International R&D Spillovers: An Application of Estimation and Inference in Panel Cointegration
| Author | Min‐Hsien Chiang,Bangtian Chen,Chihwa Kao |
| DOI | http://doi.org/10.1111/1468-0084.0610s1691 |
| Date | 01 November 1999 |
| Published date | 01 November 1999 |
INTERNATIONAL R&D SPILLOVERS: AN
APPLICATION OF ESTIMATION AND INFERENCE IN
PANEL COINTEGRATION
Chihwa Kao, Min-Hsien Chiang and Bangtian Chen
I. INTRODUCTION
In this paper, we consider the application of recent results on estimation and
inference in panel cointegration to the study of empirical economic growth.
The emergence of endogenous growth theory in the 1980s has led to a
resurgence of interest in the sources of economic growth. Coe and Helpman
(1995), among other researchers, state that commercially oriented innova-
tion efforts which respond to economic incentives are the major engine of
technological progress and productivity growth. Coe and Helpman argue
that, in a global economy, a country's productivity depends on its own R&D
efforts as well as the R&D efforts of its trading partners. Using data from
21 OECD countries plus Israel during 1971-1990, they ®nd that both
domestic and foreign R&D capital stocks have important effects on total
factor productivity (TFP). We intend to re-examine the econometric
foundation of Coe and Helpman's paper.
Coe and Helpman (1995) discovered that all of their data exhibit a clear
trend, and unit root tests on these data indicate that the TFP and both the
domestic and foreign R&D capital stocks are non-stationary. They then
con®rm the presence of cointegration for TFP and the domestic and foreign
R&D capital stocks by testing for a unit root in the residuals. In other words,
although all the variables are individually non-stationary, there exists a
linear combination of these variables so that the regression containing these
variables has a stationary error term.
Coe and Helpman's use of a cointegrating regression enables us to exploit
the relationship among the variables in levels, without transforming the
data, such as differencing, to avoid the spurious regression problem. Un-
fortunately, at the time of their article the econometrics of panel cointegra-
OXFORD BULLETIN OF ECONOMICS AND STATISTICS, SPECIAL ISSUE (1999)
0305-9049
691
#Blackwell Publishers Ltd, 1999. Published by Blackwell Publishers, 108 Cowley Road, Oxford
OX4 1JF,UK and 350 Main Street, Malden, MA 02148, USA.
We would like to thank Suzanne McCoskey, a co-editor, Anindya Banerjee, and a referee for
comments that have helped us to improve an earlier version. We also thank participants of
seminars at Syracuse University, Academia Sinica, and 1998 ASSA/CEANA Meetings. A Gauss
program for this paper can be retrieved from http://web.syr.edu/~cdkao. Address correspondence
to: Chihwa Kao, Center for Policy Research, Eggers 426, Syracuse University, Syracuse, NY
13244-1020. E-mail: cdkao@maxwell.syr.edu
tion had not yet been resolved. Among the various issues that now need to
be addressed are two directly associated with Coe and Helpman's empirical
interpretations. First, we need to know the asymptotic distribution of the
estimated cointegrating vector in panel data. It is well known that the
asymptotic distributions of estimators in pure time series regression are
dramatically affected by the presence of unit roots and the cointegration.
Accordingly, we expect that the asymptotic distributions of estimators in
panel regression might also be affected by the presence of unit roots and
cointegration. Indeed, Coe and Helpman chose not to report the t-statistic,
because the asymptotic distribution of the t-statistic was unknown. Given
that the estimated coef®cients are relatively small, we are not sure whether
these estimators are signi®cantly different from zero. Second, although it is
well known that time series regression estimates are super-consistent, it has
been found that substantial estimation bias may remain for moderate sample
sizes. We have no reason to presume that this bias will become negligible in
panel regression due to the introduction of the cross-section dimension.
Given that the estimated coef®cients in Coe and Helpman are relatively
small in magnitude, one even wonders whether those estimates are correctly
signed after the bias correction. The issues presented above cast serious
doubts on Coe and Helpman's conclusion that TFP is closely linked to
domestic and foreign R&D.
Recently, Kao and Chiang (1998) found that the limiting distributions of
OLS estimators are normally distributed with non-zero means and proposed
fully-modi®ed (FM) and dynamic OLS (DOLS) estimators in panel data.
While the limiting distribution of the OLS estimator is normal with a non-
zero mean, the FM and DOLS estimators are asymptotically normal with
zero means. Therefore, we apply Kao and Chiang's result to Coe and
Helpman's international R&D spillover regressions, and we compare the
empirical consequences of the different estimation approaches.
The paper is organized as follows. Section 2 brie¯y reviews Coe and
Helpman's model. Section 3 reviews the asymptotic theory developed by
Kao and Chiang. Section 4 presents the empirical results. Concluding
remarks are made in Section 5.
II. COE AND HELPMAN'S THEORYAND MODEL
Coe and Helpman's model is built on recent theories of innovation-driven
growth (e.g., Grossman and Helpman, 1991). Contrary to most cross-
country studies of economic growth that focus on explaining output growth
as determined by the accumulation of labor, capital, and some additional
economic and political variables, Coe and Helpman choose to focus on the
growth of TFP, which is the component of output growth that is not
attributable to the accumulation of inputs. In their account, in an economy
with two factors of production, the log of TFP is measured as
692 BULLETIN
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