Skip to main content

Special Topics in Simultaneous Equations

  • Chapter
Advanced Econometric Methods

Abstract

In this chapter we review selected special topics related to simultaneous equations. In Sections 25.2 and 25.3 we consider extensions of the tobit and probit models (Chapter 16) into the simultaneous equations framework. In Section 25.4 we consider systems of equations that describe disequilibrium situations, Section 25.5 contains a generalization of the usual error assumptions associated with simultaneous equations estimation, vector autoregressive disturbances. The important topic of rational expectations is reviewed in Section 25.6. Finally, procedures for updating parameter estimates using sample or nonsample information are considered in Section 25.7 in the context of a single equation model, and extensions to the simultaneous equations context briefly described.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Amemiya, T. (1973). Regression analysis when the dependent variable is truncated normal. Econometrica, 41, 997–1016.

    Article  Google Scholar 

  • Amemiya, T. (1974). Multivariate regression and simultaneous equation models when the dependent variables are truncated normal. Econometrica, 42, 999–1012.

    Article  Google Scholar 

  • Amemiya, T. (1979). The estimation of a simultaneous equation tobit model. International Economic Review, 20, 169–182.

    Article  Google Scholar 

  • Nelson, F. and Olson, L. (1978). Specification and estimation of a simultaneous equation model with limited dependent variables. International Economic Review, 19, 695–709.

    Article  Google Scholar 

References

  • Amemiya, T. (1974). A note on a Fair and Jaffee model. Econometrica, 42, 759–762.

    Article  Google Scholar 

  • Barro, R. J., and Grossman, H. I. (1971). A general disequilibrium model of income and employment. American Economic Review, 61, 82–93.

    Google Scholar 

  • Berndt, E. K., Hall, B. H., Hall, R. E., and Hausman, J. A. (1974). Estimation and inference in nonlinear structural models. Annals of Economic and Social Measurement, 3, 653–665.

    Google Scholar 

  • Bowden, R. J. (1978a). The Econometrics of Disequilibrium. Amsterdam: North-Holland.

    Google Scholar 

  • Bowden, R. J. (1978b). Specification, estimation and inference for model of markets in disequilibrium. International Economic Review, 19, 711–726.

    Article  Google Scholar 

  • Clower, R. W. (1965). The Keynesian counter-revolution: a theoretical appraisal. In The Theory of Interest Rates. Edited by F. M. Hakn and F. P. R. Brechling. London: Macmillan.

    Google Scholar 

  • Fair, R. C, and Jaffee, D. M. (1972). Methods of estimation for markets in disequilibrium. Econometrica, 40, 497–514.

    Article  Google Scholar 

  • Fair, R. C, and Kelejian, H. H. (1974). Method of estimation for markets in disequilibrium: a further study. Econometrica, 42, 177–190.

    Article  Google Scholar 

  • Goldfeld, S. M., and Quandt, R. E. (1975). Estimation in a disequilibrium model and the value of information. Journal of Econometrics, 3, 325–348.

    Article  Google Scholar 

  • Gourieroux, C, Laffont, J. J., and Monfort, A. (1980). Disequilibrium econometrics in simultaneous equations systems. Econometrica, 48, 75–96.

    Article  Google Scholar 

  • Hartley, M. J. (1976). The estimation of markets in disequilibrium: the fixed supply case. International Economic Review, 17, 687–699.

    Article  Google Scholar 

  • Hartley, M. J. and Mallela, P. (1977). The asumptotic properties of a maximum likelihood estimator for a model of markets in disequilibrium. Econometrica, 45, 1205–1220.

    Article  Google Scholar 

  • Ito, T. (1980). Methods of estimation for multi-market disequilibrium models. Econometrica, 48, 97–125.

    Article  Google Scholar 

  • Laffont, J. J., and Garcia, R. (1977). Disequilibrium econometrics for business loans. Econometrica, 45, 1187–1204.

    Article  Google Scholar 

  • Maddala, G. S., and Nelson, F. D. (1974). Maximum likelihood methods for models of markets in disequilibrium. Econometrica, 42, 1013–1030.

    Article  Google Scholar 

  • Patinkin, D. (1956). Money, Interest and Prices. New York: Harper & Row.

    Google Scholar 

  • Portes, R. (1977). Effective demand and spillovers in empirical two-market disequilibrium models. Harvard Institute of Economic Research Discussion Paper No. 595, Harvard University.

    Google Scholar 

  • Quandt, R. E. (1978). Tests of equilibrium vs. disequilibrium hypotheses. International Economic Review, 19, 435–452.

    Google Scholar 

  • Rosen, H. S., and Quandt, R. E. (1978). Estimation of a disequilibrium aggregate labor market. Review of Economics and Statistics, 60, 371–379.

    Article  Google Scholar 

  • Ziemer, R. F., and White, F. C. (1982). Disequilibrium market analysis: an application to the U.S. fed beef sector. American Journal of Agricultural Economics, 64, 56–62.

    Article  Google Scholar 

References

  • Baillie, R. T. (1981). Prediction from the dynamic simultaneous equation model with vector autoregressive errors. Econometrica, 49, 1331–1337.

