PDF Ebook Reproducing Business Cycle Features: How Important Is Nonlinearity Versus Multivariate Information?
Model evaluation has always been at the forefront of macroeconomic research. A modeling techniques have advanced over time, a wide variety of time-series models have sprung up to satisfy different needs, from simple univariate and multivariate linear models to more complicated univariate and multivariate nonlinear models. It is therefore important to establish an efficient and reasonable approach to model comparison and evaluation that is suitable for very different types of time-series models. In this paper, we evaluate a variety of univariate linear, univariate nonlinear, and multivariate linear models of U.S. real gross domestic product (GDP) in terms of their abilities to produce simulated data that exhibit the business cycle features in the actual GDP data. Our primary goal is to investigate the extent to which multivariate information inherent in macroeconomic variables such as the unemployment rate, inflation, interest rates, and the components of GDP can account for the apparent univariate evidence of nonlinear dynamics in U.S. GDP previously demonstrated in the literature.
The conventional methods for conducting model evaluation – hypothesis testing, out-of-sample forecast comparisons, and Bayes factors – face several drawbacks. When the models under consideration are non-nested, hypothesis testing is often intractable. Out-of-sample forecast comparisons tend to be sensitive to the particular out of sample period used. Bayes factors can be very sensitive to the specification of priors. Furthermore, Bayes factors only provide a sense of the relative performance of different models and not an absolute measure of the ability of a model to explain the dynamics in the data.
The business cycle features approach considered in this paper offers a useful alternative to the conventional methods for model evaluation. It can be viewed as being related to a broader approach to model comparison and evaluation known as “encompassing tests.” Encompassing tests evaluate the ability of models to produce simulated data that have the same behavior as sample data. In our particular case, we concentrate on features of the data that are related to business cycles. Ever since Burns and Mitchell’s (1947) extensive study of the cyclical behavior of economic activity, economists have sought to analyze economic fluctuations in terms of business cycle phases. Thus, our focus on business cycle features provides a very natural way to assess the benefit of introducing nonlinearity into time-series models, especially because many of the nonlinearities explored for GDP have been motivated as being related to the business cycle.
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