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Programming Identification Criteria in Simultaneous Equation Models

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Abstract

Examining the identification problem in the case of a linear econometric model can be a tedious task. The rank and order conditions are commonly used in identification for simultaneous equations models. The order condition of identifiability is an easy condition to compute, though maybe difficult to remember. The application of the rank condition, due to its complicated definition and its computational demands, is time consuming and contains a high risk for errors. Furthermore, possible miscalculations could lead to wrong identification results, which cannot be revealed by other indications. Thus, a safe way to test identification criteria is to make use of computer software. Specialized econometric software can off-load some of the requested computations but the procedure of formation and verification of the identification criteria are still up to the user. In our identification study we use the program editor of a free computer algebra system, Xcas. We present a routine that tests various identification conditions and classifies the equations under study as «under-identified», «just-identified», «over-identified »and «unidentified», in just one entry.

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Notes

  1. In case of fully recursive systems the rank condition may not be any longer a necessary condition. Obviously different scientific subjects and areas may use different computer algebra and identification approaches. Allowing for latent variables and multiple indicators as common in structural equation models in social sciences like sociology, psychology etc then these conditions may be less useful. For more general structural equation models with latent variables see among others Bollen and Bauldry (2010). Obviously it is worth mentioning that when there are restrictions on the covariances of the errors from different equations, the rank condition cannot be claimed to be necessary and a fully recursive model is not the only case of restrictions on error covariances.

  2. For an Xcas tutorial see Parisse (2013). Similar studies for economic applications have been carried out in Halkos and Tsilika (2011, 2012a, b).

References

  • Anderson, T. W., & Hurwitz, L. (1949). Errors and shocks in economic relationships. Econometrica, 17, 23–25.

    Article  Google Scholar 

  • Angrist, J. D., Graddy, K., & Imbens, G. W. (2000). The interpretation of instrumental variables estimators in simultaneous equations models with an application to the demand for fish. Review of Economic Studies, 67(3), 499–527.

    Article  Google Scholar 

  • Asteriou, D., & Hall, S. G. (2011). Applied econometrics (2nd ed.). Palgrave: MacMillan.

    Google Scholar 

  • Athey, S., & Haile, P. A. (2002). Identification of standard auction models. Econometrica, 70(6), 2107–2140.

    Article  Google Scholar 

  • Bekker, P. A., & Pollock, D. S. G. (1986). Identification of linear stochastic models with covariance restrictions. Journal of Econometrics, 31, 179–208.

    Article  Google Scholar 

  • Bekker, P. A. (1989). Identification in restricted factor models and the evaluation of rank condition. Journal of Econometrics, 41(1), 5–16.

    Article  Google Scholar 

  • Bekker, P. A. (1994). Counting rules for identification in linear structural models. Computational Statistics & Data Analysis, 18, 485–498.

    Article  Google Scholar 

  • Bekker, P. A., Merckens, A., & Wansbeek, T. J. (1994). Identification, equivalent models, and computer algebra. San Diego: Academic Press.

    Google Scholar 

  • Bekker, P. A., & ten Berge, J. M. F. (1997). Generic global identification in factor analysis. Linear Algebra and its Applications, 264, 255–263.

    Article  Google Scholar 

  • Benkard, C. L., & Berry, S. (2006). On the nonparametric identification of nonlinear simultaneous equations models: Comment on B. Brown(1983) and Roehrig(1988). Econometrica, 74(5), 1429–1440.

    Article  Google Scholar 

  • Bollen, K. A., & Bauldry, S. (2010). Model identification and computer algebra. Sociological Methods and Research, 39(2), 127–156.

    Article  Google Scholar 

  • Boswijk, H. P., & Doornik, J. A. (2004). Identifying, estimating and testing restricted cointegrated systems: An overview. Statistica Neerlandica, 58(4), 440–465.

    Article  Google Scholar 

  • Bowden, R. (1973). The theory of parametric identification. Econometrica, 41, 1069–1074.

    Article  Google Scholar 

  • Brown, B. W. (1983). The identification problem in systems nonlinear in the variables. Econometrica, 51(1), 175–196.

    Article  Google Scholar 

  • Brown, D. J., & Wegkamp, M. H. (2002). Weighted mean-square minimum distance from independence estimation. Econometrica, 70(5), 2035–2051.

    Article  Google Scholar 

  • Chesher, A. (2003). Identification in nonseparable models. Econometrica, 71(5), 1405–1441.

    Article  Google Scholar 

  • Deistler, M. (1976). The identifiability of linear econometric models with autocorrelated errors. International Economic Review, 17, 26–45.

