Multicollinearity Regularization Using Lasso and Ridge Regression on Economic Data

Abstract

One of the most important assumptions to consider before the adoption of a multiple regression model is the presence or otherwise of multicollinearity in the predictor variables. A Multicollinearity-free model will yield a reliable result as well as strike balance between the biasness of the estimator and the extent of variation in the predictive power of such model. This study adopts real sector data that are highly correlated, to predict the Gross Domestic Product (GDP) of Nigeria over a period of thirty-five years. The Variance Inflation Factor (VIF) from the Ordinary Least Square (OLS) regression shows that five variables out of nine predictor variables are highly correlated, the condition which renders the regression coefficient of the OLS unreliable. Ridge regression (L2) was adopted using a shrinkage value (λ) of 3.4 to penalize each of the regression coefficients. The Least Absolute Selection and Shrinkage Operation (LASSO) regression (L1) was employed to select the most significant coefficients to be included in the model. The best model from the LASSO regression indicates that industrial activities, construction, food index, population, and inflation positively affect gross domestic product of Nigeria while Electricity rate has a Negative impact on the GDP.