ras: ras Updating Proejcting

Description Usage Arguments Details Value Author(s) References See Also Examples

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

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ras(io, x1, u1, v1, tol, maxiter, type, 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: 0.001

maxiter

Numeric. The maximum number of iterations to try for convergence. Defualt: 10000

type

Character. The type of norm to use for convergence. See ?norm. Default: "o"

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] = 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

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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)

jjpwade/ioanalysis documentation built on May 6, 2019, 6:57 p.m.