It is important to understand that there are three type of models, corresponding the following diagram. The simplest type of model is a pattern in the data that we observe. A second type of model is a “mental model”. This is a structure we create in our own minds, in order to understand the patterns that we see in the observations. The third type of model is a structure of the hidden real world, which generates the patterns that we see. Some examples will be helpful in clarifying these ideas about the typology of models.
Empirical Models: The simplest kind of model consists of a pattern that we see in the observations. For example, if we see the sun rise every day for many years, this is a pattern in our experience. It leads us to conjecture the law that “the sun rises every day” – where the law extends beyond the range of our experience and observations. This is just a guess, based on patterns we see in the data. A regression model is an excellent example of an empirical model. It identifies patterns in the data, without any concern for the underlying realities. For example, a regression of Australian consumption per capita on China’s GDP gives an excellent fit –
Australian Consumption = a + b Chinese GDP per capita + error (high R-squared, significant t-stats)
This shows us that there is a pattern in the data – increases in China’s GDP go along with increases in Australian consumption. The regression cannot answer the question of why there is this pattern. Any two series of data can display correlation – time series measuring numbers of sunspots sighted on the sun’s surface can correlate with a wide variety of economic phenomena. The regression model which picks up this relationship has nothing to say about the reasons for the correlation. Given any kind of data, we can always find some regression relationship. For example, here is a regression which has a strong fit, but no meaning.
Pakistani Consumption = a + b Survival rate to age 65 of Females + c Pollution Levels by Carbon Monoxide + error
In terms of classification – we can find many different kinds of patterns in any arbitrary set of data. Whether or not the patterns have meaning depend on the real-world processes which generate these patterns. This is something which Real Models are meant to explore.
Real (Structural) Models: The empirical models look at the surface structure, the appearances, the data that is based on observations. Structural models try to explore the hidden structure underneath the appearances. Consider for example a regression of consumption per capita on GNP per capita
C = a + b Y + epsilon
From the point of view of an empirical model, this is a pattern in the data. The names of the variables do not matter. If the consumption is Australian and the GNP is Chinese, the pattern is the same as if both variables belong to the same country. The names of the variable, and the relationships between them, matter only when we think about real structural models. For example, if we think that consumers earn incomes, and then spend some proportion of the income on consumer goods, this is a real structural relationship which explains why we see the pattern in the regression relationship. This structure justifies regressing Australian consumption on Australian GDP, but not on Chinese GDP. Also, if the determinants of GDP are the production processes, we cannot reverse the variables and run a regression of GDP on Consumption. Consumption is not a determinant of GDP. For an empirical model, C on Y and Y on C are the same patterns. Correlations are symmetric, but causal relationship are one directional. Real Structural Models attempt to find hidden real variables which cause the patterns that we see. For example, the tendency of consumers to consume a proportion of their income is the hidden cause for the surface data relationship between consumption and income within a country.
Mental Models: A pattern in the data is just a pattern – there is no explanation for it. This is the Baconian model of science. If we see a pattern in the data, we deduce that a law holds which generates this model. Any pattern that we see could be a law. A mental model imagines a structure of reality which could be an explanation for the reality. For example, an aggregate consumption function can arise from individual consumers who optimize utility derived from consumption bundles subject to budget constraints. It could also arise from consumers who make completely random consumption decisions, while staying within their budget. Any imaginary structure of reality which leads to observations which match what is actually observed is a mental model.
A description of “mental model” is provided by Robert Aumann: “In my view, scientific theories are not to be considered ‘true’ or ‘false.’ In constructing such a theory, we are not trying to get at the truth, or even to approximate to it: rather, we are trying to organize our thoughts and observations in a useful manner.”
Originally, mental models were designed by thinking about what the nature of hidden reality could be, and then trying to build a mental model to match that hidden structure. However, post-Kant, the main idea became different. Trying to match hidden reality was abandoned, and instead, the goal of the model became to create a match to the observations. As a result, many concepts which are of vital importance to modelling reality were abandoned or misunderstood. For example, the idea of causation is of great importance in understanding reality. Rubbing a match against sulfur on the matchbox causes the match to burn. Learning about causation is of extreme important in learning to navigate the world we live in. Our mental models are supposed to be representations of reality. For complicated reasons, economists FORGOT this basic idea about the nature of mental models, that they are supposed to capture the hidden real mechanisms which generate the observations. This has been an empiricist tendency starting from Hume. The idea that we cannot talk about hidden unknown realities has deep roots in Western intellectual rejection of God and religion. As already discussed, Kant suggested that we can create a Copernican revolution in philosophy by changing the focus of our inquiry into the world. The following diagram explains the current Empiricist or Kantian views about models and reality. All that matters about mental models is that they should provide a match to the observations. It does not matter whether or not they match the true structures of reality which produce the observations.
Philosophers have thought for ages about the problem of how we can find out if our mental models match the reality, the hidden unknown structures. But this is the WRONG question (according to Kant and the empiricists). We can never find out the answer, because the true hidden structures of reality will NEVER be observable. So, we should abandon this ancient question. Instead, we should focus on the question of how our mind organized the observations into a coherent picture of apparent reality. The diagram below shows the Kantian shift of focus. Traditional philosophy is concerned with the question of whether or not our mental models MATCH the hidden structures of the real world. This is the question of whether or not our models are TRUE. Kant and the empiricists said that this was impossible to know. We should only be concerned about whether or not our empirical models provide a good fit for the observations. So, the question itself was changed. Instead of asking if models match reality (and hence, whether or not they are TRUE), we ask whether the output of the models provides a match to the observations.
Another useful analogy is to consider the theory of vision: How we see the world. What we REALLY see is a pair of flat 2-D upside down images of the world on our retina. Our brain has the complex task of reconstructing the real 3-D world out there from this imperfect scan of it on our retina. For more detailed discussions of this process, see “How Our Eyes See Everything Upside Down”, or “Introduction to the Science of Vision”Introduction to the Science of Vision”. Simple minds just EQUATE the mental image with the reality out there — this is the easiest model. But there are many optical illusions which can be used to show that our methods for interpreting images on our retina do not always reproduce the real world out there – A mirage, an illusion of water, being the simplest of them. The Kantian question is to consider how our mind creates a 3-D image of reality from the imperfect 2-D pair of images available as observations. The Real Philosophers ask about the match between our mental image and the complex reality.
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