Dynamic Hierarchical Factor Models ∗

This paper presents an approach to dynamic factor modeling in which variations can be idiosyncratic, block-specific, or common across blocks and units. Existing two level factor models do not usually account for variations at the block level which implies that these can be confounded with genuine common co-movements in the data. Specifying the block structure also facilitates interpretation of shocks to economic activity. Our approach is aimed at three types of applications: (i) decomposition of variance to assess the relative importance of different shocks, (ii) understanding how block-specific shocks impact overall economic activity, and (iii) monitoring and economic forecasting. We estimate a three level model for housing and find evidence of aggregate housing shocks, but these are small relative to common regional shocks and shocks to individual series within regions. We also estimate a model for real economic activity excluding housing. The 315 time series are organized into six blocks according to the timing of data releases. The results suggest that block-specific variations are important. Data released in the household survey component of the monthly employment situation report turn out to be mostly idiosyncratic and bear little information about the state of real economic activity. Finally, we estimate a four level model consisting of 402 series organized into an output, an employment, and a demand block that each are broken down into sub-blocks. According to this model, the level of real economic activity at the end of our sample in February 2008 was about 1.5 standard deviations below average, but still well above the level of 3 standard deviations below average reached at the trough of the recession in 2001. ∗We would like to thank Evan LeFlore for excellent research assistance on this project. The first author would like to acknowledge financial support from the National Science Foundation under grant SES 0549978. The views expressed in this paper are those of the authors and do not necessarily reflect the views of the Federal Reserve Bank of New York or the Federal Reserve System. †Columbia University, 420 W. 118 St., MC 3308, New York, NY 10025. [email protected] ‡Federal Reserve Bank of New York, 33 Liberty St., New York, NY 10045. [email protected] §Federal Reserve Bank of New York, 33 Liberty St., New York, NY 10045. [email protected]