On randomness and probability in economics

11 June, 2018 at 11:50 | Posted in Statistics & Econometrics | 10 Comments

Modern mainstream economics relies to a large degree on the notion of probability. To at all be amenable to applied economic analysis, economic observations have to be conceived as random events that are analyzable within a probabilistic framework. But is it really necessary to model the economic system as a system where randomness can only be analyzed and understood when based on an a priori notion of probability?

slide_1When attempting to convince us of the necessity of founding empirical economic analysis on probability models,  neoclassical economics actually forces us to (implicitly) interpret events as random variables generated by an underlying probability density function.

This is at odds with reality. Randomness obviously is a fact of the real world. Probability, on the other hand, attaches (if at all) to the world via intellectually constructed models, and a fortiori is only a fact of a probability generating (nomological) machine or a well constructed experimental arrangement or ‘chance set-up.’

Just as there is no such thing as a ‘free lunch,’ there is no such thing as a ‘free probability.’

To be able at all to talk about probabilities, you have to specify a model. If there is no chance set-up or model that generates the probabilistic outcomes or events – in statistics one refers to any process where you observe or measure as an experiment (rolling a die) and the results obtained as the outcomes or events (number of points rolled with the die, being e. g. 3 or 5) of the experiment – there strictly seen is no event at all.

Probability is a relational element. It always must come with a specification of the model from which it is calculated. And then to be of any empirical scientific value it has to be shown to coincide with (or at least converge to) real data generating processes or structures – something seldom or never done.

And this is the basic problem with economic data. If you have a fair roulette-wheel, you can arguably specify probabilities and probability density distributions. But how do you conceive of the analogous nomological machines for prices, gross domestic product, income distribution etc? Only by a leap of faith. And that does not suffice. You have to come up with some really good arguments if you want to persuade people into believing in the existence of socio-economic structures that generate data with characteristics conceivable as stochastic events portrayed by probabilistic density distributions.

We simply have to admit that the socio-economic states of nature that we talk of in most social sciences – and certainly in economics – are not amenable to analyze as probabilities, simply because in the real world open systems there are no probabilities to be had!

The processes that generate socio-economic data in the real world cannot just be assumed to always be adequately captured by a probability measure. And, so, it cannot be maintained that it even should be mandatory to treat observations and data – whether cross-section, time series or panel data – as events generated by some probability model. The important activities of most economic agents do not usually include throwing dice or spinning roulette-wheels. Data generating processes – at least outside of nomological machines like dice and roulette-wheels – are not self-evidently best modelled with probability measures.

If we agree on this, we also have to admit that much of modern neoclassical economics lacks sound foundations.

When economists and econometricians – often uncritically and without arguments — simply assume that one can apply probability distributions from statistical theory on their own area of research, they are really skating on thin ice.

This importantly also means that if you cannot show that data satisfies all the conditions of the probabilistic nomological machine, then the statistical inferences made in mainstream economics lack sound foundations!

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  1. In a separate post today Prof . Syll wisely accepts empirical evidence as the basis for his rejection of “The Permanent Income Hypothesis”.
    But sadly, and inconsistently, whenever he writes about econometrics, he neglects the evidence that the notion of probability is extremely useful if not fundamental to the success of most human endeavors.
    .
    Prof . Syll complains that “Modern mainstream economics relies to a large degree on the notion of probability”.
    However, there is overwhelming evidence that the notion of probability was also a vital factor influencing the survival of our ancestors and our own evolution.
    The physiology and psychology of humans evolved over many millennia. So it is reasonable to suppose that the thinking processes of prehistoric peoples must have had many of the features of modern men. As for modern humans, Y = f(X) + U is probably a good representation of how our ancestors used knowledge to plan their hunting, fishing, foraging, marauding, philandering etc.
    For example, for a fishing expedition:
    Y= weight of fish caught on past expeditions (= expected weight for the next expedition)
    X = length of time spent fishing, time of day, length of time from previous expedition, height of water, distance from home, weather etc
    U = unexplained effect of other factors and measurement/memory errors.
    They generally expected U to be close to some average value (e.g zero), while very large values of U were regarded as unlikely. In other words, they regarded U as having a bell shaped (roughly normal) probability distribution.
    .
    Obviously primitive humans did not formalise their thinking in algebra.
    Even so their elementary econometrics worked! Our ancestors thrived in the struggle for survival.
    .
    Of course, in the distant past, like today, there were some humans who rejected or were less good at econometric thinking. These tended to die early with fewer offspring.
    So most our ancestors were not like this – most were generally successful at using experience to make plans using the notion of probability. Otherwise we would not be here.

    • Kingsley,

      Animals are still here after hundreds of millions of years, does that mean they also have an innate sense of probability and how it might be used for survival? Does this mean they have the powers of conscious thought?

      (Personally, I believe the notion of probability is bulldust anyway.)

