ras: ras Updating Proejcting

In ioanalysis: Input Output Analysis

Description

Uses the ras technique to update the matrix of technical input coefficients A. You must have knowledge of or forecasts for the following three objects: (1) row sums u1 of A, (2) column sums v1 of A, and (3) total production x1.

Usage

ras(io, x1, u1, v1, tol, maxiter, verbose = FALSE)

Arguments

io	An InputOutput class object from as.inputoutput
x1	Vector. The forecast for future total production of each region-sector combination, matching the X object in io
u1	Vector. The forecast for future row sums of the matrix of technical input coefficients in A from io
v1	Vector. The forecast for future column sums of the matrix of technical input coefficients in A from io
tol	Numeric. The tolerance for convergence. Default: 1e-06
maxiter	Numeric. The maximum number of iterations to try for convergence. Defualt: 10000
verbose	Logical. If TRUE will print the iteration and norm at each step. This is useful if the dataset is large. Deafult: FALSE

Details

Uses the ras iterative technique for updating the matrix of technical input coefficients. This takes the form:

lim_{n \Rightarrow ∞} A^{2n} = lim_{n \Rightarrow ∞} [\hat{R}^n ... \hat{R}^1]A_t[\hat{S}^1 ... \hat{S}^n] = \hat{A}_{t+1}

where R^1 = diag(u_{t+1}/u_0), u_0 = A_tX, and u_{t+1} = u1. Similarly S^1 = diag(v_{t+1}/v_0), v_0 = XR^1A_t.

Each iteration calculates the full ras object; that is, 2 steps are caluclated per iteration.

See Blair and Miller (2009) for more details.

Value

Produces the forecast of the matrix of technical input coefficients given the forecasted row sums, column sums, and total production.

Author(s)

John J. P. Wade

References

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

See Also

as.inputoutput, lq

Examples

data(toy.IO)
class(toy.IO)

set.seed(117)
growth <- 1 + 0.1 * runif(10)
sort(growth)

X <- toy.IO$X
X1 <- X * growth
U <- rowSums(toy.IO$Z)
U1 <- U * growth
V <- colSums(toy.IO$Z)
V1 <- V * growth

ras <- ras(toy.IO, X1, U1, V1, maxiter = 10, verbose = TRUE)

Example output

Loading required package: ggplot2
Loading required package: plot3D
Loading required package: lpSolve
Warning message:
no DISPLAY variable so Tk is not available 
[1] "InputOutput"
 [1] 1.000117 1.004538 1.007363 1.013443 1.043169 1.044370 1.046505 1.053531
 [9] 1.071782 1.075570
  Iteration: 1   RMSE: 0.000887824134655695 
  Iteration: 2   RMSE: 2.64050640741665e-05 
  Iteration: 3   RMSE: 1.33487833734874e-06 
  Iteration: 4   RMSE: 7.71764009426244e-08 

ioanalysis documentation built on Jan. 13, 2021, 5:16 p.m.