The assumption of additivity and linearity means that the outcome variable is, in reality, linearly related to any predictors … and that if you have several predictors then their combined effect is best described by adding their effects together …
This assumption is the most important because if it is not true then even if all other assumptions are met, your model is invalid because you have described it incorrectly. It’s a bit like calling your pet cat a dog: you can try to get it to go in a kennel, or to fetch sticks, or to sit when you tell it to, but don’t be surprised when its behaviour isn’t what you expect because even though you’ve called it a dog, it is in fact a cat. Similarly, if you have described your statistical model inaccurately it won’t behave itself and there’s no point in interpreting its parameter estimates or worrying about significance tests of confidence intervals: the model is wrong.
On Monday the World Bank made it official that Paul Romer will be the new chief economist. This nomination can be seen as a big step back toward the infamous Washington Consensus, which World Bank and IMF seemed to have left behind. This is true, even though Paul Romer has learned quite well to hide the market fundamentalist and anti-democratic nature of his pet idea – charter cities – behind a veil of compassionate wording …
Since about 2009 he has been promoting so-called charter cities as a model for development … His proposal amounts to declaring enlightened colonialism to be the best (or even only) way toward development of poor countries, and a good substitute to development aid …
Romer has in mind a version of the Hong Kong case, without the coercion. His cities are supposed to be extreme forms of free enterprise zones which some developing countries, including China, have been experimenting with for quite a while. The idea of the latter is to attract foreign investors by exempting them from certain regulations, duties etc. His charters cities go further. They build on the wholesale abrogation of all laws of the respective country. For countries with dysfunctional public institutions he suggested that they lease out the regions, where these charter cities are to be build, long-term to a consortium of enlightend industrial countries, which would do the management. What the British extracted at gunpoint from China, developing countries are expected to give voluntarily today. A World Bank manager commented on the idea in 2010 on the blog of the World Bank by quoting a magazine article, which called it “not only neo-medieval, but also neo-colonial”.
The libertarian spirit of the idea of the man who will be the World Bank’s chief economist from September reminds of the Washington Consensus that ruled into the 1990s. This is a name for the ideological position, enforced by World Bank and IMF, that the best and only way to development is the scrapping of government regulation and giving companies a maximum of freedom to go about their business.
What we discover is that the cash value of these laws lies beneath the surface — in the extent to which they approximate the behaviour of real gases or substances, since such substances do not exist in the world …
Notice that we are here regarding it as grounds for complaint that such claims are ‘reduced to the status of definitions’ … Their truth is obtained at a price, namely that they cease to tell us about this particular world and start telling us about the meaning of words instead …
The ultimate reduction to triviality makes the claim definitionally true, and obviously so, in which case it’s worth nothing to those who already know the language …
One of the main cruxes of economics laws — and regularities — is that they only hold ceteris paribus. That fundamentally means that these laws/regularites only hold when the right conditions are at hand for giving rise to them. Unfortunately, from an empirical point of view, those conditions are only at hand in artificially closed nomological models purposely designed to give rise to the kind of regular associations that economists want to explain. But, really, since these laws/regularities do not exist outside these ‘socio-economic machines,’ what’s the point in constructing these non-existent laws/regularities? When the almost endless list of narrow and specific assumptions necessary to allow the ‘rigorous’ deductions are known to be at odds with reality, what good do these models do?
Take ‘The Law of Demand.’
Although it may (perhaps) be said that neoclassical economics had succeeded in establishing The Law – when the price of a commodity falls, the demand for it will increase — for single individuals, it soon turned out, in the Sonnenschein-Mantel-Debreu theorem, that it wasn’t possible to extend The Law to apply on the market level, unless one made ridiculously unrealistic assumptions such as individuals all having homothetic preferences – which actually implies that all individuals have identical preferences.
This could only be conceivable if there was in essence only one actor – the (in)famous representative actor. So, yes, it was possible to generalize The Law of Demand – as long as we assumed that on the aggregate level there was only one commodity and one actor. What generalization! Does this sound reasonable? Of course not. This is pure nonsense!
How has neoclassical economics reacted to this devastating findig? Basically by looking the other way, ignoring it and hoping that no one sees that the emperor is naked.
