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Prompt:
Sunday, September 13, 2026
Saturday, September 12, 2026
The trouble some issues encountered while modelling the economic growh together with a new exponential modelling
The following text is AI (ChatGPT plus) generated with reference to my current issue in mathematical modelling of the macroeconomic growth theory.
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This week I had an interesting little incident at the boundary between economics and mathematics.
I was checking an exponential model for an economic growth / Total Factor Productivity (TFP) problem. After going back to the mathematical formulation and implementing it carefully in MATLAB, the objective function showed a clear minimum.
At first sight, that sounds encouraging: the optimisation problem has a well-defined solution.
However, when I reconstructed the corresponding TFP trajectory using the parameters associated with that minimum, the result did not reproduce the observed trajectory satisfactorily.
So I found myself in an interesting situation:
the mathematics said, “Here is the optimum,” while the economic data replied, “Not so fast.” 😅
This does not necessarily mean that the exponential approach is mathematically wrong. Rather, it raises a more interesting question: is this particular model structure appropriate for representing the empirical behaviour of TFP?
At the moment, I am therefore also comparing the result with a penalised smoothing spline, which appears to represent the trajectory more naturally.
For me, this has been a useful reminder that finding a mathematically neat optimum is not the same thing as finding a good empirical model. Optimisation, model specification, and interpretation all have to work together.
The investigation is still ongoing, so this is not a final conclusion — just one of those small research episodes where economics and mathematics refuse to cooperate quite as politely as expected.
Friday, September 11, 2026
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