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I'm currently undertaking postgraduate theory units in microeconomics and macroeconomics for the first time and it seems like I am supposed to turn into an applied mathematician, not an economist.

I understand the value of math, but it seems like many of the complex models I am learning have no direct value, just indirect value by the knowledge they bring and the opportunity to "see the bigger picture". In physics, math not only helps us think, but is essential to understand the mechanisms of nature. In economics, I feel as though mathematics creates a false sense of precision, though I may be wrong.

I speculate that if I were to speak to most CEO's in the world, they would have never heard of elementary concepts such as marginal revenue or marginal cost, and they definitely wouldn't incorporate complex economic models into their decision systems.

The models I am learning in macroeconomics: Overlapping Generation Model, Ramsey Model, Solow Model, the Permanent Income Hypothesis and so forth. Do central banks actively use these models or similar models in their decision systems? If they do, does anyone else?

Likewise in Microeconomics: Producer and Consumer Theory (advanced), Contract Design, Advanced Game Theory, Bayesian Econometrics, Asymmetric Information, Price Discrimination and so forth. Just how valuable are they?

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    $\begingroup$ What do you count as a practicing economist? You mention CEO but that would not count in my view and I think in view of most people as practicing economists. Economists working for central banks, government and also for business do use empirical and numerical models that are often rooted in theoretical math models as well $\endgroup$
    – 1muflon1
    Jun 9, 2022 at 10:56
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    $\begingroup$ I would say Bayesian econometrics is part of econometrics, not microeconomics. $\endgroup$ Jun 9, 2022 at 11:13
  • $\begingroup$ I was just using the CEO point as an example that complex models may seldom be used in business decision making. I understand complex macroeconomic models are typically used in the public sector, which is why I mentioned central banks. Even at central banks though, the complexity of the models used do not really compare to the complexity of models taught in graduate programs. As far as businesses go, I am sure some use empirical and numerical models , but I find it hard to believe an ordinary business, perhaps even fantastic ones, incorporate complex microeconomic theory into decisions $\endgroup$
    – Eli J
    Jun 9, 2022 at 11:16
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    $\begingroup$ An example: To use or understand Nash equilibrium you don't need to fully understand the Nash theorem. In most of the economics, maths is used to derive results not apply it. This doesn't diminish the importance of deriving results. Derivations convert intuitions and hunches into concrete results. Without them using intuitions will always leave application uncertain. $\endgroup$
    – Dayne
    Jun 9, 2022 at 11:41
  • $\begingroup$ I voted to close because I was torn between answering it and looking at the irrelevancy of answering it. Your question is ill-posed. The simple answer is "yes," these models are used and "no," nobody probably uses almost any of them. The problem, for example, if you were hired by the PGA, you would find that the economics of professional golf does not match anything you were taught. You would also find that specific contract specifications and structures cause modifications of what you were taught. Now you can build a working model that is valid. $\endgroup$ Jun 11, 2022 at 5:15

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Do practicing economists actually use complex mathematics?

I think by "practicing economists" you actually refer to those who work outside academia with "Economist" as part of their job titles. I'll call these professional economists to distinguish them from the academic economists who "practice" economics in universities/colleges.

Clearly, (some) academic economists use complex math in their everyday research. To get a clear sense of the complexity involved in such work, just flip through any article in Econometrica to get an idea. On the other hand, there are other academic economists whose work make contributions not by their mathematical complexity but by applying innovative methodology/design or examining novel datasets. For this category, consult any paper you read as an undergraduate student.

For professional economists, the landscape is not that different. As an example from the public sector, the FEDS' Finance and Economics Discussion Series feature both math-intensive and math-light papers. The former, though smaller in number, is by no means negligible.

I would say that situation is similar for professional economists in the private sector, although it's harder to find direct evidence, since a lot of their work is proprietary. As an indirect proof, consider the business of economic consulting as exemplified by NERA, a leading economic consultancy in the US. The firm has been known to

methodically applying microeconomic theory to litigation and regulatory matters. The firm applies econometric and statistical analysis to provide strategy, studies, reports, expert testimony, and policy recommendations for government authorities, law firms, and corporations.

In short, the economic models that you learn in graduate school do get used in a non-negligible fraction of both academic and professional work, though not as much as applied econometrics. Sometimes those models require "customization", which in turn requires a solid understanding of the standard version.

There could be many reasons why graduate programs decide to train students to the level of mathematical rigor that is typically seen today, and not all of those reasons are related to whether one can use the mathematical knowledge in his/her future work.

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