Regression Part-9 Model Specification Flashcards
What is model specification bias?
CLRM assumption that model must be correctly specified
What are the attributes of a good model?
- Parsimony (few variables good)
- Identifiability (estimated parameters have unique values)
- Goodness of Fit (using evaluation criteria)
- Theoretically sound
- Exogenous regressors (X uncorrelated with error)
- Data coherency (residuals must be white noise)
What are types of model specification errors?
- Omission of a relevant variable(s).
- Inclusion of unnecessary variable(s).
- Implementing a wrong functional form.
- Errors of measurement
What is underfitting?
If we omit a variable
What is overfiiting?
If we include irrelevant variable
What is the difference between model specification and model misspecification?
Model specification error - we have a true model in mind
Model misspecification - we donβt know the true model
What leads to errors in measurement?
Using proxies in the implemented model
What are the consequences of Omitted Variable bias?
- If X3 is correlated with X2 then missepcified model coeffs are inconsistent and biased; The alpha2 overestimates the beta2
- Var(alpha2) > var(beta2) (overestimated)
- The intercept may be underestimated
- Standard errors increase; R squared decrease
What are the consequences of Irrelevant Variable inclusion bias?
- the ols estimators are unbiased and consistent; LUE not Best
- Var of new model more than true model;
- var(alpha2)/var(beta2) = 1/(1-r23squared) or the VIF
What is the consequence of the two bias?
Underfitting
Overfitting
Coefficients of the variables -
- Biased and inconsistent
- Unbiased and consistent
Error variance
- Incorrectly estimated
- Correctly estimated
Hypothesis testing proc.
- Might be invalid
- Still valid
Variances of coefficients
-Inefficient
-Inefficient (larger
What is the consequence of incorrect functional form?
incorrect or illogical values of estimated coefficients
What is the reasons of errors in measurement bias ?
nonresponse errors, reporting errors, and computing errors
What is the consequence of errors in measurement bias on Y?
- The OLS estimators are unbiased.
- The variances are unbiased.
- The estimated variances of the estimators are larger than true model
What is the consequence of errors in measurement bias on X?
- The OLS estimators are biased.
- They are also inconsistent; that is, they remain biased even if the sample size increases indefinitely.
What is remedy of error in measurement bias?
- use instrumental or proxy variables.
- the data are measured as accurately as possible; avoid errors of recording, rounding, or omission