Identifying Nonlinear Components by Random Fields in the US GNP Growth. Implications for the Shape of the Business Cycle

Christian M. Dahl 1 , 1  and Gloria Gonzalez-Rivera 2 , 2
  • 1 Purdue University,
  • 2 University of California, Riverside,

Within a flexible parametric regression framework (Hamilton, 2001) we provide further evidence on the existence of a nonlinear component in the quarterly growth rate of the US real GNP. We implement a battery of new tests for neglected nonlinearity based on the theory of random fields (Dahl and Gonzalez-Rivera, 2003). We find that the nonlinear component is driven by the fifth lag of the growth rate. We show that our model is superior to linear and nonlinear parametric specifications because it produces a business cycle that when dissected with the BBQ algorithm mimics very faithfully the characteristics of the actual US business cycle. On understanding the relevance of the fifth lag, we find that the nonparametrically estimated conditional mean supports parametric specifications that allow for three phases in the business cycle: rapid linear contractions, aggressive short-lived convex early expansions, and moderate/slow relatively long concave late expansions.

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SNDE recognizes that advances in statistics and dynamical systems theory can increase our understanding of economic and financial markets. The journal seeks both theoretical and applied papers that characterize and motivate nonlinear phenomena. Researchers are required to assist replication of empirical results by providing copies of data and programs online. Algorithms and rapid communications are also published.