What is a model? How does it relate to reality? This question has been discussed thoroughly in previous post on Models and Reality , and briefly in previous lectures. Western understanding of models was derailed by a complex set of historical accidents. This is a tangled tale with bewildering twists and turns, some aspects of which are discussed in “Deification of Science and Its Disastrous Consequence“, and some others in Logical Positivism and Islamic Economics . The reason we need to tell this story is because without understanding it, it is impossible to understand why Friedman could say, without being laughed out of court, that “Truly important and significant hypotheses will be found to have “assumptions” that are wildly inaccurate descriptive representations of reality, and, in general, the more significant the theory, the more unrealistic the assumptions.” Similarly, how could Lucas and Sargent make assumptions that are certifiably crazy, and receive Nobel Prizes and accolades? To understand why completely crazy understanding of models currently dominates the economics profession, it is necessary to understand some aspects of this story. Nonetheless, it is too long and difficult a task, so we will vastly oversimplify, and pin all the blame on poor stodgy German philosopher Kant — not that he does not deserve a lot of blame, but he also had a lot of accomplices, both before and after. A more nuanced account must be left for a much longer treatment by someone much more knowledgeable about Western philosophy and intellectual history. For students of economics, a brief explanation can be provided by looking at a key turning point, called a “Copernican Revolution” by Kant himself:
Kant’s Blunder: Kant argued that the nature of hidden reality, which generates the observations that we see, CANNOT be known to us. This is true almost by definition, since observations are all we can see – we can only guess at the nature of the hidden reality (Thing-In-Itself), and our guesses can never be confirmed by cross-checking against the truth, because the truth about hidden reality will never be accessible to us. So far so good – we have no disagreement with this. HOWEVER, from the impossibility of getting certain knowledge about hidden reality, Kant argued that we should ABANDON this pursuit, and give up on trying to make guesses, which can never be confirmed, about hidden realities. Instead we should focus on a different problem: how does our mind assemble and organize what we observe, to create a coherent mental picture of reality. A diagram can help us to understand Kant:
The underlying idea, which I have called Kant’s Blunder, is that if we have to guess at something, and can never be certain about our guess, then we should not make such guesses. This is an outcome of the idea that REASONING is the central tool for the acquisition — while guesswork, intuition, plausiblity, heart-knowledge — these are all anti-thetical to rational knowledge. This drive for certainty based on logic and rationality, which is embedded with current Western conceptions of knowledge, has led to hopelessly bad misconceptions about the nature of knowledge, and how we should approach the acquisition of knowledge. Western philosophy has been unable to recover from the false track on which Kant put it; as a result, current concepts about the nature of models and their relation to reality are hopelessly muddled. See my lecture on The Search for Knowledge to understand more details about an Islamic approach to knowledge, and how it is dramatically different from Western conceptions. Despite the fact that Kant is seriously wrong, and his misconception is seriously damaging to our quest for knowledge, his ideas became widely accepted, and continue to underlie modern notions of knowledge in the West.
Why is Kant wrong? Basically the idea that knowledge must be JTB: Justified True Belief, sets the bar for knowledge too high. This level of certainty is almost impossible to achieve. We operate in our daily lives with a much lower level of certainty. The idea that if we cannot achieve certainty, we should ABANDON the attempt to guess, would lead to paralysis. When I am driving, I am constantly guessing at what other drivers intend to do – whether they are going to go speeding through the red light, or stop, for example. Very often, my life, and that of others depends on such guesses. We don’t think that since I cannot be sure about such guesses – how can I be certain about the intentions of the person sitting behind the wheel – I should abandon the attempt to make such guesses. Simlarly, in our personal relationships, in nearly all important aspects of our life experiences, our decisions are guided by guesses about possible future outcomes which would result from our actions. Abandoning making such guesses because we cannot have certainty about them is almost unthinkable. Yet this is precisely the principle that Kant advocates.
Once we accept the idea of Kant, that there is no need to check for a match between our mental models and the hidden reality which generates the observations, there is no longer any need to confine our models to sensible ideas about what might be hidden beneath the surface observations. The only criteria for a good model is whether or not it can generate a good match to observations. This is sometimes called “Saving the Appearances”. An example will serve to illustrate and clarify.
When I was in graduate school at Stanford, top ranked game theorists Robert Aumann and Mordecai Kurz, discussed a paper in our classes regarding tax structure. They considered a game where any coalition can form, and the majority coalition can enforce any tax rule it likes on the whole group. This game turns out to have a trivial solution. If N+1 is the smallest majority coalition, this coalition will form and tax away EVERYTHING from the minority, taking it for themselves. Now this has no resemblance to the tax structures we see in the real world. So this is not a good model. Aumann and Kurz thought about how to get more realistic outcomes. They modified the game as follows. Those in the minority have one additional move which they can make. They can simply burn their entire endowment, instead of giving it up in taxes. This forces the majority to make less draconian tax levies, to ensure that the minority prefers to pay taxes rather than burn their possessions. With this slight modification, the tax structures which emerge from solving the game appear a lot more realistic. The paper they co-authored looks at the match between the outcomes of the game and real world tax rules in the USA, and finds it a reasonable fit.
