Linear Regression Limit Theory for Nonstationary Panel Data

This paper develops a regression limit theory for nonstationary panel data with large
numbers of cross section (n) and time series ( T )observations. The limit theory allows for
both sequential limits, wherein T +m followed by n +m, and joint limits where T, n +m
simultaneously; and the relationship between these multidimensional limits is explored.
The panel structures considered allow for no time series cointegration, heterogeneous
cointegration, homogeneous cointegration, and near-homogeneous cointegration. The
paper explores the existence of long-run average relations between integrated panel
vectors when there is no individual time series cointegration and when there is heterogeneous
cointegration. These relations are parameterized in terms of the matrix regression
coefficient of the long-run average covariance matrix. In the case of homogeneous and
near homogeneous cointegrating panels, a panel fully modified regression estimator is
developed and studied. The limit theory enables us to test hypotheses about the long run
average pararneters both within and between subgroups of the full population.
KEYWORDS:Nonstationary panel data, long-run average relations, multidimensional
limits, panel cointegration regression, panel spurious regression.

1. INTRODUCTION
THEREHAS BEEN MUCH RECENT EMPIRICAL econometric work on economic
models that uses panel data for which the time series component is nonstationary.
Testing growth convergence theories in macroeconomics and estimating
long-run relations between international financial series such as relative prices
and exchange rates, and spot and future exchange rates are a few examples. This
work has been facilitated by the construction and availability of a number of
important panel data sets covering different individuals, regions, and countries
over a relatively long time period, a notable example being the Penn World
table. For such cases a new nonstationary panel data limit theory which allows
for large n and large T asymptotics is useful. Much past panel data research has
focused on identifying and estimating effects from stationary panels with a large
cross section data dimension ( n )but with few time series (TI observations. In
such cases a large n, fixed T limit theory is natural and Chamberlain (19841,
Hsiao (1986), Matyas and Sevestre (1992), and Baltagi (1995) review much of
this research.