Working Paper: CEPR ID: DP2338
Authors: Mario Forni; Marc Hallin; Marco Lippi; Lucrezia Reichlin
Abstract: This paper analyzes identification conditions, and proposes an estimator, for a dynamic factor model where the idiosyncratic components are allowed to be mutually non-orthogonal. This 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 propose an estimator of the common components and prove convergence as both time and cross-sectional size go to infinity at appropriate rates. Simulations yield encouraging results in small samples. We use our model to construct an index of the state of the economy for the European currency area. Such an index is defined as the common component of real GDP within a model including several macroeconomic variables for each European country.
Keywords: coincident indicators; dynamic factor models; dynamic principal components
JEL Codes: C13; C33; C43
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| common and idiosyncratic components (D80) | asymptotic identification (C51) |
| cross-sectional dimension increases (C21) | recovery of common component of economic indicators (E20) |
| first q dynamic principal component series converge to the factor space (C38) | projection of observable variables on these components converges to the common component (C39) |
| estimator for the common components (C51) | converges as both time and cross-sectional dimensions approach infinity (C32) |
| common component (Y20) | consistently estimated despite nonorthogonality of idiosyncratic components (C51) |
| identified components (Y90) | economic index constructed from GDP data of member countries (E01) |