    Article  Google Scholar 

  • Deistler, M. (1978). The structural identifiability of linear models with autocorrelated errors in the case of affine cross-equation restrictions. Journal of Econometrics, 8, 23–31.

    Article  Google Scholar 

  • Deistlet, M., & Schrader, J. (1979). Linear models with autocorrelated errors: Structural identifiability in the absence of minimality assumption. Econometrica, 47, 495–504.

    Article  Google Scholar 

  • Drèze, J. H. (1974). Bayesian theory of identification in simultaneous equation models. In S. E. Fienberg & A. Zellner (Eds.), Studies in Bayesian econometrics and statistics. Amsterdam: North-Holland.

    Google Scholar 

  • Duncan, O. D., & Featherman, D. L. (1972). Psychological and cultural factors in the process of occupational achievement. Social Science Research, 1, 121–145.

    Article  Google Scholar 

  • Fisher, F. M. (1959). Generalization of the rank and order conditions for identifiability. Econometrica, 27, 431–447.

    Article  Google Scholar 

  • Fisher, F. M. (1961). Identifiability criteria in nonlinear systems. Econometrica, 29, 574–590.

    Article  Google Scholar 

  • Fisher, F. M. (1963). Uncorrelated disturbances and identifiability criteria. International Economic Review, 4, 134–152.

    Article  Google Scholar 

  • Fisher, F. M. (1965). Identifiability criteria in nonlinear systems: A further note. Econometrica, 33, 197–205.

    Article  Google Scholar 

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

    Google Scholar 

  • Geraci, V. J. (1976). Identification of simultaneous equation models with measurement error. Journal of Econometrics, 4, 263–284.

    Article  Google Scholar 

  • Goldberger, A. S. (1972). Structural equation methods in the social sciences. Econometrica, 40, 979–1002.

    Article  Google Scholar 

  • Goldberger, A. S. (1974). Unobservable variables in econometrics. In P. Zarembka (Ed.), Frontiers of Econometrics (pp. 193–213). New York: Academic.

    Google Scholar 

  • Greenslade, J. V., & Hall, S. G. (2002). On the identification of cointegrated systems in small samples: A modelling strategy with an application to uk wages and prices. Journal of Economic Dynamics and Control, 26(9–10), 1517–1537.

    Article  Google Scholar 

  • Guerre, E., Perrigne, I., & Vuong, Q. (2000). Optimal nonparametric estimation of first-price auctions. Econometrica, 68(3), 525–574.

    Article  Google Scholar 

  • Gujarati, D. N. (2003). Basic Econometrics (4th ed.). Boston: McGraw Hill.

    Google Scholar 

  • Halkos, G. E. & Tsilika, K. D. (2011). Xcas as a programming environment for stability conditions of a class of linear differential equation models in economics: 9th International Conference of Numerical Analysis and Applied Mathematics (ICNAAM), AIP Conf. Proc. 1389, (pp. 1769–1772) Halkidiki.

  • Halkos, G. E., & Tsilika, K. D. (2012a). Computing optimality conditions in economic problems. Journal of Computational Optimization in Economics and Finance, 3(3), 1–13.

    Google Scholar 

  • Halkos, G. E., & Tsilika, K. D. (2012b). Stability analysis in economic dynamics: A computational Approach. MPRA paper (Vol. 41371). Munich: University Library of Munich.

    Google Scholar 

  • Harvey, A. (1990). The Econometric analysis of time series (2d ed.). Cambridge: The MIT Press.

    Google Scholar 

  • Hatanaka, M. (1975). On the global identification of the dynamic simultaneous equations model with stationary disturbances. International Economic Review, 16, 545–554.

    Article  Google Scholar 

  • Hausman, J. A., & Taylor, W. B. (1980). Identification in simultaneous equation systems with covariance restrictions. MIT, mimeo.

  • Hausman, J. A., & Hausman, J. A. (1983). Specification and estimation of simultaneous equation models. Handbook of Econometrics (pp. 392–448). Amsterdam: North Holland.

    Google Scholar 

  • Hood, W. C., & Koopmans, T. C. (Eds.). (1953). Studies in econometric method, cowles commission monograph 14. New York: Wiley.

    Google Scholar 

  • Hsiao, C. (1976). Identification and estimation of simultaneous equation models with measurement error. International Economic Review, 17, 319–339.

    Article  Google Scholar 

  • Hsiao, C. (1977). Identification for a linear dynamic simultaneous error shock model. International Economic Review, 18, 181–194.

    Article  Google Scholar 

  • Johansen, S. (1995). Identifying restrictions of linear equations with applications to simultaneous equations and cointegration. Journal of Econometrics, 69(1), 111–132.

