Structural Changes in Models for I(1) and I(2) Converging Series
Giuliana Passamani
Department of Economics, University of Trento, Trento, TN, Italy

The paper deals with the problem of assessing stochastic convergence between two series as in Bernard and Durlauf (1995), but we consider also the possibility of structural changes occurring in the period of observation. We move from the work of Strazicich et al. (2004), where they show that stochastic relative convergence is achieved when, controlling for at most two endogenously determined structural breaks in level and trend, the null hypothesis of a unit root in the log difference of the two series is rejected. Rejection implies their conditional convergence, or, in other terms, that the relation between the two series is stationary, apart from a possible deterministic term, that is there is evidence of a cointegration relation such that shocks to it have only temporary effects. The aim of the paper is to show that we can still detect stochastic converging series even if we fail to reject the null hypothesis of a unit root in the log difference of the two series. This is the case when the estimated cointegration relation between the series show some non-stationarity of the I(1) type, due to the presence of structural breaks in trend or in level in the differenced observed series. In such case we cannot simply conclude that the series are diverging, but we should also consider the possibility of stochastic relative convergence analyzing the series using an I(2) model and controlling for possible structural breaks as in Juselius (2006, chapters 16-18). This is particular useful when the observed time series show evidence of regime changes. The empirical analysis refers to the catching up process in Central and Eastern European countries and the convergence of their economies towards the average economy of EU15 countries, in particular with respect to purchasing power parity. The structural changes occurring are the ones related to the recent economic crisis. We will show that rejecting convergence in the I(1) model still allows to asses convergence in the I(2) model, where convergence is driven by an I(2) common stochastic trend.


Bernard, A. B., Durlauf, S. N. (1995): “Convergence in international output”, Journal of Applied Econometrics, 10, 97-108

Juselius K. (2006), “The Cointegrated VAR Model. Methodology and Applications”, Oxford: Oxford University Press.

Strazicich M. C., Lee J., Day E. (2004), “Are incomes converging among OECD countries? Time series evidence with two structural breaks”, Journal of Macroeconomics, 26, 131-145.

Keywords: Structural changes; Stochastic relative convergence; I(2) common stochastic trend

Biography: Presenter: Prof. Giuliana Passamani, Professor of Economic Statistics, Department od Economics, University of Trento.