Chapter 13 Model Selection Criteria and Tests.ppt

Chapter 13Model Selection: Criteria and Tests
One CLRM assumption is: The model used in empirical analysis is “correctly specified”
No theoretically relevant variable has been excluded from the model.
No unnecessary or irrelevant variables are included in the model.
The functional form of the model is correct
“Correct specification ”of a model means:
The Attributes of a Good Model  ——Criteria to judge a model:
1. Principle of parsimony
A model should be kept as simple as possible.
2. Identifiability
For a given set of data the estimated parameters must have unique values
3. Goodness of fit.
Model is judged good by the higher adjusted R2(= )
4. Theoretical consistency
In constructing a model we should have some theoretical underpinning
5. Predictive power
Choose the model whose theoretical predictions are borne out by actual experience.
Types of Specification Errors
a Relevant Variable: “Underfitting” or “Underspecifying” a Model
True model: Yt=B1+B2X2t+B3X3t+μt ()
Misspecified model: Yt=A1+A2X2t+μt ()
(1)If X2,X3 are correlated:
◎a1 and a2 are biased, a1 , a2 can have an upward or downward bias
E(a1 )≠B1 E(a1 )= B1 +B3( ()
E(a2 ) ≠B2 E(a2 )= B2 +B3b32
◎ a1 and a2 are inconsistent.
(2)If X2 and X3 are not correlated
a2 is unbiased, consistent, b32 will be zero
a1 biased, unless is zero in the model()
The consequences of omitting variable bias (X3)
(3)The error variance estimated from the misspecified model is a biased estimator of the true error variance σ2
——The conventionally estimated variance of a2 is a biased estimator of the variance of the true estimator b2
∵ E[var(a2 )]=var(b2 )+
∴Var(a2 ) will overestimate the true variance of b2 , that is, it will have a positive bias.
(4)The usual confidence interval and hypothesis-testing procedures are unreliable.
The confidence interval will be wider.
Inclusion of irrelevant variables will certainly increase R2,which might increase the predictiv