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A Monte Carlo Study of the Residuals of System Estimators in the Presence of Multicollinearity

Yıl 2024, Sayı: 41, 13 - 21, 26.12.2024
https://doi.org/10.26650/ekoist.2024.41.1251589

Öz

Residual analysis is often used to evaluate the precision of the parameter estimates of econometric models. Analysis of residuals from regression is an important way of assessing the performance of a regression model in achieving the goal of accounting for the independent variable under the underlying assumption. With the Monte Carlo Simulation (MCS) of a data set of sample size 40 over varied replications R = 20, 50, 100 and 150, we used residual analysis to study the relative performance of six estimators of a simultaneous equation model under varied multicollinearity conditions. We found that the two-stage least squares (2SLS), Limited Information Maximum Likelihood (LIML), and Three-Stage Least Squares (3SLS) estimators generated virtually similar estimates. This is in agreement with the theory. In addition, the results revealed that notwithstanding the level of multicollinearity, Ordinary Least Squares (OLS), followed by Indirect Least Squares (ILS), produced the lowest Sum of Squared Residuals (SSR) of parameter estimates, an indication of the robustness of OLS in the presence of multicollinearity. This result also showed that the single equation estimators (OLS and ILS) performed better than the system estimators under the condition of multicollinearity to which we subjected our model. Furthermore, the Sum of Squared Residuals (SSR) generated for cases of low multicollinearity are lower than those generated for cases of high multicollinearity.

Destekleyen Kurum

None

Kaynakça

  • Albert J. and Chib S. (1995), “Bayesian residual analysis for binary response regression models”, Biometrika, Vol. 82, Issue 4, No. 1, pp. 747-769. google scholar
  • Ardalani-Farsa M. and Zolfaghari S. (2010), “Chaotic time series prediction with residual analysis method using hybrid Elman-NARX neural networks”, Neurocomputing, Vol. 73, Issues 13-15, pp. 2540-2553. google scholar
  • Baddeley, A., Turner, R., Moller, J. and Hazelton, M. (2005), “Residual Analysis for Spatial Point Processes” Journal of the Royal Statistical Society. Series B (Statistical Methodology) Volume 67, No. 5, pages 617-666. google scholar
  • Chaloner, K. and Brant, R. (1988), “A Bayesian approach to outlier detection and residual analysis”, Biometrika, Volume 75, Issue 4, 1, pages 651-659. google scholar
  • Chaloner K. (1991), “Bayesian residual analysis in the presence of censoring”, Biometrika, Vol. 78, Issue 3, No. 1, pp. 637-644. google scholar
  • Chesher A and Irish M (1987), “Residual analysis in the grouped and censored normal linear model”, Journal of Econometrics, Vol. 34, Issues 1-2, pages 33-61. google scholar
  • Clements, R. A., Schoenberg, F. P. and Schorlemmer, D. (2011), “Residual Analysis Methods for Space-Time Point Processes with Applications to Earthquake Forecast Models in California”. The Annals of Applied Statistics Vol. 5, No. 4, pages. 2549-2571. google scholar
  • Farias R. B. A. and Branco M. D. (2012), “Latent residual analysis in binary regression with skewed link”, (Contributions to the 10th Bayesian Statistics Brazilian Meeting), Brazilian Journal of Probability and Statistics, Vol. 26, No. 4, pp. 344 357. google scholar
  • Johnston, J. (1991), Econometrics Methods, McGraw-Hill Book Company. google scholar
  • Schoenberg F. P. (2003), “Multidimensional Residual Analysis of Point Process Models for Earthquake Occurrences”, Journal of the American Statistical Association Vol. 98, No. 464, pages 789-795. google scholar
  • Jalilian, A. H. and Vahidi-Asl, M. Q. (2011), “Residual Analysis for Inhomogeneous Neyman-Scott Processes”, Scandinavian Journal of Statistics. Volume 38, No. 4, pages 617-630. google scholar
  • Nagar, A.L. (1960), “A Monte Carlo Study of Alternative Simultaneous Equation Estimators”, Econometrica, Vol. 28, No. 3, pages 573-590. google scholar
  • Oduntan, Emmanuel A. and Iyaniwura, J. O. (2021) "A Monte Carlo Simulation Framework on the Relative Performance of System Estimators in the Presence of Multicollinearity" Cogent Social Sciences, Vol. 7, Issue 1. google scholar
  • Ogata Y. (1988), “Statistical Models for Earthquake Occurrences and Residual Analysis for Point Processes”, Journal of the American Statistical Association, Vol. 83, Issue 401. google scholar
  • Pagan, A.R. and Hall, A.D. (1983), “Diagnostic tests as residual analysis”, Econometric Reviews, Volume 2, Issue 2. google scholar
  • Zhuang J. (2006), “Second-Order Residual Analysis of Spatiotemporal Point Processes and Applications in Model Evaluation”, Journal of the Royal Statistical Society, (Statistical Methodology), Series B, 68, No. 4. google scholar
Yıl 2024, Sayı: 41, 13 - 21, 26.12.2024
https://doi.org/10.26650/ekoist.2024.41.1251589