Modern mainstream neoclassical textbooks try to describe and analyze complex and heterogeneous real economies with a single rational-expectations-robot-imitation-representative-agent. That is, with something that has absolutely nothing to do with reality. And – worse still – something that is not even amenable to the kind of general equilibrium analysis that they are thought to give a foundation for, since Hugo Sonnenschein (1972) , Rolf Mantel (1976) and Gerard Debreu (1974) unequivocally showed that there did not exist any condition by which assumptions on individuals would guarantee neither stability nor uniqueness of the equlibrium solution.
Of course one could say that it is too difficult on undergraduate levels to show why the procedure is right and to defer it to masters and doctoral courses. It could justifiably be reasoned that way – if what you teach your students is true, if The Law of Demand is generalizable to the market level and the representative actor is a valid modeling abstraction! But in this case it’s demonstrably known to be false, and therefore this is nothing but a case of scandalous intellectual dishonesty. It’s like telling your students that 2 + 2 = 5 and hope that they will never run into Peano’s axioms of arithmetics.
As Hans Albert has it:
The neoclassical style of thought – with its emphasis on thought experiments, reflection on the basis of illustrative examples and logically possible extreme cases, its use of model construction as the basis of plausible assumptions, as well as its tendency to decrease the level of abstraction, and similar procedures – appears to have had such a strong influence on economic methodology that even theoreticians who strongly value experience can only free themselves from this methodology with difficulty …
Clearly, it is possible to interpret the ‘presuppositions’ of a theoretical system … not as hypotheses, but simply as limitations to the area of application of the system in question. Since a relationship to reality is usually ensured by the language used in economic statements, in this case the impression is generated that a content-laden statement about reality is being made, although the system is fully immunized and thus without content. In my view that is often a source of self-deception in pure economic thought …
Although the expected utility theory is obviously both theoretically and descriptively inadequate, colleagues and microeconomics textbook writers gladly continue to use it, as though its deficiencies were unknown or unheard of.
Daniel Kahneman writes — in Thinking, Fast and Slow — that expected utility theory is seriously flawed since it doesn’t take into consideration the basic fact that people’s choices are influenced by changes in their wealth. Where standard microeconomic theory assumes that preferences are stable over time, Kahneman and other behavioural economists have forcefully again and again shown that preferences aren’t fixed, but vary with different reference points. How can a theory that doesn’t allow for people having different reference points from which they consider their options have an almost axiomatic status within economic theory?
The mystery is how a conception of the utility of outcomes that is vulnerable to such obvious counterexamples survived for so long. I can explain it only by a weakness of the scholarly mind … I call it theory-induced blindness: once you have accepted a theory and used it as a tool in your thinking it is extraordinarily difficult to notice its flaws … You give the theory the benefit of the doubt, trusting the community of experts who have accepted it … But they did not pursue the idea to the point of saying, “This theory is seriously wrong because it ignores the fact that utility depends on the history of one’s wealth, not only present wealth.”
On a more economic-theoretical level, information theory — and especially the so called Kelly criterion — also highlights the problems concerning the neoclassical theory of expected utility.
Suppose I want to play a game. Let’s say we are tossing a coin. If heads comes up, I win a dollar, and if tails comes up, I lose a dollar. Suppose further that I believe I know that the coin is asymmetrical and that the probability of getting heads (p) is greater than 50% – say 60% (0.6) – while the bookmaker assumes that the coin is totally symmetric. How much of my bankroll (T) should I optimally invest in this game?
A strict neoclassical utility-maximizing economist would suggest that my goal should be to maximize the expected value of my bankroll (wealth), and according to this view, I ought to bet my entire bankroll.
Does that sound rational? Most people would answer no to that question. The risk of losing is so high, that I already after few games played — the expected time until my first loss arises is 1/(1-p), which in this case is equal to 2.5 — with a high likelihood would be losing and thereby become bankrupt. The expected-value maximizing economist does not seem to have a particularly attractive approach.
So what’s the alternative? One possibility is to apply the so-called Kelly criterion — after the American physicist and information theorist John L. Kelly, who in the article A New Interpretation of Information Rate (1956) suggested this criterion for how to optimize the size of the bet — under which the optimum is to invest a specific fraction (x) of wealth (T) in each game. How do we arrive at this fraction?
When I win, I have (1 + x) times as much as before, and when I lose (1 – x) times as much. After n rounds, when I have won v times and lost n – v times, my new bankroll (W) is
(1) W = (1 + x)v(1 – x)n – v T
[A technical note: The bets used in these calculations are of the “quotient form” (Q), where you typically keep your bet money until the game is over, and a fortiori, in the win/lose expression it’s not included that you get back what you bet when you win. If you prefer to think of odds calculations in the “decimal form” (D), where the bet money typically is considered lost when the game starts, you have to transform the calculations according to Q = D – 1.]
