Academic journal article Economic Inquiry

Business Cycle Asymmetry: A Deeper Look

Academic journal article Economic Inquiry

Business Cycle Asymmetry: A Deeper Look

Article excerpt

I. INTRODUCTION

The behavior of macroeconomic variables over phases of the business cycle has long been an object of interest to economists. A critical aspect of this is the symmetry or asymmetry of business cycles. An asymmetric cycle is one in which some phase of the cycle is different from the mirror image of the opposite phase; for example, contractions might be steeper, on average, than expansions. Although asymmetries were noted by early business cycle researchers, the issue has only recently been examined empirically.(1) This recent interest arises from a desire to carefully document the stylized facts of business fluctuations and because linear structural and time series models cannot represent asymmetric behavior under standard assumptions.

Neftci |1984~(2) and DeLong and Summers |1986~ reported evidence that increases in the unemployment rate are steeper than decreases. The evidence on the asymmetry of real GNP is less clear, however. Falk |1986~--using Neftci's procedure--found that real GNP does not exhibit this type of asymmetry. However, Hamilton |1989~ showed that a particular nonlinear (asymmetric) model for real GNP growth rates dominates linear models.

All of the above research has focused on asymmetries--or nonlinearities--in the rate of change of business cycle variables; that is, these researchers compare periods of increase to periods of decrease. Brock and Sayers |1988~ expanded the search for asymmetry by applying a test that identifies any form of nonlinearity or asymmetry. Brock and Sayers find evidence of nonlinear structure--in the postwar period--in employment, unemployment, and industrial production. One problem with their test, however, is that it cannot distinguish among different types of asymmetries.

This paper sharpens the asymmetry evidence by distinguishing two types of asymmetry that could exist separately or simultaneously.(3) The first type of asymmetry--which has been investigated in most of the research described above--occurs when contractions are steeper than expansions. I refer to this type of asymmetry as steepness. The second--and as yet not explicitly considered--type of asymmetry occurs when troughs are deeper than peaks are tall. I refer to this type of asymmetry as deepness.

These two types of asymmetry are illustrated in Figure 1 for a trendless time series. The first panel shows a symmetric cycle. The second panel shows a cycle exhibiting steepness, which pertains to relative slopes or rates of change and compares mirror images across imaginary vertical axes placed at peaks and troughs.(4) The third panel shows a cycle exhibiting deepness, which pertains to relative levels and compares mirror images across a horizontal axis (the dashed line in the figure). The final panel in the figure shows a cycle exhibiting both deepness and steepness.

In section II, I discuss the implications of asymmetry. Tests for deepness and steepness are presented in section III, and detrending is discussed. In section IV, I provide evidence of deepness in unemployment and industrial production; the evidence for real GNP is weaker. Previous evidence of steepness in unemployment is also confirmed. In section V, I discuss Monte Carlo simulations that demonstrate that these tests are actually able to identify different types of asymmetry. Section VI concludes.

II. IMPLICATIONS OF ASYMMETRY

Asymmetry in business cycle time series is important for macroeconometrics because linear and Gaussian models are incapable of generating asymmetric fluctuations.(5) Consider a variable |x.sub.t~, generated by a linear, Gaussian, and stationary autoregressive moving average (ARMA) process, and its infinite moving average representation:

(1a) A(L) ||chi~.sub.t~ = B(L) ||epsilon~.sub.t~

(1b) ||chi~.sub.t~ = |A.sup.-1~(L) B(L) ||epsilon~.sub.t~

where A(L) and B(L) are finite polynomials in the lag operator L and ||epsilon~.sub.t~ is an i. …

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