of the general model he has set up, and the empirical trends predicted by that model. This is the kind of thing I'm looking for: a holistic, falsifiable approach. I don't see either of those things in EM.

    5. "This kind of paper wouldn't have been written by heterodox economists, that's the point!"

      Are you so sure? You give two reasons

      (i) that the model is in a 'preferred framework': "OLG modelling in general, microfoundations, optimisation etc." As I explained, there is no microfoundations or optimisation of any consequence in this paper. Are heterodox macroeconomists not allowed to do OLG?

      (ii) that this is a simple model that focuses on a key mechanism. But as I tried to explain in my post, this is how you build and understand more complex - indeed general - models. Are heterodox economists superhuman so they do not need to do this kind of abstraction? Nick Edmonds in the post referred to in his comment above shows how its easy to put banks into the model.

    6. (i) The mechanics of intertemporal optimisation are the direct reason that the interest rate falls, no?

      (ii) It's perfectly fine building models that start from a simple framework and then get more complex. If EM (or anyone else) go on to build a more comprehensive model that actually produces falsifiable predictions, and which can account for multiple macroeconomic phenomena, as opposed to just a negative NRoI, I'll swallow my words.

      However, it seems that macro frameworks like OLG are continually being pushed in mutually conflicting directions, with every version of the model being defended on the grounds that it's "just a simplification", but with no clear progress towards a comprehensive theory.

      A harsh way of putting it is that macro is driven by the latest fad, and fails to offer any ex ante understanding of the actual economy. There's a financial crisis - everyone starts including 'financial frictions'. Larry Summers mentions Secular Stagnation - someone runs and makes a model that seems to produce it. Whatever the next thing is, I doubt macroeconomists will see it beforehand, but I'm sure they'll find a way to put it into their framework a couple of years after it's happened. I just don't see how any of this furthers our understanding of anything except macro models themselves.

    7. (i) The interest rate moves to equate the supply and demand for loans. I assume that is allowed in heterodox models. So I still think the paper would make a good, if simple, heterodox model.

      (ii) I don't think modelling financial frictions is following the 'latest fad'. Nor, after what seems like at least a decade of low real interest rates, is it a fad to wonder how persistent low rates might be. And there are more elaborate models out there that collect together many mechanisms - I mentioned one in my post.

      (iii) Macroeconomics is not always behind the curve. Macroeconomics said austerity would delay the recovery, and it did. Macroeconomics said higher levels of government debt following the recession would not push up interest rates, and it was right. New Keynesian analysis said QE would not raise inflation, and it was correct.

    8. I was going to give you the last word (for now!) but just to clear a couple of things up:

      (i) Heterodox (at least what you might call left-heterodox) models do not use loanable funds theory, so the interest rate does not serve that purpose.

      (iii) (a) Even macroeconomists aren't in agreement over this issue: there are plenty of high profile, Nobel-winning macroeconomists using their models to say something different to you.

      (b) It's possible to be right for the wrong reasons. There are quite a few theories that are consistent with the observations you point out, which is why I want to have more realistic, less abstract mechanisms so we can understand not only what is happening but why.

    9. UE, re point (i) - although I am no supporter of "loanable funds" theory, I disagree with you here. The interest rate does move to equate supply of and demand for loans. Interest rates on lending relate to cost of funding. That applies as much in an endogenous money model where banks are capital constrained as it does an an exogenous money model.

      Real interest rates have actually been falling for decades in the Western world. The question is why. May I add my two-pennyworth to this? I don't think the demographics question is a sufficient explanation - actually I think it is largely incidental. I think this is about the purpose for which the vast majority of loans are made. I'd suggest that in countries where there is substantial home ownership and much of it is mortgaged, real interest rates must fall over time in order to maintain positive real returns on property investment. Unlike land, property is naturally a depreciating asset. But in much of the Western world, residential property is the largest form of long-term savings for most people, and they have come to expect it to yield a positive return. Therefore house prices must rise over time. As most house purchases are made with mortgages, if wages don't keep pace with house prices (and they have not since the 1970s) then over time interest rates must fall. If they don't, eventually the property market collapses - and no government is going to allow large numbers of (mainly older) people to suffer significant realised or unrealised losses on their property investments. I may be completely wide of the mark here, but indirect or direct government intervention to encourage property prices to rise seems likely to depress interest rates. Governments have been encouraging property prices to rise faster than incomes for the last forty years.