The bankroll increases multiplicatively — “compound interest” — and the long-term average growth rate for my wealth can then be easily calculated by taking the logarithms of (1), which gives
(2) log (W/ T) = v log (1 + x) + (n – v) log (1 – x).
If we divide both sides by n we get
(3) [log (W / T)] / n = [v log (1 + x) + (n – v) log (1 – x)] / n
The left hand side now represents the average growth rate (g) in each game. On the right hand side the ratio v/n is equal to the percentage of bets that I won, and when n is large, this fraction will be close to p. Similarly, (n – v)/n is close to (1 – p). When the number of bets is large, the average growth rate is
(4) g = p log (1 + x) + (1 – p) log (1 – x).
Now we can easily determine the value of x that maximizes g:
(5) d [p log (1 + x) + (1 – p) log (1 – x)]/d x = p/(1 + x) – (1 – p)/(1 – x) =>
p/(1 + x) – (1 – p)/(1 – x) = 0 =>
(6) x = p – (1 – p)
Since p is the probability that I will win, and (1 – p) is the probability that I will lose, the Kelly strategy says that to optimize the growth rate of your bankroll (wealth) you should invest a fraction of the bankroll equal to the difference of the likelihood that you will win or lose. In our example, this means that I have in each game to bet the fraction of x = 0.6 – (1 – 0.6) ≈ 0.2 — that is, 20% of my bankroll. Alternatively, we see that the Kelly criterion implies that we have to choose x so that E[log(1+x)] — which equals p log (1 + x) + (1 – p) log (1 – x) — is maximized. Plotting E[log(1+x)] as a function of x we see that the value maximizing the function is 0.2:
The optimal average growth rate becomes
(7) 0.6 log (1.2) + 0.4 log (0.8) ≈ 0.02.
If I bet 20% of my wealth in tossing the coin, I will after 10 games on average have 1.0210 times more than when I started (≈ 1.22).
This game strategy will give us an outcome in the long run that is better than if we use a strategy building on the neoclassical economic theory of choice under uncertainty (risk) – expected value maximization. If we bet all our wealth in each game we will most likely lose our fortune, but because with low probability we will have a very large fortune, the expected value is still high. For a real-life player – for whom there is very little to benefit from this type of ensemble-average – it is more relevant to look at time-average of what he may be expected to win (in our game the averages are the same only if we assume that the player has a logarithmic utility function). What good does it do me if my tossing the coin maximizes an expected value when I might have gone bankrupt after four games played? If I try to maximize the expected value, the probability of bankruptcy soon gets close to one. Better then to invest 20% of my wealth in each game and maximize my long-term average wealth growth!
When applied to the neoclassical theory of expected utility, one thinks in terms of “parallel universe” and asks what is the expected return of an investment, calculated as an average over the “parallel universe”? In our coin toss example, it is as if one supposes that various “I” are tossing a coin and that the loss of many of them will be offset by the huge profits one of these “I” does. But this ensemble-average does not work for an individual, for whom a time-average better reflects the experience made in the “non-parallel universe” in which we live.
The Kelly criterion gives a more realistic answer, where one thinks in terms of the only universe we actually live in, and ask what is the expected return of an investment, calculated as an average over time.
Since we cannot go back in time — entropy and the “arrow of time ” make this impossible — and the bankruptcy option is always at hand (extreme events and “black swans” are always possible) we have nothing to gain from thinking in terms of ensembles and “parallel universe.”
Actual events follow a fixed pattern of time, where events are often linked in a multiplicative process (as e. g. investment returns with “compound interest”) which is basically non-ergodic.
Instead of arbitrarily assuming that people have a certain type of utility function – as in the neoclassical theory – the Kelly criterion shows that we can obtain a less arbitrary and more accurate picture of real people’s decisions and actions by basically assuming that time is irreversible. When the bankroll is gone, it’s gone. The fact that in a parallel universe it could conceivably have been refilled, are of little comfort to those who live in the one and only possible world that we call the real world.
