Lucrezia Reichlin

The Generalized Dynamic-Factor Model: Identification and Estimation

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 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.

The Generalized Dynamic Factor Model: One-Sided Estimation and Forecasting

This article proposes a new forecasting method that makes use of information from a large panel of time series. Like earlier methods, our method is based on a dynamic factor model. We argue that our method improves on a standard principal component predictor in that it fully exploits all the dynamic covariance structure of the panel and also weights the variables according to their estimated signal-to-noise ratio. We provide asymptotic results for our optimal forecast estimator and show that in finite samples, our forecast outperforms the standard principal components predictor.

A Quasi Maximum Likelihood Approach for Large Approximate Dynamic Factor Models

Is maximum likelihood suitable for factor models in large cross-sections of time series? We answer this question from both an asymptotic and an empirical perspective. We show that estimates of the common factors based on maximum likelihood are consistent for the size of the cross-section (n) and the sample size (T), going to infinity along any path, and that maximum likelihood is viable for n large. The estimator is robust to misspecification of cross-sectional and time series correlation of the idiosyncratic components. In practice, the estimator can be easily implemented using the Kalman smoother and the EM algorithm as in traditional factor analysis.

Opening the Black Box: Structural Factor Models with Large Cross-Sections

This paper shows how large-dimensional dynamic factor models are suitable for structural analysis. We argue that all identification schemes employed in SVAR analysis can be easily adapted in dynamic factor models. Moreover, the “problem of fundamentalness”, which is intractable in structural VARs, can be solved, provided that the impulse-response functions are sufficiently heterogeneous. We provide consistent stimators for the impulse-response functions, as well as (n, T) rates of convergence. An exercise with US macroeconomic data shows that our solution of the fundamentalness problem may have important empirical consequences.

Segmented Trends and Non-stationary Time Series

Since the influential work of Charles R. Nelson and Charles Plosser (1982), many empirical studies have concluded that macroeconomic time series are difference stationary. This paper proposes the segmented trend model as an alternative in which the series is the sum of a nonstationary trend and a stationary cycle, and where the trend shows infrequent shifts. The paper proposes tests between the difference stationary, and segmented trends models and applies these to the data of Nelson and Plosser. In general, the results indicate that prices are difference stationary but quantities follow segmented trend processes. Copyright 1989 by Royal Economic Society. (This abstract was borrowed from another version of this item.)

A Measure Of Comovement For Economic Variables: Theory And Empirics

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.

Do Financial Variables Help Forecasting Inflation and Real Activity in the Euro Area

The Paper uses a large data set, consisting of 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 index and to evaluate the role of financial variables in forecasting. We considered two models which allow forecasting based on large panels of time series: Forni, Hallin, Lippi, and Reichlin (2000, 2001c) and Stock and Watson (1999). Performance of both models was compared to that of a simple univariate AR model. Results show that multivariate methods outperform univariate methods for forecasting inflation at one, three, six, and twelve months and industrial production at one and three months. We find that financial variables do help forecasting inflation, but do not help forecasting industrial production. (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.)

Monetary Policy in Real Time

We analyze the panel of the Greenbook forecasts (sample 1970-1996) and a large panel of monthly variables for the United States (sample 1970-2003) and show that the bulk of dynamics of both the variables and their forecasts is explained by two shocks. A two-factor model that exploits, in real time, information on many time series to extract a two-dimensional signal produces a degree of forecasting accuracy of the federal funds rate similar to that of the markets and, for output and inflation, similar to that of the Greenbook forecasts. This leads us to conclude that the stochastic dimension of the U.S. economy is two. We also show that dimension two is generated by a real and nominal shock, with output mainly driven by the real shock, and inflation mainly driven by the nominal shock. The implication is that, by tracking any forecastable measure of real activity and price dynamics, the central bank can track all fundamental dynamics in the economy.

The generalized dynamic factor model consistency and rates

Abstract A factor model generalizing those proposed by Geweke (in: D.J. Aigner and A.S. Goldberger, Latent Variables in Socio-Economic Models, North-Holland, Amsterdam, 1977), Sargent and Sims (New Methods in Business Research, Federal Reserve Bank of Minneapolis, Minneapolis, 1977), Engle and Watson (J. Amer. Statist. Assoc. 76 (1981) 774) and Stock and Watson (J. Business. Econom. Statist. 20 (2002) 147) has been introduced in Forni et al. (Rev. Econ. Statist. 80 (2000) 540), where consistent (as the number n of series and the number T of observations both tend to infinity along appropriate paths (n,T(n))) estimation methods for the common component are proposed. Rates of convergence associated with these methods are obtained here as functions of the paths (n,T(n)) along which n and T go to infinity. These results show that, under suitable assumptions, consistency requires T(n) to be at least of the same order as n, whereas an optimal rate of n is reached for T(n) of the order of n2. If convergence to the space of common components is considered, consistency holds irrespective of the path (T(n) thus can be arbitrarily slow); the optimal rate is still n , but only requires T(n) to be of the order of n.

Coincident and Leading Indicators for the Euro Area

This paper proposes a new way to compute a coincident and a leading indicator of economic activity. Our methodology, based on Forni, Hallin, Lippi and Reichlin (2000), reconciles dynamic principal components analysis with dynamic factor analysis. It allows us to extract indicators from a large panel of economic variables (many variables for many countries). The procedure is used to estimate coincident and leading indicators for the EURO area. Unlike other methods used in the literature, the procedure takes into consideration the cross-country as well as the within-country correlation structure and exploit all information on dynamic cross-correlation.(This abstract was borrowed from another version of this item.)