Calzolari, Giorgio and Panattoni, Lorenzo (1988): Mode predictors in nonlinear systems with identities. Published in: International Journal of Forecasting. Working paper presented at the European Meeting of the Econometric Society, Bologna, 1988. pp.129 No. 6 (1990): pp. 317326.

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Abstract
For a nonlinear system of simultaneous equations, the mode of the joint distribution of the endogenous variables in the forecast period is proposed as alternative to the more usual deterministic or mean predictors. A first method follows from maximizing the joint density of a subset of the endogenous variables, corresponding to stochastic equations only (analogously to FIML estimation, where identities are first substituted into stochastic equations). Then a more general approach is developed, which maintains the identities. The model with identities is viewed as a mapping between the space of the random errors and a hypersurface in the space of the endogenous variables; the probability density is defined, and maximization is performed on such a hypersurface. Experimental results on these two mode predictors (and comparisons with deterministic and mean predictors) are provided for a macro model of the Italian economy.
Item Type:  MPRA Paper 

Original Title:  Mode predictors in nonlinear systems with identities 
Language:  English 
Keywords:  Nonlinear econometric models, simultaneous equations, deterministic predictor, mean predictor, joint density function. 
Subjects:  C  Mathematical and Quantitative Methods > C6  Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C63  Computational Techniques ; Simulation Modeling C  Mathematical and Quantitative Methods > C3  Multiple or Simultaneous Equation Models ; Multiple Variables 
Item ID:  28845 
Depositing User:  Giorgio Calzolari 
Date Deposited:  10 Apr 2011 08:14 
Last Modified:  05 May 2019 06:22 
References:  Amemiya, T. (1983): "Nonlinear Regression Models", in in Handbook of Econometrics, ed. by Z. Griliches and M. D. Intriligator. Amsterdam: NorthHolland Publishing Company, Vol. I, 333389. Anderson,T.W. (1958), An Introduction to Multivariate Statistical Analysis, New York, John Wiley. Bianchi, C., G. Calzolari, and P. Corsi (1976): "Divergences in the Results of Stochastic and Deterministic Simulation of an Italian NonLinear Econometric Model", in Simulation of Systems, ed. by L. Dekker. Amsterdam: NorthHolland Publishing Company, 653661. Bianchi, C., and G. Calzolari (1980): "The OnePeriod Forecast Errors in Nonlinear Econometric Models", International Economic Review 21, 201208. Brillet, J.L., G.Calzolari, and L.Panattoni (1986): "Coherent Optimal Prediction with Large Nonlinear Systems: An Example Based on a French Model". Paris: INSEE, Service des Programmes, discussion paper presented at the European Meeting of the Econometric Society. Budapest, September 15. Brown, B. W., and R. S. Mariano (1984): "ResidualBased Procedures for Prediction and Estimation in a Nonlinear Simultaneous System", Econometrica 52, 321343. Brown, B. W., and R. S. Mariano (1985): "Reduced Variance Prediction in Nonlinear Simultaneous System". Rice University, discussion paper presented at the World Congress of the Econometric Society. M.I.T, Cambridge, MA, August 1724. Brundy, J. M., and D. W. Jorgenson (1971): "Efficient Estimation of Simultaneous Equations by Instrumental Variables", The Review of Economics and Statistics 53, 207224. Calzolari, G. (1979): "Antithetic Variates to Estimate the Simulation Bias in NonLinear Models", Economics Letters 4, 323328. Damiani, M. (1987): "Uno Schema Macroeconomico di Simulazione per l'Economia Italiana". Universita' di Perugia, Facolta' di Scienze Politiche, mimeo. Dennis, J.E., and J.J. More' (1977): "QuasiNewton Methods, Motivation and Theory", SIAM Review 19, 4689. Dutta, M., and E. Lyttkens (1974): "Iterative Instrumental Variables Method and Estimation of a Large Simultaneous System", Journal of the American Statistical Association 69, 977986. Fair, R. C. (1980): "Estimating the Expected Predictive Accuracy of Econometric Models", International Economic Review 21, 355378. Fisher, P., and M. Salmon (1986): "On Evaluating the Importance of Nonlinearity in Large Macroeconometric Models", International Economic Review 27, 625646. Hadley, G. (1961): Linear Algebra. Reading, MA: Addison  Wesley. Hall, S. G. (1984): "The Application of Stochastic Simulation Techniques in the National Institute's Model 7". London: NIESR, discussion paper No. 65. Hall, S. G. (1986): "The Importance of NonLinearities in Large Forecasting Models with Stochastic Error Processes", Journal of Forecasting 5, 205215. 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., 299319. Kendall,M.G. e A.Stuart (1969), The Advanced Theory of Statistics, Vol.I, London, Charles Griffin. Mariano, R. S., and B. W. Brown (1983): "Asymptotic Behavior of Predictors in a Nonlinear Simultaneous System", International Economic Review 24, 523536. McCarthy, M. D. (1972): "Some Notes on the Generation of PseudoStructural 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, 185191. 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, 425456. Oberhofer,W. (1971), "On the Treatment of Definition Equations in Likelihood Functions", Universitaet Bonn, Institut fuer Gesellschafts und Wirtschafts wissenschaften, Wirtschaftstheoretische Abteilung, discussion paper No.14. Rothenberg,T.J. and C.T.Leenders (1964), "Efficient Estimation of Simultaneous Equation Systems", Econometrica 32, 5716. Sikorski, R. (1969): Advanced Calculus. Functions of Several Variables. Warszawa: PWN  Polish Scientific Publishers. Sylos Labini, P. (1987): The Theory of Unemployment, too, is Historically Conditioned" Banca Nazionale del Lavoro Quarterly Review 163, 37943a. Wallis,K.F. (1982), "Time Series versus Econometric Forecasts: A NonLinear Regression CounterExample", Economics Letters, 10, pp. 309315. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/28845 