ioanalysis (version 0.3.4)

ras: ras Updating Proejcting

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

Value

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

Details

Uses the ras iterative technique for updating the matrix of technical input coefficients. This takes the form: $$lim_{n \Rightarrow \infty} A^{2n} = lim_{n \Rightarrow \infty} [\hat{R}^n ... \hat{R}^1]A_t[\hat{S}^1 ... \hat{S}^n] = \hat{A}_{t+1}$$ 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.

References

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

See Also

as.inputoutput, lq

Examples

# NOT RUN {
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)
# }