%0 Journal Article
%T Effets des erreurs dans les coefficients structuraux d¡¯un mod¨¨le intersectoriel £¿ rectangulaire £¿. Une approche de type Monte-Carlo
%A Autin
%A Claude
%A Fearnley
%A Jacques
%A Rioux
%A Ronald
%J -
%D 1975
%R https://doi.org/10.7202/800607ar
%X The most simple rectangular input-output models use two rectangular matrices: R a market coefficient matrix, A* a production coefficient matrix. A given exogenous demand Xo determines the sectorial activity levels X* = [I ¡ª RA*]-1Xo. We assume that A* is random with expectation A. We study the distribution of the "error" X* ¡ª X with X = [I ¡ª RA]-1Xo.(1) For the statistically independent elements of A*, we analytically prove that X < EX*.(2) In the more realistic case of statistically dependent elements of A*.(a) One submatrix of A* with T non zero elements is chosen. The probabilistic model which generates the T coefficients is as follows: a* = (1 ¡ª ¦Ì)a + ¦Ì(S/n) b* o¨´ a* is the vector of the T random elements, a is the expectation of a* whose components are observed values of a real input-output model, S is the sum of components of a, ¦Ì is a parameter between zero and one, b* is a multinomial random vector with T components and parameters n, number of drawings during an experiment, and a/S, the corresponding probabilities.We control the variability of a* through ¦Ì and n. For a given experiment, we get a realisation of A* and we compute X*. K independent experiments allow us to estimate the expectation and the variance-covariance matrix of X*, simultaneous confidence intervals for the expectation of the components of X*, and also a few global measures of errors on X*.The Canadian model for 1961 (16 productive sectors, 40 commodities), is tested with that model.The main result is: the relative errors, measured according to the variation coefficients, are greatly reduced when we pass from the "errors" on a* to the corresponding "errors" on X*.(b) The same random model is also simultaneously applied to 2 or 3 sub-matrices of A*
%U https://www.erudit.org/en/journals/ae/1975-v51-n1-ae3130/800607ar/