Saturday, 18 August 2012

The Lucas Critique and Internal Consistency


For those interested in microfoundations macro. Unlike earlier posts, I make no judgement about the validity or otherwise of the microfoundations approach, but instead just try and clarify two different motivations behind microfoundations.

When I discuss the microfoundations project, I say that internal consistency is the admissibility criteria for microfounded models. I am not alone in stressing the role of internal consistency: for example in the preface to their highly acclaimed macroeconomics textbook, Obstfeld and Rogoff (1996) argue that a key problem with the pre microfoundations literature is that it “lacks the microfoundations needed for internal consistency”. However when others talk about microfoundations, they often say they are designed to avoid the Lucas critique. This post argues that the latter is just a particular case of the former.

What do we mean when we say a model is internally consistent? Most obviously, we mean that individual agents within the model behave consistently in making their own decisions. A trivial example is if the model contains a labour supply equation and a consumption function that are supposed to represent the behaviour of the same agent. In that case we would want the agent to behave consistently. An agent that became more impatient, and so wanted to consume more by borrowing, but also wanted to work more hours (and so exhibit less impatience in their consumption of leisure), would appear to behave inconsistently unless their preferences or prices also changed.

Suppose instead of a labour supply equation, we had wage setting by unions. In this case we have a consistency issue between two sets of agents: consumers and unions. If we wanted to model unions as representing consumers as workers, we would want to align their preferences, so we are back to the previous case. However, there may be reasons why we do not want to do this. If we did not, we would want to make sure these agents interrelated in a sensible way.

What is meant by a sensible way? Consumer’s decisions will almost certainly depend on expectations about the wages unions set. Lucas called rational expectations a ‘consistency axiom’. If, for example, the union started being more concerned about employment than wages, we might expect consumers to recognise this in thinking about how their future income might evolve.

The Lucas critique is just an example of consistency between agents. The question is whether the private sector agents in the model react in a sensible way to policy changes. The classical example of the Lucas critique is inflation expectations. If monetary policy changes to become much harder on inflation, then rational agents will incorporate that into the way they form inflation expectations. A model that did not have that feedback would be ‘subject to the Lucas critique’.

Discussion of the Lucas critique often involves the need to model in terms of ‘deep’ parameters. A deep parameter (like impatience) is one that is independent of (exogenous to) the rest of the model. Here the parameters of the rule agents’ use to forecast inflation are not deep parameters, because (under rational expectations) they depend on how policy is made. But we can have a similar discussion about workers and unions: if the latter aimed at representing the former, then union attitudes to the wage/employment trade off should not be independent of worker preferences. Internal consistency is again more general than the Lucas critique.

Now obviously the Lucas critique is a particularly important kind of inconsistency if you are interested in analysing policy. But it is not the only kind of inconsistency that matters. A very good example of this is Woodford’s derivation of a social welfare function from the utility function of agents. Before this work, macroeconomists had typically assumed that a benevolent policy maker would minimise some quadratic combination of excess inflation and output, but this was disconnected from consumers’ utility. This had no bearing on the Lucas critique, which applies to any policy, benevolent or not. However it was a glaring example of inconsistency – why wasn’t the policy maker maximising the representative agent’s utility? After Woodford’s analysis, nearly every macroeconomics paper followed his example: not because it did anything about the Lucas critique, but because it solved an internal consistency issue.

Why does putting the Lucas critique in its proper place matter? I can think of two reasons. First, if you believe that avoiding the Lucas critique means you necessarily have a microfounded model, you are wrong. (In contrast, an internally consistent model will avoid the Lucas critique.) Second, it has a bearing on the idea often put forward that microfounded models are just for policy analysis, but not for forecasting. If we think that microfoundations is all about the Lucas critique, then this mistake is understandable (although still a mistake). But if microfoundations is about internal consistency, then it is easier to see how a microfounded model could be much better at forecasting as well as policy analysis.

14 comments:

  1. This whole discussion of consistency depends on very strong assumptions -- for example you say that a model can't be considered micro-founded unless consistency can be analytically proved!! This seems really excessive.

    But I'm more concerned about the assumptions about agents of the sort you discuss in your post on the hetrodox vs. superhuman agent. I believe these are simply unnecessary, unrealistic and therefore inappropriate.

