The Frisch model of business cycles – A spurious doctrine, but a mysterious success （1999）
Introduction：A central issue in business-cycle theory is the nature and origin of persistent business cycles. There are mainly two lines of economic thinking: the endogenous school and the exogenous school (Zarnowitz 1992). Schumpeter considered business cycles as the life rhythm of an economic organism (1939).Goodwin introduced the nonlinear and chaotic oscillator to describe persistent business cycles (1951, 1990). However, early evidence of economic chaos has received little interest in mainstream economics, because the existence of economic chaos may imply serious challenges to the foundations of equilibrium theory and parametric econometrics (Barnett and Chen 1988; Chen 1988a, 1993a, 1996a, 1996b; Brock and Sayers 1988). In contrast, the exogenous school represents mainstream economics since the 1930s; whose founder was Ragnar Frisch (Kydland 1995).
Hayek realized that empirical features of business cycles were difficult to understand by equilibrium theory (Hayek 1933). However, Frisch suggested that a noise-driven damped oscillator might explain both market stability and persistent cycles, which he claimed in an informal paper in 1933 (Frisch 1933). Contrary to Frisch’s belief, physicists had known since 1930 that a harmonic oscillator under Brownian motion could not produce persistent oscillations (Uhlenbeck and Ornstein 1930; Wang and Uhlenbeck 1945). Today Frisch’s belief is still widely held among economists and econometricians. Indeed, it is a mystery as to why Frisch never published his promised paper, and why the first Nobel Prize in economics was awarded to an unproved and wrong idea. Reexamining the Frisch model will help us to understand the origin of equilibrium belief in economic thinking.
In this chapter, we will give a brief history of the Frisch model, and then discuss its theoretical and empirical implications. We will show that the linear deterministic model of business cycles has structural instability. The effect of external noise to a linear oscillator can be studied by the Langevin equation and the Fokker–Planck equation. We may obtain the analytical solution for a harmonic oscillator under Brownian motion. Its exponential decay in amplitude and autocorrelations indicate that white noise is not capable of producing persistent cycles. We can directly estimate the intrinsic frequency and friction coefficient from real US GDP data. We then will discuss the main implications from the Brownian motion of a harmonic oscillator, and basic problems of the linear model of business-cycle theory.
Chen, Ping. The Frisch Model of Business Cycles – a Spurious Doctrine, but a Mysterious Success (1999), Also, in Chen (2010), Chapter 12, pp.239-250.
