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This paper shows how large-dimensional dynamic factor models are suitable for structural analysis. We establish sufficient conditions for identification of the structural shocks and the associated impulse-response functions. In particular, we argue that, if the data follow an approximate factor structure, the "problem of fundamentalness", which is intractable in structural VARs, can be solved provided that the impulse responses are sufficiently heterogeneous. Finally, we propose a consistent method (and n, T rates of convergence) to estimate the impulse-response functions, as well as a bootstrapping procedure for statistical inference. Non Technical SummaryAgents and policy makers have access to rich information, coming from data on different sectors of the economy. However, standard macro time series models are typically based on few selected variables. Recent econometric literature has introduced models that can exploit large data-sets and still retain simplicity (parsimony). These models -known in the literature as dynamics factor models -are based on the idea that the macroeconomy is driven by few shocks, common to all variables. Since a robust empirical characteristics of macroeconomic time series is that they exhibit strong co-movements, common shocks generate the bulk of the observed dynamics in macro variables.Dynamic factor models have been shown to be successful to forecast macroeconomic variables, but only few applications have considered these models for identifying and estimating structural shocks, as, for example, it is done in the VAR literature.The aim of this paper is to develop the estimation and identification theory needed to study structural shocks and their impulse response functions in dynamic factor models.The analysis of the paper and the empirical application we present show that dynamic factor models are suitable for structural macroeconomic modelling and constitute an interesting alternative to structural VARs. In particular, if the information used by economic agents cannot be captured by the small set of variables considered in a typical VAR, an econometric model based on large information can recover the structural shocks while the small VAR cannot. The factor model framework is also useful when the aim is to study the effect of macroshocks on many variables in the economy, possibly sectoral and regional, rather than studying the effect of these shocks to core macro variables only.

The paper uses a large data set, made up by 447 monthly macroeconomic time series concerning the main countries of the Euro area to simulate out-of-sample predictions of the Euro area industrial production and the harmonized inflation indexes and to evaluate the role of financial variables in forecasting. We considered two models which allows forecasting based on large panels of time series: Forni, Hallin, Lippi and Reichlin (2001b) and Stock and Watson (1999). Performance of both models were compared to that of a simple univariate AR model. Results show that, in general, multivariate methods outperform univariate methods and that financial variables help forecasting inflation, but do not help forecasting industrial production. We also show that Forni et al.'s method outperforms SW's. JEL subject classification : C13, C33, C43.

This paper, along with the companion paper Forni, Hallin, Lippi, and Reichlin (2000, Review of Economics and Statistics 82, 540–554), introduces a new model—the generalized dynamic factor model—for the empirical analysis of financial and macroeconomic data sets characterized by a large number of observations both cross section and over time. This model provides a generalization of the static approximate factor model of Chamberlain (1983, Econometrica 51, 1181–1304) and Chamberlain and Rothschild (1983, Econometrica 51, 1305–1324) by allowing serial correlation within and across individual processes and of the dynamic factor model of Sargent and Sims (1977, in C.A. Sims (ed.), New Methods in Business Cycle Research, pp. 45–109) and Geweke (1977, in D.J. Aigner & A.S. Goldberger (eds.), Latent Variables in Socio-Economic Models, pp. 365–383) by allowing for nonorthogonal idiosyncratic terms. Whereas the companion paper concentrates on identification and estimation, here we give a full characterization of the generalized dynamic factor model in terms of observable spectral density matrices, thus laying a firm basis for empirical implementation of the model. Moreover, the common factors are obtained as limits of linear combinations of dynamic principal components. Thus the paper reconciles two seemingly unrelated statistical constructions.

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. (c) 2010 The President and Fellows of Harvard College and the Massachusetts Institute of Technology.

Key words and phrases: High -dimensional time series. Generalized dynamic factor models.Vector processes with singular spectral density. One-sided representations of dynamic factor models. Consistency and rates.

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