Different kinds of models

Most people assume that computer based models are just on type. But here are three important classes of model you may encounter and the advantages of the new agent-based modelling. Lets dive in.

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Modelling is a method for predicting the future based on an understanding of past events. It allows us to predict possible outcomes in various situations. Models are deployed in weather forecasting, financial planning, sales forecasting, traffic estimations, etc.

In simple terms, you develop a model by analysing the data of past events using logic. The model is used to predict possible outcomes. Then, you observe the new data and verify if your model is correct or not. If not, you improve your model and repeat this process.

In modern research, we encounter three important classes of models. Until now, we were limited by computing power and mathematical design limitations. But now, we will be able to tackle new kinds of problems AND old problems, but differently.

Fundamental Models

These are based on modelling the fundamental realities that explain the observable phenomenon. These are often based on immutable laws such as the laws of physics.

Consider Newton's Law of Gravity and Newton’s laws of motion. Using these laws, we were able to model the behaviour of planets. You are also able to back-calculate the position of the planets at any date, and you are able to predict their position at any date in the future. These models allowed us to send a man to the moon.

Statistical /Probabilistic/ Econometric Models

These models are designed to choose the best subset of fundamental variables that explain past events most closely. These models can be improved by adding more of the right variables. However, the models can be misled by adding the wrong type of variables. These models are not seeking the fundamental underlying theory, OR the theory is not immutable and can change with behaviours or feedback loops. Hence, these models are theory-agnostic.

Most models in finance and economics fall in this class.

Agent-based Models

A newer class of models is agent-based models. These were conceptualised in the 1940s (yeas others came before that!) With the growth in computing power, these are now ready to be utilised in many fields.

These models use fundamental models on the individual element. Each element is given rules based on their observed behaviour. Each element is then modelled, and we get a forecast for individual elements. The elements are then aggregated across the entire population.

The model was first used in cellular biology, where each cell was one element. These are becoming increasingly important in social sciences, where a person is the individual element.

The differences

There are critical differences in these three classes of models:

1. Fundamental Models are based on eternal laws. They are like Shruti in the Vedas.

   1. The true test of the model is often how well it predicts the future. Most forecasts are wrong if you consider exact observations. The forecast needs to be directionally correct and closest to the future observation.

   2. Technically speaking, when observed reality deviates from the calculations given by such models, we start looking for variables outside of the model.

   3. That sounds too complicated. So, let me share a story: When scientists used Newton’s laws to calculate Mercury’s orbit, the results didn’t align with actual observations. This discrepancy led them to hypothesize the existence of an unseen planet between Mercury and the Sun, which they named Vulcan, believing it was causing Mercury to wobble. However, Vulcan was never discovered. The anomaly was later resolved by Albert Einstein's Theory of General Relativity, which revealed that Newton’s laws were incomplete in this context. Einstein’s theory provided accurate predictions of Mercury’s orbit, improving our understanding of the forces at play.

2. The statistical/probabilistic/econometric class models are actually error-minimizing models.

   1. As described earlier, we add some more variables to get the model closer to reality. However, sometimes adding relevant variables too INCREASES the error. This anomalous behaviour is a result of our incomplete understanding of the fundamentals.

   2. Now, imagine a case where a new variable becomes influential. In such scenarios, past data is not relevant. That is why most econometric models became confused after COVID affected the economic data unexpectedly.

   3. Since these models are top-down, they ignore many self-cancelling variables. The importance of such variables remains hidden.

3. Agent-based models are incentive optimizing.

   1. The forecasts that result from these models are emergent properties.

   2. The degrees of freedom and variables affecting one element are easier to model than modelling everything all at once. With substantial computing power, we can now aggregate complex individual agent models into a system.

   3. Since these models optimize incentives at the individual level, they are better suited to behavioural analysis and social sciences where the governing laws are not immutable.

   4. Our understanding of social systems is about change drastically.

In Sum

Agent-based models have opened up another avenue for understanding the world. We need to think of ways to incorporate them into our modelling.

Before I close, it is important to note some realities. Most real-life models (not fundamental models) are hybrid models. They mix and match across classes. Because of the ways in which mix-and-match is executed, many errors arise, and much insight is suppressed. So be careful. Remember, the tool you use is a function of many variables, including the class of model you are using.

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