Econometrics pp 268-306 | Cite as

Simultaneous Equations Model

  • Badi H. Baltagi


Economists formulate models for consumption, production, investment, money demand and money supply, labor demand and labor supply to attempt to explain the workings of the economy. These behavioral equations are estimated equation by equation or jointly as a system of equations. These are known as simultaneous equations models. Much of todays econometrics have been influenced and shaped by a group of economists and econometricians known as the Cowles Commission who worked together at the University of Chicago in the late 1940’s, see Chapter 1. Simultaneous equations models had their genesis in economics during that period. Haavelmo’s (1944) work emphasized the use of the probability approach to formulating econometric models. Koopmans and Marschak (1950) and Koopmans and Hood (1953) in two influential Cowles Commission monographs provided the appropriate statistical procedures for handling simultaneous equations models. In this chapter, we first give simple examples of simultaneous equations models and show why the least squares estimator is no longer appropriate. Next, we discuss the important problem of identification and give a simple condition that helps check whether a specific equation is identified. Sections 11.2 and 11.3 give the estimation of a single and a system of equations using instrumental variable procedures while, section 11.4 gives a necessary and sufficient condition for identification. Section 11.5 gives a test of over-identification restrictions whereas, section 11.6 gives a Hausman specification test. Section 11.7 concludes with an empirical example.


Instrumental Variable Exogenous Variable Endogenous Variable Trade Credit Demand Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Anderson, T.W. and H. Rubin (1950), “The Asymptotic Properties of Estimates of the Parameters of a Single Equation in a Complete System of Stochastic Equations,” Annals of Mathematical Statistics, 21: 570–582.CrossRefGoogle Scholar
  2. Baltagi, B.H. (1989), “A Hausman Specification Test in a Simultaneous Equations Model,” Econometric Theory, Solution 88.3.5, 5: 453–467.Google Scholar
  3. Basmann, R.L. (1957), “A Generalized Classical Method of Linear Estimation of Coefficients in a Structural Equation,” Econometrica, 25: 77–83.CrossRefGoogle Scholar
  4. Basmann, R.L. (1960), “On Finite Sample Distributions of Generalized Classical Linear Identifiability Tests Statistics,” Journal of the American Statistical Association, 55: 650–659.CrossRefGoogle Scholar
  5. Durbin, J. (1954), “Errors in Variables,” Review of the International Statistical Institute, 22: 23–32.CrossRefGoogle Scholar
  6. Farebrother, R.W. (1985), “The Exact Bias of Wald’s Estimator,” Econometric Theory, Problem 85.3.1, 1: 419.Google Scholar
  7. Farebrother, R.W. (1991), “Comparison of t-Ratios,” Econometric Theory, Solution 90.1.4, 7: 145–146.Google Scholar
  8. Fisher, F.M. (1966), The Identification Problem in Econometrics ( McGraw-Hill: New York).Google Scholar
  9. Haavelmo, T. (1944), “The Probability Approach in Econometrics,” Supplement to Econometrica, 12.Google Scholar
  10. Hall, A. (1993), “Some Aspects of Generalized Method of Moments Estimation,” Chapter 15, Handbook of Statistics, Volume 11, North Holland, Amsterdam.Google Scholar
  11. Hansen, L. (1982), “Large Sample Properties of Generalized Method of Moments Estimators,” Econometrica, 50: 646–660.Google Scholar
  12. Hausman, J.A. (1978), “Specification Tests in Econometrics,” Econometrica, 46: 1251–1272.CrossRefGoogle Scholar
  13. Hausman, J.A. (1983), “Specification and Estimation of Simultaneous Equation Models,” Chapter 7, Handbook of Econometrics, Vol. I, eds. Z Griliches and M.D. Intriligator, North Holland, Amsterdam.Google Scholar
  14. Holly, A. (1987), “Identification and Estimation of a Simple Two-Equation Model,” Econometric Theory, Problem 87.3.3, 3: 463–466.Google Scholar
  15. Holly, A. (1988), “A Hausman Specification Test in a Simultaneous Equations Model,” Econometric Theory, Problem 88.3.5, 4: 537–538.Google Scholar
  16. Holly, A. (1990), “Comparison of t-ratios,” Econometric Theory, Problem 90.1.4, 6: 114.Google Scholar
  17. Kapteyn, A. and D.G. Fiebig (1981), “When are Two-Stage and Three-Stage Least Squares Estimators Identical?,” Economics Letters, 8: 53–57.CrossRefGoogle Scholar
  18. Koopmans, T.C. and J. Marschak (1950), Statistical Inference in Dynamic Economic Models ( John Wiley and Sons: New York).Google Scholar
  19. Koopmans, T.C. and W.C. Hood (1953), Studies in Econometric Method ( John Wiley and Sons: New York).Google Scholar
  20. Laffer, A.B., (1970), “Trade Credit and the Money Market,” Journal of Political Economy, 78: 239–267.CrossRefGoogle Scholar
  21. Lott, W.F. and S.C. Ray (1992), Applied Econometrics: Problems with Data Sets ( The Dryden Press: New York).Google Scholar
  22. Mariano, R.S. (1982), “Analytical Small-Sample Distribution Theory in Econometrics: The Simultaneous Equations Case,” International Economic Review, 23: 503–534.CrossRefGoogle Scholar
  23. Nelson, C.R. and R. Startz (1990), “The Distribution of the Instrumental Variables Estimator and its t-Ratio when the Instrument is a Poor One,” Journal of Business, 63: S 125–140.CrossRefGoogle Scholar
  24. Sapra, S.K. (1997), “Equivariance of an Instrumental Variable (IV) Estimator in the Linear Regression Model,” Econometric Theory, Problem 97.2.5, 13: 464.Google Scholar
  25. Singh, N. and A N. Bhat (1988), “Identification and Estimation of a Simple Two-Equation Model,” Econometric Theory, Solution 87.3.3, 4: 542–545.Google Scholar
  26. Theil, H. (1953), “Repeated Least Squares Applied to Complete Equation Systems,” The Hague, Central Planning Bureau (Mimeo).Google Scholar
  27. Theil, H. (1971), Principles of Econometrics ( Wiley: New York).Google Scholar
  28. Wooldridge, J.M. (1990), “A Note on the Lagrange Multiplier and F Statistics for Two Stage Least Squares Regression,” Economics Letters, 34: 151–155.CrossRefGoogle Scholar
  29. Wald, A. (1940), “Fitting of Straight Lines if Both Variables are Subject to Error,” Annals of Mathematical Statistics, 11: 284–300.CrossRefGoogle Scholar
  30. Wu, D.M. (1973), “Alternative Tests of Independence Between Stochastic Regressors and Disturbances,” Econometrica, 41: 733–740.CrossRefGoogle Scholar
  31. Zellnner, A. and Theil, H. (1962), “Three-Stage Least Squares: Simultaneous Estimation of Simultaneous Equations,” Econometrica, 30: 54–78.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin · Heidelberg 1998

Authors and Affiliations

  • Badi H. Baltagi
    • 1
  1. 1.Department of EconomicsTexas A&M UniversityCollege StationUSA

Personalised recommendations