New Econometric Methods For Parameter Instability

Econometric relationships are plagued by various forms of instabilities along different dimensions. In cross sections, it is often found that individuals display some degree of heterogeneity. In time series, triggering events, such as pandemics and new regulations, change the relationships among the variables over time. Over the last seventy years, there has been a surge in methodologies and modelling approaches to deal with both cross-sectional heterogeneity as well as time-varying parameters in econometric analyses. These approaches vary from the two-sample problem to grouping structures, to face cross-sectional heterogeneity, and from simple one-time exogenous breaks models to more elaborated endogenous time-varying processes to account for time variations in the parameters of interest. This dissertation contributes to the econometrics of parameter instability over time by analyzing and proposing methods to deal with this type of issue. The dissertation is developed along three chapters. The first chapter serves as an introduction to the econometrics of parameter instability. In particular, after a general review of the problem of parameter instability in econometrics, we introduce and review two particular classes of econometric methods to deal with parameter instabilities. The two methods that we introduce in the first chapter, Markov switching models and real-time tests for structural breaks, are the main focus of the following two chapters of this dissertation. In the second chapter we study the question of temporal aggregation of Markov switching models. Markov switching models have been widely used in economics and finance, yet no exhaustive treatment of their implications for temporally aggregated data has been advanced. We characterize in detail the effects of temporal aggregation of flow and stock variables following a wide range of multivariate Markov switching processes. The stochastic properties as well as the implications of temporal aggregation on the underlying Markov chain are also studied. The results show that the natural time unit of the data plays a fundamental role, and therefore considerable time should be spent in deciding at which frequency the data should be modelled. The third chapter (co-authored with Eduardo Rossi and Lorenzo Trapani) deals with real-time tests for structural breaks. We first extend the class of available weighted-monitoring tests considering a heavily weighted boundary function. These new tests allow to have minimal detection delay when the break point is early in the monitoring horizon. Since the location of the future break point is unknown, we propose a new class of real-time tests which combines different weighting functions, so to have minimal detection delays, regardless of the location of the break point in the monitoring horizon. For both procedures the full asymptotic theory is derived, and extensive Monte Carlo simulations show the finite sample properties of the statistics.