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4.2. Long-run relationship
Once the order of integration of the series has been analyzed, we will estimate
the long-run or cointegration relationship for each country separately. Given the
(relatively small) time dimension of the series in our sample, we will estimate and test
the coefficients of the cointegration equation by means of the Dynamic Ordinary Least
Squares (DOLS) method put forward by Stock and Watson (1993), following the
methodology proposed by Shin (1994). This estimation method provides a robust
correction for the possible presence of endogeneity in the explanatory variables, as well
as, serial correlation in the error terms of the OLS estimation. Also, to overcome the
problem of the low power of the classical cointegration tests in the presence of
persistent roots in the residuals of the cointegration regression, Shin (1994) suggests a
new test where the null hypothesis is that of cointegration. We estimate a long-run
dynamic equation including the leads and lags of all the explanatory variables, the socalled
DOLS regression. In our case this relation is the following:
y t
= α 0
+ α 1
t + β k
x t
+
q
γ j
j=−q
∑ Δx t − j
+ ε t
(6)
where y t is TFP growth, t is a linear trend and x t are the explanatory variables: a
measure of the domestic stock of knowledge (measured through domestic patents), a
measure of the imports of knowledge (measured through foreign patents using an
import weighting scheme) and a measure of human capital, as explained in the previous
section. The parameter β k is the long-run cointegrating coefficient estimated between
TFP growth and the explanatory variable k (or long-run elasticity).
In the above empirical model we will test for the type of cointegration (either
stochastic or deterministic) using the Shin (1994) tests. The Shin tests we evaluate are
based on the calculation of a LM statistic from the DOLS residuals, namely C μ and C τ ,
to test for deterministic (when α 1 = 0) and stochastic (when α 1 ≠ 0) cointegration,
respectively. If there is cointegration in the demeaned specification given in (6), that
occurs when α 1 = 0, this corresponds to deterministic cointegration, which implies that
the same cointegrating vector eliminates deterministic trends as well as stochastic
trends. But if the linear stationary combinations of I(1) variables have nonzero linear
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