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Structural econometrics

from Lars Syll

In a blog post the other day, Noah Smith returned again to the discussion about the ’empirical revolution’ in economics and how to — if it really does exist — evaluate it. Counter those who think quasi-experiments and RCTs are the true solutions to finding causal parameters, Noah argues that without structural models

empirical results are only locally valid. And you don’t really know how local “local” is. If you find that raising the minimum wage from $10 to $12 doesn’t reduce employment much in Seattle, what does that really tell you about what would happen if you raised it from $10 to $15 in Baltimore?

That’s a good reason to want a good structural model. With a good structural model, you can predict the effects of policies far away from the current state of the world.

If only that were true! But it’s not.

Structural econometrics — essentially going back to the Cowles programme — more or less takes for granted the possibility of a priori postulating relations that describe economic behaviours as invariant within a Walrasian general equilibrium system. In practice that means the structural model is based on a straightjacket delivered by economic theory. Causal inferences in those models are — by assumption — made possible since the econometrician is supposed to know the true structure of the economy. And, of course, those exact assumptions are the crux of the matter. If the assumptions don’t hold, there is no reason whatsoever  to have any faith in the conclusions drawn, since they do not follow from the statistical machinery used!  

Structural econometrics aims to infer causes from probabilities, inferred from sample data generated in non-experimental settings. Arguably, it is the most ambitious part of econometrics. It aims to identify economic structures, robust parts of the economy to which interventions can be made to bring about desirable events. This part of econometrics is distinguished from forecasting econometrics in its attempt to capture something of the ‘real’ economy in the hope of allowing policy makers to act on and control events …

LierBy making many strong background assumptions, the deductivist [the conventional logic of structural econometrics] reading of the regression model allows one — in principle — to support a structural reading of the equations and to support many rich causal claims as a result. Here, however, the difficulty is that of finding good evidence for many of the assumptions on which the approach rests. It seems difficult to believe, even in cases where we have good background economic knowledge, that the background information will be sufficiently to do the job that the deductivist asks of it. As a result, the deductivist approach may be difficult to sustain, at least in economics.

The difficulties in providing an evidence base for the deductive approach show just how difficult it is to warrant such strong causal claims. In short, as might be expected there is a trade-off between the strength of causal claims we would like to make from non-experimental data and the possibility of grounding these in evidence. If this conclusion is correct — and an appropriate elaboration were done to take into account the greater sophistication of actual structural econometric methods — then it suggests that if we want to do evidence-based structural econometrics, then we may need to be more modest in the causal knowledge we aim for. Or failing this, we should not act as if our causal claims — those that result from structural econometrics — are fully warranted by the evidence and we should acknowledge that they rest on contingent, conditional assumptions about the economy and the nature of causality.

Damien Fennell

Maintaining that economics is a science in the ‘true knowledge’ business, yours truly remains a skeptic of the pretences and aspirations of — both structural and non-structural — econometrics. So far, I cannot see that it has yielded much in terms of relevant, interesting economic knowledge. Over all the results have been bleak indeed.

Firmly stuck in an empiricist tradition, econometrics is only concerned with the measurable aspects of reality. But there is always the possibility that there are other variables — of vital importance and although perhaps unobservable and non-additive, not necessarily epistemologically inaccessible — that were not considered for the econometric modeling.

Most econometricians still concentrate on fixed parameter models and the structuralist belief/hope that parameter-values estimated in specific spatio-temporal contexts are exportable to totally different contexts. To warrant this assumption one, however, has to convincingly establish that the targeted acting causes are stable and invariant so that they maintain their parametric status after the bridging. The endemic lack of predictive success of the econometric project indicates that this hope of finding fixed parameters is a hope for which there really is no other ground than hope itself.

Most of the assumptions that econometric modeling presupposes  are not only unrealistic — they are plainly wrong.

If economic regularities obtain they do it (as a rule) only because we engineered them for that purpose. Outside man-made ‘nomological machines’ they are rare, or even non-existant. Unfortunately that also makes most of the achievements of both structural and non-structural econometric forecasting and ‘causal explanation’ rather useless.

41svIj0RdVLInvariance assumptions need to be made in order to draw causal conclusions from non-experimental data: parameters are invariant to interventions, and so are errors or their distributions. Exogeneity is another concern. In a real example, as opposed to a hypothetical, real questions would have to be asked about these assumptions. Why are the equations “structural,” in the sense that the required invariance assumptions hold true? Applied papers seldom address such assumptions, or the narrower statistical assumptions: for instance, why are errors IID?

