634 Panel Methods to Test for Unit Roots and Cointegration
Finally, the Industry Growth Accounting Database provides information on labor
skills in three categories and on investment and capital services (three information
and communications technologies (ICT) asset categories and three non-ICT cate-
gories). The countries covered are Australia, Canada, the United States and four
European countries (France, Germany, the Netherlands and the United Kingdom).
The information is provided in order to allow for a decomposition of output growth
into the contributions of labor and capital and total factor productivity using the
growth-accounting methodology.
This chapter deals with particular aspects of the study of such large economic
datasets, with a view to using this data to analyze economic hypotheses of interest.
13.1.1 An example: economic convergence in the sense of
Evans and Karras (1996)
The available large datasets, containing income and other macroeconomic vari-
ables, lead us to choose economic convergence as a motivating example. This
allows us to discuss some of the possibilities that macro-panel data offer and some
issues that arise.^1
There is an abundance of definitions of convergence in the literature. Given that
we consider panel data, we focus on those put forward in Evans and Karras (1996)
(abbreviated henceforth as EK). These essentially coincide with the definitions of
Bernard and Durlauf (1995, 1996), formulated within a time series context.^2 Three
features of EK are of interest to us, within the context of this chapter. First, that the
paper studied convergence within the framework of a dataset in which the cross-
section dimensionNand time series dimensionTwere both used (in contrast
to using only theTdimension and investigating the hypothesis on a country-
by-country basis or only along the cross-sectional dimension). Second, the data
could be taken to be integrated of order one (or, loosely speaking, needing first-
differencing for stationarity). And third, and most importantly, the hypothesis of
interest could be formulated in terms of testing for a unit root, in this case at least, in
an autoregressive model. This threefold combination of a so-called macro-panel of
data (involving gathering together time series information on a variable or a set of
variables with the cross-sectional or cross-country information on these variables)
with the problem of testing for a non-stationary root, where the hypothesis is
formulated as such, gives our chapter its name and decides its focus.
Thus, denote log per capita GDP byyi,t, referred to for simplicity as income, in
countryiin yeart, considered to be valued at constant and common international
prices. This variable is observed for a collection ofi=1,...,Ncountries over the
yearst=1,...,T. Several underlying theoretical formulations of growth models
lead to balanced growth paths for each of the economies to which each of the
economies converges in the long run. Under some additional assumptions the
balanced growth paths of the economies are parallel to each other. Such a set-up
is the starting point of EK’s statistical definition of economic convergence, which
we give below:
Definition (general): Denote byyi,t+jincome in countryiat timet+jand assume
that there exists a processatand finite parametersμ 1 ,...,μNfor which it holds