Our coin toss example can be applied to more traditional economic issues. If we think of an investor, we can basically describe his situation in terms of our coin toss. What fraction (x) of his assets (T) should an investor – who is about to make a large number of repeated investments – bet on his feeling that he can better evaluate an investment (p = 0.6) than the market (p = 0.5)? The greater the x, the greater is the leverage. But also – the greater is the risk. Since p is the probability that his investment valuation is correct and (1 – p) is the probability that the market’s valuation is correct, it means the Kelly criterion says he optimizes the rate of growth on his investments by investing a fraction of his assets that is equal to the difference in the probability that he will “win” or “lose.” In our example this means that he at each investment opportunity is to invest the fraction of x = 0.6 – (1 – 0.6), i.e. about 20% of his assets. The optimal average growth rate of investment is then about 2 % (0.6 log (1.2) + 0.4 log (0.8)).
Kelly’s criterion shows that because we cannot go back in time, we should not take excessive risks. High leverage increases the risk of bankruptcy. This should also be a warning for the financial world, where the constant quest for greater and greater leverage – and risks – creates extensive and recurrent systemic crises. A more appropriate level of risk-taking is a necessary ingredient in a policy to come to curb excessive risk taking.
The works of people like Kelly and Kahneman show that expected utility theory is indeed a serious case of theory-induced blindness that transmogrifies truth.
Chameleons arise and are often nurtured by the following dynamic. First a bookshelf model is constructed that involves terms and elements that seem to have some relation to the real world and assumptions that are not so unrealistic that they would be dismissed out of hand. The intention of the author, let’s call him or her “Q,” in developing the model may to say something about the real world or the goal may simply be to explore the implications of making a certain set of assumptions. Once Q’s model and results become known, references are made to it, with statements such as “Q shows that X.” This should be taken as short-hand way of saying “Q shows that under a certain set of assumptions it follows (deductively) that X,” but some people start taking X as a plausible statement about the real world. If someone skeptical about X challenges the assumptions made by Q, some will say that a model shouldn’t be judged by the realism of its assumptions, since all models have assumptions that are unrealistic. Another rejoinder made by those supporting X as something plausibly applying to the real world might be that the truth or falsity of X is an empirical matter and until the appropriate empirical tests or analyses have been conducted and have rejected X, X must be taken seriously. In other words, X is innocent until proven guilty. Now these statements may not be made in quite the stark manner that I have made them here, but the underlying notion still prevails that because there is a model for X, because questioning the assumptions behind X is not appropriate, and because the testable implications of the model supporting X have not been empirically rejected, we must take X seriously. Q’s model (with X as a result) becomes a chameleon that avoids the real world filters.
The best way to illustrate what chameleons are is to give some actual examples …
In April 2012 Harry DeAngelo and René Stulz circulated a paper entitled “Why High Leverage is Optimal for Banks.” The title of the paper is important here: it strongly suggests that the authors are claiming something about actual banks in the real world. In the introduction to this paper the authors explain what their model is designed to do:
“To establish that high bank leverage is the natural (distortion-free) result of intermediation focused on liquid-claim production, the model rules out agency problems, deposit insurance, taxes, and all other distortionary factors. By positing these idealized conditions, the model obviously ignores some important determinants of bank capital structure in the real world. However, in contrast to the MM framework – and generalizations that include only leverage-related distortions – it allows a meaningful role for banks as producers of liquidity and shows clearly that, if one extends the MM model to take that role into account, it is optimal for banks to have high leverage.” [emphasis added]
Their model, in other words, is designed to show that if we rule out many important things and just focus on one factor alone, we obtain the particular result that banks should be highly leveraged. This argument is for all intents and purpose analogous to the argument made in another paper entitled “Why High Alcohol Consumption is Optimal for Humans” by Bacardi and Mondavi. In the introduction to their paper Bacardi and Mondavi explain what their model does:
“To establish that high intake of alcohol is the natural (distortion free) result of human liquid-drink consumption, the model rules out liver disease, DUIs, health benefits, spousal abuse, job loss and all other distortionary factors. By positing these idealized conditions, the model obviously ignores some important determinants of human alcohol consumption in the real world. However, in contrast to the alcohol neutral framework – and generalizations that include only overconsumption- related distortions – it allows a meaningful role for humans as producers of that pleasant “buzz” one gets by consuming alcohol, and shows clearly that if one extends the alcohol neutral model to take that role into account, it is optimal for humans to be drinking all of their waking hours.”[emphasis added]
Deangelo and Stulz model is clearly a bookshelf theoretical model that would not pass through any reasonable filter if we want to take its results and apply them directly to the real world. In addition to ignoring much of what is important (agency problems, taxes, systemic risk, government guarantees, and other distortionary factors), the results of their main model are predicated on the assets of the bank being riskless and are based on a posited objective function that is linear in the percentage of assets funded with deposits. Given this the authors naturally obtain a corner solution with assets 100% funded by deposits. (They have no explicit model addressing what happens when bank assets are risky, but they contend that bank leverage should still be “high” when risk is present) …
DeAngelo and Stulz paper is a good illustration of my claim that one can generally develop a theoretical model to produce any result within a wide range. Do you want a model that produces the result that banks should be 100% funded by deposits? Here is aset of assumptions and an argument that will give you that result. That such a model exists tells us very little. By claiming relevance without running it through the filter it becomes a chameleon …
Whereas some theoretical models can be immensely useful in developing intuitions, in essence a theoretical model is nothing more than an argument that a set of conclusions follows from a given set of assumptions. Being logically correct may earn a place for a theoretical model on the bookshelf, but when a theoretical model is taken off the shelf and applied to the real world, it is important to question whether the model’s assumptions are in accord with what we know about the world. Is the story behind the model one that captures what is important or is it a fiction that has little connection to what we see in practice? Have important factors been omitted? Are economic agents assumed to be doing things that we have serious doubts they are able to do? These questions and others like them allow us to filter out models that are ill suited to give us genuine insights. To be taken seriously models should pass through the real world filter.
