Financial Risk Manager Part 1

In the presence of near multicollinearity, the OLS estimator will still be consistent, unbiased, and efficient. This happens because none of the four Gauss-Markov assumptions of the Classical Linear Regression Model (CLRM) have been violated.

Key Points:

1. Near multicollinearity is defined as a situation where there is a high, but not perfect, correlation between two or more explanatory variables.
2. Gauss-Markov assumptions include:
   • Linearity
   • Non-collinearity (no perfect multicollinearity)
   • Exogeneity (zero conditional mean)
   • Homoscedasticity (constant variance)
   • No autocorrelation
3. Near multicollinearity does not violate the non-collinearity assumption, which only requires that there is no perfect linear relationship between regressors.
4. Practical implications: While the OLS estimator remains BLUE (Best Linear Unbiased Estimator) under near multicollinearity, the estimates may have:
   • High standard errors
   • Unstable coefficient estimates
   • Difficulty in interpreting individual coefficients
   • But the estimator properties (consistency, unbiasedness, efficiency) are preserved.

Note: There is no definitive threshold for what constitutes "high" correlation in near multicollinearity, but it typically refers to correlation coefficients above 0.7-0.8.