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).