    Article  Google Scholar 

  • Brundy, J. M. and Jorgenson, D. W. (1971). Efficient estimation of simultaneous equations by instrumental variables. Review of Economics and Statistics, 53, 207–224.

    Article  Google Scholar 

  • Dhrymes, P. J. and Erlat, H. (1974). Asymptotic properties of full information estimators in dynamic autoregressive simultaneous equation models. Journal of Econometrics, 2, 247–259.

    Article  Google Scholar 

  • Fair, R. C. (1970). The estimation of simultaneous equation models with lagged endogenous variables and first order serially correlated errors. Econometrica, 38, 507–516.

    Article  Google Scholar 

  • Granger, C. W. J. and Newbold, P. (1977). Forecasting Economic Time Series. New York: Academic Press.

    Google Scholar 

  • Guilkey, D. K. (1974). Alternative tests for a first-order vector autoregressive error specification. Journal of Econometrics, 2, 95–104.

    Article  Google Scholar 

  • Guilkey, D. K. (1975). A test for the presence of first-order vector autoregressive errors when lagged endogenous variables are present. Econometrica, 43, 711–717.

    Article  Google Scholar 

  • Guilkey, D. K. and Schmidt, P. (1973). Estimation of seemingly unrelated regressions with vector autoregressive errors. Journal of the American Statistical Association, 68, 642–647.

    Article  Google Scholar 

  • Hannan, E. J. and Terrell, R. D. (1973). Multiple equation systems with stationary errors. Econometrica, 41, 299–320.

    Article  Google Scholar 

  • Hatanaka, M. (1976). Several efficient two-step estimators for the dynamic simultaneous equations model with autoregressive disturbances. Journal of Econometrics, 4, 189–204.

    Article  Google Scholar 

  • Hendry, D. F. (1981). Maximum likelihood estimation of systems of simultaneous regression equations with errors generated by a vector autoregressive process. International Economic Review, 12, 257–272.

    Article  Google Scholar 

  • Knight, J. L. (1982). Asymptotic distribution of restricted reduced forms and dynamic multipliers in a linear dynamic model with vector autoregressive errors. International Economic Review, 23, 553–563.

    Article  Google Scholar 

  • Maritz, A. (1978). A note of correction to Guilkey’s test for serial independence in simultaneous equations models. Econometrica, 46, 471.

    Article  Google Scholar 

  • Schmidt, P. (1974). The asymptotic distribution of forecasts in the dynamic simulation of an econometric model. Econometrica, 42, 303–309.

    Article  Google Scholar 

  • Wallis, K. F. (1967). Lagged dependent variables and serially correlated errors: a reappraisal of three-pass least squares. Review of Economics and Statistics, 49, 555–567.

    Article  Google Scholar 

References

  • Aoki, M. and Canzoneri, M. (1979). Reduced forms of rational expectations models. Quarterly Journal of Economics, 93, 59–71.

    Article  Google Scholar 

  • Carlson, J. A. (1977). A study of price forecasts. Annals of Economics and Social Measurement, 6, 27–56.

    Google Scholar 

  • Chavas, J. and Johnson, S. R. (1983). Rational expectations in econometric models. In New Directions in Econometric Modeling and Forecasting in U.S. Agriculture. Edited by C. R. Rausser. New York: Elsevier-North Holland.

    Google Scholar 

  • Dalkey, N. C, Rourke, D. L., Lewis, R., and Snyder, D. (1972). Studies in the Quality of Life; Delphi Decision Making. Lexington, MA: Lexington Books.

    Google Scholar 

  • Feldstein, M. (1971). The error of forecast in econometric models when the forecastperiod exogenous variables are stochastic. Econometrica, 39, 55–60.

    Article  Google Scholar 

  • Gardner, B. L. (1976). Futures prices in supply analysis. American Journal of Agricultural Economics, 58, 81–84.

    Article  Google Scholar 

  • Granger, C. W. J. and Newbold, P. (1977). Forecasting Economic Time Series. New York: Academic Press.

    Google Scholar 

  • Hoffman, D. L. and Schmidt, P. (1981). Testing the restrictions implied by the rational expectations hypothesis. Journal of Econometrics, 15, 265–87.

    Article  Google Scholar 

  • Johnson, S. R. and Rausser, G. C. (1983). Composite forecasting in commodity systems. In New Directions in Econometric Modeling and Forecasting in U.S. Agriculture. Edited by G. C. Rausser. New York: Elsevier North-Holland.

    Google Scholar 

  • McCallum, B. T. (1976a). Rational expectations and the estimation of econometric models: an alternative procedure. International Economic Review, 17, 485–490.

    Article  Google Scholar 

  • McCallum, B. T. (1976b). Rational expectations and the natural rate hypothesis: some consistent estimates. Econometrica, 44, 42–52.

    Article  Google Scholar 

  • Mullineaux, D. J. (1978). On testing for rationality: another look at the Livingston price expectations data. Journal of Political Economy, 86, 329–336.

    Article  Google Scholar 

  • Muth, J. F. (1961). Rational expectations and the theory of price movements. Econometrica, 29, 315–335.

