Home > Uncategorized > On randomness and probability in economics

On randomness and probability in economics

from Lars Syll

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!

  1. June 18, 2018 at 7:28 pm

    I have often noticed that people who are older than 25 or so and who never learned to drive a car are very likely to never learn to drive. Indeed I have seen such people bridle at the suggestion they should learn even though driving is, well, useful if not necessary.
    I believe this is true for those who never learned in their youth about ordinary differential equations, coupled ordinary differential equations, or nonlinear coupled differential equations. When I see Steve Keen kajoling Paul Krugman to consider learning about this and Krugman’s reaction against learning this important math skill I see poor Keen shocked to see the same reaction I have seen in one who is too old to learn how to drive.

    • Craig
      June 18, 2018 at 9:26 pm

      Keen is good at looking at problems like the fact that neo-liberalism is incorrect in using only linear equations. He’s not so good at perceiving either the current problematic paradigm of Finance, namely Debt/Burden as virtually the only vehicle and form for the distribution of credit/money, or the new paradigm of Direct and Reciprocal Monetary Gifting.

      Also, being somewhat overly abstract as nearly all economists are he doesn’t contemplate the present time actions of commerce (exchange). Nor does he have a good understanding of the digital nature of the discipline that underlies that exchange and how that nature could be utilized to linearize tremendously beneficial monetary and economic policy effects DIRECTLY to the individual AND RECIPROCALLY to enterprise.

      Hence he’s still trapped within the current paradigm and can only suggest “epicycle” policies instead of realizing the paradigm changing ones derived from directly looking at the above.

  2. June 19, 2018 at 6:48 am

    It is necessary to remember Warren Weaver’s three classes of problems which were exposed in his seminal Science and Complexity paper (1948):

    http://rule11.tech/papers/1948%20Science%20and%20complexity%20%28Weaver%29.pdf

    Weaver was in information theory an eminent researcher who has a co-authored book with Claude Shannon. Excepting problems of simplicity, which were targets of modern physics until the 19th century, Weaver distinguished problems of disorganized complexity and organized complexity. Probability theory is extremely useful for problems of disorganized complexity. It was successfully applied to statistical mechanics and then quantum statistical mechanics. However, Weaver knew well that there are many fields which cannot be treated as disorganized complexity (or simplicity). At the occasion he retires from the Science and Medicine Division of Rockefeller Foundation, he expressed his view on which direction the sciences should be developed in the next half century. This was a bit too premature prediction, because real science of complexity barely starts in 1970’s.

    Economy belongs to the problems of organized complexity. Probability and statistics have only limited applicability. Complex systems of the second category (i.e. disorganized complexity) should develop new methods and tools of analysis. Mainstream economists did not proceeded in this direction and was satisfied with what they can do with probability and statistics. They are attacking problems of organized complexity with the means and tools which were successful for problems of disorganized complexity.

    P.S. Ordinary differential equations (whether they are linear or non-linear) are essentially tools for problems of simplicity. Mathematics has not yet developed suitable tools to attack problems of organized complexity. This is one of reasons that we should expect much in agent-based simulation. In short, theory and mathematics are the first mode of scientific method, experimentation the second mode. We need the third mode of scientific research method. See my paper:

    A Guided Tour of the Backside of Agent-Based Simulation.

    • Craig
      June 20, 2018 at 2:42 am

      That is a very good post and set of observations. However, economic theory is actually paradigm hypnotized organized complexity.

      • June 21, 2018 at 9:15 am

        Craig
        Thank you for your kind comment. Would you like to explain more concretely what you mean by “paradigm hypnotized organized complexity”? We may deepen our argument by chance.

      • Craig
        June 21, 2018 at 5:39 pm

        Being hypnotized is an unconscious state. Current paradigms are largely unconsiously accepted norms. Thus old/current paradigms generally lack full examination, and new ones are generally either rejected as illogical or not reacted to at all because the individual has no frame of reference regarding it.

        The current virtually monopolistic monetary paradigm for the vehicle and distribution of credit/money described as Privately Created Debt ONLY is a form of hypnotization that has become the unconsciously accepted norm, and its organized complexity and enforced lack of directness to the individual is coalescing as we sit debating instead of organizing.

