Stochastic input-output modeling

Gurgul, Henryk (2007): Stochastic input-output modeling. Published in: Managerial Economics , Vol. 1, No. 2 (2007): pp. 57-70.

Abstract

Input-output data (IO data) are compiled by survey methods, which are based on a sample. It is well known, that IO matrices are not stable over time. Therefore different actualizations methods have been developed. Econometric methods play important role in the realization of input-output matrices. These methods, on the basis of the relevant data, can facilitate the formulation of IO value forecasts. Established parameter and random term estimators are a source of uncertainty for IO parameters. In a historical perspective the author discusses stochastic methods in IO theory as well as their applications.

• Item Type: MPRA Paper
• Language: English
• Keywords: input-output, stochastic analysis
• Subjects: E - Macroeconomics and Monetary Economics > E0 - General; E - Macroeconomics and Monetary Economics > E0 - General > E00 - General

References

[1a] Bidard C., Schatteman T., The Spectrum of Random Matrices, “Economic Systems Research-Journal of International Input-Output Association” 2001, vol. 13, s. 289-298.

[1b] Białas S., Gurgul H., On hypothesis about the second eigenvalue of the Leontief matrix, “Economic Systems Research“, vol. 10, s. 285-289.

[2] Briggs F.E., On Problems of Estimation in Leontief Models, “Econometrica” 1957, vol. 25, s. 444-455.

[3] Bródy A., The Second Eigenvalue of the Leontief Matrix, “Economic Systems Research-Journal of International Input-Output Association” 1997, vol. 9, s. 253-258.

[4] Brown D.M., Giarratani F., Input-output as a Simple Econometric Model: A Comment, “Review of Economics and Statistics” 1979, vol. 61, s. 621-623.

[5] Bullard C.W., Sebald A.R., Effects of Parametric Uncertainty and Technological Change on Input-Output Models, “Review of Economics and Statistics” 1977, vol. 59, s. 75-81.

[6] Christ C.F., A Review of Input-Output Analysis, [w:] Input-Output Analysis: An Appraisal. Studies in Income and Wealth, National Bureau of Economic Research 1955, vol. 18, Princeton, NJ: Princeton University Press, s. 137-169.

[7] Czamanski S., Malizia E.E., Applicability and Limitations in the Use of National Input-Output Tables for Regional Studies, “Papers of the Regional Science Association” 1969, vol. 23, s. 65-77.

[8] Ćmiel A., Gurgul H., Dynamic input-output models with stochastic time lags, “International Journal of Systems Science” 1997, vol. 27, s. 857-861.

[9] Ćmiel A., Gurgul H., Dynamic Input-Output Models with Stochastic Matrices and Time Lags, “Economic Systems Research-Journal of International Input-Output Association” 1996, vol. 8, s. 133-143.

[10] Ćmiel A., Gurgul H., Stochastic Backward-Lag-Type Leontief Model, “The Central European Journal for Operations Research and Economics” 1997, vol. 5, s. 34-45.

[11] Ćmiel A., Gurgul H., One Sector Stochastic Growth Model, “Systems Analysis Modelling Simulations” 1999, vol. 36, s. 225-234.

[12] Dewyer P.S., Waugh F.V., On Errors in Matrix Inversion, “Journal of American Statistial Association” 1953, vol. 68, s. 289-319.

[13] Evans W.D., The Effect of Structural Matrix Errorson Interindustry Relations Estimates, Econometrica 1954, vol. 22, s. 461-480.

[14] Ganseman D., Stochastic Input-Output Analysis: A Simulation Study “Environment and Planning” 1982, vol. 14, s. 1425-1435.

[15] Garhart R.E., Jr., The Role of Error Structure in Simulations on Regional Input-output Analysis, “Journal of Regional Science” 1985, vol. 25, s. 353-366.

[16] Gerking S.D., Reconciling ‘Rows Only’ and ‘Colums Only’ Coeffi cients in an Input-Output Model, “International Regional Science Review” 1976a. vol. 1, s. 30-46.

[17] Gerking S.D., Input-Output as a Simple Econometric Model, “Review of Economics and Statistics” 1976b, vol. 58, s. 274-282.

[18] Gerking S.D., Reconciling Reconcilation Procedures in Regional Input-Output Analysis, “International Regional Science Review” 1979. vol. 4, s. 23-36, s. 38-40.

[19] Gerking S.D., Pleeter S., Minimum Variance Sampling in Input-Output Analysis, “Review of Regional Studies” 1977, vol. 7, s. 60-80.

[20] Giarratani F., Evidence on the Structure of Errors, Paper presented to the British Section Regional Science Association, September 1986, Bristol.

[21] Goicoechea A., Hansen D. R., An Input-Output Model with Stochastic Parameters, AIIE Transactions 1978, vol. 10, s. 285-291.

[22a] Gurgul H., Recursive approach of updating input-output coeffi cients, [w:] U. Derigs, A. Bachem & A. Drexl (eds.), “Operations Research Proceedings 1994” 1995, s. 370-375.

[22b] Hanseman D., Stochastic Input-Output Analysis: A simulation study, “Environment and Planning”, vol. 14, 1982, s. 1425-1435.

[23] Hanseman D., Gustafson E.F., Stochastic Input-Output Analysis: A Comment, “Review of Economics and Statistics” 1981, vol. 63, s. 468-470.

