Konvergence theory

Epilogue [to my thoughts] and prologue [to this note]

Reality is for losers.

Normative

Convergence theory, or the catch-up hypothesis (Abramovitz 1986), can be summarised as follows:

Setting the variable x as time and the variable y as any proxy for divergence as you see fit, the convergence function is:

y=a/x+b+E, where the constant a>0, the constant b is any real number, E is the error term, and x>0

Most economists like to accept this highly idealised model, attributing any deviation to the error term E. This is perhaps broadly similar to how economists use the A technology or productivity parameter in growth models. But here, I show below, the overly idealised model is neither accurate nor is it unavoidable to use.

A more realistic model of convergence, henceforward called konvergence to distinguish between Abramovitz's (1986) model and my own, is shown below:

1) y=a/x+b+E for 0<x<π where the constant a>0, the constant b is any real number, and E is the error term;
2) y=cx+F for π<x<µ where the constant c>0 and F is the error term;
3) and convergence in the conventional shape for x>µ.

Positive

For later.