ECON 6306 Lecture Notes - Lecture 9: Heteroscedasticity, Statistical Hypothesis Testing, Nonparametric Statistics
11 May 2018
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Violations of OLS assumption
The assumptions of OLS are:
• No correlation between residuals and predicted y variable.
• No correlation between residuals of different observations.
• No correlation between residuals and x variables.
These assumptions are often violated but we can solve them while staying within the OLS domain. The
benefits of OLS are:
• Simplicity of interpretation
• Forced independence between residuals and x variables; and between residuals and predicted y
variable
• Residuals are expected to sum to zero and form a normal distribution which means easier
hypothesis testing through t tests.
• The slope coefficients we get are best linear unbiased estimators (BLUE). Violations result in us
not getting BLUE estimators but we can solve this problem with OLS extensions
• Slope coefficients are unbiased, consistent and efficient
Problems with violations
As noted above, violations result in our estimates being not BLUE anymore. A summary of the effects on
beta coefficients is given below
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Document Summary
The assumptions of ols are: no correlation between residuals and predicted y variable, no correlation between residuals of different observations, no correlation between residuals and x variables. These assumptions are often violated but we can solve them while staying within the ols domain. Violations result in us not getting blue estimators but we can solve this problem with ols extensions: slope coefficients are unbiased, consistent and efficient. As noted above, violations result in our estimates being not blue anymore. A summary of the effects on beta coefficients is given below. Heteroscedasticity means that the residuals are correlated with the predicted y variable. The residual plot for a heteroskedastic model shows unequal variance. More details on fixing heteroscedasticity are given in later lectures. The problem associated with heteroscedasticity is that our p values are no longer reliable. Non normality t and f-test become unreliable for small sample sizes.
