If the classical linear regression model (CLRM) doesn't work for your data because one of its assumptions doesn't hold, then you have to address the problem before you can finalize your analysis. Fortunately, one of the primary contributions of econometrics is the development of techniques to address such problems or other complications with the data that make standard model estimation difficult or unreliable.
The following table lists the names of the most common estimation issues, a brief definition of each one, their consequences, typical tools used to detect them, and commonly accepted methods for resolving each problem.
| Problem | Definition | Consequences | Detection | Solution |
|---|---|---|---|---|
| High multicollinearity | Two or more independent variables in a regression model exhibit a close linear relationship. | Large standard errors and insignificant
t-statistics Coefficient estimates sensitive to minor changes in model specification Nonsensical coefficient signs and magnitudes |
Pairwise correlation coefficients Variance inflation factor (VIF) |
1. Collect additional data. 2. Re-specify the model. 3. Drop redundant variables. |
| Heteroskedasticity | The variance of the error term changes in response to a change in the value of the independent variables. | Inefficient coefficient estimates Biased standard errors Unreliable hypothesis tests |
Park test Goldfeld-Quandt test Breusch-Pagan test White test |
1. Weighted least squares (WLS) 2. Robust standard errors |
| Autocorrelation | An identifiable relationship (positive or negative) exists between the values of the error in one period and the values of the error in another period. | Inefficient coefficient estimates Biased standard errors Unreliable hypothesis tests |
Geary or runs test Durbin-Watson test Breusch-Godfrey test |
1. Cochrane-Orcutt transformation 2. Prais-Winsten transformation 3. Newey-West robust standard errors |