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
How to detect Unnecessary variables specification errors?
We can use the πΉ and π‘ tests to assess the statistical significance of variables or we can also use the Partial πΉ test for assessing the significance of a subset of variables (anova of (new model, old model)
How to detect Omitted variables specification errors?
Informal - residual plot - if pattern then omission
Formal - Ramseyβs RESET (Regression Specification Error Test)
What are the steps in Ramseys RESET?
- Obtain predicted values of Y
- Rerun model with predY squared, and cubed
- Find out F value
- If F significant then misspecified model
It is a test of misspecification only says if there is but not where
What is the Mckinnon White Davidson test
This test is used to choose between the linear and log-linear regression models.
To see if one specification is better than the other, we can use the MWD test.
π»0: linear model π is a linear function of πs
π»1: Log-Linear model: ln π is a linear function of πs or a log of the π
What Steps in MWD test?
- Estimate the linear model and obtain the estimated π values
- Estimate the log-linear model and obtain the estimated ln π values
- Obtain π1π = ln ππ β lnππ
- Regress π on the πs and π1π.
Reject π»0 if the coefficient of π1π is statistically significant by the usual π‘-test. - Obtain π2π = exp(lnYi) - Yi
- Regress ln π on the πs or logs of πs and π2π
Reject π»1 if the coefficient of π2 in the preceding equation is statistically significant.
The idea behind the MWD test is that if the linear model is in fact the correct model, the constructed variable π1π should not be significant. The same comment applies to the alternative hypothesis π»1
What is the order of harsher penalties imposed by model selection criterias?
r squared< adj r squared< AIC< SIC