UNIVERSITÄT POTSDAM - Prof. Dr. Paul JJ Welfens

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2
R adj.
0.9970 0.9967 0.9969 0.9966
DW-test 2.0108 2.1136 -- --
EG-test (28.6) b) (28.5) -- --
-5.3968 -5.6735 -- --
(0.0859) c) (0.0261) -- --
F-test of the 1.4396
restriction (0.2345) c)
a)
Empirical t-values are in brackets, but statistical conclusions on the basis of usual t-tests are only
permitted if the third step of the Engle/Yoo procedure has been applied.
b)
Number of observations available after forming lags and first differences and number of I(0) variables
in brackets.
c)
Significance levels in brackets.
The estimation results for the unrestricted and restricted version of this long-term production
function are reported in Table 8. A view of the t-values calculated for the estimates
of the third step of the Engle / Yoo procedure shows that all coefficients of the
unrestricted as well as the restricted estimation are unequal to zero at a significance
level of 1 %. Therefore, all three indicator variables have a highly significant power of
explanation. Furthermore, the magnitudes of their coefficients verify that the factors
approximated by the indicator variables make contributions to real gross value-added
that cannot be neglected. The estimates of the coefficients of the factors capital and
labor also seem to be very reliable. They are rather similar to the estimates in
SCHRÖER / STAHLECKER (1996) where a long-term Cobb-Douglas production
function is estimated using quarterly data from 1970 until 1989. SCHRÖER /
STAHLECKER (1996) introduced after a data mining process a dummy variable which
changes the slope of the time trend to approximate a change of technical progress. The
R 2 s of 0.9977 and 0.9974 for the first step of the Engle / Granger procedure and
0.9976 and 0.9966 for the third step of the Engle / Yoo procedure indicate a very good
fitting of the models to the observed data. The DW test statistics suggest that the presence
of first order autocorrelation can be excluded. Turning to the EG test statistics it
can be seen that the unrestricted as well as the restricted production function forms a
cointegration relation at significance levels of 8.59 % and 2.61 %. Therefore the sum of
the partial production elasticities is now permitted beyond all usual significance levels
as the F-test shows. Based on these estimation and testing results, the restricted product
function containing all three indicator variables is superior to other augmented production
functions with only one or two indicator variables which had been considered during
the empirical investigation, but are not reported here due to the limitation of space.