La varianza delle previsioni nei modelli econometrici

Calzolari, Giorgio (1987): La varianza delle previsioni nei modelli econometrici. Published in: CLEUP Editore - Padova - Italy , Vol. 3, No. Serie didattica (November 1987): pp. 1-230.

Abstract

In econometric models specified as systems of simultaneous equations, forecast errors can be regarded as random variables whose variances can be investigated, analyzed and estimated. This book summarizes results available in the literature for linear and nonlinear econometric models, when forecasts are one-step ahead or multi-steps ahead. Theoretical, practical and computational problems are considered. Complete data-sets and detailed numerical results are provided for several models; these results can be replicated by econometric researches when "tuning" their computer algorithms.

• Item Type: MPRA Paper
• English Title: Forecast variance in econometric models
• Language: Italian
• Keywords: Econometric models; simultaneous equations, forecast; variance of forecast error
• Subjects: C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C53 - Forecasting and Prediction Methods ; Simulation Methods

References

Ahlstedt, M. (1986): Small Sample Estimation and Stochastic Simulation of an Econometric Model. Helsinki: Suomen Pankki (Bank of Finland), Institute for Economic Research, Series D, No. 63.

Amemiya, T. (1977): "The Maximum Likelihood and the Nonlinear Three-Stage Least Squares in the General Nonlinear Simultaneous Equation Model", Econometrica 45, 955-968.

Amemiya, T. (1983): "Non-linear Regression Models", in in Handbook of Econometrics, ed. by Z. Griliches and M. D. Intriligator. Amsterdam: North-Holland Publishing Company, Vol. I, 333-389.

Amirkhalkhali, S., and A. Naini (1985): "On the Predictive Efficiency in Simultaneous Equation Models: A Simulation Study". Halifax: Saint Mary's University, Department of Economics, Discussion Paper.

Baillie, R. T. (1981): "Prediction from the Dynamic Simultaneous Equation Model with Autoregressive Errors", Econometrica 49, 1331-1337.

Berndt, E. K., B. H. Hall, R. E. Hall, and J. A. Hausman (1974): "Estimation and Inference in Nonlinear Structural Models", Annals of Economic and Social Measurement 3, 653-665.

Belsley, D. A. (1980): "On the Efficient Computation of the Nonlinear Full-Information Maximum-Likelihood Estimator", Journal of Econometrics 14, 203-225.

Bianchi, C., and G. Calzolari (1980): "The One-Period Forecast Errors in Nonlinear Econometric Models", International Economic Review 21, 201-208.

Bianchi, C., and G. Calzolari (1982): "Evaluating Forecast Uncertainty Due to Errors in Estimated Coefficients: Empirical Comparison of Alternative Methods", in Evaluating the Reliability of Macro-Economic Models, ed. by G. C. Chow and P. Corsi. New York: John Wiley & Sons, Inc., 251-277.

Bianchi, C., and G. Calzolari (1983): "Standard Errors of Forecasts in Dynamic Simulation of Nonlinear Econometric Models: Some Empirical Results", in Time Series Analysis: Theory and Practice 3, ed. by O. D. Anderson. Amsterdam: North-Holland Publishing Company, 177-198.

Bianchi, C., G. Calzolari, and P. Corsi (1976): "Divergences in the Results of Stochastic and Deterministic Simulation of an Italian Non-Linear Econometric Model", in Simulation of Systems, ed. by L. Dekker. Amsterdam: North-Holland Publishing Company, 653-661.

Bianchi, C., G. Calzolari, and P. Corsi (1979): "A Note on the Numerical Results by Goldberger, Nagar and Odeh", Econometrica 47, 505-506.

Bianchi, C., G. Calzolari e F. Sartori (1982): "Stime 2SLS con Componenti Principali di un Modello Non Lineare dell'Economia Italiana", Note Economiche 2, 114-137.

Brillet, J. L. (1981): "Mini-DMS: Modele Macroeconomique de Simulation". Paris: INSEE, Archives & Documents No. 35.

Brown, B. W., and R. S. Mariano (1984): "Residual-Based Procedures for Prediction and Estimation in a Nonlinear Simultaneous System", Econometrica 52, 321-343.

Brundy, J. M., and D. W. Jorgenson (1971): "Efficient Estimation of Simultaneous Equations by Instrumental Variables", The Review of Economics and Statistics 53, 207-224.

Calzolari, G. (1979): "Antithetic Variates to Estimate the Simulation Bias in Non-Linear Models", Economics Letters 4, 323-328.

Calzolari, G. (1981): "A Note on the Variance of Ex-Post Forecasts in Econometric Models", Econometrica 49, 1593-1595.