[24] Jackson R.W., The ‘Full Distribution’ Approach to Aggregate Representation in the Input-Output Modeling Framework, “Journal of Regional Science” 1986, vol. 26, s. 515-530.

[25] Jensen R.C., The Concept of Accuracy in Regional Input-Output Models, “International Regional Science Review” 1980, vol. 5, s. 139-154.

[26] Lahiri S., Satchell S., Properties of the Expected Value of the Leontief Inverse: Some Further Results, “Mathematics for Social Science” 1986, vol. 11, s. 69-82.

[27] Leontief W., Some Basic Problems of Empirical Input-Output Analysis, [w:] Input-Output Analysis: An Appraisal. Studies in Income and Wealth, National Bureau of Economic Research 1955, Princeton, NJ: Princeton University Press, vol. 18, s. 9-22.

[28] Malizia E., Bond D.L., Empirical Tests of the RAS Method of Interindustry Coeffi cient Adjustment, “Journal of Regional Science” 1974, vol. 14, s. 355-365.

[29] McCamley F., Schreiner D., Muncrief G., A Method for Estimating the Sampling Variances of Multipliers Derived from a From-To-Model, “Annals of Regional Science” 1973, vol. 7, s. 81-89.

[29’] McMenamin D.G., Haring J.V., An Appraisal of Nonsurvey Techniques for Estimating Regional Input-Output Models, “Journal of Regional Science” 1974, vol. 14, s. 191-205.

[30] Miernyk W.H., Comments on Recent Developments in Input-Output Analysis, “International Regional Science Review” 1976, vol. 1, s. 47-55.

[31] Miernyk W.H., Reply to Reconciling Reconciliation Procedures in Regional Input-Output Analysis “International Regional Science Review” 1979, vol. 4, s. 36-38.

[31’] Miernyk W.H. et al., Simulating Regional Economic Development, “Lexington“, Massachusetts, 1970.

[32] Molnar G., Simonovits A., The Subdominant Eigenvalue of a Large Stochastic Matrix, “Economic Systems Research-Journal of International Input-Output Association” 1998, vol. 10, s. 79-82.

[33] Morrison W. I., Smith P., Non-Survey Input-Output Techniques at the Small Area Level: An Evaluation, “Journal of Regional Science” 1974, vol. 14, s. 1-14.

[34] Park S., On Input-Output Multipliers with Errors in Input-Output Coefficients, “Journal of Economic Theory” 1973, vol. 6, s. 399-403.

[35] Park S., Mohtadi M., Kubursi A., Errors in Regional Nonsurvey Input-Output Models: Analytical and Simulation Results, “Journal of Regional Science” 1981, vol. 21, s. 321-340.

[36] Quandt R., Probabilistic Errors in the Leontief Systems, “Naval Research Logistics Quarterly” 1958, vol. 5, s. 155-170.

[37] Quandt R., On the Solution of Probabilistic Leontief Systems, “Naval Research Logistics Quarterly” 1959, vol. 6, s. 295-305.

[38] Rao C.R., Advanced Statistical Methods in Biometric Research, New York: Hafner Press 1952.

[39] Round J.I., An Interregional Input-Output Approach to the Evaluation of Nonsurvey Methods, “Journal of Regional Science” 1978, vol. 18, s. 179-194.

[40] Rey S. J., West G.R. Janikas M.V., Uncertainty in Integrated Models, “Economic System Research-Journal of International Input-Output Association” 2004, vol. 16, s. 259-277.

[41] Schaffer W.A., Chu K., Nonsurvey Techniques for Constructing Regional Interindustry Models, “Papers of the Regional Science Association” 1969, vol. 23, s. 83-101.

[42] Sebald A.V., An Analysis of the Sensitivity of Large Scale Input-Output Models to Parametric Uncertainties, Center for Advanced Computation Document No. 122. Urbana, II: University of Illinois at Urbana-Champaign 1974.

[43] Simonovits A., A Note on the Underestimation and Overestimation of the Leontief Inverse, “Econometrica” 1975, vol. 43, s. 493-498.

[44] Sherman J., Morrison W. J., Adjustment of an Inverse Matrix Corresponding to a Change in One Element of a Given Matrix, “Annals of Mathematical Statistics” 1950, vol. 21, s. 124-127.

[44’] Stevens B.H., Treyz G.I., Lahr M.L., On the comparative accuracy of RPC estimating techniques, [w:] Miller R.E., Polenske K.R., Rose A.Z., (eds) Frontiers of Input-Output Analysis. Oxford, Oxford University Press 1989, s. 245-267.

[45] Stevens B.H., Trainer G.A., Error Generation in Regional Input-Output Analysis and Its Implication for Non-Survey Models [w:] Economic Impact Anlysis: Methodology and Application, edited by Saul Pleeh. Boston: Martinus Nijhoff 1980, s. 68-84.

[46] Theil H., Applied Economic Forecasting, Amsterdam, The Netherlands: North Holland 1966.

[47] West G.R., An Effi cient Approach to the Estimation of Regional Input-Output Tables, “Environment and Planning” 1981, vol. 13, s. 857-867.

[48] West G.R., Sensitivity and Key Sector Analysis in Input-Output Models, “Australian Economic Papers” 1982, vol. 21, s. 365-378.

[49] West G.R., A Stochastic Analysis of an Input-Output Model, “Econometrica” 1986, vol. 54, s. 363-374.

[50] Wibe S., The Distribution of Input Coeffi cients, “Economics of Planning“ 1982, vol. 2, s. 65-70.