        The only reason why the new paradigm of Direct and Reciprocal Monetary Gifting is not accepted and applauded is because:

        1) economists are not looking at the integratively micro-foundational character of double entry bookkeeping,

        2) its digital character (equal amounts of debits and credits equal to zero) is not being recognized

        3) the point of sale throughout the entirety of the economic/productive process is a temporary summing and ending point for all costs and prices for any item or service and the point of retail sale is the TERMINAL summing and
        ending point for same….and the terminal EXPRESSION POINT for any and all types of inflation as well.

        Thus, along with a universal dividend, a digital policy at these points of sale of equal discounts to the consumer and rebates back to merchants giving the discount would enable us to vastly increase individual purchasing power which would equally benefit both the individual and enterprise….and again, as retail sale is the terminal expression point for all inflation, not only eliminate inflation…but painlessly and beneficially integrate price deflation into profit making systems.

      • June 21, 2018 at 6:40 pm

        Dear Craig,
        I understand how economics is hypnotized paradigm. I agree with you. Those who believe in neoclassical theory are hypnotized.

        The question we must ask is how to dehypnotize those (perhaps including us). It must need a new paradigm.

      • Craig
        June 21, 2018 at 6:47 pm

        I hasten to add that this paradigm hypnotized organized complexity is also a mental-theoretical barrier to recognizing that the entire concept of “free” markets is fallacious. Markets are not just unstable….they are chaotic, that is they in fact are not bounded at all on the lower end by cost nor the upper end by price. In the temporal universe there is no such thing as total freedom….only freedom amongst known, rational and ethical barriers.

        Thus the dominatingly smothered economy by Private Finance’s monopolistic paradigm of Debt Only is the parasitical present “answer”…..and the incisive, proactive and tremendously beneficial policies of the new paradigm are the wise actual answer.

      • Craig
        June 21, 2018 at 7:09 pm

        We de-hypnotize ourselves and others by looking at and playing out the double entry bookkeeping/micro-foundational policy effects I outlined….and then integrating the very correct macro-economic critiques of neo-liberalism with those micro policies. And then begin organizing a movement to communicate the benefits of those policies to the small to medium sized business community and every individual who has the common sense to accept gifts of income and price reduction.

        In other words the integration of heterodox macro critique and the policies I outline IMPLEMENT the new paradigm….so lets take that ball and score six or seven social and political touchdowns with it.

  3. Helen Sakho
    June 19, 2018 at 12:11 pm

    I shall look up your paper, time allowing.
    But as my own Categories and emerging Subcategories were already oversaturated with nonsense for decades, could I respectfully ask you to take a look at chapter 3 or 4 of my PhD (written decades ago), which is now available online free of charge on Research Methodology?
    In all probability, you and I might well have something in common, except technological-animation skills of which I confess publicly I am profoundly sceptical to say the least. Written works are far more superior, simply because they cannot be changed, mimicked or erased all the time.

    • June 19, 2018 at 2:31 pm

      Helen,
      could you give me the reference to your PhD dissertation? I have searched it but could not find out a good one.

  4. Helen Sakho
  5. Helen Sakho
    June 22, 2018 at 2:22 pm

    You are welcome Yoshinori, I hope you find of some use.

  6. June 26, 2018 at 4:55 am

    Dear Helen Sakho

    After reading Chapter 4 of your dissertation paper, I found it very difficult to explain what is problems of organized complexity.

    You argue mainly qualitative research. For example, you enumerate four of five methods that Creswell examined in their Qualitative Inquiry and Research Design. They are: biography, grounded theory, ethnography, and case study. Certainly, they are methods which are related to organized complexity. But, main focus is different. In case of organized complexity, inquiries are addressed to understand the relations between elements of a large system. If we take an example of economy, it is a system composed of many human agents and firms. Enormous number of transactions is always taking place. Problems of organized complexity try to understand these processes which are generated by actions of those economic agents.

    I have no intention to deny the significance of such researches likw qualitative research and grounded theory method in particular. But in view of problems of organized complexity, they seem to be preparatory works before attacking problems of organized complexity. Exploring organized complexity requires accumulation of qualitative and descriptive knowledge on individuals (or individual firms). To know how firms behave is important, but we cannot know how economy works by only having knowledge of firms. Behavior of a total system is not the sum of individual behaviors. In my understanding, Warren Weaver wanted to explore those complex relations, which we have not yet a good tool to analyze.

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