Statistical inference — a self-imposed limitation

14 January, 2017 at 12:21 | Posted in Statistics & Econometrics | 2 Comments

koopmansThe tool of statistical inference becomes available as the result of a self-imposed limitation of the universe of discourse. It is assumed that the available observations have been generated by a probability law or stochastic process about which some incomplete knowledge is available a priori …

It should be kept in mind that the sharpness and power of these remarkable tools of inductive reasoning are bought by willingness to adopt a specification of the universe in a form suitable for mathematical analysis.

Yes indeed — using statistics and econometrics to make inferences you have to make lots of (mathematical) tractability assumptions. And especially since econometrics aspires to explain things in terms of causes and effects, it needs loads of assumptions, such as e.g. invariance, additivity and linearity.

Limiting model assumptions in economic science always have to be closely examined since if we are going to be able to show that the mechanisms or causes that we isolate and handle in our models are stable in the sense that they do not change when we ‘export’ them to our ‘target systems,’ we have to be able to show that they do not only hold under ceteris paribus conditions. If not, they are of limited value to our explanations and predictions of real economic systems.

Unfortunately, real world social systems are usually not governed by stable causal mechanisms or capacities. The kinds of ‘laws’ and relations that econometrics has established, are laws and relations about entities in models that presuppose causal mechanisms being invariant, atomistic and additive. But — when causal mechanisms operate in the real world they mostly do it in ever-changing and unstable ways. If economic regularities obtain they do so as a rule only because we engineered them for that purpose. Outside man-made ‘nomological machines’ they are rare, or even non-existant.

So — if we want to explain and understand real-world economies we should perhaps be a little bit more cautious with using universe specifications ‘suitable for mathematical analysis’ …



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  1. Hello.
    I read some articles of your blog and the book “Statistical Models: Theory and Practice” by David Freedman and now I am aware of the limitations of statistical inference and when I can not get reliable results.
    Now I’d need a good book or other type of resource (beginner graduate level) for learning in which contexts and how I can make use of statistical models and more specifically econometrics as a tool. What would you recommend?
    For example, to evaluate broadly the impact of certain economic policies, compute Keynesian multipliers related to reduction of taxes or increased expenditure, ecc.

  2. The caution and timidity of philosophers contrasts starkly with the practical need for risk-taking in everyday life. On the one hand we have the dithering hesitations Koopmans and Prof. Syll in this post. Their motto seems to be “fools rush in where angels fear to tread”. Their caution echoes Aristotle:
    “It is the mark of an educated mind to rest satisfied with the degree of precision which the nature of the subject admits and not to seek exactness where only an approximation is possible.” – Aristotle: Nicomeachean Ethics, Book 1, Chapter 3 [350 BC]
    In contrast, econometricians make explicit assumptions which sometimes permit useful conclusions to be drawn from data. And like econometricians, ordinary folk make practical judgments every day based on probability assumptions, e.g. when crossing a busy road on foot or driving a car. Experience (not logic) teaches us that many outcomes in nature and in human behavior have bell shaped (roughly normal) probability distributions. Of course, we sometimes make errors or have bad luck, but that’s part of life.
    Acceptance of the need to take risks accords with common experience and wisdom:
    “He who doesn’t risk, doesn’t drink champagne” – Ukrainian proverb
    “A ship is safe in harbor, but that’s not what ships are for.” William G.T. Shedd
    “There are risks and costs to action. But they are far less than the long-range risks of comfortable inaction.” – John F. Kennedy
    “Take calculated risks – that is quite different from being rash.” – General George S. Patton
    “The fearful and unbelieving shall have their part in the lake which burneth with fire and brimstone” (Revelation 21:8, KJV)
    “Unhardy is unsely“ [Timidity is unhappy] – Chaucer: The Canterbury Tales: The Reeve’s Tale [c. 1374]
    A translation of more of the latter is below:
    John lies still for a short time, feeling sorry for himself.
    “Alas,” he says, “this is a cruel joke; now I can see that I am the only fool here.”
    “My colleague is getting compensation for his grievance; he has the miller’s daughter in his arms. He has taken a chance, and fulfilled his needs, while I lie like a sack of rubbish in my bed.”
    “And when this joke is told one day, I shall be considered an ass, a weakling!”
    “I will arise and take a chance, too, by my faith!’ Nothing ventured, nothing gained, or so men say.
    And so John gets out of bed and creeps softly to …
    The continuation to this bawdy tale must be censured here, but can be found at
    or in

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