Page 124 - Azerbaijan State University of Economics

Yadulla Hasanli, Gunay Rahimli, Fuad Quliyev, Mattia Ferrari: Evaluation of Sectoral
Foreign Trade Elasticities of Azerbaijan

, the corresponding values of the explanatory variables ( , , … , ) for =

2

1
1,2, … , are obtained. Thus,

Yi = Fi (a1, a2 ,...., an; Xi1, Xi2 ,...., Xin )+ Ui, i= m,1 , (7)

where denotes the disturbance term. The objective in (7) is to identify values of the

parameters , , … , such that the theoretical values of the dependent variable are
1

2
as close as possible to the observed values. In other words, the deviations must be

minimized. The parameters satisfying this condition are typically estimated using the
method of least squares.

The Armington and CET functions employed in our study are nonlinear with respect
to their parameters, similar to the CES production function. It should be noted that if
a function is nonlinear in variables (but linear in parameters), linearization is
straightforward. Because statistical values of the variables are drawn from
observations, the function can be linearized regardless of the specific type of
nonlinearity. For example, consider the Cobb–Douglas production function:

= ,

where denotes GDP, capital, and labor, while , , and are the parameters.
Taking logarithms of both sides yields:

log ( ) = log ( ) + log ( ) + log ( )

By defining log ( ) = , log ( ) = , log ( ) = , and log ( ) = , the model
∗
∗
∗
∗
becomes a linear specification:

∗
∗
= + + .
∗
∗

In any applied econometric software package (such as EViews or SPSS), the
parameters of such linear regression models can be estimated using various methods,
including ordinary least squares (OLS). The Gauss–Markov assumptions and the
Gauss–Markov theorem apply to regression models that are linear—in other words,
linear in parameters. Although certain extensions of the Gauss–Markov framework
exist, there is no general theorem that guarantees the Gauss–Markov conditions or
BLUE-type optimality for regression models that are nonlinear in parameters
(Verbeek, M., (2017). Consequently, for nonlinear specifications such as the CES
function, numerical estimation methods remain the standard and accepted approach
in applied research.

Therefore, for nonlinear-in-parameter models, the minimization of the objective
function

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