Extended nonlinear feedback model for describing episodes of high inflation

Abstract

An extension of the nonlinear feedback (NLF) formalism to describe regimes of hyper- and high-inflation in economy is proposed in the present work. In the NLF model the consumer price index (CPI) exhibits a finite time singularity of the type $1/(t_c -t)^{(1- \beta)/\beta}$, with $\beta>0$, predicting a blow up of the economy at a critical time $t_c$. However, this model fails in determining $t_c$ in the case of weak hyperinflation regimes like, e.g., that occurred in Israel. To overcome this trouble, the NLF model is extended by introducing a parameter $\gamma$, which multiplies all therms with past growth rate index (GRI). In this novel approach the solution for CPI is also analytic being proportional to the Gaussian hypergeometric function $_2F_1(1/\beta,1/\beta,1+1/\beta;z)$, where $z$ is a function of $\beta$, $\gamma$, and $t_c$. For $z \to 1$ this hypergeometric function diverges leading to a finite time singularity, from which a value of $t_c$ can be determined. This singularity is also present in GRI. It is shown that the interplay between parameters $\beta$ and $\gamma$ may produce phenomena of multiple equilibria. An analysis of the severe hyperinflation occurred in Hungary proves that the novel model is robust. When this model is used for examining data of Israel a reasonable $t_c$ is got. High-inflation regimes in Mexico and Iceland, which exhibit weaker inflations than that of Israel, are also successfully described.