lecture 11 Flashcards
what is a restricted model?
one in which some parameters
have been set to particular values rather than being estimated.
We will be concerned with linear restrictions i.e. restrictions which
take the form:
𝑅𝜃=𝑟
R is an g x k matrix, θ is a k x 1 vector and r is a g x 1 vector
(a B1 B2) and you impost B1=b2=1 what would you realise
non linear restrictions cant be written in the borm of B1*b2=1
what are the three classical approaches to testing linear restrictions
likelihood ratio, Wald and Lagrange multiplier approaches.
what is the likelihood ratio
The Likelihood ratio test is based on
the difference between the log-
likelihoods of the restricted and
unrestricted cases
what is the wald test?
The Wald test is based on the
difference between the restricted
and unrestricted parameter estimate
what is the lagrange multiplier
The Lagrange multiplier test is based
on the slope of the log-likelihood
function at the restricted parameter
value
what is an example of a wald testing procedure, AND ONE ADVANTAGE
student t test
Bhat-Bbar/SE(Bhat)
One advantage of the Wald testing procedure is that we only
have to estimate the unrestricted model.
What is an example of the likelihood ratio
𝐹=(𝑅𝑅𝑆𝑆−𝑈𝑅𝑆𝑆)/𝑈𝑅𝑆𝑆 (𝑁−𝑘)/𝑟
F test
The F-test is most easy applied when it is relatively easy to
estimate both the unrestricted and restricted models.
why is the F statistic always positive
Restrictions always increase the residual sum of squares.
Therefore the F statistic is always positive.
give all the reasons why a regression model may be misspecified
An incorrect choice of functional form
- Omitted variable bias
- Inclusion of irrelevant variables
- Measurement error in the regressors
- Correlation of the independent variables with the error
ommitted variable and inclusion of irrelevant variable
removing a relavant variables will make the OLS biased to a variable
adding irrelavant variables will make the OLS inefficient
hwoever there is a trade off between the 2