Öz

Kaynakça

  • Albert J. and Chib S. (1995), “Bayesian residual analysis for binary response regression models”, Biometrika, Vol. 82, Issue 4, No. 1, pp. 747-769. google scholar
  • Ardalani-Farsa M. and Zolfaghari S. (2010), “Chaotic time series prediction with residual analysis method using hybrid Elman-NARX neural networks”, Neurocomputing, Vol. 73, Issues 13-15, pp. 2540-2553. google scholar
  • Baddeley, A., Turner, R., Moller, J. and Hazelton, M. (2005), “Residual Analysis for Spatial Point Processes” Journal of the Royal Statistical Society. Series B (Statistical Methodology) Volume 67, No. 5, pages 617-666. google scholar
  • Chaloner, K. and Brant, R. (1988), “A Bayesian approach to outlier detection and residual analysis”, Biometrika, Volume 75, Issue 4, 1, pages 651-659. google scholar
  • Chaloner K. (1991), “Bayesian residual analysis in the presence of censoring”, Biometrika, Vol. 78, Issue 3, No. 1, pp. 637-644. google scholar
  • Chesher A and Irish M (1987), “Residual analysis in the grouped and censored normal linear model”, Journal of Econometrics, Vol. 34, Issues 1-2, pages 33-61. google scholar
  • Clements, R. A., Schoenberg, F. P. and Schorlemmer, D. (2011), “Residual Analysis Methods for Space-Time Point Processes with Applications to Earthquake Forecast Models in California”. The Annals of Applied Statistics Vol. 5, No. 4, pages. 2549-2571. google scholar
  • Farias R. B. A. and Branco M. D. (2012), “Latent residual analysis in binary regression with skewed link”, (Contributions to the 10th Bayesian Statistics Brazilian Meeting), Brazilian Journal of Probability and Statistics, Vol. 26, No. 4, pp. 344 357. google scholar
  • Johnston, J. (1991), Econometrics Methods, McGraw-Hill Book Company. google scholar
  • Schoenberg F. P. (2003), “Multidimensional Residual Analysis of Point Process Models for Earthquake Occurrences”, Journal of the American Statistical Association Vol. 98, No. 464, pages 789-795. google scholar
  • Jalilian, A. H. and Vahidi-Asl, M. Q. (2011), “Residual Analysis for Inhomogeneous Neyman-Scott Processes”, Scandinavian Journal of Statistics. Volume 38, No. 4, pages 617-630. google scholar
  • Nagar, A.L. (1960), “A Monte Carlo Study of Alternative Simultaneous Equation Estimators”, Econometrica, Vol. 28, No. 3, pages 573-590. google scholar
  • Oduntan, Emmanuel A. and Iyaniwura, J. O. (2021) "A Monte Carlo Simulation Framework on the Relative Performance of System Estimators in the Presence of Multicollinearity" Cogent Social Sciences, Vol. 7, Issue 1. google scholar
  • Ogata Y. (1988), “Statistical Models for Earthquake Occurrences and Residual Analysis for Point Processes”, Journal of the American Statistical Association, Vol. 83, Issue 401. google scholar
  • Pagan, A.R. and Hall, A.D. (1983), “Diagnostic tests as residual analysis”, Econometric Reviews, Volume 2, Issue 2. google scholar
  • Zhuang J. (2006), “Second-Order Residual Analysis of Spatiotemporal Point Processes and Applications in Model Evaluation”, Journal of the Royal Statistical Society, (Statistical Methodology), Series B, 68, No. 4. google scholar
Toplam 16 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Ekonometri (Diğer)
Bölüm ARAŞTIRMA MAKALESI
Yazarlar

Emmanuel Oduntan 0000-0002-6115-480X

Yayımlanma Tarihi 26 Aralık 2024
Gönderilme Tarihi 8 Kasım 2023
Kabul Tarihi 15 Ekim 2024
Yayımlandığı Sayı Yıl 2024 Sayı: 41

Kaynak Göster

APA Oduntan, E. (2024). A Monte Carlo Study of the Residuals of System Estimators in the Presence of Multicollinearity. EKOIST Journal of Econometrics and Statistics(41), 13-21. https://doi.org/10.26650/ekoist.2024.41.1251589