17 General Criticism of the Classical Growth Models
The basic problem of economic growth models is
to solve by model the dependence of growth of GDP Y from its influencing
main factors X. The undisputed most important parameter is the capital K
and its availability for investment and consumption. In addition, other
influencing factors X may come with, but is not known on an ad hoc basis
whether and how this might be. There are now basic mathematical and physical
reasons, such as a reliable model can be constructed.
From purely mathematical reasons applies:
a) We have to determine at least the dependent time evolution of at
least two functions, namely Y(t) and K(t).
b) It follows thus mathematically essential that we need at least a system
of two linearly independent but coupled differential equations to derive this functions. This is a necessary condition by
mathematics.
c) For a realistic model, but this is still not a sufficient condition. For
physical reasons, a sufficient condition is, that of
course only if the model and real data come close enough to each other, in
past and future as well, then the model works well.
d) Although this additional condition can be achieved in various ways more or
less well, but it is clear from the science that this can be achieved only in a
perfect way by field theoretical approaches. This means it must serve
consistency on the basis of sources and sinks and of invariants.
Virtually all classical economic growth models fail, however, already at the indispensable necessary condition by mathematics, condition (b).
For those whom the foundations of mathematical and physical analysis are not familiar, I will take this condition into some simpler words: The problem is always that one makes the math questions in order to get an helpful answer. If one asks the wrong question, one gets a bad answer. So its essential, if you ask for functions, you have always to formulate the questions by differential calculus as only this mathematical gadgets delivers functions as an answer.
On the other side function always just deliver numbers or series of numbers as an answer. If you now construct any model by defining a function Y=f(K) or Y=f(L) and so forth in the beginning, the answer will always be a series of numbers depending on your own assumptions for K or L in this samples, regardless of the mathematically complexity and even correctness of the complete derivation following.