Dynamic models for a fast changing world

PRIN Project 2020 · Local coordinator: Giacomo Bormetti · Principal Investigator: Fulvio Corsi

In recent years, shocks of different nature to the socio-economic system have become increasingly frequent (financial crisis, technological innovations, climate changes, pandemics). As forcefully argued by Robert E. Lucas in 1976, rational agents will adapt to the new conditions expected to prevail after the shock by changing their behavior, thereby inducing variability in the parameters of econometric models. To the econometric community, this represents a formidable challenge of increasing relevance that clearly imposes the adoption of dynamic models with time-varying parameters.

In this project, we aim to cope with this challenging task by developing new econometric models with time-varying parameters based on the recently introduced Score-Driven (SD) approach. SD models represent a general class of observation-driven models where parameters evolve over time based on past observations. We argue that the adoption of SD models to describe the dynamics of socio-economic systems is particularly convenient for two main reasons: (i) economically, contrary to existing approaches where parameters follow a stochastic process with random and exogenous shocks, SD models might allow the evolution of the parameters to be driven by actual realized past shocks, thus opening the possibility to gauge the impact of observed shocks or hypothetical policy interventions on the future evolution of the model parameters; (ii) computationally, since SD models are susceptible to straightforward maximum likelihood estimation, they are able to effectively deal with high-dimensional problems and large amount of data.

This project comprises different lines of research, which are both theoretical (T) and applied (A). From the theoretical point of view, we plan to shed light on some important yet unexplored aspects of SD models:

  • T1. their statistical properties when employed as approximate filters for high-dimensional, non-linear non-Gaussian state-space models;

  • T2. their ability in recovering approximate estimates and filtering densities of continuous-time models;
  • T3. the connections of such models with Bayesian approximation methods and some recently introduced Machine Learning approaches.

The possible fields of application of this general class of econometric models are extensive. We plan to focus on the following topics:

  • A1. Structural Vector Auto-Regressive models with time-varying parameters driven by past structural shocks, which would allow to provide an interesting econometric answer to the profound Lucas critique on macroeconometrics models;

  • A2. high-dimensional covariance matrix forecasting in the presence of estimation errors and non-linearity
  • A3. testing and forecasting of temporal networks with dynamic nodes dependencies;

  • A4. econometric analysis of microstructure models at high (tick-by-tick) and ultra-high (limit order book) frequency.

The research group is composed of four units: University of Pisa, Scuola Normale Superiore, University of Verona, and University of Bologna. Units will proceed in strong integration and collaboration. However, there is some diversification of work between them. Bologna Unit will act as leading participant for lines of research T3, A1, A2, A3, and A4.