    Article  Google Scholar 

  • Nelson, C. R. (1975a). Rational expectations and the estimation of econometric models. International Economic Review, 16, 555–561.

    Article  Google Scholar 

  • Nelson, C. R. (1975b). Rational expectations and predictive economic models. Journal of Business, 47, 331–343.

    Google Scholar 

  • Nerlove, M. (1972). Lags in economic behavior. Econometrica, 40, 221–251.

    Article  Google Scholar 

  • Nerlove, M. (1958). Adaptive expectations and cobweb phenomena. Quarterly Journal of Economics, 73, 227–240.

    Article  Google Scholar 

  • Peck, A. E. (1976). Futures markets, supply responses and price stability. Quarterly Journal of Economics, 90, 407–423.

    Article  Google Scholar 

  • Popkin, J. (1975). Some avenues for the improvement of price forecasts generated by macroeconomic models. American Journal of Agricultural Economics, 57, 157–163.

    Article  Google Scholar 

  • Sargent, T. J. (1978). Rational expectations, econometric exogeneity and consumption. Journal of Political Economy, 86, 673–700.

    Article  Google Scholar 

  • Sargent, T. J. and Wallace, N. (1975). Rational expectations, the optimal monetary instrument and the optimal money supply rule. Journal of Political Economy, 83, 241–254.

    Article  Google Scholar 

  • Turnovsky, S. J. (1979). Futures markets, private storage, and price stabilization. Journal of Political Economy, 12, 301–327.

    Google Scholar 

  • Woglom, J. (1979). Rational expectations and monetary policy in a simple macroeconomic model. Quarterly Journal of Economics, 59, 91–105.

    Article  Google Scholar 

References

  • Anderson, B. D. O. and Moore, J. B. (1978). Optimal Filtering. Englewood Cliffs, N.J.: Prentice-Hall, Inc. 1978.

    Google Scholar 

  • Belsey, D. A. (1973a). On the determination of systematic parameter variation in the linear regression model. Annals of Economics and Social Measurement, 2, 487–494.

    Google Scholar 

  • Belsey, D. A. (1973b). The applicability of the Kaiman filter in the determination of systematic parameter variation. Annals of Economics and Social Measurement, 2, 531–533.

    Google Scholar 

  • Brook, R. and Wallace, T. D. (1973). A note on extraneous information in regression. Journal of Econometrics, 1, 315–316.

    Article  Google Scholar 

  • Chow, G. C. (1975). Analysis and Control of Dynamic Economic Systems. New York: Wiley.

    Google Scholar 

  • Chow, G. C. (1981). Econometric Analysis by Control Methods. New York: Wiley.

    Google Scholar 

  • Conard, W., and Corrado, C. (1979). Applications of the Kaiman filter to revisions in monthly retail sales estimates. Journal of Economic Dynamics and Control, 1, 177–198.

    Article  Google Scholar 

  • Covey-Crump, P. A. K. and Silvey, S. D. (1970). Optimal regression designs with previous observations. Biometrika, 62, 551–566.

    Article  Google Scholar 

  • Guttman, I. (1971). A remark on the optimal regression designs with previous observations of Covey-Crump and Silvey. Biometrica, 64, 683–684.

    Article  Google Scholar 

  • Kaiman, R. E. (1960). A new approach to linear filtering and prediction problems. Journal of Basic Engineering, D, 82, 95–108.

    Google Scholar 

  • Kiefer, J. (1958). On the nonrandomized optimality and randomized nonoptimality of symmetrical designs. Annals of Mathematical Statistics, 29, 675–699.

    Article  Google Scholar 

  • MacRae, E. C. (1977). Optimal experimental design for dynamic econometric models. Annals of Economic and Social Measurement, 6, 399–405.

    Google Scholar 

  • Murata, Y. (1982). Optimal Control Methods for Linear Discrete-Time Economic Systems. New York: Springer-Verlag.

    Book  Google Scholar 

  • Rausser, G. C., Mundlak, Y., and Johnson, S. R. (1983). Structural change, updating and forecasting. In New Directions in Econometric Modeling and Forecasting in U.S. Agriculture. Edited by G. Rausser. New York: Elsevier-North Holland.

    Google Scholar 

  • Sage, A. P., and Melsa, J. L. (1971). Estimation Theory with Applications to Communications and Control. New York: McGraw-Hill.

    Google Scholar 

  • Silvey, S. D. (1969). Multicollinearity and imprecise estimation. Journal of the Royal Statistical Society, B, 31, 539–552.

    Google Scholar 

  • Theil, H. (1971). Principles of Econometrics. New York: Wiley.

    Google Scholar 

  • Theil, H. (1974). Mixed estimation based on quasi-prior judgements. European Economic Review, 5, 33–40.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 1984 Springer Science+Business Media New York

About this chapter

Cite this chapter

Fomby, T.B., Johnson, S.R., Hill, R.C. (1984). Special Topics in Simultaneous Equations. In: Advanced Econometric Methods. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-8746-4_25

Download citation

  • DOI: https://doi.org/10.1007/978-1-4419-8746-4_25

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-96868-1

  • Online ISBN: 978-1-4419-8746-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics