Page 123 - Azerbaijan State University of Economics

THE JOURNAL OF ECONOMIC SCIENCES: THEORY AND PRACTICE, V.82, # 2, 2025, pp. 117-137

price method, system of equations method, trade cost method, and markup method for
assessing Armington elasticities. Annabi, N.; Cockburn, J.; Decaluwé, B. (2006) focus
on the estimation of functional forms and their parameters used in general equilibrium
models, the mathematical and methodological foundations of CES-type function
parameter estimation — including Armington and CET functions—and information
on the methods employed in existing research. In practice, when constructing general
equilibrium models, trade elasticities are estimated using econometric or entropy
methods. In some cases, researchers rely on elasticity values from other countries
available in literature, or occasionally on their own judgment. Although econometric
methods are the most widely used, they require the availability of relevant indicators
for a given country and their necessary dynamics. The econometric approach involves
evaluating the first-order condition of the optimization problem using the linear least
squares method or estimating the parameters of the CES function using the nonlinear
least squares method.

In our study, Armington and CET elasticities are estimated for the oil, non-oil, and
service sectors. As observed in the literature review, when data are available,
econometric methods are the most commonly used approach for estimating
elasticities. The first-order condition obtained from solving the optimization problem
is convenient for econometric evaluation using linear least squares (LS). However,
due to difficulties in obtaining the necessary sectoral-level price data, we will estimate
CES-type Armington and CET functions using the nonlinear least squares method.

METHODOLOGY
Although the CES function has a more general structure and allows for the
consideration of various aspects of economic agents’ behavior, its nonlinearity - even
after logarithmization - prevents evaluation using the linear least squares method.
Therefore, the nonlinear least squares method is employed to estimate this function
(Kubaniva, M.; Tabata, M.; Hasebe, Y. (1991)).

Assume that the theoretical form of a nonlinear function F, which characterizes the
dependence of the dependent variable Y on the explanatory variables X1, X2 ,...., Xn, is
known:

Y = F (X1, X2 ,...., Xn )

However, the values of the parameters a1, a2 ,...., an associated with the explanatory
variables X1, X2 ,...., Xn are unknown. Each parameter reflects the effect of the

explanatory variable on the dependent variable . These parameters must therefore

be estimated. For this purpose, observations are collected. For each observed value

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