Economists typically use seasonally adjusted data in which the assumption is imposed that seasonality is uncorrelated with trend and cycle. The importance of this assumption has been highlighted by the Great Recession. The paper examines an unobserved components model that permits nonzero correlations between seasonal and nonseasonal shocks. Identification conditions for estimation of the parameters are discussed from the perspectives of both analytical and simulation results. Applications to UK household consumption expenditures and US employment reject the zero correlation restrictions and also show that the correlation assumptions imposed have important implications about the evolution of the trend and cycle in the post-Great Recession period.

In the aftermath of the global financial crisis, competing measures of the trend in macroeconomic variables such as U.S. real GDP have featured prominently in policy debates. A key question is whether large shocks to macroeconomic variables will have permanent effects—i.e., in econometric terms, do the data contain stochastic trends? Unobserved-components models provide a convenient way to estimate stochastic trends for time series data, with their existence typically motivated by stationarity tests that allow at most a deterministic trend under the null hypothesis. However, given the small sample sizes available for most macroeconomic variables, standard Lagrange multiplier tests of stationarity will perform poorly when the data are highly persistent. To address this problem, we propose the use of a likelihood ratio test of stationarity based directly on the unobserved-components models used in estimation of stochastic trends. We demonstrate that a bootstrap version of this test has far better small-sample properties for empirically relevant data-generating processes than bootstrap versions of the standard Lagrange multiplier tests. An application to U.S. real GDP produces stronger support for the presence of large permanent shocks using the likelihood ratio test than using the standard tests.

This paper considers a correlated unobserved-components model for output, employment, and hours in order to disentangle the causes for the last three jobless recoveries. The composition of the structural shocks during recessions and the periods immediately following recessions has changed, as have the responses of employment and hours to those shocks. Recessions before 1984 were followed by recoveries driven by positive permanent shocks to output, whereas post-1984 recessions were followed by weak recoveries in demand. Employment is more sensitive to demand shocks post-1984, leading to weak recoveries in employment. In addition, hours and employment were complements before 1984, but are treated as substitutes after 1984. Much of the initial decrease in demand is now absorbed on the intensive margin.

Does excluding food and energy prices from the Consumer Price Index (CPI) produce a measure that better captures permanent price changes? To examine this question, we decompose CPI inflation and “core” inflation into their permanent and transitory components, using a correlated unobserved-components model. The stationarity of inflation may be time-varying, so we examine the performance of the core measure of inflation separately for periods in which inflation is I(1) and I(0). For a period in which inflation appears to be I(1), we find that core inflation and the permanent component of overall inflation are closely related, but there are some caveats. For a period in which inflation appears to be I(0), we decompose the core and overall price levels and find that the permanent component of the core CPI is much more volatile than the actual core series and that the core excludes volatile permanent shocks to the overall price level.