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Simultaneous Equation Models

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Financial Econometrics, Mathematics and Statistics

Abstract

Based upon the discussion of single-equation models in the previous two chapters, in this chapter, we discuss simultaneous equation models, including the basic definition, their specification, and identification. The estimation methods for simultaneous equation models include two-stage least squares estimation method and three-stage least squares estimation method. Some examples of applying simultaneous equation models in finance research are also provided.

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Notes

  1. 1.

    The discussions of the order condition draw heavily from Ramanathan (1995).

  2. 2.

    For more detailed discussions of the rank condition, see econometric books such as Greene (2017), Judge et al. (1985), Fisher (1966), Blalock (1969), and Fogler and Ganapathy (1982).

  3. 3.

    3SLS is a combination of 2SLS and the seemingly uncorrelated regression (SUR) method proposed by Zellner (1962). SUR method will be discussed in the next chapter in detailed.

  4. 4.

    For more detailed discussions, see Ghosh (1991), Judge et al. (1985), and Greene (2017).

Bibliography

  • Blalock, H. M. (1969). Theory construction: From verbal to mathematical formulations. Englewood Cliffs, New Jersey: Prentice Hall.

    Google Scholar 

  • Chen, C. R., Steiner, T., & Whyte, A. (2006). Does stock option-based executive compensation induce risk-taking? An analysis of the banking industry. Journal of Banking and Finance, 30, 915–946.

    Article  Google Scholar 

  • Chen, C. R., & Lee, C. F. (2010). Application of simultaneous equation in finance research. In C. F. Lee et al. (Eds.), Handbook of quantitative finance and risk management (Vol. 3). New York: Springer.

    Google Scholar 

  • Cochran, W. G. (1972). Some effects of errors of measurement on multiple correlation coefficients. Journal of American Statistical Association, 65, 22–34.

    Article  Google Scholar 

  • Fama, E. F. (1968). Risk, return and equilibrium: Some clarifying comments. Journal of Finance, 23(1), 29–40.

    Article  Google Scholar 

  • Fisher, F. M. (1966). The identification problem in econometrics. NY, New York: McGraw-Hill.

    Google Scholar 

  • Fogler, H. R., & Ganapathy, S. (1982). Financial econometrics. Englewood Cliffs, New Jersey: Prentice Hall.

    Google Scholar 

  • Ghosh, S. K. (1991). Econometrics: Theory and applications. Englewood Cliffs, New Jersey: Prentice Hall.

    MATH  Google Scholar 

  • Greene, W. H. (2017). Econometric analysis. Upper Saddle River, New Jersey: Prentice Hall.

    Google Scholar 

  • Haitovsky, Y. (1969). A note on the maximization of R. The American Statistician, 23, 20–21.

    Google Scholar 

  • Judge, G. G., Griffiths, W. E., Hill, R. C., Lütkepohl, H., & Lee, T. (1985). The theory and practice of econometrics. NY, New York: Wiley.

    MATH  Google Scholar 

  • Klein, L. R., & Nakamura, M. (1962). Singularity in the equation systems of econometrics: Some aspects of the problem of multicollinearity. Internal Economic Review, 3, 274–299.

    Google Scholar 

  • Kmenta, J. (1971). Element of econometric. New York: The MacMillan Company.

    MATH  Google Scholar 

  • Lee, C.-F., Lee, A. C., & Lee, J. (2010). Handbook of quantitative finance and risk management. New York: Springer.

    Google Scholar 

  • Lee, C.-F. (1976). A note on the interdependent structure of security returns. Journal of Financial and Quantitative Analysis.

    Google Scholar 

  • Lee, C.-F., Hu, C., & Foley, M. (2018). Inside debt, firm risk and investment decision. Working paper. Rutgers University.

    Google Scholar 

  • Lee, C.-F., Liang, W. L., Lin, F. L., & Yang, Y. (2016). Applications of simultaneous equations in finance research: Methods and empirical results. Review of Quantitative Finance and Accounting, 47(4), 943–971.

    Article  Google Scholar 

  • Lee, C.-F., & Nieh, C.-C. (2001). Dynamics relationship between stock prices and exchange rates for G-7 countries. The Quarterly Review of Economics and Finance, 41(4), 477–490.

    Google Scholar 

  • Lintner, J. (1965). Security prices, risk and maximal gains from diversification. Journal of Finance, 20, 587–616.

    Google Scholar 

  • Mossin, J. (1966). Equilibrium in a capital asset market. Econometrica, 34, 768–783.

    Article  Google Scholar 

  • Ramanathan, R. (1995). Introductory econometrics with application. Fort Worth, Texas: The Dryden Press.

    Google Scholar 

  • Sharpe, W. F. (1964). Capital asset prices: A theory of market equilibrium under conditions of risks. Journal of Finance, 19, 425–442.

    Google Scholar 

  • Simkowitz, M. A., & Logue, D. E. (1973). The interdependent structure of security returns. Journal of Financial and Quantitative Analysis, 8(2), 259–272.

    Article  Google Scholar 

  • Wang, C. J. (2015). Instrumental variable approach to correct for endogeneity in finance. In C. F. Lee & J. Lee (Eds.), Handbook of financial econometrics and statistics (pp. 2577–2600). New York: Springer.

    Google Scholar 

  • Zellner, A. (1962). An efficient method of estimating seemingly unrelated regressions and tests for aggregation bias. Journal of the American Statistical Association, 348–368.

    Article  MathSciNet  Google Scholar 

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Correspondence to Cheng-Few Lee .

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Lee, CF., Chen, HY., Lee, J. (2019). Simultaneous Equation Models. In: Financial Econometrics, Mathematics and Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-9429-8_4

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