Difference between revisions of "Ghosh Model"

Latest revision as of 18:12, 16 November 2023

Definition

A Ghosh Model is a category of Supply Side Input–Output Models that represent an alternative type of Input-Output Model to the more commonly used demand side Leontief Model.

The two categories of models are based on the same set of economic data^[1] but interpret and use them differently.

Structure

Contrary to the static IO quantity model, the static IO price model (or Gosh model) is downstream oriented. It captures the effects of input factors, such as wages, on sectoral production prices. As such, they assume that cost/price changes are passed on completely and directly (cost push/through). The price model is not relevant in the context of classical EIA and EEIO analyses.

The Ghosh Model approach is made operational by essentially transposing the vertical (column) view of an Input-Output model to a horizontal (row) one. Instead of dividing each column of Primary Input $Z$ by the gross output of the sector associated with that column, the suggestion is to divide each row of Z by the gross output of the sector associated with that row.

If we denote by $B$ the direct-output coefficients matrix that results, these $b_{ij}$ coefficients represent the distribution of sector i’s outputs across sectors j that purchase inter-industry inputs from i. These are frequently called allocation coefficients, as opposed to technical coefficients.

Formula

The model uses the same quantities that underpin the demand-driven model, namely Z, f, and v, from which x follows as

x = Z i + f

or, as,

x = i Z + v

x^{T} = x^{T} B + v^{T}

where v is Value Added or primary factors and B is the distribution coefficients matrix, calculated by the elements of the SAM divided by the total of their corresponding row. The Ghosh multipliers matrix is derived as

G = (I - B)^{-1}

In the downstream or Ghosh model, a matrix of direct sales A, is defined as the inter-industrial flows from an industry i to an industry j per gross input of i.

An element of the total sales matrix, or Ghosh inverse, represents the amount of gross input into industry j that absorbed, or utilised a unit of primary inputs v into industry i.

Further Resources

References

↑ R.E. Miller and P.D. Blair, Input-Output Analysis: Foundations and Extensions, Second Edition, Cambridge University Press, 2009

[1] R.E. Miller and P.D. Blair, Input-Output Analysis: Foundations and Extensions, Second Edition, Cambridge University Press, 2009

[1]

@@ Line 1: / Line 1: @@
 == Definition ==
-A '''Ghosh Model''' is a category of ''Supply Side'' Input–Output Models that represent an alternative type of [[Input-Output Model]] to the ''demand side'' [[Leontief Model]].
+A '''Ghosh Model''' is a category of ''Supply Side'' Input–Output Models that represent an alternative type of [[Input-Output Model]] to the more commonly used ''demand side'' [[Leontief Model]].
-The two categories are based on the same set of data<ref>R.E. Miller and P.D. Blair, Input-Output Analysis: Foundations and Extensions, Second Edition, Cambridge University Press, 2009</ref> but interpret them differently.
+The two categories of models are based on the same set of economic data<ref>R.E. Miller and P.D. Blair, Input-Output Analysis: Foundations and Extensions, Second Edition, Cambridge University Press, 2009</ref> but interpret and use them differently.
 == Structure ==
-Contrary to the static IO quantity model, the static IO price model (or Gosh model) is ''downstream'' oriented. It captures the effects of input factors, such as wages, on sectoral production prices. As such, they assume that cost/price changes are passed on completely and directly (''cost push/through''). The price model is not relevant in the context of classical EIA and EEIO analyses.
+Contrary to the static IO ''quantity'' model, the static IO ''price'' model (or Gosh model) is ''downstream'' oriented. It captures the effects of [[Input Factor | input factors]], such as wages, on sectoral production prices. As such, they assume that cost/price changes are passed on completely and directly (''cost push/through''). The price model is not relevant in the context of classical EIA and EEIO analyses.
-The Ghosh Model  approach is made operational by essentially ''transposing'' the vertical (column) view of an IO model to a horizontal (row) one. Instead of dividing each column of [[Primary Input]] <math>Z</math> by the gross output of the sector associated with that column, the suggestion is to divide each row of Z by the gross output of the sector associated with that row.
+The Ghosh Model  approach is made operational by essentially ''transposing'' the vertical (column) view of an Input-Output model to a horizontal (row) one. Instead of dividing each ''column'' of [[Primary Input]] <math>Z</math> by the gross output of the sector associated with that column, the suggestion is to divide each ''row'' of Z by the gross output of the sector associated with that row.
-If we denote by <math>B</math> the direct-output coefficients matrix that results, these <math>b_{ij}</math> coefficients represent the distribution of sector i’s outputs across sectors j that purchase interindustry inputs from i. These are frequently called allocation coefficients, as opposed to technical coefficients.
+If we denote by <math>B</math> the direct-output coefficients matrix that results, these <math>b_{ij}</math> coefficients represent the distribution of sector i’s outputs across sectors j that purchase inter-industry inputs from i. These are frequently called ''allocation coefficients'', as opposed to technical coefficients.
 == Formula  ==
-Uses the same quantities that underpin the demand-driven model namely Z, f, and v, from which x follows as x = Z i + f or as x  = i Z + v
+The model uses the same quantities that underpin the demand-driven model, namely Z, f, and v, from which x follows as
+:<math>
+x = Z i + f
+</math>
+or, as,
+:<math>
+x  = i Z + v
+</math>
 :<math>
@@ Line 18: / Line 26: @@
 </math>
-where v is value added or primary factors and B is the distribution coefficients matrix, calculated by the elements of the SAM divided by the total of their corresponding row. The Ghosh multipliers matrix is derived as
+where v is [[Value Added]] or primary factors and B is the distribution coefficients matrix, calculated by the elements of the SAM divided by the total of their corresponding row. The Ghosh multipliers matrix is derived as
 :<math>
@@ Line 24: / Line 32: @@
 </math>
-In the downstream or Ghosh model, a matrix of direct sales A, is defined as the inter-industrial flows a ij  tij =xi from an industry i to an industry j per gross input of i.
+In the downstream or Ghosh model, a matrix of direct sales A, is defined as the inter-industrial flows from an industry i to an industry j per gross input of i.
-An element lij of the total sales matrix, or Ghosh inverse L (I  Ā1 , represents the amount of gross input x0 v0 (I-Ā) into industry j that absorbed, or utilised a unit of primary inputs v into industry i. The prime denotes transposition.
+An element of the total sales matrix, or Ghosh inverse, represents the amount of gross input into industry j that absorbed, or utilised a unit of primary inputs v into industry i.
 == See Also ==
@@ Line 32: / Line 40: @@
 == Further Resources ==
-* [https://www.openriskacademy.com/mod/page/view.php?id=800 Crash Course on Input-Output Model Mathematics]
+* [https://www.openriskacademy.com/course/view.php?id=70 Crash Course on Input-Output Model Mathematics]
+* [https://www.openriskacademy.com/course/view.php?id=64 Introduction to Input-Output Models using Python]
 == References ==