      • Henry,
        There is interesting evidence that “Apes are intuitive statisticians”.
        “In a series of 7 experiments, Bonobos, Chimpanzees, Gorillas and Orangutans drew flexible statistical inferences from populations to samples. These inferences, furthermore, were truly based on statistical information regarding the relative frequency distributions in a population, and not on absolute frequencies. Intuitive statistics in its most basic form is thus an evolutionarily more ancient rather than a uniquely human capacity.”
        https://www.ncbi.nlm.nih.gov/pubmed/24440657

        • Kingsley,

          Any evidence that fish or beetles are “intuitive statisticians”?

          • Henry,
            Fish, insects, plants and rocks are also interesting, but these are rather irrelevant.
            .
            There is clear evidence that at a relatively late stage of their evolution APES acquired notions of probability . The ability to make decisions based on assessments of probabilities plainly enhanced their survival prospects, especially in the case of the most advanced and successful apes, namely HUMANS.
            .
            Prof Syll’s theorizes that in “real world open systems there are no probabilities to be had!”. However, the evidence is clear: humans and other apes DO have notions of probability which are important for their success in life.

            • Kingsley,

              “Fish, insects, plants and rocks are also interesting, but these are rather irrelevant.”

              They are not irrelevant.

              You are making the argument that humans survived because they somehow used probability to survive.

              I’m suggesting that it follows from your argument that if animals have also survived then they have also somehow used probability to survive.

              However, I think it might be difficult to argue that animals in general (such as fish and beetles) used probability to survive.

              It follows that your argument that humans used probability to survive is weakened, if not invalid, or reduced to a wild assertion.

              The abstract of the paper you quoted says there is evidence that primates and human infants use intuitive statistics. The abstract makes no reference, as far as I can see, to using this intuitive instinct to survive. This your surmise.

              I would say rather than invoking the notion of probability to survive, it might be better to see survival as a learning process. And, of course, there is much evidence that animals learn.

              • Henry,
                Different species have different survival skills. Many species have special abilities, e.g:
                bats – echolocation
                sharks – electroreception
                snakes – venomous bites
                dogs – acute sense of smell
                humans – high intelligence, including probabilistic thinking.
                Echolocation is essential for bats even though other species do not have this faculty.
                Probabilistic thinking is essential for humans even though other species do not have this faculty.
                .
                You express doubts about whether probabilistic thinking gives humans a survival advantage. However:
                – most of the distinctive features of a species evolved for a reason
                – there is much evidence that humans do commonly assess prospective risks and rewards when planning actions, and that success at doing this increases their chances of success in life.
                .
                This is certainly not a new idea. For example:
                “We are pattern seekers, believers in a coherent world, in which regularities appear not by accident but as a result of mechanical causality or of someone’s intention. We do not expect to see regularity produced by a random process, and when we detect what appears to be a rule, we quickly reject the idea that the process is truly random. Random processes produce many sequences that convince people that the process is not random after all. You can see why assuming causality could have evolutionary advantages. It is part of the general vigilance that we have inherited from ancestors.”
                Daniel Kahneman (2002 Nobel Prize in Economics) – “Thinking, Fast and Slow”

                “Reasoning under uncertainty is the bread and butter of everyday life. Many areas of psychology, from cognitive, developmental, social, to clinical, are interested in how individuals make inferences and decisions with incomplete information. The ability to reason under uncertainty necessarily involves probability computations, be they exact calculations or estimations. ”
                Denison & Xu 2014
                https://www.researchgate.net/publication/259504371_The_origins_of_probabilistic_inference_in_human_infants
                .
                A study of indigenous Maya people finds probabilistic reasoning does not depend on formal education.
                https://www.nature.com/news/humans-have-innate-grasp-of-probability-1.16271
                .
                Are great apes able to reason from multi-item samples to populations of food items?
                https://www.psych.uni-goettingen.de/de/development/pdfs/Eckert_et_al_2017-American_Journal_of_Primatology.pdf
                .
                S Placi – ‎2018 – Do long-tailed macaques engage in intuitive statistics?
                https://www.biorxiv.org/content/biorxiv/early/2018/01/17/247635.full.pdf

      • The full unpaywalled paper is available at:
        http://www.eva.mpg.de/documents/Elsevier/Rakoczy_Apes_Cognition_2014_1920316.pdf

    • I think your “probable” reconstruction of primitive thought says more about you than ancient humans or animals. When you spend enough time outdoors immersed in nature, you don’t worry about time. You learn to take what comes, without needing to predict and plan. Functions are a terrible way to represent nature. Water for example has no mathematical equation of state because water, like so much in nature, is inconsistent, contradictory, not susceptible to math. Math assumes the Law of Noncontradiction but nature does not. Math harps on consistency at the expense of completeness; nature is complete and inconsistent.

      Animal studies, again, say more about the researchers than about animals.

  2. “Just as there is no such thing as a ‘free lunch,’”

    Right now you can borrow US dollars, swap into Euros, and get paid back more dollars than you have to pay back. The persistent, decades-long violation of covered interest parity in currency swap markets is a free lunch.


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