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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. Copyright Springer Science+Business Media New York 2015

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  • George Halkos & Kyriaki Tsilika, 2015. "Programming Identification Criteria in Simultaneous Equation Models," Computational Economics, Springer;Society for Computational Economics, vol. 46(1), pages 157-170, June.
  • Handle: RePEc:kap:compec:v:46:y:2015:i:1:p:157-170
    DOI: 10.1007/s10614-014-9444-9
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    1. Emmanuel Guerre & Isabelle Perrigne & Quang Vuong, 2000. "Optimal Nonparametric Estimation of First-Price Auctions," Econometrica, Econometric Society, vol. 68(3), pages 525-574, May.
    2. Hsiao, Cheng, 1977. "Identification for a Linear Dynamic Simultaneous Error-Shock Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 18(1), pages 181-194, February.
    3. Donald J. Brown & Marten H. Wegkamp, 2002. "Weighted Minimum Mean-Square Distance from Independence Estimation," Econometrica, Econometric Society, vol. 70(5), pages 2035-2051, September.
    4. Hatanaka, Michio, 1975. "On the Global Identification of the Dynamic Simultaneous Equations Model with Stationary Disturbances," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 16(3), pages 545-554, October.
    5. Brown, Bryan W, 1983. "The Identification Problem in Systems Nonlinear in the Variables," Econometrica, Econometric Society, vol. 51(1), pages 175-196, January.
    6. Greenslade, Jennifer V. & Hall, Stephen G. & Henry, S. G. Brian, 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, Elsevier, vol. 26(9-10), pages 1517-1537, August.
    7. Rosa L. Matzkin, 2003. "Nonparametric Estimation of Nonadditive Random Functions," Econometrica, Econometric Society, vol. 71(5), pages 1339-1375, September.
    8. Susan Athey & Philip A. Haile, 2002. "Identification of Standard Auction Models," Econometrica, Econometric Society, vol. 70(6), pages 2107-2140, November.
    9. Rosa L. Matzkin, 2008. "Identification in Nonparametric Simultaneous Equations Models," Econometrica, Econometric Society, vol. 76(5), pages 945-978, September.
    10. Bekker, Paul A., 1989. "Identification in restricted factor models and the evaluation of rank conditions," Journal of Econometrics, Elsevier, vol. 41(1), pages 5-16, May.
    11. Whitney K. Newey & James L. Powell & Francis Vella, 1999. "Nonparametric Estimation of Triangular Simultaneous Equations Models," Econometrica, Econometric Society, vol. 67(3), pages 565-604, May.
    12. Andrew C. Harvey, 1990. "The Econometric Analysis of Time Series, 2nd Edition," MIT Press Books, The MIT Press, edition 2, volume 1, number 026208189x, December.
    13. Hausman, Jerry A., 1983. "Specification and estimation of simultaneous equation models," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 1, chapter 7, pages 391-448, Elsevier.
    14. Joshua D. Angrist & Kathryn Graddy & Guido W. Imbens, 2000. "The Interpretation of Instrumental Variables Estimators in Simultaneous Equations Models with an Application to the Demand for Fish," Review of Economic Studies, Oxford University Press, vol. 67(3), pages 499-527.
    15. C. Lanier Benkard & Steven Berry, 2006. "On the Nonparametric Identification of Nonlinear Simultaneous Equations Models: Comment on Brown (1983) and Roehrig (1988)," Econometrica, Econometric Society, vol. 74(5), pages 1429-1440, September.
    16. Johansen, Soren, 1995. "Identifying restrictions of linear equations with applications to simultaneous equations and cointegration," Journal of Econometrics, Elsevier, vol. 69(1), pages 111-132, September.
    17. Kenneth A. Bollen & Shawn Bauldry, 2010. "Model Identification and Computer Algebra," Sociological Methods & Research, , vol. 39(2), pages 127-156, November.
    18. Deistler, Manfred, 1978. "The structural identifiability of linear models with autocorrelated errors in the case of cross-equation restrictions," Journal of Econometrics, Elsevier, vol. 8(1), pages 23-31, August.
    19. H. Peter Boswijk & Jurgen A. Doornik, 2004. "Identifying, estimating and testing restricted cointegrated systems: An overview," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 58(4), pages 440-465, November.