Chameleons are models that are offered up as saying something significant about the real world even though they do not pass through the filter. When the assumptions of a chameleon are challenged, various defenses are made (e.g., one shouldn’t judge a model by its assumptions, any model has equal standing with all other models until the proper empirical tests have been run, etc.). In many cases the chameleon will change colors as necessary, taking on the colors of a bookshelf model when challenged, but reverting back to the colors of a model that claims to apply the real world when not challenged.
Reading Pfleiderer’s absolutely fabulous gem of an article reminded me of what H. L. Mencken once famously said:
There is always an easy solution to every problem – neat, plausible and wrong.
Pfleiderer’s perspective may be applied to many of the issues involved when modeling complex and dynamic economic phenomena. Let me take just one example — simplicity.
When it come to modeling I do see the point emphatically made time after time by e. g. Paul Krugman in simplicity — as long as it doesn’t impinge on our truth-seeking. “Simple” macroeconomic models may of course be an informative heuristic tool for research. But if practitioners of modern macroeconomics do not investigate and make an effort of providing a justification for the credibility of the simplicity-assumptions on which they erect their building, it will not fulfill its tasks. Maintaining that economics is a science in the “true knowledge” business, I remain a skeptic of the pretences and aspirations of “simple” macroeconomic models and theories. So far, I can’t really see that e. g. “simple” microfounded models have yielded very much in terms of realistic and relevant economic knowledge.
All empirical sciences use simplifying or unrealistic assumptions in their modeling activities. That is not the issue – as long as the assumptions made are not unrealistic in the wrong way or for the wrong reasons.
But models do not only face theory. They also have to look to the world. Being able to model a “credible world,” a world that somehow could be considered real or similar to the real world, is not the same as investigating the real world. Even though — as Pfleiderer acknowledges — all theories are false, since they simplify, they may still possibly serve our pursuit of truth. But then they cannot be unrealistic or false in any way. The falsehood or unrealisticness has to be qualified.
Explanation, understanding and prediction of real world phenomena, relations and mechanisms therefore cannot be grounded on simpliciter assuming simplicity. If we cannot show that the mechanisms or causes we isolate and handle in our models are stable, in the sense that what when we export them from are models to our target systems they do not change from one situation to another, then they – considered “simple” or not – only hold under ceteris paribus conditions and a fortiori are of limited value for our understanding, explanation and prediction of our real world target system.
The obvious ontological shortcoming of a basically epistemic – rather than ontological – approach, is that “similarity” or “resemblance” tout court do not guarantee that the correspondence between model and target is interesting, relevant, revealing or somehow adequate in terms of mechanisms, causal powers, capacities or tendencies. No matter how many convoluted refinements of concepts made in the model, if the simplifications made do not result in models similar to reality in the appropriate respects (such as structure, isomorphism etc), the surrogate system becomes a substitute system that does not bridge to the world but rather misses its target.
Constructing simple macroeconomic models somehow seen as “successively approximating” macroeconomic reality, is a rather unimpressive attempt at legitimizing using fictitious idealizations for reasons more to do with model tractability than with a genuine interest of understanding and explaining features of real economies. Many of the model assumptions standardly made by neoclassical macroeconomics – simplicity being one of them – are restrictive rather than harmless and could a fortiori anyway not in any sensible meaning be considered approximations at all.
