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.

This paper proposes a measure of dynamic comovement between (possibly many) time series and names it cohesion. The measure is defined in the frequency domain and is appropriate for processes that are costationary, possibly after suitable transformations. In the bivariate case, the measure reduces to dynamic correlation and is related, but not equal, to the well known quantities of coherence and coherency. Dynamic correlation on a frequency band equals (static) correlation of bandpass-filtered series. Moreover, long-run correlation and cohesion relate in a simple way to co-integration. Cohesion is useful to study problems of business-cycle synchronization, to investigate short-run and long-run dynamic properties of multiple time series, and to identify dynamic clusters. We use state income data for the United States and GDP data for European nations to provide an empirical illustration that is focused on the geographical aspects of business-cycle fluctuations.

This paper proposes a factor model with infinite dynamics and nonorthogonal idiosyncratic components. The model, which we call the generalized dynamic-factor model, is novel to the literature and generalizes the static approximate factor model of Chamberlain and Rothschild (1983), as well as the exact factor model à la Sargent and Sims (1977). We provide identification conditions, propose an estimator of the common components, prove convergence as both time and cross-sectional size go to infinity at appropriate rates, and present simulation results. We use our model to construct a coincident index for the European Union. Such index is defined as the common component of real GDP within a model including several macroeconomic variables for each European country.

Removal of short-run dynamics from a stationary time series to isolate the medium- to long-run component can be obtained by a bandpass filter. However, bandpass filters are infinite moving averages and can therefore deteriorate at the end of the sample. This is a well-known result in the literature isolating the business cycle in integrated series. We show that the same problem arises with our application to stationary time series. In this paper, we develop a method to obtain smoothing of a stationary time series by using only contemporaneous values of a large data set, so that no end-of-sample deterioration occurs. Our method is applied to the construction of New Eurocoin, an indicator of economic activity for the euro area, which is an estimate, in real time, of the medium- to long-run component of GDP growth. As our data set is monthly and most of the series are updated with a short delay, we are able to produce a monthly real-time indicator. As an estimate of the medium- to long-run GDP growth, Eurocoin performs better than the bandpass filter at the end of the sample in terms of both fitting and turning-point signaling.