Asymmetric Business Cycles and the Skew Factor

Cycle Skew Factor

The business cycle is a fundamental concept in macroeconomics. The economy has been characterized by an increasingly negative cyclical asymmetry over the last three decades.

As a result, booms are increasingly smoother and longer-lasting than recessions.

An extensive literature has examined in detail the statistical properties of this empirical regularity and confirmed that the extent of contractions tends to be sharper and faster than that of expansions. The 'skew factor' allows the representation of an asymmetric shape for business cycles in a cyclic model.

Examples

skew = +0.25

skew= +0.5

skew=+0.75

skew = - 0.25

skew = - 0.5

skew = -0.75

$\frac{(a + \cos x) \cos n + b \sin x \sin n}{\sqrt{(a + \cos x)^{2} + {(b \sin x)}^{2}}}$

Desmos interactive playbook: https://www.desmos.com/calculator/ejq06faf93

Math Equation

To apply the cycle skew, the cycle skew equation is used instead of a pure sin(x) formula:

Where:

a = skew factor
b = 1.0
n = PI / 2

Math LaTeX Code:

\frac{(a+\cos x)\cos n+b\sin x\sin n}{\sqrt{(a+\cos x)^2+\left(b\sin x\right)^2}}

Asymmetric Business Cycles and the Skew Factor

Cycle Skew Factor

Examples

Math Equation

Further Reading