Employment and Business Cycle Asymmetries: A Data Based Study

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Does the magnitude of a trough in employment differ from the magnitude of a peak in employment, and is the time employment spends in rising from a trough to a peak longer than the time spends in falling from a peak to a trough? In this paper we measure the “asymmetry of magnitudes” and the “asymmetry of durations” of seven US postwar employment series. The series are detrended using the Hodrick-Prescott filter prior to the analysis. Appropriate measurements of the two types of asymmetry are the skewness of the detrended series and the skewness of the first differenced detrended series, respectively. Monte Carlo and bootstrapping procedures are used to evaluate the significance levels. Five out of seven series show negative skewnesses in levels as well as in first differences. The skewnesses of “magnitudes” and “durations” of US aggregate employment are significant, and yield –0.50 and –0.60 respectively.

In the second part of the paper a nonlinear AR model is derived from the theory of Hermitian type polynomials that have the potential to realize stochastic asymmetric self-sustained oscillations. In contrast with the standard linear AR model, the nonlinear AR model, fitted to the employment series, accurately generates the two types of asymmetry.