# Ghosh Model

## 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 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 the direct-output coefficients matrix that results, these 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

or, 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

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.

## See Also

## Further Resources

## References

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