Nonlinear Business Cycle Dynamics: Cross-Country Evidence on the Persistence of Aggregate Shocks

I. INTRODUCTION Economists have long been interested in the dynamics of business cycles, particularly regarding the symmetry of expansions and contractions. More recently, the specification of stochastic trends in economic growth has generated concerns about the relative persistence of positive and negative shocks to the economy. Several papers have looked at the persistence of business cycles, including Nelson and Plosser [1982], Campbell and Mankiw [1987], Cochrane [1988], Diebold and Rudebusch [1989], Balke and Fomby [1990], Zelhorst and de Haan [1994], and Bradley and Jansen [1995]. While results vary, especially on the issue of a unit root in output, the overarching result is that output fluctuations are highly persistent. One question not asked by the above authors is whether business cycle dynamics are asymmetric. This issue has been investigated by Neftci [1984], Falk [1986], DeLong and Summers [1986], Hamilton [1989], Diebold and Rudebusch [1990], and Terasvirta and Anderson [1991]. These authors take a variety of approaches but they reach a general conclusion that there is some evidence of asymmetric business cycle dynamics. However, most of these studies ask if contractions are shorter and steeper than expansions. Except Hamilton [1989], they do not ask if there is a difference in persistence due to the asymmetries. In a recent paper, Beaudry and Koop [1993] propose a set of methods for simultaneously examining these two questions. Specifically, Beaudry and Koop (BK) recommend the augmentation of the standard ARMA representation of real output growth through the inclusion of a nonlinear term that captures the relative state of the economy. This augmentation provides for nonlinear dynamics and the possibility of asymmetric dynamic responses to positive and negative shocks. In addition, calculation of the implied impulse responses permits detection of the relative persistence implied by the combination of asymmetric cycle dynamics and stochastic trend. Based upon their analysis of U.S. data, BK conclude that the response of the economy to positive and negative shocks is indeed asymmetric and "the imposition of symmetry on impulse responses has likely led to misleading measures of persistence." [BK, p. 162] As a result BK conclude "We find that the effects of negative shocks to be mainly temporary and the effects of positive shocks to be very persistent." [BK, p. 162]. If BK's results are correct, they have strong implications for the way macro economists view economic fluctuations and will, in their words, "contribute to a reappraisal of some macroeconomic theories." That is, BK's results suggest that macroeconomic models must be revised to provide for temporary effects of negative shocks but permanent effects of positive shocks. Because of the potential importance of BK's results, we examine the robustness of those results by modifying and extending BK's proposed methods of testing. Not only do we extend the analysis to the other six G7 countries besides the United States, but also we redefine, in a sensible way, the nature of the nonlinear dynamics. Overall, our results from other economies provide only mixed support for the asymmetry of cyclical dynamics and the lack of persistence of negative shocks. II. THE MODEL TO BE ESTIMATED In the BK framework, the estimated model includes an asymmetric response term. The asymmetry is generated by a variable that measures the strength of a recession. The variable is calculated as the distance between current real GDP and the previous peak level of real GDP. That is, BK define a measure they call Current Depth of the Recession (CDR) where: (1) [CDR.sub.t] = max [{[Y.sub.t-j]}.sub.j [greater than or equal to] 0 - [Y.sub.t]. With this definition in place, BK recommend augmenting an autoregressive model of real GDP growth as: (2) [Phi](L) [Delta] [Y.sub.t] = [Delta] +[[Omega](L) - 1] [CDR.sub. …