1106 The Econometrics of Convergence
how convergence under a cross-section test can, in fact, imply a failure of con-
vergence under a time series test, because of these different assumptions. To be
clear, it is possible for data from a stationary process to exhibitβ-convergence, for
example, but it is not clear what the economic interpretation is.
Harvey and Carvalho (2002) and Carvalho and Harvey (2005a, 2005b) propose
a number of time series analyses of convergence which distinguish between eval-
uating whether countries have converged, and whether countries are converging.
The idea of this framework is to interpret convergence as involving adjustments
of output in a given country to gaps between its past output and that of other
countries. It allows one to evaluate the presence of common deterministic trends,
as well as tendencies for economies to adjust based on differences with the rest
of the world. Relative to the other unit root tests, this approach allows for level
differences between economies and so distinguishes between convergence to a
common level and convergence to common growth paths. Harvey and Carvalho
(2002) use this approach to conclude that there is convergence between the US
and Japanese growth paths; Carvalho and Harvey (2005a, 2005b) find both con-
vergence and divergence between Euro zone countries and various pairs of US
regions respectively. An additional finding of these papers is that unit root tests
of convergence are highly sensitive to the inclusion of time trends and constant
terms.
Phillips and Sul (2006) extend the distinction between economies that have con-
verged and economies that are converging, by explicitly addressing the question of
invariance of the time series process for output. Their analysis focuses on models
of the form:
yi,t=bi,tβt+κi,t, (23.16)whereβtis a common trend (deterministic and/or stochastic) andκi,tis a cyclical
term. The key advance in this formulation is thatbi,t, the weights on the com-
mon trend, are allowed to vary both with respect to the country and with respect
to time. This approach allows one to estimate a transition curve for individual
economies which, by tracing outbi,tβt, allows for explicit evaluation of how the
long-run components of national output co-evolve. Their analysis finds evidence
of convergence for the OECD member countries and for US states, but not for a
broader sample of countries drawn from the Penn World Table.
23.7 The economics of convergence
The various approaches to convergence that we have discussed are all purely sta-
tistical, so it remains to consider convergence as an economic concept, in order
to assess what can be learned from econometric studies. In this section we pro-
vide some definitions of convergence that, while statistical in nature, can be used
to move between the economic notion of convergence and the statistical notions
that have been employed to assess it.
Broadly speaking, we take the substantive economic content of the conver-
gence hypothesis to be the claim that initial conditions have no effect on long-run