a ij ¼
z ij
x ij
ð3:3Þ
According to the structure of the IOM, these coefficients (a ij ) are fixed because
they represent the technological capacity of the society. They only vary if there are
significant technological changes that modify the productive structure of the society.
Thus, the matrix of technological coefficients (A) can be defined. Through a series of
algebraic operations from Eq. (3.2), the following expression can be obtained:
X ¼ I À A
ð
Þ
À1 ∙ Y
ð3:4Þ
In Eq. (3.4), the element (I À A)
À1 is known as the Leontief inverse matrix (L ).
The structure of this equation will be used to determine the impact of the technological change in Ecuador on the national economy, considering the impacts per se due
to the change in the refining structure, known as direct effects, and the impacts along
the productive chains, known as induced effects.
Following the national accounts provided by the Central Bank of Ecuador, the
model’s reference year is 2015, generating an input–output matrix of 71 sectors (Z I ).
Based on the theory shown, we obtain the respective technical coefficients (a ijI ) and
consequently an initial matrix of technical coefficients (A I ), considering Ecuador’s
current refining capacity.
The literature review about the application of this model to the Ecuadorian
economy includes estimates of the transport sector demand (CEPAL 2017), analysis
of the impact of variations in the agricultural sector (Banderas and Hidalgo 2013),
identification of key sectors in the national economy (Fernández 2009), estimates of
the contribution of the construction sector to national GDP (Yagual Velástegui et al.
2018), and estimates of input–output matrices for the provinces of Guayas (Palma
Luna and Vega Ramírez 2016) and Carchi (Fundación Alianza Estratégica 2015).
3.4.2 General Equilibrium Model
The general equilibrium model (GEM) is based on the theory of general equilibrium
proposed by Walras. It is worth noting that the complexity of the model due to the
significant number of equations, number of variables and iterations between them,
made it difficult to enhance its development for several years. However, due to
advancements in computer and high-speed processors, the development of models
based on this theory was possible.
The theory of general equilibrium stems from the premise of the existence of an
equilibrium between the different actors in the market. As such, this type of model
seeks to explain the behaviour and interactions of the actors when faced with
alterations to the condition of equilibrium, using mathematical equations for the
supply (producers) and demand (consumers) of products or services according to the
realities of each society.
46
D. Ortega-Pacheco et al.
z ij
x ij
ð3:3Þ
According to the structure of the IOM, these coefficients (a ij ) are fixed because
they represent the technological capacity of the society. They only vary if there are
significant technological changes that modify the productive structure of the society.
Thus, the matrix of technological coefficients (A) can be defined. Through a series of
algebraic operations from Eq. (3.2), the following expression can be obtained:
X ¼ I À A
ð
Þ
À1 ∙ Y
ð3:4Þ
In Eq. (3.4), the element (I À A)
À1 is known as the Leontief inverse matrix (L ).
The structure of this equation will be used to determine the impact of the technological change in Ecuador on the national economy, considering the impacts per se due
to the change in the refining structure, known as direct effects, and the impacts along
the productive chains, known as induced effects.
Following the national accounts provided by the Central Bank of Ecuador, the
model’s reference year is 2015, generating an input–output matrix of 71 sectors (Z I ).
Based on the theory shown, we obtain the respective technical coefficients (a ijI ) and
consequently an initial matrix of technical coefficients (A I ), considering Ecuador’s
current refining capacity.
The literature review about the application of this model to the Ecuadorian
economy includes estimates of the transport sector demand (CEPAL 2017), analysis
of the impact of variations in the agricultural sector (Banderas and Hidalgo 2013),
identification of key sectors in the national economy (Fernández 2009), estimates of
the contribution of the construction sector to national GDP (Yagual Velástegui et al.
2018), and estimates of input–output matrices for the provinces of Guayas (Palma
Luna and Vega Ramírez 2016) and Carchi (Fundación Alianza Estratégica 2015).
3.4.2 General Equilibrium Model
The general equilibrium model (GEM) is based on the theory of general equilibrium
proposed by Walras. It is worth noting that the complexity of the model due to the
significant number of equations, number of variables and iterations between them,
made it difficult to enhance its development for several years. However, due to
advancements in computer and high-speed processors, the development of models
based on this theory was possible.
The theory of general equilibrium stems from the premise of the existence of an
equilibrium between the different actors in the market. As such, this type of model
seeks to explain the behaviour and interactions of the actors when faced with
alterations to the condition of equilibrium, using mathematical equations for the
supply (producers) and demand (consumers) of products or services according to the
realities of each society.
46
D. Ortega-Pacheco et al.