journal of forest science

5 years interval). If a manager goes through this procedure
for every year, he can develop a mean annual increment
(MAI) curve to aid him to make management
decisions.
or predicting eucalyptus plantation growth and yield,
the system of equations in different estimation methods
can be expressed as follows:
NOLS method,
[– 2.6583(1/t2 – 1/t1) – 5.0887(1/H2 – 1/H1) + 1.0039 (ln G2 – ln G1)]
V2 = V1 e
[(t1/t2) ln G1 + 2.9772(1 – t1/t2) + 0.6416(1 – H1/H2)]
G2 = e
H2 = 29.3852 {1 – [ln (1 – e–0.131 t2 )]/[ln(1 – e –0.131 t1 )]} H1 [ln (1 – e –0.131 t2 )/ln (1 – e –0.131 t1 )]
N3SLS method,
[– 3.0736(1/t2 – 1/t1) – 4.3678(1/H2 – 1/H1) + 0.9798(ln G2 – ln G1)]
V2 = V1 e
[(t1/t2) ln G1 + 3.0316(1 – t1/t2) + 0.5482(1 – H1/H2)]
G2 = e
H2 = 28.7501 {1 – [ln (1 – e–0.138 t2 )]/[ln(1 – e –0.138 t1 )]} H1 [ln (1 – e –0.138 t2 )/ln (1 – e –0.138 t1 )]
NSUR method,
[– 2.8140(1/t2 – 1/t1) – 5.013(1/H2 – 1/H1) + 0.9798(ln G2 – ln G1)]
V2 = V1 e
[(t1/t2) ln G1 + 3.1647(1 – t1/t2) + 0.3294(1 – H1/H2)]
G2 = e
H2 = 29.43 {1 – [ln (1 – e–0.129 t2 )]/[ln(1 – e –0.129 t1 )]} H1 [ln (1 – e –0.129 t2 )/ln (1 – e –0.129 t1 )]
CONCLUSIONS
A simultaneously interdependent system of three nonlinear
equations for predicting stand volume yield, stand
basal area and stand dominant height growth has been
presented and discussed for eucalyptus plantations grown
in the Central interior of Portugal. The ordinary least
squares (OLS) estimation method and system estimation
methods such as seemingly unrelated regression (SUR)
and three-stage least squares (3SLS) from econometrics
were used to estimate the structural parameters simultaneously,
and then the statistics of estimated results from
the system methods were compared to those obtained
from ordinary least squares. The results indicate that there
is a small difference between the three approaches in the
particular case but the system estimation methods perform
better for the simultaneously interdependent system
of equations in theory, especially, the 3SLS technique
accounts for both simultaneity bias and contemporaneous
correlations of the system of equations. Therefore,
the appropriate system estimation methods are recommended
for estimating parameters in simultaneously interdependent
systems of forestry equations. Moreover,
when there is a demand for the parameters to be the same
in both the growth and yield equations in the system of
equations, the system estimation methods would be more
adequate than the ordinary least squares method.
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