    You seem to argue these assumptions are necessary. In that post you said "If you do not assume rational expectations, what do you assume?"

    In fact you can assume only very local knowledge and very basic choice -- kind of like gas molecules bumping around, converging on a global equilibrium. Eric Smith and Duncan Foley have done this in "Classical thermodynamics and economic general equilibrium theory" JEDC 32, 7-65.
    http://www.santafe.edu/~desmith/PDF_pubs/DYNCON2011.pdf

    Turns out you can build quite powerful and useful models without unrealistic assumptions. Then you can *add* more rationality, knowledge, and behavioral biases incrementally in an empirically guided way.

    Foley has elsewhere written much more on this kind of model.

    If you take this approach, then most of the conundra you are wrestling with in the current post are not problematic. Individual behavior can be inconsistent (as it often is) and yet macro behavior approximates consistency.

    I'd very much like to understand why this approach isn't more widely pursued.

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    1. Also note that generally these models are fairly tractable, so analytic results about consistency etc. are easier to derive.

      And there's a very powerful, well understood set of tools in statistical mechanics available to build, analyze and prove results about these models.

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  2. Ditto. (Even if I would have said 'conundrUMS' ;)

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  3. Simon, there are several notions of consistency that a model could satisfy, and not all of them are methodologically desirable. One wants individual decisions to respect budget constraints both within individuals (if I consume more with no change in income I must borrow or reduce saving) and across individuals (if I buy more of your output your income must rise). But the rational expectations assumes much more than this: it requires the mutual consistency of individual plans. So if I plan to retire early and move to warmer shores, someone today must anticipate the greater demand for housing in Florida that will arise in a decade. This assumption is indefensible in the absence of complete futures and contingency markets - there is simply no mechanism to bring about such consistency. Moreover, I would argue that the most interesting macroeconomic phenomena, booms and busts for example, arise through the resolution of plans that are found to have been inconsistent.

    Related thoughts here:

    http://rajivsethi.blogspot.com/2010/11/foley-sidrauski-and-microfoundations.html

    I've been enjoying your posts on microfoundations, though have never commented before.

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    1. Bravo, Rajiv!

      You write, "I would argue that the most interesting macroeconomic phenomena, booms and busts for example, arise through the resolution of plans that are found to have been inconsistent."

      This was one of Frank Hahn's central themes in his under-appreciated critique of rational expectations models that piggy-back on GE results without incorporating complete markets in contingent claims.

      And thanks, Simon, for all your interesting posts on this subject.

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    2. derrida derider22 August 2012 03:42

      Actually it is a central insight of Keynes' General Theory. Friedman used to accuse Keynesians of "forgetting things we used to know" - surely RE people have done the same here.

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  4. I note that the "deep parameters" are two things, because the word "eexogenous" has two meanings. They are parameters which we have reason to hope are exogenous to the economy and, in particular, not influenced by policy. But exogenous also just means unmodelled. No one thinks that technology is really exogenous (it doesn't fall out of the sky). It is treated as exogenous in many models exactly because technological progress is too complicated for us to model.

    The jump to assuming that, since we don't understand it, we can assume that it is not influenced by policy is completely unjustified and absurd. Please google phlogistonomics and Noah Smith. Micro founded New Keynesian economics in particular is lousy with variables which are treated as exogenous to the model simply for convenience and which then are assumed to be policy invariant for no comprehensible reason.

    The usual rant follows.


    Certainly a micro founded model could be much better at forecasting. In fact they give terrible forecasts. This was not expected by those who started developing such models. The idea that a model which does not fit the data can be useful for policy analysis has no possible philosophical basis. It is what one would expect from supporters of a completely failed research program. For example, fundamentalist Christians say that the assumption that the bible is inerrant is useful for policy analysis. They respond to the inconsistencies between the bible and the evidence by saying the world works in mysterious ways. I think their approach to reasoning about the world is indistinguishable from say Prescott's. If there is any meaningful difference, I would like to know what it is.

    More generally, I think that anyone who say a model is useful for policy analysis even if it doesn't yield good out of sample forecasts rejects the scientific method as such. Such people may be third rate mathematicians or ideologues, but they definitely aren't social scientists.

    As an aside, I don't accept that only rational expectations are consistent. Any simple model of irrationality will give predictable deviations between forecasts and reality (somewhat like the easily predictable excess returns described in financial markets in the 60s which persist to this day). But a complicated theory of irrationality does not imply an inconsistent model. It implies no model (as the term is used by economists).




