Aggregate Output Measurements: A Common Trend Approach

The authors analyze a model for N different measurements of a persistent latent time series when measurement errors are mean-reverting, which implies a common trend among measurements. The authors study the consequences of overdifferencing, finding potentially large biases in maximum likelihood estimators (MLE) of the dynamics parameters and reductions in the precision of smoothed estimates of the latent variable, especially for multiperiod objects such as quinquennial growth rates. The authors also develop an R2 measure of common trend observability that determines the severity of misspecification. Finally, the authors apply their framework to US quarterly data on GDE and GDI, obtaining an improved aggregate output measure.