Identifying Structural Breaks in Cointegrated Vector Autoregressive Models*

Abstract

This article suggests an alternative formulation of the cointegrated vector autoregressive (VAR) model such that the coefficients for the deterministic terms have straightforward interpretations. These coefficients can be interpreted as growth rates and cointegration mean level coefficients and express long-run properties of the model. For example, the growth rate coefficients tell us how much to expect (unconditionally) the variables in the system to grow from one period to the next, representing the underlying (steady state) growth in the variables. The estimation of the proposed formulation is made operationally in GRaM, which is a program for Ox Professional. GRaM can be used for analysing structural breaks when the deterministic terms include shift dummies and broken trends. By applying a formulation with interpretable deterministic components, different types of structural breaks can be identified. Shifts in both intercepts and growth rates, or combinations of these, can be tested for. The ability to distinguish between different types of structural breaks makes the procedure superior compared with alternative procedures. Furthermore, the procedure utilizes the information more efficiently than alternative procedures. Finally, interpretable coefficients of different types of structural breaks can be identified.

Global shocks and their impact on the Tanzanian economy

“…In modelling structural breaks, the paper draws on the conventional (multivariate) cointegration approach in Johansen et al (2000) and Hungnes (2010), which accommodates different types of structural breaks. Specifically, using such a multivariate framework, hypothesis testing on breaks in trend slopes (or shifts in growth rates) can be formulated and properly tested.…”

Adjustment and Long‐Run Economic Performance in 18 African Countries

“…This paper uses a structural break approach to study the impact on long‐run growth paths of the introduction of SAPs. In particular, we employ the multivariate cointegration model in Hungnes (), which is an alternative formulation of the conventional cointegration model in Johansen et al . () and accommodates different types of structural breaks.…”

“…In particular, an algorithm searching for breaks developed by Doornik et al . () and the procedure in Hungnes () were used to determine the existence, timing and significance of breaks in mean macroeconomic growth rates.…”

“…This necessitates reformulating the model in Equation such that the deterministic terms are easily identifiable and directly interpretable. Hungnes () suggests an alternative formulation that facilitates the decomposition of all deterministic terms into components that induce growth in the system, Δ x t , and those that capture the means of cointegration relations, β ′ x t : where D t contains the deterministic variables in Equation , and γ is a vector of coefficients to D t . Note that δ ≡ β ′ γ measures the effect of the deterministic variables, D t , on the long‐run relations, β ′ x t .…”

“…We identify and test for trend breaks using univariate as well as multivariate statistical procedures. In particular, an algorithm searching for breaks developed by Doornik et al (2013) and the procedure in Hungnes (2010) were used to determine the existence, timing and significance of breaks in mean macroeconomic growth rates.…”