Why Are Beveridge-Nelson and Unobserved-Component Decompositions of GDP So Different?

Abstract

this paper where the two cycle components are plotted, and has been widely noted; see Watson (1986), Stock and Watson (1988) among others. It should surprise us that the unobserved component (UC) and Beveridge-Nelson (BN) methods produce very different trend-cycle decompositions since both are modelbased. Each implies an ARIMA representation. Neither imposes smoothness in the trend component a priori as does the smoother of Hodrick and Prescott (1997) or as in the polar case of a linear trend that forces all variation, save constant growth, into the cycle. The UC and BN both "let the data speak for itself" in this regard. While it is often stated that BN assumes a perfect negative correlation between trend and cycle innovations, that is a property of the estimated trend and cycle, not the unobserved components, and it is a property shared with the UC decomposition. This paper attempts to find out why we do not, after decades of research, have a consistent picture of how variation in a series like real GDP should be allocated between trend and cycle. Briefly, section 1 demonstrates the theoretical equivalence between the approaches. Section 2 investigates the source of the difference observed in practice. Section 3 concludes. 3