Financial Risk Manager Part 1
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Jessica Pearson, FRM, builds a model to study the annual salaries of individuals in a certain developed country. The model incorporates just 2 independent variables – age and experience. She is surprised for ending up with a negative value for the coefficient of experience, which seems to be somewhat counterintuitive. Furthermore, the coefficients have low t-statistics but otherwise the model has a high R². Which of the following is the most likely cause of such results?
Explanation:
Explanation
Multicollinearity is the most likely cause of these results for several reasons:
Key Indicators of Multicollinearity:
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Negative coefficient for experience: This is counterintuitive since we would expect experience to have a positive relationship with salary. When two variables are highly correlated (age and experience), the regression model struggles to separate their individual effects, which can lead to unstable and even negative coefficients.
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Low t-statistics: Multicollinearity inflates the standard errors of the coefficients, making them less statistically significant (lower t-statistics) even when the overall model fits well.
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High R²: The model still explains a large portion of the variance in salaries, which is consistent with multicollinearity - the correlated variables together explain the dependent variable well, but individually their contributions are hard to distinguish.
Why Other Options Are Incorrect:
- A. Heteroskedasticity: This affects the variance of error terms but doesn't typically cause negative coefficients or the specific pattern of low t-statistics with high R².
- C. Homoskedasticity: This is actually a desirable property of regression models, not a problem that would cause these symptoms.
- D. Serial correlation: This relates to time series data where errors are correlated over time, which isn't indicated in this cross-sectional salary study.
The Root Cause:
Age and experience are naturally highly correlated - as people get older, they typically gain more work experience. This high correlation creates multicollinearity, making it difficult for the regression model to determine the unique contribution of each variable to salary determination.