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Investigating the two parameter analysis of Lipovetsky for simultaneous systems

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Abstract

Two stage least squares regression analysis is the most practical statistical technique that is used in the analysis of structural equations. This study demonstrates the utility of some biased estimation methods when there is inherent multicollinearity among exogenous variables of a simultaneous system. Two stage ridge estimator is one of the biased estimators encountered in this model. In the light of the two parameter ridge estimator of Lipovetsky and Conklin (Appl Stoch Mod Bus Ind 21:525–540, 2005) in linear regression model, we propose two stage two parameter ridge estimator in the simultaneous equations model. Due to the fact that Lipovetsky and Conklin’s two parameter ridge estimator is superior to the ridge and ordinary least squares estimators, we expect the superiority of our new two stage two parameter ridge estimator to the two stage ridge estimator and the two stage least squares estimator. This superiority is proved theoretically. A data analysis involved with Klein Model I is examined to illustrate the mastery of the two stage two parameter ridge estimator in the sense of mean square error. In addition, an extensive Monte Carlo experiment is conducted. It is recommended that investigators who develop simultaneous equations models may perform the new estimator to eliminate the effect of multicollinearity on parameter estimates.

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References

  • Agunbiade DA (2007) A Monte Carlo approach to the estimation of a just identified simultaneous three-equations model with three multicollinear exogenous variables. Unpublished Ph.D. Thesis, University of Ibadan, Nigeria

  • Agunbiade DA (2011) Effect of multicollinearity and the sensitivity of the estimation methods in simultaneous equation model. J Mod Math Stat 5(1):9–12

    Article  MathSciNet  Google Scholar 

  • Agunbiade D, Iyaniwura JO (2010) Estimation under multicollinearity: a comparative approach using Monte Carlo methods. J Math Stat 6(2):183–192

    Article  Google Scholar 

  • Capps O Jr, Grubbs WD (1991) A Monte Carlo study of collinearity in linear simultaneous equation models. J Stat Comput Simul 39:139–162

    Article  Google Scholar 

  • Farebrother RW (1976) Further results on the mean square error of ridge regression. J R Stat Soc Ser B 38:248–250

    MathSciNet  MATH  Google Scholar 

  • Geweke J (1999) Using simulation methods for bayesian econometric models: inference, development and communication. Econom Rev 18(1):1–73

    Article  MathSciNet  Google Scholar 

  • Güler H, Gültay B, Kaçıranlar S (2017) Comparisons of the alternative biased estimators for the distributed lag models. Commun Stat Simul Comput 46(4):3306–3318

    Article  MathSciNet  Google Scholar 

  • Hendry DF (1976) The structure of simultaneous equation estimators. J Econom 4:51–88

    Article  MathSciNet  Google Scholar 

  • Hoerl AE, Kennard RW (1970) Ridge regression: biased estimation for nonorthogonal problems. Technometrics 12(1):55–67

    Article  Google Scholar 

  • Johnston J, Dinardo JE (1997) Econometric methods. McGraw-Hill, New York

    Google Scholar 

  • Klein LR (1950) Economic fluctuation in the United States, 1921-1941. Wiley, New York

    Google Scholar 

  • Lipovetsky S (2006) Two parameter ridge regression and its convergence to the eventual pairwise model. Math Comput Model 44:304–318

    Article  MathSciNet  Google Scholar 

  • Lipovetsky S (2010) Enhanced ridge regressions. Math Comput Model 51:338–348

    Article  MathSciNet  Google Scholar 

  • Lipovetsky S, Conklin WM (2005) Ridge regression in two parameter solution. Appl Stoch Mod Bus Ind 21:525–540

    Article  MathSciNet  Google Scholar 

  • Özbay N, Kaçıranlar S (2017) The Almon two parameter estimator for the distributed lag models. J Stat Comput Simul 87(4):834–843

    Article  MathSciNet  Google Scholar 

  • Özbay N, Toker S (2018) Multicollinearity in simultaneous equations system: evaluation of estimation performance of two-parameter estimator. Comput Appl Math. https://doi.org/10.1007/s40314-018-0628-0

    Article  MathSciNet  MATH  Google Scholar 

  • Park SB (1982) Some sampling properties of minimum expected loss (MELO) estimates of structural coefficients. J Econom 18:295–311

    Article  Google Scholar 

  • Toker S, Kaçıranlar S (2013) On the performance of two parameter ridge estimator under the mean square error criterion. Appl Math Comput 219:4718–4728

    MathSciNet  MATH  Google Scholar 

  • Toker S, Kaçıranlar S, Güler H (2018) Two-stage Liu estimator in a simultaneous equations model. J Stat Comput Simul 88(11):2066–2088

    Article  MathSciNet  Google Scholar 

  • Trenkler G, Toutenburg H (1990) Mean squared error matrix comparisons between biased estimators-an overview of recent results. Stat Pap 31:165–179

    Article  MathSciNet  Google Scholar 

  • Vinod HD, Ullah H (1981) Recent advances in regression methods. Marcel Dekker, New York Inc

    MATH  Google Scholar 

  • Wagnar HM (1958) A Monte Carlo study of estimates of simultaneous linear structural equations. Econometrica 26:117–133

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgments

This paper is supported by Çukurova University Scientific Research Projects Unit Project Number: FBA-2018-9770.

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  1. Department of Statistics, Faculty of Science and Letters, Çukurova University, Adana, Turkey

    Selma Toker

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  1. Selma Toker
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Correspondence to Selma Toker.

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Toker, S. Investigating the two parameter analysis of Lipovetsky for simultaneous systems. Stat Papers 61, 2059–2089 (2020). https://doi.org/10.1007/s00362-018-1021-1

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  • DOI: https://doi.org/10.1007/s00362-018-1021-1

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