If economists aren’t able to show that the mechanisms or causes that they isolate and handle in their “simple” models are stable in the sense that they do not change when exported to their “target systems”, they do only hold under ceteris paribus conditions and are a fortiori of limited value to our understanding, explanations or predictions of real economic systems.
That Newton’s theory in most regards is simpler than Einstein’s is of no avail. Today Einstein has replaced Newton. The ultimate arbiter of the scientific value of models cannot be simplicity.
As scientists we have to get our priorities right. Ontological under-labouring has to precede epistemology.
Footnote: And of course you understood that the Bacardi/Mondavi paper is fictional. Or?
Ja hur ska man reagera på dessa uttryck för oförblommerat svinaktig rasism?
Kanske med att lyssna på Olof Palme
Reasoning is the process whereby we get from old truths to new truths, from the known to the unknown, from the accepted to the debatable … If the reasoning starts on firm ground, and if it is itself sound, then it will lead to a conclusion which we must accept, though previously, perhaps, we had not thought we should. And those are the conditions that a good argument must meet; true premises and a good inference. If either of those conditions is not met, you can’t say whether you’ve got a true conclusion or not.
Neoclassical economic theory today is in the story-telling business whereby economic theorists create make-believe analogue models of the target system – usually conceived as the real economic system. This modeling activity is considered useful and essential. Since fully-fledged experiments on a societal scale as a rule are prohibitively expensive, ethically indefensible or unmanageable, economic theorists have to substitute experimenting with something else. To understand and explain relations between different entities in the real economy the predominant strategy is to build models and make things happen in these “analogue-economy models” rather than engineering things happening in real economies.
Neoclassical economics has since long given up on the real world and contents itself with proving things about thought up worlds. Empirical evidence only plays a minor role in economic theory, where models largely function as a substitute for empirical evidence. The one-sided, almost religious, insistence on axiomatic-deductivist modeling as the only scientific activity worthy of pursuing in economics, is a scientific cul-de-sac. To have valid evidence is not enough. What economics needs is sound evidence.
Avoiding logical inconsistencies is crucial in all science. But it is not enough. Just as important is avoiding factual inconsistencies. And without showing — or at least warrantedly arguing — that the assumptions and premises of their models are in fact true, mainstream economists aren’t really reasoning, but only playing games. Formalistic deductive “Glasperlenspiel” can be very impressive and seductive. But in the realm of science it ought to be considered of little or no value to simply make claims about the model and lose sight of reality.
Econometricians usually think that the data generating process (DGP) always can be modelled properly using a probability measure. The argument is standardly based on the assumption that the right sampling procedure ensures there will always be an appropriate probability measure. But – as always – one really has to argue the case, and present warranted evidence that real-world features are correctly described by some probability measure.
There are no such things as free-standing probabilities – simply because probabilities are strictly seen only defined relative to chance set-ups – probabilistic nomological machines like flipping coins or roulette-wheels. And even these machines can be tricky to handle. Although prob(fair coin lands heads|I toss it) = prob(fair coin lands head & I toss it)|prob(fair coin lands heads) may be well-defined, it’s not certain we can use it, since we cannot define the probability that I will toss the coin given the fact that I am not a nomological machine producing coin tosses.
No nomological machine – no probability.
A chance set-up is a nomological machine for probabilistic laws, and our description of it is a model that works in the same way as a model for deterministic laws … A situation must be like the model both positively and negatively – it must have all the characteristics featured in the model and it must have no significant interventions to prevent it operating as envisaged – before we can expect repeated trials to give rise to events appropriately described by the corresponding probability …
Probabilities attach to the world via models, models that serve as blueprints for a chance set-up – i.e., for a probability-generating machine … Once we review how probabilities are associated with very special kinds of models before they are linked to the world, both in probability theory itself and in empirical theories like physics and economics, we will no longer be tempted to suppose that just any situation can be described by some probability distribution or other. It takes a very special kind of situation withe the arrangements set just right – and not interfered with – before a probabilistic law can arise …
Probabilities are generated by chance set-ups, and their characterisation necessarily refers back to the chance set-up that gives rise to them. We can make sense of probability of drawing two red balls in a row from an urn of a certain composition with replacement; but we cannot make sense of the probability of six per cent inflation in the United Kingdom next year without an implicit reference to a specific social and institutional structure that will serve as the chance set-up that generates this probability.