When Can Trend-Cycle Decompositions Be Trusted?

Abstract

In this paper, we examine the results of GDP trend-cycle decompositions from the estimation of bivariate unobserved components models that allow for correlated trend and cycle innovations. Three competing variables are considered in the bivariate setup along with GDP: the unemployment rate, the inflation rate, and gross domestic income. We find that the unemployment rate is the best variable to accompany GDP in the bivariate setup to obtain accurate estimates of its trend-cycle correlation coefficient and the cycle. We show that the key feature of unemployment that allows for precise estimates of the cycle of GDP is that its nonstationary component is "small" relative to its cyclical component. Using quarterly GDP and unemployment rate data from 1948:Q1 to 2015:Q4, we obtain the trend-cycle decomposition of GDP and find evidence of correlated trend and cycle components and an estimated cycle that is about 2 percent below its trend at the end of the sample.

A hitchhiker’s guide to empirical macro models

“…The procedure is typically run on a single time series, but the setup can be easily made multivariate, see e.g. Gonzalez-Astudillo and Roberts (2016), or Grant and Chan (2017). In this case, one can assume that there are common trends, or common cycles, or both.…”

The Real‐Time Properties of the Bank of Canada's Staff Output Gap Estimates

“…Additionally, we also estimate three multivariate models: first, (viii) the Clark () bivariate unobserved components model with GDP and unemployment. Gonzalez‐Astudillo and Roberts () show that the unemployment rate is the most informative variable to add along GDP to accurately estimate trend‐cycle decomposition in bivariate unobserved components models. Second, two multivariate BN decompositions: (ix) one including GDP growth and the change in the unemployment rate, and (x) another including GDP growth, the change in the unemployment rate, the change in the consumer price index (CPI) and the change in the 3‐month treasury bill rate…”

The Credit Cycle and Measurement of the Natural Rate of Interest

“…Admittedly, this task is extremely data demanding. We therefore augment purely empirical analysis with Monte Carlo experiments, which are commonly applied in the analysis of trend/cycle decomposition (Nelson, 1988, Basistha, 2007, and Gonzalez-Astudillo and Roberts, 2016. This approach allows us to generate a large number of artificial credit cycles and examine the fluctuations of the natural rate of interest in the proximity of credit cycle peaks.…”