    10. And I have just realised that Simon said more-or-less the same about interest rates and house prices in his next blogpost. I hadn't read it when I posted the above. Simon, I think you and I disagree over causation, though. You argue that rising house prices are driven by falling interest rates. I think it is the other way round - that it is upwards pressure on house prices (and other asset prices too, though I think this is less significant in most Western countries) that causes interest rates to fall.

    11. Yes, Frances: you are absolutely right. I'm so used to being an endogenous money warrior I simply read what Simon said as 'equates the demand and supply for loanable funds'. My mistake.

  5. UE shows us how not to read an economics paper. As usual, he puts an apple on trial for not being an orange and finds it guilty.

    Plus US spouts nonsense. UE writes: " My problem is that by making D exogenous, EM essentially assume what they want to prove."

    But EM want to prove that deleveraging "can .. lead to a permanent reduction in the real rate of interest under flexible prices."

    Obviously "making D exogenous" does not amount to assuming that result.

    1. Is there any criteria you would put forward that would show this model is wrong?

  6. Isn’t any flow of savings that finance is unable to intermediate (assuming it occurs on a large enough scale) a good enough reason to say the natural interest rate can be negative for a period of time? Say, as one example, that a portion of society is attempting to accumulate “permanent wealth.” They are accumulating wealth far beyond what they, or their children (or even grandchildren), are likely to consume. There are all kinds of rational motives for doing this; for example, having and bequeathing the power and influence that comes only with wealth, or, say they want their descendants to be able to live off the interest of their wealth into the indefinite future. How can you intermediate a flow of savings that isn’t going to be consumed in any reasonable length of time? (Maybe I’m wrong and you can in fact do it, but I don’t see how.) Certainly anecdotal, if not empirical, evidence is that accumulation of savings and planned consumption are decoupled beyond a certain level of wealth—and there may be rational motives behind this.

    I can think of other examples of flows of savings that are not, practically speaking, intermediate-able (short of some kind of financial innovation that has not, and may never, come along).

    Is my premise wrong: that a large flow of savings that cannot be intermediated is enough to have a negative real interest rate? **Please let me know if this is off base.**

    Thank you for the great blog!

    1. Mark,

      I'm sure Simon will respond, but I hope you don't mind me commenting too.

      If by "cannot be intermediated" you mean cannot be used productively in the present, then yes, that would cause interest rates to fall. The real return on unproductive capital is negative. The question is why there is apparently more global capital than can be productively used at present.

    2. Hi Frances. Thank you for your reply! Yes, that is what I meant by “cannot be intermediated.” I was being sloppy with word usage, but I figured people would know what I meant. With my comment, I was trying to see if I could bypass the “alternative assets” and the “existence of land” (from Nick Rowe) arguments, though I’m not sure if I succeeded or not.

      If I understand correctly (which may or may not be the case), *it is the implied future consumption from savings that provides the link to current investment*. In “theory,” the financial sector -- through innovation and maturity transformation -- should be able to find ways to intermediate current savings that will be consumed in the future. But if there is a significant amount of current savings that is totally decoupled from any future expenditure, then finance cannot do its job. To be honest, I don’t fully understand the land argument so I’m not sure if this works in that context.

      The Eggertsson and Mehrotra paper doesn’t prove secular stagnation can be a stable equilibrium, but if, in fact, a “permanent” pool of savings can produce negative real interest rate in a stable equilibrium, then we’ve at least identified *one* way in which it is possible. If there is one, there may be others. Of course there needs to be an explanation for accumulating “permanent” wealth, but that doesn’t seem particularly problematic to me.

      Thanks again!

    3. Just a note: I switched from a flow argument in my first comment to a stock of "permanent savings." That was intentional but I didn't explain myself. I think it works either way (stock or flow), but a stock was more pertinent to my second comment. Also, I'm putting quotes around "permanent" (or "permanent savings") because I don't think there is really such a thing as truly permanent savings. But practically speaking one might treat it as permanent. Thanks.

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