Academic journal article Journal of Money, Credit & Banking

Time Irreversibility and Business Cycle Asymmetry

Academic journal article Journal of Money, Credit & Banking

Time Irreversibility and Business Cycle Asymmetry

Article excerpt

BUSINESS CYCLE ASYMMETRY has been a topic of great interest to economists ever since the work by Burns and Mitchell (1946). More recently, the seminal article by Neftci (1984) stimulated renewed interest in the subject and introduced both new concepts of "asymmetry" and new ways to measure the effect. This resurgence in interest in the topic has been contemporaneous with the equally important renewed interest in dynamics and the presence of nonlinearity in structural economic relationships.

In this paper we combine these ideas by utilizing an important concept in dynamics, "time reversibility," in order to clarify some issues in the analysis of business cycle asymmetry.(1) We will also provide a link between aspects of asymmetry and the fundamental concepts of time reversibility and its inverse "time irreversibility." In the process we will shed some further light on the Blatt (1980) criticism of the Frisch-Slutsky impulse propagation mechanisms as models of aggregate business activity.

One of the difficulties in examining the notion of asymmetry is that rigorous definitions are difficult to formulate, even though the intuitive idea is clear. A major problem, of course, is that if asymmetries in the duration of expansions and contractions are linked to the National Bureau of Economic Research (NBER) definitions of turning points, the statistics to be used to evaluate the former depend in subtle ways on the statistics used to define the latter. Neftci (1984, p. 310) recognized this difficulty and devised a method to measure the degree of asymmetry. Others have explored alternative concepts of asymmetry, such as, DeLong and Summers (1986), Sichel (1993), and McQueen and Thorley (1993). The outcome of these and other efforts has enriched the analysis of business cycles in that we can now identify many different definitions of asymmetry, each of which focuses on a different aspect of the general concept, although there is some overlap between the competing definitions. We believe that the introduction of the concepts of time reversibility and its inverse will not only provide a new perspective on the idea, but will also provide a unified framework for the current alternative definitions.

The outline of the paper is as follows. We begin with a discussion of various concepts of asymmetry and provide an intuitive definition of the idea of time reversibility and its inverse in the next section. In that section we discuss the economic importance of the concept of time reversibility and its relationship to the various definitions of business cycle asymmetry. The following section provides a formal definition of time reversibility and examines some of the properties of the concept. A statistical tool for identifying time-irreversible stochastic processes, the symmetric-bicovariance function, is introduced in this section.

The time reversibility (TR) test statistic is presented in section 3. In section 4 the TR test statistics are calculated for a set of business cycle indicators. We apply the TR test to the well-known Nelson and Plosser (1982) representative annual macroeconomic dataset recently extended by Schotman and Van Dijk (1991) and to the international annual dataset studied by Backus and Kehoe (1992). Our results provide evidence that some business cycle fluctuations are time irreversible, showing that some business cycle components are asymmetric in a way to be made precise in the next two sections.

Section 5 provides a characterization of the business cycle asymmetry detected by the TR tests discussed in the previous sections. Section 6 concludes the paper.

1. SOME ALTERNATIVE DEFINITIONS OF ASYMMETRY AND TIME REVERSIBILITY

The original Burns and Mitchell notion was intuitively appealing, and their conclusion about many U.S. aggregate economic time series was that upswings are longer and slower than downswings. Thus, the Burns and Mitchell concept involves the idea that the duration and slope of expansions is not symmetric with contractions. …

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