Growth Trends and Systematic Patterns of Booms and Busts‐Testing 200 Years of Business Cycle Dynamics

Abstract

We study the dynamic pattern of business cycles using US GDP data between 1790 and 2015. To address difficulties in trend and cycle decomposition, we introduce a semiparametric estimation approach with an iterative plug‐in (IPI) algorithm for endogenous bandwidth selection. This algorithm identifies continuously moving growth trends with trend‐supporting growth periods. A simulation study demonstrates the value‐added of our trend identification. Afterwards, nonlinear SETAR models are fitted parametrically. Further, we test the trend using a recently developed test and the estimated SETAR models against their linear alternatives. The results indicate asymmetric characteristics during booms and busts.

Improved Output Gap Estimates and Forecasts Using a Local Linear Regression

“…We focus on the estimation quality at these points and use an asymmetric boundary kernel to obtain stable boundary estimates, which are the key to obtaining reliable real-time output gap estimates. Ref [14] use an additive component model:…”

“…, T, x t = t/T denotes the rescaled time, m(x) is some smooth function and ξ t denotes a zero mean stationary process. Thus, a data-driven local polynomial estimator for the smooth trend function is used in line with [14] without any parametric assumptions on ξ t . Under the assumption of short-range dependence the authors use the following Equation (2) for estimating the trend m(x t ) by minimizing the locally weighted least squares:…”

“…Since the local linear estimator, where p = 1, results in the most stable boundary estimates (for two-sided filters), it seems a logical choice for estimating the output gap. In order to estimate the bandwidth in a data-driven manner, we follow [14], where the bandwidth is estimated by minimizing the asymptotic mean integrated squared error (AMISE):…”

“…Therefore, any analyses need to provide additional information that can be used to estimate a more precise output gap. To use all available information in the sense of applying a two-sided filter, the local polynomial regression of [14] may be a better alternative for estimating the output gap. This method in its local linear (LLR) version also improves the estimation quality at boundary points, since an asymmetric boundary kernel is introduced to enhance the estimation quality at time series endpoints (real-time reliability).…”

“…We then extend the method to forecast output gaps. Moreover, the univariate LLR of [14] is extended to multivariate analysis to examine the contribution of multivariate methods. Besides introducing this methodology, we also compare the gaps produced using the LLR with those using the HP filter for (i) statistically based estimations and (ii) the production function approach used by the OECD.…”