Let's Get Real: A Factor Analytical Approach to Disaggregated Business Cycle Dynamics

Abstract

This paper develops a method for analysing the dynamics of large cross-sections based on a factor analytic model. We use law of large numbers arguments to show that the number of common factors can be determined by a principal components method, the economy-wide shocks can be identified by means of simple structural VAR techniques and that the parameters of the unobserved factor model can be estimated consistently by applying OLS equation by equation. We distinguish between a technological and a non-technological shock. Identification is obtained by minimizing the negative realizations of the technology shock. Empirical results on 4-digit industrial output and productivity for the U.S. economy from 1958 to 1986 show that: (1) at least two economy-wide shocks, both having a long-run effect on sectoral output, are needed to explain the common dynamics; (2) although the technological shock accounts for at least 50% of the aggregate dynamics of output, it cannot by itself explain dynamics at business cycle frequencies; (3) sector-specific shocks explain the main bulk of total variance but generate mainly high frequency dynamics; (4) both the technological and the non-technological component of output show a peak for positive sectoral comovements of output at business cycle frequencies; (5) technological shocks are strongly correlated with the growth rates of the investment in machinery and equipment sectors and their inputs. Many interesting questions about cyclical fluctuations and economic growth can be answered only by studying the dynamic behaviour of sectoral variables. When data contain information on time for a large cross-section of sectors, traditional econometric techniques used in the macroeconomic literature such as Vector Autoregressive (VAR) and Vector Autoregressive Moving Average (VARMA) models are not appropriate since they require the estimation of too many parameters. This is why new methods which allow for the reduction of the parameter space need to be developed. The objective of this paper is both methodological and descriptive. At the methodological level we develop a simple framework for the dynamic analysis of large cross-sections. The basic model is a dynamic factor analytic model as in Sargent and Sims (1977). The sectoral variables are decomposed into two unobservable components: a common component, driven by macroeconomic shocks, and a purely sectoral component. When