An Extensive Study on the Disturbances Generated by Collinearity in a Linear Regression Model with Three Explanatory Variables

In econometric models, linear regressions with three explanatory variables are widely used. As examples can be cited: Cobb-Douglas production function with three inputs (capital, labour and disembodied technical change), Kmenta function used for approximation of CES production function parameters, error-correction models, etc. In case of multiple linear regressions, estimated parameters values and some statistical tests are influenced by collinearity between explanatory variables. In fact, collinearity acts as a noise which distorts the signal (proper parameter values). This influence is emphasized by the coefficients of alignment to collinearity hazard values. The respective coefficients have some similarities with the signal to noise ratio. Consequently, it may be used when the type of collinearity is determined. For these reasons, the main purpose of this paper is to identify all the modeling factors and quantify their impact on the above-mentioned indicator values in the context of linear regression with three explanatory variables.