Handling Multicollinearity Problems in Indonesia's Economic Growth Regression Modeling Based on Endogenous Economic Growth Theory
Penanganan Masalah Multikolinieritas pada Pemodelan Pertumbuhan Ekonomi Indonesia Berdasarkan Teori Pertumbuhan Ekonomi Endogenous
DOI:
https://doi.org/10.29244/ijsa.v6i2p214-230Keywords:
endogenous economic growth, lasso, multicollinearityAbstract
One of the multiple linear regression applications in economics is Indonesia’s economic growth model based on the theory of endogenous economic growth. Endogenous economic theory is the development of classical theory which cannot explain how the economy grows in the long run. The regression model based on the theory of endogenous economic growth used many independent variables, which caused multicollinearity problems. In this study, the multiple linear regression model using the least-squares estimation method and some methods to handle the multicollinearity problem was implemented. Variable selection methods (backward, forward, and stepwise), principal component regression (PCR), partial least square (PLS), and regularization methods (Ridge, Lasso, and Elastic Net) were applied to solve the multicollinearity problem. Variable selection method with backward, forward, and stepwise has not been able to overcome the problem of multicollinearity. In contrast, Principal Component Regression, PLS regression, and regularization regression methods overcame the multicollinearity problem. We used "leave one out cross-validation" (LOOCV) to determine the best method for handling multicollinearity problems with the smallest mean square of error (MSE). Based on the MSE value, the best method to overcome the multicollinearity problem in the economic growth model based on endogenous economic growth theory was the Lasso regression method.
Downloads
References
Apriansyah D, Kusuma AW. 2019. Asosiasi Single Nucleotide Polymorphism dan fenotipe pada penyakit diabetes mellitus tipe 2 menggunakan stepwise regression. Departemen Ilmu Komputer. Bogor: IPB University.
Arashi M, Roozbeh M, Hamzah NA, Gasparini M. 2021. Ridge Regression And Its Applications In Genetic Studies. PLoS ONE 16(4): e0245376. https://doi.org/10.1371/journal.pone.0245376.
Artigue H, Smith G. 2019. The principal problem with principal components regression. Cogent Mathematics and Statistics.https://doi.org/10.1080/25742558.2019.1622190
Fanny R, Djuraidah A, Alamudi A. 2018. Pendugaan produktivitas penangkapan bagan perahu dengan regresi gulud, lasso, dan elastic-net. Xplore 2(2):7-14.
Hastie T, Tibshirani R, Friedman J. 2008. The elements of statistical learning second edition. California: Springer Series in Statistics.
Hoerl AE, Kennard RW. 1970. Ridge regression: biased estimation for nonorthogonal problems. Technometrics 12(1).
Kayanan M, Wijekoon P. 2019. Performance of Lasso and Elastic Net Estimators un Misspecified Linear Regression Model. Ceylon Journal of Science 48: 293-299.
Kusuma GW, Wulansari IY. 2019. Analisis Kemiskinan dan Kerentanan Kemiskinan dengan Regresi Gulud, Lasso, dan Elastic-Net di Provinsi Jawa Tengah Tahun 2017. Seminar Nasional Official Statistics 2019.
Korkmazoglu OB, Kemalbay G. 2012. Econometrics application of partial least squares regression: an endogeneous growth model for Turkey. Procedia- Social and Behavioral Sciences 62:906-910.
Liu W, Li Q. 2017. An Efficient Elastic Net With Regression Coefficients Method for Variable Selection of Spectrum Data. PLoS ONE 12(2): e0171122. doi:10.1371/journal.pone.0171122.
Marcus LG, Wattimanela JH, Lesnussa AY. 2012. Analisis regresi komponen utama untuk mengatasi masalah multikolinieritas dalam analisis regresi linier berganda. Jurnal Barekeng 6(1): 31-40.
Montgomery DC, Peck EA, Vining GG. 2012. Introduction to linear regression analysis fifth edition. New Jersey: John Wiley & Sons.
Neog Y, Gaur AK. 2020. Tax Structure and Economic Growth: A Study of Selected Indian States. Journal of Economic Structure 2020 9:38.
Ng KS. 2013. A simple explanation of partial least squares. Australian National University.
Pomfret R. 1997. Growth and transition: why has China’s performance so different?. Journal of Comparative Economics 25: 422-440.
Romer PM. 1994. The origins of endogenous growth. Journal of Economic Perspectives 8(1): 3-22.
Soleh AM, Aunuddin. 2013. Lasso: solusi alternatif seleksi peubah dan penyusutan koefisien model regresi linier. Forum Statistika dan Komputasi: Indonesian Journal of Statistics 18(1): 21-27.
Soleh AM, Wigena AH, Djuraidah A, Saefuddin A. 2015. Statistical downscaling to predict monthly rainfall using linear regression with L1 regularization (Lasso). Applied Mathematical Sciences 9(8): 5361-5369.
Tasel F, Bayarcelik B. 2013. The Effect of Schooling Enrolment Rates on Economic Sustainability. 9th International Strategic Management Conference, Procedia - Social and Behavioral Sciences 99 (2013): 104–111.
Tibshirani R. 1996. Regression shrinkage and selection via the Lasso. J.R Statist. Soc. B 58(1): 267-288.
Wang K, Chen Z. 2016. Stepwise regression and all possible subsets regression in education. Electronic Internasional J of Efucation, Arts and Science. 2(2016):60-81
Zareen S, Qayyum A. 2014. An Analysis of the Impact of Government Size on Economic Growth of Pakistan: An Endogenous Growth. Research Journal Social Science 4(1): 61-80.
Zifarelli A, Giglio M, Menduni G, Sampaolo A, Patimisco P, Passaro VMN, Wu H, Dong L, Spagnolo V. 2020. Partial Least Squares Regression as a Tool to Retrieve Gas Concentrations in Mixtures Detected Using Quartz-Enhanced Photoacoustic Spectroscopy. Analytical Chemistry 2020, 92: 11035-11043.
Zou H, Hastie T. 2005. Regularization and variable selection via the elastic net. J.R. Statist. Soc. B 67(2): 301-320.