    Article  Google Scholar 

  • Judge, G. G., Griffiths, W. E., Cartel Hill, R., Lutkepohl, H., & Lee, T. C. (1985). The theory and practice of Econometrics, Wiley series in probability and mathematical statistics (2nd ed.). New York: Wiley.

    Google Scholar 

  • Kadane, J. B. (1974). The role of identification in bayesian theory. In S. E. Fienberg & A. Zellner (Eds.), Studies in Bayesian Econometrics and statistics. Amsterdam: North-Holland.

    Google Scholar 

  • Kelly, J. S. (1971). The identification of ratios of parameters in unidentified equations. Econometrica, 39, 1049–1051.

    Article  Google Scholar 

  • Kelly, J. S. (1975). Linear cross-equation constraints and the identification problem. Econometrica, 43, 125–140.

    Article  Google Scholar 

  • Koopmans, T. C. (1949). Identification problems in economic model construction. Econometrica, 17(2), 125–144.

    Article  Google Scholar 

  • Koopmans, T. C., & Reiersol, O. (1950). The identification of structural characteristics. Annals of Mathematical Statistics, 21(2), 165–181.

    Article  Google Scholar 

  • Koopmans, T. C., Rubin, H., & Leipnik, R. B. (1950). Measuring the equation systems of dynamic economics. In T. C. Koopmans (Ed.), Statistical inference in dynamic economic models, cowles commission monograph 10. New York: Wiley.

    Google Scholar 

  • Merckens, A., & Bekker, P. A. (1993). Identification of simultaneous equation models with measurement error: A computerized evaluation. Statistica Neerlandica, 47(4), 233–244.

    Article  Google Scholar 

  • Newey, W. K., Powell, J. L., & Vella, F. (1999). Nonparametric estimation of triangular simultaneous equations models. Econometrica, 67(3), 565–603.

    Article  Google Scholar 

  • Newey, W. K., & Powell, J. L. (2003). Instrumental variable estimation of nonparametric models. Econometrica, 71(5), 1565–1578.

    Article  Google Scholar 

  • Matzkin, R. (2003). Nonparametric estimation of nonadditive random functions. Econometrica, 71(5), 1332–1375.

    Article  Google Scholar 

  • Matzkin, R. L. (2008). Identification in nonparametric simultaneous equations models. Econometrica, 76(5), 945–978.

    Article  Google Scholar 

  • McFadden, D. (1999). Chapter 6. Simultaneous equations. Lecture notes for Economics 240B, Berkeley. Resource document. http://emlab.berkeley.edu/users/mcfadden/e240b_f01/ch6.pdf. Accessed 17 Feb 2013.

  • Parisse, B. An introduction to the Xcas interface. Resource document. http://www-fourier.ujf-grenoble.fr/~parisse/giac/tutoriel_en.pdf. Accessed 17 Feb 2013.

  • Richmond, J. (1974). Aggregation and identification. International Economic Review, 17, 47–56.

    Article  Google Scholar 

  • Roehrig, C. S. (1988). Conditions for identification in nonparametric and parametric models. Econometrica, 56(2), 433–447.

    Article  Google Scholar 

  • Rothenberg, T. J. (1973). Identification in parametric models. Econometrica, 39, 577–592.

    Article  Google Scholar 

  • Wald, A. (1950). Note on the identification of economic relations. In Statistical inference in dynamic economic models, Cowles Commission Monograph 10. New York: Wiley.

  • Wegge, L. (1965). Identifiability criteria for a system of equations as a whole. Australian Journal of Statistics, 7, 67–77.

    Article  Google Scholar 

  • Wiley, D. E. (1973). The identification problem for structural equation models with unmeasured variables. In A. S. Goldberger & O. D. Duncan (Eds.), Structural equation models in the Social Sciences (pp. 69–84). New York: Seminar Press.

  • Zellner, A. (1971). An introduction to Bayesian inference in Econometrics. New York: Wiley.

    Google Scholar 

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Acknowledgments

We would like to thank the Editor Professor Hans Amman and an anonymous reviewer for the comments provided in relation to an earlier version of our paper. Any remaining errors are solely the authors’ responsibility.

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  1. Laboratory of Operations Research, Department of Economics, University of Thessaly, Korai 43, 38 333 , Volos, Greece

    George E. Halkos & Kyriaki D. Tsilika

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  1. George E. Halkos
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Correspondence to George E. Halkos.

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Halkos, G.E., Tsilika, K.D. Programming Identification Criteria in Simultaneous Equation Models. Comput Econ 46, 157–170 (2015). https://doi.org/10.1007/s10614-014-9444-9

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