    20. Kelly, Jerry S, 1971. "The Identification of Ratios of Parameters in Unidentified Equations," Econometrica, Econometric Society, vol. 39(6), pages 1049-1051, November.
    21. Elodie Guerre & I. Perrigne & Q.H. Vuong, 2000. "Optimal nonparametric estimation of first-price auctions [[Estimation nonparamétrique optimale des enchères au premier prix]]," Post-Print hal-02697497, HAL.
    22. Roehrig, Charles S, 1988. "Conditions for Identification in Nonparametric and Parametic Models," Econometrica, Econometric Society, vol. 56(2), pages 433-447, March.
    23. Bowden, Roger J, 1973. "The Theory of Parametric Identification," Econometrica, Econometric Society, vol. 41(6), pages 1069-1074, November.
    24. A. Merckens & P. A. Bekker, 1993. "Identification of simultaneous equation models with measurement error: a computerized evaluation," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 47(4), pages 233-244, December.
    25. Bekker, Paul A. & Pollock, D. S. G., 1986. "Identification of linear stochastic models with covariance restrictions," Journal of Econometrics, Elsevier, vol. 31(2), pages 179-208, March.
    26. Kelly, Jerry S, 1975. "Linear Cross-Equation Constraints and the Identification Problem," Econometrica, Econometric Society, vol. 43(1), pages 125-140, January.
    27. Deistler, Manfred, 1976. "The Identifiability of Linear Econometric Models with Autocorrelated Errors," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 17(1), pages 26-46, February.
    28. Bekker, Paul A., 1994. "Counting rules for identification in linear structural models," Computational Statistics & Data Analysis, Elsevier, vol. 18(5), pages 485-498, December.
    29. Andrew Chesher, 2003. "Identification in Nonseparable Models," Econometrica, Econometric Society, vol. 71(5), pages 1405-1441, September.
    30. Hsiao, Cheng, 1976. "Identification and Estimation of Simultaneous Equation Models with Measurement Error," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 17(2), pages 319-339, June.
    31. Deistler, Manfred & Schrader, Jurgen, 1979. "Linear Models with Autocorrelated Errors: Structural Identifiability in the Absence of Minimality Assumptions," Econometrica, Econometric Society, vol. 47(2), pages 495-504, March.
    32. Goldberger, Arthur S, 1972. "Structural Equation Methods in the Social Sciences," Econometrica, Econometric Society, vol. 40(6), pages 979-1001, November.
    33. Halkos, George & Tsilika, Kyriaki, 2012. "Stability analysis in economic dynamics: A computational approach," MPRA Paper 41371, University Library of Munich, Germany.
    34. Whitney K. Newey & James L. Powell, 2003. "Instrumental Variable Estimation of Nonparametric Models," Econometrica, Econometric Society, vol. 71(5), pages 1565-1578, September.
    35. Geraci, Vincent J., 1976. "Identification of simultaneous equation models with measurement error," Journal of Econometrics, Elsevier, vol. 4(3), pages 263-283, August.
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    Cited by:

    1. Halkos, George & Tsilika, Kyriaki, 2014. "Perspectives on integrating a computer algebra system into advanced calculus curricula," MPRA Paper 63898, University Library of Munich, Germany.
    2. Halkos, George & Tsilika, Kyriaki, 2012. "Constructing a Generator of Matrices with Pattern," MPRA Paper 43614, University Library of Munich, Germany.
    3. Halkos, George & Tsilika, Kyriaki, 2016. "Measures of correlation and computer algebra," MPRA Paper 70200, University Library of Munich, Germany.
    4. George E. Halkos & Kyriaki D. Tsilika, 2018. "Programming Correlation Criteria with free CAS Software," Computational Economics, Springer;Society for Computational Economics, vol. 52(1), pages 299-311, June.

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    More about this item

    Keywords

    Simultaneous equations; Order and rank conditions; Computer algebra system Xcas; C10; C30; C51; C63;
    All these keywords.

    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General

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