On the traditional approach of matching model with reality, we would IMMEDIATELY reject Aumman-Kurz taxation model — it is completely ludicrous, and has no relationship with how tax laws are made in the Congress. However, on the Kantian understand of models, this lack of realism has no bearing on whether or not the model is good. This is exactly in line with the Friedman quote, that models can be “wildly inaccurate” as descriptions of reality. This then is the conventional Western understanding of models, as exposited in modern textbooks of economic theory, which cite Friedman’s methodological approach with approval.
In our Macro course, we will work with a radically different understanding of what models are, and how they function. Models are not meant for producing a match to observations. Nor do they provide accurate maps of the hidden reality which produced the observations. Rather, models are extreme simplifications of a complex reality, designed to enable us to understand the real world. Models are meant to be easy to understand, to strip away elements which are not essential, and to highlight and focus on the central elements of the real world which produce the phenomenon we would like to study. It must be emphasized that the goal of models is to help us UNDERSTAND reality — not necessarily to facilitate predictions, nor to produce good match to observations. Again it is helpful to provide an explicit example.
What Keynes was trying to understand was unemployment. According to economic theory, the free market automatically eliminates unemployment. Anyone who wants a job at the going wage rate can find one. This is in conflict with our own observations and experience — all of the students are anxious about whether or not they will be able to find jobs after graduation! Keynes also witnessed large scale unemployment in England, and in other advanced economies of the time. He wanted to understand why this happened, especially since it was in conflict with dominant economic theories at that time. Models help us to achieve such understanding. To see how, let us try to construct a model in which we can see the phenomenon of unemployment.
Note that our model must contain some employers and some employees. That is why we have some landlords, and some laborers in our models. Now let us look for the simplest possible model in which unemployment can be observed. As students soon saw in class, with fixed proportions technology, every landlord can only employ laborers upto the number of acres that he has — with 5 Acres, a maximum of 5 laborers. Beyond that, laborers cannot add to production and are useless. So a clear and simple model with unemployment is one where we have an excess of labor, beyond the maximum possible to employ usefully. Note that even though this model is completely unrealistic and inaccurate, it provides a reasonable explanation for unemployment which would be transferable to the far more complicated real world. If labor is already being utilized in all jobs, and the economy is at its maximum possible productive capacity, then further labor cannot be used, and will therefore be unemployed.
However, this simple model is NOT useful for understanding the kind of unemployment witnessed by Keynes. That is because the economy was functioning at full capacity just prior to the Great Depression, and unemployment rates were near 3% in the USA. This shot up to nearly 25%, and remained above 10% until WW2. So economy was not working at full capacity. Hence the mystery: the economy was capable of providing jobs to nearly all seekers, and had done so in the past. Without any material changes, the same economy was not providing jobs. We seek to build a model to understand why.
The simple model discussed earlier has some very interesting features. The marginal product for each laborer is 10 units of corn — this remains constant from the 1st to the 40th laborer. The real wage is significantly lower — it is 7.5 units of corn in the baseline model. Every landlord wants to hire more laborer. All laborers want to get jobs because they would starve to death otherwise. Now it is a real puzzle as to WHY unemployment would exist in such a model. If we can make plausible how unemployment could arise in such a model, we have some hope of understanding how it could happen in the real world. Note that our model, while extremely simple, is nonetheless fairly realistic. The assumptions are line with reasonable beliefs about the real world. The point of simplicity is NOT to be wildly unrealistic — the point is to show that all of extremely complex worldly structures are not needed to produce (and hence to understand) unemployment. If we can produce unemployment with an extremely small number of operational factors which drive the model, then we have an explanation of unemployment, which leads us to some understanding of the real world mechanisms which cause unemployment. This is always subject to Kant’s warning — we can never be sure of the truth of our models. But we make plans for tomorrow without being sure that we will be alive; similarly, working with models, and with guesswork, without certainties, is part of the human condition. In fact it is not at all easy to come up with a model which will produce unemployment under the set of conditions which the model satisfies — marginal product of labor is higher than wages, so every landlord wants to hire, and the economy has ample capacity — many more acres of land than laborers required to work them. It was the genius of Keynes to discover a REASONABLE model (not a grotesque Friedmanian caricature of a model) which could create unemployment for reasons which we can understand. This model was discussed in the previous lectures, and will be discussed some more today. This particular post is restricted to a discussion of the approach to modeling we take in this course, and how this is different from the standard approach currently in use in economics.