Common Stochastic Trends And Aggregation In Heterogeneous Panels

In nonstationary heterogeneous panels where the number of units is finite and where each unit cointegrates, a large number of conditions needs to be satisfied for cointegration to be preserved in the aggregate relationship. In reality, the conditions most likely will not hold. This paper takes a closer look at what happens when the conditions are violated. In this case, the question of whether an aggregate relationship is observationally equivalent to a cointegrating equation is of particular interest. We derive a measure of the degree of noncointegration of the aggregate estimates, and we explore its asymptotic properties.We thank Stephen Hall for inspiring discussions and comments during the initial stage of this research. We are grateful to participants in the 9th Conference on Panel Data (Geneva, June 22–23, 2000) and the 2000 Meeting of the Society for Economic Dynamics (San José, Costa Rica, June 29–July 2, 2000) and to colleagues at the University of Bergamo (Italy), London Business School (UK), and Cass Business School (UK) for useful comments. We have enormously benefited from comments and suggestions from two anonymous referees, the editor, Peter C.B. Phillips, and the co-editor, Bruce Hansen. The usual disclaimer applies. G. Urga acknowledges ESRC (Project R022251032) for financial support. Lorenzo Trapani acknowledges financial support from Cass Business School (RAE Development Funds Scheme) and ESRC Postdoctoral Fellowship Scheme (A.N. PTA-026-27-1107).