Calzolari, G. (1987): "Forecast Variance in Dynamic Simulation of Simultaneous Equation Models". Pisa: Centro Scientifico IBM (in corso di stampa su Econometrica 55/56).

Calzolari, G., and P. Corsi (1977): "Stochastic Simulation as a Validation Tool for Econometric Models", in Models for Regional Planning and Policy-Making, ed. by A. Straszak, and B. V. Wagle. Peterlee: IBM UKSC 0097, 359-369.

Calzolari, G., and L. Panattoni (1984): "Evaluating Forecast Uncertainty in Econometric Models: The Effect of Alternative Estimators of Maximum Likelihood Covariance Matrix". Pisa: Centro Scientifico IBM, articolo presentato a The Fourth International Symposium on Forecasting, London Business School, 8-11 Luglio.

Calzolari, G., and L. Panattoni (1987): "Alternative Estimators of FIML Covariance Matrix: A Monte Carlo Study". Pisa: Centro Scientifico IBM (in corso di stampa su Econometrica 56).

Calzolari, G., and F. P. Sterbenz (1986): "Control Variates to Estimate the Reduced Form Variances in Econometric Models", Econometrica 54, 1483-1490.

Campos, J. (1986): "Confidence Intervals for the Sum of Forecasts". Caracas: Banco Central de Venezuela, Departamento de Modelos y Analisis Coyuntural, Discussion Paper.

Chernoff, H., and N. Divinsky (1953): "The Computation of Maximum-Likelihood Estimates of Linear Structural Equations", in Studies in Econometric Method, ed. by W. C. Hood and T. C. Koopmans. New York: John Wiley & Sons, Inc., Cowles Commission Monograph No. 14, 236-302.

Chong, Y. Y., and D. F. Hendry (1986): "Econometric Evaluation of Linear Macro-Economic Models", The Review of Economic Studies 53, 671-690.

Christ, C. F. (1966): Econometric Models and Methods. New York: John Wiley & Sons, Inc.

Contini, B. (1973): Introduzione alla Econometria. Bologna: Societa' editrice il Mulino.

Cooper, J. P., and S. Fischer (1974): "Monetary and Fiscal Policy in the Fully Stochastic St. Louis Econometric Model", Journal of Money, Credit, and Banking 6, 1-22.

Corker, R., R. Ellis and S. Holly (1983): "Uncertainty and Forecasting Precision". London Business School, Centre for Economic Forecasting, Discussion Paper No.98.

Cramer, H. (1946): Mathematical Methods of Statistics. Princeton: Princeton University Press.

Denton, F. T., and E. H. Oksanen (1972): "A Multi - Country Analysis of the Effects of Data Revisions on an Econometric Model", Journal of the American Statistical Association 67, 286-291.

Denton, F. T., and E. H. Oksanen (1973): "Data Revisions and Forecasting Accuracy: An Econometric Analysis Based on Preliminary and Revised National Accounting Estimates", The Review of Income and Wealth 19, 437-452.

Dhrymes, P. J. (1970): Econometrics: Statistical Foundations and Applications. New York: Harper & Row.

Dhrymes, P. J. (1971): "A Simplified Structural Estimator for Large-Scale Econometric Models", Australian Journal of Statistics 13, 168-175.

Di Fonzo, T. (1986): "Revisioni Occasionali e Cambiamenti di Base: Un' Analisi di Sensitivita' delle Stime di Modelli", in Errori nei Dati Preliminari, Previsioni e Politiche Economiche, a cura di U. Trivellato. Padova: CLEUP, 241-265.

Dutta, M., and E. Lyttkens (1974): "Iterative Instrumental Variables Method and Estimation of a Large Simultaneous System", Journal of the American Statistical Association 69, 977-986.

Fair, R. C. (1980): "Estimating the Expected Predictive Accuracy of Econometric Models", International Economic Review 21, 355-378.

Faliva, M. (1987): Econometria: Principi e Metodi. Torino: UTET.

Fisher, P., and M. Salmon (1986): "On Evaluating the Importance of Nonlinearity in Large Macroeconometric Models", International Economic Review 27, 625-646.

Freedman, A. D., and S. C. Peters (1984): "Bootstrapping an Econometric Model: Some Empirical Results", Journal of Business and Economics Statistics 2, 150-158.

Fuller, W. A. (1980): "The Use of Indicator Variables in Computing Predictions", Journal of Econometrics 12, 231-243.

Gallant, A. R. (1977): "Three-Stage Least-Squares Estimation for a System of Simultaneous, Nonlinear, Implicit Equations", Journal of Econometrics 5, 71-88.