The tension here is worth considering. We want to use regression to draw causal inferences from non-experimental data. To do that, we need to know that certain parameters and certain distributions would remain invariant if we were to intervene. Invariance can seldom be demonstrated experimentally. If it could, we probably wouldn’t be discussing invariance assumptions. What then is the source of the knowledge?

“Economic theory” seems like a natural answer, but an incomplete one. Theory has to be anchored in reality. Sooner or later, invariance needs empirical demonstration, which is easier said than done.

  1. Yu
    May 16, 2017 at 3:32 am

    I have been following your discussions on regression. Thank you very much for indicating the hidden assumptions inside regressions. However, I want to remind you that it is possible to get “relatively good’ result when the assumptions fail. For example, linear and quadratic discriminant analysis in machine learning require data are Gaussian when we derive the method. But when it is applied in reality, at least for my experience during course homework, this method gives a surprisingly good predictions even when the data are apparently not Gaussian. I have not figured out why though.

    For a structural model, I think predictability for non seen data is core. We may first make some ridiculous assumptions to build a model, and then we relax the assumptions and test it against the data. I am still learning Econ, but it seems not many textbooks carefully discuss hidden model assumptions.

  2. May 18, 2017 at 7:26 am

    The questions to ask are how and are the “structures” which suggest an economic transaction or market created. Markets, as economists describe them require not just calculative agents but also agents with information on all the possible states of the world, on the nature of the
    actions which can be undertaken and on the consequences of these different actions, once
    they have been undertaken. Uncertainties in human actions, their results, and reactions to them make this impossible. So, economists “hedge” their bet. They propose ways around these uncertainties. Of course, they keep these “under wraps.” They might undermine confidence in the discipline of economics. These “quiet” solutions include such as the following. The most “orthodox” solution is that of contingent contracts. Contingent contracts are revisable contracts; their renegotiation is planned, thus taking into account the occurrence of events specified beforehand. Such contracts’ range of coverage is small and complex uncertainties quickly overwhelm them. A second solution economists offer is a “focal point.” Economists presume that the agents share common knowledge which guarantees the coordination. The nature of this knowledge is highly variable. It may pertain to a shared culture, rules, procedures, routines, or conventions which guarantee the adjustments and predictability of actions. Whether we talk about a common culture or of shared rules or conventions, we encounter the same stumbling block: a rule, convention or cultural device does not govern action completely since they comprise irreducible margins of interpretation. These margins of interpretation can be removed only during interaction, negotiation, or discussion. A subtler solution to the question of coordination is to admit that beneath the contracts and the rules, there is a “primitive” reality without which coordination would not be possible. An understanding of this ultimate basis is the purpose of the notion of a social network or, more broadly, the notion of embeddedness as initially formulated by Polanyi and later refined by Granovetter in two brief seminal articles. If agents can calculate their decisions, it is because they are entangled in a web of relations and connections; they do not have to open up to the world because they contain their world. Agents are actor-worlds. Closer, but we still haven’t explained the existence of calculative agents who sign contracts. Instead of explaining that homo clausus needs to open up in order to become economicus, an attempt is made to explain how homo apertus can withdraw into himself and become calculative. To explain the emergence of calculating agents and of a great divide between
    agents and goods, we must discard the over-social networks of Polanyi and Granovetter. if calculations are to be performed and completed, the agents and goods involved in these calculations must be “disentangled and framed.” In short, a clear and precise boundary must be drawn between the relations which the agents will take into account and which will serve in their calculations, on the one hand, and that multitude of relations which will be spawned by the calculation as such, on the other. This is impossible in any absolute sense since economic agents are always entangling the two and overflowing the calculative framework set up. These three transformations are needed to create the framing necessary for a market that matches economics textbooks:
    • existence of a perfectly qualified product;
    • existence of a clearly constituted supply and demand;
    • organization of transactions allowing for the establishment of an equilibrium price. M.-F. Garcia describes the transformation of the table strawberry market in the Sologne region of France intended to create such a textbook market. The conclusion that can be drawn from this simple experiment is fundamental: yes, homo economicus does exist, but is not an a-historical reality; it does not describe the hidden nature of the human being. It is the result of a process of configuration. The history of the strawberry market shows what this framing consists of, that it often fails, and that the market participants will alter it for varied reasons. Of course, it mobilizes material and metrological investments, but we should not forget the essential contribution of economics in the performing of the economy. The study of this contribution constitutes a vast project for economics and the social sciences future. One, so far not obtained.

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