Skip to main content

Reduced Form Estimation and Prediction in Simultaneous Equations Models

  • Chapter
  • 445 Accesses

Abstract

In this chapter we turn our attention from point estimation of the structural coefficients of a simultaneous equations model to the efficient estimation of the reduced form equation Y = X II + V and its use for forecasting future values of the endogenous variables given values (either known or forecasted) of the predetermined variables. Assuming the appropriateness of the initial model specification, efficient estimation requires the utilization of all available information. As we shall see, the ordinary least squares estimator, \( \hat \Pi = \left( {X'X} \right)^{ - 1} X'Y \), of the reduced form parameters does not utilize all available information and as a result there exist more efficient ways to estimate Π. Such methods are discussed in Section 23.2.

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

Buying options

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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Amemiya, T. (1966). On the use of principal components of independent variables in two-stage least squares estimation. International Economic Review, 7, 283–303.

    Article  Google Scholar 

  • Dhrymes, P. (1973). Restricted and unrestricted reduced forms: asymptotic distribution and relative efficiency. Econometrica, 41, 119–134.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Fisher, F. (1966). The Identification Problem in Econometrics. New York: McGraw-Hill.

    Google Scholar 

  • Goldberger, A. (1964). Econometric Theory. New York: Wiley.

    Google Scholar 

  • Kakwani, N. and Court, R. (1972). Reduced form coefficient estimation and forecasting from a simultaneous equation model. The Australian Journal of Statistics, 14, 143–160.

    Article  Google Scholar 

  • Knight, J. (1977). On the existence of moments of the partially restricted reduced form estimators from a simultaneous-equation model. Journal of Econometrics, 5, 315–322.

    Article  Google Scholar 

  • Maasoumi, E. (1978). A modified Stein-like estimator for the reduced form coefficients in simultaneous equations. Econometrica, 46, 695–705.

    Article  Google Scholar 

  • McCarthy, M. (1972). A note on the forecasting properties of the two stage least squares restricted reduced forms—the finite sample case. International Economic Review, 13, 757–761.

    Article  Google Scholar 

  • McCarthy, M. (1981). A note on the moments of partially restricted reduced forms. Journal of Econometrics, 17, 383–387.

    Article  Google Scholar 

  • Nagar, A. and Sahay, S. (1978). The bias and mean square error of forecasts from partially restricted reduced forms. Journal of Econometrics, 7, 227–244.

    Article  Google Scholar 

  • Schmidt, P. (1976). Econometrics. New York: Marcel Dekker.

    Google Scholar 

  • Schmidt, P. (1978). A note on dynamic simulation forecasts and stochastic forecastperiod exogenous variables. Econometrica, 46, 1227–1230.

    Article  Google Scholar 

  • Swamy, P. (1980). A comparison of estimators for undersized samples. Journal of Econometrics, 14, 161–182.

    Article  Google Scholar 

  • Swamy, P. and Mehta, J. (1980). On the existence of moments of partially restricted reduced form coefficients. Journal of Econometrics, 14, 183–194.

    Article  Google Scholar 

  • Swamy, P. and Mehta, J. (1981). On the existence of moments of partially restricted reduced form estimators: a comment. Journal of Econometrics, 17, 389–392.

    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). Reduced Form Estimation and Prediction in Simultaneous Equations Models. In: Advanced Econometric Methods. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-8746-4_23

Download citation

  • DOI: https://doi.org/10.1007/978-1-4419-8746-4_23

  • 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