Ghizzetti, A. (1960-61): Lezioni di Analisi Matematica, Vol. I. Roma: Libreria Eredi Virgilio Veschi.

Ghizzetti, A. (1961-62): Lezioni di Analisi Matematica, Vol. II. Roma: Libreria Eredi Virgilio Veschi.

Giannini, C., and R. Mosconi (1986): "Predictions from Unrestricted VAR Models with Deterministic Components". Universita' di Pavia: Quaderni dell'Istituto di Scienze Economiche e Statistiche, CR-14.

Girshick, M. A., and T. Haavelmo (1953): "Statistical Analysis of the Demand for Food: Examples of Simultaneous Estimation of Structural Equations", in

Studies in Econometric Method, ed. by W. C. Hood and T. C. Koopmans. New York: John Wiley & Sons, Inc., Cowles Commission Monograph No. 14, 92-111.

Goldberger, A. S., A. L. Nagar and H. S. Odeh (1961): "The Covariance Matrices of Reduced-Form Coefficients and of Forecasts for a Structural Econometric Model", Econometrica 29, 556-573.

Grassini, M. (1971): Lezioni di Econometrica. Pisa: CNUCE, Centro Nazionale Universitario di Calcolo Elettronico.

Haitovsky, Y., and N. Wallace (1972): "A Study of Discretionary and Nondiscretionary Monetary and Fiscal Policies in the Context of Stochastic Macroeconometric Models", in The Business Cycle Today, Fiftieth Anniversary Colloquium I, ed. by V. Zarnowitz. New York: National Bureau of Economic Research, Columbia University Press, 261-309.

Hall, S. G. (1986): "The Importance of Non-Linearities in Large Forecasting Models with Stochastic Error Processes", Journal of Forecasting 5, 205-215.

Hatanaka, M. (1978): "On the Efficient Estimation Methods for the Macro-Economic Models Nonlinear in Variables", Journal of Econometrics 8, 323-356.

Hausman, J. A. (1974): "Full Information Instrumental Variables Estimation of Simultaneous Equations Systems", Annals of Economic and Social Measurement 3, 641-652.

Hendry, D. F. (1971): "Maximum Likelihood Estimation of Systems of Simultaneous Regression Equations with Errors Generated by a Vector Autoregressive Process", International Economic Review 12, 257-272.

Hendry, D. F. (1984): "Monte Carlo Experimentation in Econometrics", in Handbook of Econometrics, ed. by Z. Griliches and M. D. Intriligator. Amsterdam: North-Holland Publishing Company, Vol. II, 937-976.

Hooper, J. W., and A. Zellner (1961): "The Error of Forecast for Multivariate Regression Models", Econometrica 29, 544-555.

Howrey, E. P., and H. H. Kelejian (1971): "Simulation versus Analytical Solutions: the Case of Econometric Models", in Computer Simulation Experiments with Models of Economic Systems, ed. by T. H. Naylor. New York: John Wiley & Sons, Inc., 299-319.

Howrey, E. P., and L. R. Klein (1972): "Dynamic Properties of Nonlinear Econometric Models", International Economic Review 13, 599-618.

Intriligator, M. D. (1978): Econometric Models, Techniques, and Applications. Englewood Cliffs, New Jersey: Prentice-Hall, Inc. Distributed by North-Holland Publishing Company, Amsterdam.

Johnson, N. L., and S. Kotz (1970): Continuous Univariate Distributions, Vol. I. Boston: Houghton Mifflin Company.

Klein, L. R. (1950): Economic Fluctuations in the United States, 1921-1941. New York: John Wiley & Sons, Inc., Cowles Commission Monograph No. 11.

Klein, L. R. (1974): A Textbook of Econometrics. Englewood Cliffs, New Jersey: Prentice-Hall, Inc.

Klein, L. R., A. Doud, and E. Sojo (1985): "Simplification of Large Scale Macroeconometric Models", Eastern Economic Journal 11, 28-40.

Lorenzoni, L. (1986): "Applicazione della Teoria del Controllo ad un Modello IS - LM Stimato per l'Italia". Universita' di Siena: Facolta' di Scienze Economiche e Bancarie, Tesi di Laurea.

Mairesse, J. (1982): "Discussion", in Evaluating the Reliability of Macro-Economic Models, ed. by G. C. Chow and P. Corsi. New York: John Wiley & Sons, Inc., 277-279.

Makridakis, S., and S. C. Wheelwright (1978): Forecasting Methods and Applications. New York: John Wiley & Sons, Inc.

Malinvaud, E. (1968): Statistical Methods of Econometrics. Amsterdam: North-Holland Publishing Company.

Mariano, R. S., and B. W. Brown (1983): "Asymptotic Behavior of Predictors in a Nonlinear Simultaneous System", International Economic Review 24, 523-536.

McCarthy, M. D. (1972): "Some Notes on the Generation of Pseudo-Structural Errors for Use in Stochastic Simulation Studies", in Econometric Models of Cyclical Behavior, ed. by B. G. Hickman. New York: National Bureau of Economic Research, Studies in Income and Wealth No. 36, Columbia University Press, 185-191.

Moy, W. A. (1971): "Variance Reduction", in Computer Simulation Experiments with Models of Economic Systems, ed. by T. H. Naylor. New York: John Wiley & Sons, Inc., 269-289.

Nagar, A. L. (1969): "Stochastic Simulation of the Brookings Econometric Model", in The Brookings Model: Some Further Results, ed. by J. S. Duesenberry, G. Fromm, L. R. Klein, and E. Kuh. Amsterdam: North Holland, 425-456.

Nissen, D. H. (1968): "A Note on the Variance of a Matrix", Econometrica 36, 603-604.

Oliver, J. (1980): "An Algorithm for Numerical Differentiation of a Function of One Real Variable", Journal of Computational and Applied Mathematics 6, 145-153.

Pagan, A. R., and D. F. Nicholls (1984): "Estimating Predictions, Prediction Errors and Their Standard Deviations Using Constructed Variables", Journal of Econometrics 24, 293-310.

Peters, S. C., and D. A. Freedman (1985): "Using the Bootstrap to Evaluate Forecasting Equations", Journal of Forecasting 4, 251-262.

Phillips, P. C. B., and M. R. Wickens (1978): Exercises in Econometrics. Oxford: Philip Allan Publishers Limited, Vol. II.

Rao, C. R. (1973): Linear Statistical Inference and its Applications. New York: John Wiley & Sons, Inc.

Rettore, E. e U. Trivellato (1986): "Effetti dei Dati Provvisori sull'Errore di Previsione di Modelli ad Equazioni Simultanee", in Errori nei Dati Preliminari, Previsioni e Politiche Economiche, a cura di U. Trivellato. Padova: CLEUP, 267-284.

Salkever, D. S. (1976): "The Use of Dummy Variables to Compute Predictions, Prediction Errors and Confidence Intervals", Journal of Econometrics 4, 393-397.

Sampoli, L. (1986): "Costruzione e Convalida di un Modello Macroeconomico per l'Italia". Universita' di Siena: Facolta' di Scienze Economiche e Bancarie, Tesi di Laurea.

Sartori, F. (1978): "Caratteristiche e Struttura del Modello", in Un Modello Econometrico dell'Economia Italiana; Caratteristiche e Impiego. Roma: Ispequaderni 1, 9-36.

Schink, G. R. (1971): "Small Sample Estimates of the Variance Covariance Matrix of Forecast Error for Large Econometric Models: The Stochastic Simulation Technique". University of Pennsylvania: Graduate School of Arts and Sciences, Ph. D. Dissertation.

Schmidt, P. (1973): "The Asymptotic Distribution of Dynamic Multipliers", Econometrica 41, 161-164.

Schmidt, P. (1974): "The Asymptotic Distribution of Forecasts in the Dynamic Simulation of an Econometric Model", Econometrica 42, 303-309.

Schmidt, P. (1977): "Some Small Sample Evidence on the Distribution of Dynamic Simulation Forecasts", Econometrica 45, 997-1005.

Slutsky, E. (1925): "Ueber Stochastische Asymptoten und Grenzwerte", Metron 5, No. 3.

Sterbenz, F. P. (1981): "Stochastic Simulation of the Linkage of Macroeconomic Models and Techniques for Generating Pseudorandom Vectors with Desirable Properties". University of Pennsylvania: Graduate School of Arts and Sciences, Ph. D. Dissertation.

Sterbenz, F. P., and G. Calzolari (1987): "The Impact of Structural Error Specifications on the Simulation of Nonlinear Econometric Models". Columbus: Ohio State University, Discussion Paper.

Theil, H. (1971): Principles of Econometrics. New York: John Wiley & Sons, Inc.

Trivellato, U., and E. Rettore (1986): "Preliminary Data Errors and Their Impact on the Forecast Error of Simultaneous Equations Models", Journal of Business & Economic Statistics 4, 445-453.

Yamamoto, T. (1980): "On the Treatment of Autocorrelated Errors in the Multiperiod Prediction of Dynamic Simultaneous Equation Models", International Economic Review 21, 735-748.

Zacks, S. (1971): The Theory of Statistical Inference. New York: John Wiley & Sons, Inc.

Zaghini, E. (1970): Lezioni di Econometrica. Roma: Edizioni dell'Ateneo.