Model Misspecification Flashcards
Model Misspecification - Omitted variable
If we omit a significant variable from our model, the error term will capture the missing.
Model Misspecification - Inappropriate form of variable
Failing to account for non-linearity
Causes: Conditional heteroscedasticity
To fix it we can use natural log to transform the variable to be linear.
Model Misspecification - Inappropriate Scaling
Causes Conditional heteroscedasticity and multicollinearity
Model Misspecification - Inappropriate Pooling of Data
Causes Conditional heteroscedasticity and Serial correlation
- Conditional heteroscedasticity
- Serial Correlation
What is Unconditional heteroscedasticity
Var(error) not correlated with independent X variable.
No issue with interference.
What is Conditional heteroscedasticity
Var(error) are correlated with independent X variable
F-test is unreliable since MSE is a biased estimator of the true population variance.
variance at one time step has a positive relationship with variance at one or more previous time steps. This implies that periods of high variability will tend to follow periods of high variability and periods of low variability will tend to follow periods of low variability.
What does the Breusch Pagan BP tets do?
Tests for heteroskedasticity
The formula for BP test statistics
n * R-Square
BP test
Test statistics > Critical value
Reject the null.
No heteroskedasticity
homoskedasticity is present - Constant vartiance
- H0: No heteroskedasticity - homoskedasticity is present
- Ha: Heteroskedasticit
BP test
Test statistics < Critical value
Reject the null
There is Heteroskedasticity
- H0: No heteroskedasticity
- Ha: Heteroskedasticity
What is serial correlation?
Errors correlated across the observation
Positive Serial Correlation
Positive residuals is most likely followed by positive residuals
Negative residuals is most likely followed by negative residuals
Negative Serial Correlation
Negative residual is most likely followed by positive residual
Positive residual is most likely followed by negative residual
Multicollinearity
2 or more independent variables are highly correlated or there is an approximate linear relationship among the IVs.
Inflates the standard error
Coefficients will be consistent but imprecise and unreliable
Inflated SE and insignificant T-Statistics, but possibly significant F-Statistics
How to detect multicollinearity?
Variance inflation factor
1 / (1- R Square)
We want VIF as low as possible
> 5 Concerning
10 Multicollinearity
How to fix multicollinearity?
- Increase sample size
- Excluding one or more of the regression variables.
- Use a different proxy for one of the variables
What does the BP test for ?
Conditional Heteroskedasticity
What is the most common problem in trend models?
Serial correlation
Trend models often have the limitation that their errors are serially correlated. This is due to the fact that predictions in the trend models are based soley on what time period it is, and thus they fail to account for significant trends in the data such as recession.
Chi-Squar degree of freedom > BP
No Evidence of Conditional Heterskedatisicty
BP test > Chi-Squar Degree of Freedom
Evidence of Conditional Heterskedatisicty
Spurious Correlation
Two or more events or variables are associated but not causally related, due to either coincidence or the presence of a certain third, unseen factor.
Caused by innapropriately pooled data.
Characteristics of Multicolinearity
Even though we have a independent variable that is not statistically significant.
High R-Square
Significant F - Statistics
