GLASS - The Global Augmented State Space Error Correction Model: Structure Theory, Estimation and Inference

• Applicant: Professor Dr. Dietmar Bauer
• Subject Area: Statistics and Econometrics
• Term: since 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 469278259

Increased economic and financial integration, increased availability of large-scale (multi-country) data sets and scientific progress in econometric modelling of high-dimensional time series have led to important advances in multi-country modelling. These advances have occurred both in economic theory driven models and reduced form time series models specified using statistical tools rather than economic theory. For empirical application any model class under consideration has to deal with the curse-of-dimensionality or, put differently, complexity reduction. In this project we aim to (i) explore and (ii) extend the linkages between two prominent econometric approaches for modelling high-dimensional (structured) time series, global vector autoregressive (GVAR) and generalized dynamic factor models (GDFMs). GVAR models achieve complexity reduction by strongly restricting the impact of the variables of all other countries on the evolution of the variables in each country considered. The impact of other countries on the evolution is purged in the so-called star and global variables. The corresponding restrictions on the one hand rest upon numerous posited exogeneity constraints and also limit the flexibility of modelling the long-run (cointegration) behavior of the joint system. Whilst in particular “structural forms” of GVAR models can be seen as semi-structural models, GDFMs have a strong reduced form character, relating in particular the co-movements of series to a small number of unobserved and statistically identified common factors. This approach is very efficient in complexity reduction, but limits in particular structural analysis and interpretations.Starting from the underlying assumption that all variables are generated by a vector autoregressive moving average (VARMA) process this project proposes – using appropriate state space representations – the Global Augmented State Space (GLASS) model to (i) address open issues with respect to exogeneity and cointegration properties in GVAR-type models in a model-class that is invariant to linear transformations and (ii) to investigate in detail the relationship between (VARMA) GDFMs and GLASS-type models. The structure of state space models with the latent (potentially low-dimensional) state vector describing the dynamics of the observables is very similar to the structure of GDFMs; providing the entry point for studying the relationships. A key issue to be addressed to study the links across model classes is a detailed understanding of both finite-N (in GVAR settings) as well as N-asymptotic (GDFMs) properties and their interrelationships. Based upon the structure theory, GLASS will develop estimation and inference tools allowing for structural analysis in high-dimensional cointegrated systems. The procedures and tools will be made available to the public by means of well-tested and robust code. GLASS is a high-dimensional and structural extension of our earlier project EICIP.

• DFG Programme: Research Grants
• International Connection: Austria
• Partner Organisation: Fonds zur Förderung der wissenschaftlichen Forschung (FWF)
• Cooperation Partner: Professor Dr. Martin Wagner