Multicolinearity

Problem

Consider \(y_i=β_1+β_2x_{i,2}+β_3x_{i,3}+ε_i\) where \(y_i\) is investment as a proportion of GDP in country \(i\) , \(x_{i,2}\) is the average temperature of the country in degrees Celsius and \(x_{i,3}\) is the average temperature of the country in degrees Fahrenheit. Will it be possible to estimate this model using OLS? If not, why not?

Solution

No. \(x_{i,3}\) is a linear function of \(x_{i,2}\) so there is a perfect linear relationship between them and a correlation of 1. You would have perfect multicollinearity and the OLS estimates do not exist.