# lq: Simple Location Quotient Updating In ioanalysis: Input Output Analysis

## Description

Uses simple linear quotient technique to update the matrix of technical input coefficients (A)

## Usage

 1 lq(io) 

## Arguments

 io An InputOutput class object from as.inputoutput

## Details

Uses the simple linear quotient technique as follows:

lq_i = \frac{X_i^r / X^r}{X_i^n / X^n}

where X^n is the total production, X^r is the total production for region r, X^r_i is the production for region r sector i, and X^n_i is the total production for the ith sector.

Then lq is converted such that if lq_i > 1, then lq_i = 1. Then lq is converted into a diagonal matrix of values less than or equal to 1, which gives us our final results

\hat{A} = A lq

## Value

Produces the forecast of the matrix of technical input coefficients (A) using the Slq technique.

John J. P. Wade

## References

Blair, P.D. and Miller, R.E. (2009). "Input-Output Analysis: Foundations and Extensions". Cambridge University Press

Nazara, Suahasil & Guo, Dong & Hewings, Geoffrey J.D., & Dridi, Chokri, 2003. "PyIO. Input-Output Analysis with Python". REAL Discussion Paper 03-t-23. University of Illinois at Urbana-Champaign. (http://www.real.illinois.edu/d-paper/03/03-t-23.pdf)

## Examples

 1 2 3 4 data(toy.IO) class(toy.IO) Anew <- lq(toy.IO) 

### Example output

Loading required package: ggplot2