    Notably Lucas and Prescott were very interested in forecasting and hypothesis testing. They were also very interested in taking models seriously, that is treating them as hypotheses to be tested. Sargent did that and rejected their models. Their reaction was to decide that hypothesis testing is not relevant to macroeconomics. Notably, Sargent described these conversations soon after being awarded the Nobel memorial prize.

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  5. "An agent that became more impatient, and so wanted to consume more by borrowing, but also wanted to work more hours (and so exhibit less impatience in their consumption of leisure), would appear to behave inconsistently unless their preferences or prices also changed."

    So, if someone decides to form a small business and borrows money to buy equipment and works longer hours in hopes of making the business a success, then he or she is inconsistent. Hmmm....

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    1. Consumption and investment are generally treated differently in macroeconomics. Borrowing to invest is not the same as borrowing to consume. A closer analogy would be somebody who decided to work more hours and suddenly started buying a new car, a Rolex, some electronic gadget every month, and so on on a credit card, while making the minimum credit payment every month. This is certainly possible, but yes it would be inconsistent.

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  6. Rational expectations is the Lucas' solution to the inconsistency issue raised by the Lucas critique: if a model is based on rational agents, and those agents have expectations, then those agents necessarily have rational expectations. That's consistent. And from a theoretical point of view, it is also quite interesting. The problem is that the model bears little resemblance with the reality.
    Many explanations can probably be found, but there are two that I would like to propose:
    - Economic agents are not that rational as individuals (they don't maximize their utility) as individuals. There are even less so as a collective aggregate of individuals (herd behavior).
    - Most economic agents don't make predictions. They have no expectations at all. If the economy is depressed, they believe it will remain depressed (and vice-versa).
    A model based on non-rational expectation-free agents would be consistent. It would not satisfy the Lucas critique, but that does not matter because the critique would not be relevant in that context.

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    1. I mostly agree but guess that you don't go far enough. For example agents may not believe anything about the future, not even that it will be like the present, they may just spend based on their income and endowment.

      Note that there are many mechanisms that can produce the appearance of (some approximation to) rational choice -- for example imitation of surviving actors. But the intertemporal implications are of course different.

      Looking at the financial crisis, which is a more credible explanation of the actual choices of financial actors?
      1) Make a rational decision based on all the information available.
      2) Do what seemed to work recently for other actors "near" you.

      And, to repeat, you can get simple tractable equilibrium models just fine with assumption (2). So why is it ignored?

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    2. Actually we can rework the point about how actors make choices to address the question of why more modest assumptions about rationality don't get traction in economics:

      Looking at the economic profession, which is a more credible explanation of how economists choose models and assumptions?
      1) They make rational decisions based on all the information available.
      2) They do what seemed to work recently for other actors "near" them.

      So unfortunately this approach predicts its own lack of adoption.

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  7. Now I understand why the Phillips Curve has lasted as long as it has. I think if one listens to Lucas today, I would concede that the above discussion suggests that our discipline hasn't learned very much since Lucas 1976. Honestly, the FED is chasing 6.5 and 2 on the Phillips Curve. Does anybody really believe that is tenable? Fact is, agents responded very rationally to real low rates and because of a lack of Fin. Reg., TBTF, et al structural methodological inadequacies, we created a boom that would otherwise not have occurred under normal price discovery. Moreover, since policy has not allowed for price discovery since 2008, we are apt to repeat the very same mistake. That we relaxed mark to market.....do we dummy up for moral hazard? Are we factoring in these kinds of structural anomalies such as the FED's balance sheet, that it represents over 30% of the bond market, and that debt servicing costs are imposing significant budget constraints? Its an interesting discussion talking about the rationality of agents and structural consistency. But, the Bernanke FED is coercively forcing behaviour that simply would not otherwise occur in the market place in its current policy absence. Does it really matter what individual agents really think in this context? My guess is probably not. I don't have an axe to grind with you fine practitioners of macro economics. However, I am finding that my discipline is sorely lacking in its ability to observe reality and is instead getting increasingly lost in quantitative exercises that really have no bearing on the economic problem, in my opinion. Respectfully, Michael P. Ivy, Edmonton, Alberta.

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