What’s the value of mathematical models? Are economists true scientists or politicians disguised as scientists?

Despite the risk of “Mathiness” and a critical reduction of complexity, I argue that mathematical models should be devoted high value for their ability to efficiently describe scientific insights into the world-in-itself [1]. Furthermore, the choice of underlying assumptions, deriving real-world recommendations from the model, and working on it as a scientist are normative (and therefore political) actions.

Willing to comprehend their complex surrounding, humankind developed systematic approaches to un­der­­stand, describe, and communicate the world-in-itself. With the help of language, numbers, (ma­the­mat­i­cal) symbols, as well as agreed scientific methods, like mutually-shared definitions, falsifiability, ob­ser­va­tions, or experiments, scientists create a less complex (and therefore understandable) copy of parts of the world-in-itself: scientific insights.

Within the methods to describe the world-in-itself, numbers, mathematical symbols, and variables (es­pe­ci­ally in comparison to words and sentences) have proven to offer great benefits to their users: Precision (as numbers and symbols within mathematics are consistently defined), efficiency (as mathematics ex­clu­des [semantic] ambiguities), brevity (as variables or symbols can cover long definitions in one character), comprehensiveness (as mathematical description follow strict syntactical rules), and com­pa­ra­bi­li­ty/trans­fera­bility (as the “language of mathematics” is understood worldwide). Therefore, mathematical approa­ches have also been adapted to less mathematized fields of science, like social sciences or humanities.

The aggregation of numbers, symbols, and variables to mathematical model is highly popular in eco­no­mics. Here, mathematized economic models serves two purposes: They are either used as means of ex­pla­nation to a proposed advancement of economic theory (e.g., Foundational models[2], Toy models) and means of validating theoretic description empirically (e.g., DSGE models, partially Policy models). Or, they are used to draw real-world normative recommendations or prognosis from their employment (e.g., Fore­casting models, partially Policy models).

Assessing the value of mathematical models, we can apply a complexity and a quality criterium: first, the ability of models to efficiently describe insights into the world-in-itself, considering its degree of ab­strac­tion and (harmful) reduction of complexity (complexity criterium); second, the ability of models to fulfil their theo­retical/empirical or normative purpose (quality criterium). With regards to the complexity criterium, ma­thematical models are valuable as they offer a precise, lean, and transferrable economic understanding of the world-in-itself; yet, they create the illusion of simplicity as its complexity is reduced drastically and the remains are hidden inside its very efficient notation. This bears the risk of researchers falling into the trap of the “Ricardian Vice”, as well as skipping a step-by-step replicability of mathematized model, which gives leverage to pseudo-mathe­ma­tiz­ed models (referred to as “Mathiness” by Paul Romer). In a second step, value is added to a mathe­ma­ti­cal model if it en­han­ces or validates theory or draws normative conclusions that are brought forward con­vin­cingly in a political discussion (quality criterium). Notably the latter can be difficult to achieve as en­com­passing real-world modelling requires a big reduction of complexity.

Breaking science down to a choice of axioms (or assumptions), scientific methods, and a narrative of the world-in-itself, makes every scientist a politician. Engaging for one field of science means choosing one set of axioms, methods, and narrative over others, and this is a normative (and hence political) decision. After de­ciding for one approach to the world-in-itself and within the rules and assumptions of his/her field, the theo­­retical and empirical work produces insights and validations that are not more political than the con­tin­uous upholding of the initial political statement for this scientific approach and against others. Nor­ma­tive fin­dings are, to the contrary and regardless of the field of science, political as they leave their scientific system and try to formulate “absolute Truth” about the world-in-itself – independently from their axiomatic fundament.

[1] The world-in-itself is a borrowing from Immanuel Kant’s concept of the “thing-in-itself”, the real existence of objects before any human perception.

[2] The following five types of exemplary macro models refer to Blanchard (2017): “On the Need of (At Least) Five Classes of Macro Models”.

This OnePager is part of a six piece series written for the course "Advanced Economics: Economic Theory & Policy" at Hertie School of Governance, lectured by Prof Jean Pisani-Ferry, Chief Economist of the French President and Professor at Hertie School of Governance and SciencePo.