3 main topics
1) test for misspecification
2) dealing with outliers
3) bootstrap method for calc SE
Testing for misspecification
- omitted functions of explanatory variables
- log (Wage) = B0+B1Educ+B2exper+u
omitting exper2 result in biased estimator because exper ^2 can be correlated with education - if omitted, it will not properly describe / maximize the relationship of X to Y
Test for misspecification
1) Ramsey REST Test
2) David Mackinnon Test
Ramsey REST Test
- reg specification error test
- to see if non-linear functions of Xi are significant
- determine how many function of fitted values to include in expanded reg (^2/^3)
hypothesis
H0 = S1 = S2 = 0 (no misspecification)
H1 = S1 = S2 =/= 0
(misspecification), there’s omitted relationship
positives of test
preserves degrees of freedom
negatives of test
does not indicate specific source of misspecification
David Mackinnon Test
(nonnested alternative)
- decide whether an IND Var should be in level or log form
test 1
only tests y hat
test 2
tests log and y hat
Outliers
- observation that when removed from regression, results substantial change in OLS estimator
bootstrap method for estimating SE
- about what happens when statistical inference is unavailable or unreliable
what causes hyp testing to be invalid
- errors are not normally distributed
Monte Carlo Approach
replicate DGP thus, derive parameters of the sampling distribution
MCA steps
1) Run OLS on orig data, treat est. as true parameters value
2) treat the values of explanatory variables as “Fixed in repeated samples”
3) generate value on DEP VAR based on error from random number generator
4) estimate new parameters
5) repeat 1000+ times
6) calculate stand dev of parameters
MCA drawback
- generating new errors for “repeated samples” requires specifying the distribution from which those errors came
Contradicts: we don’t know the distribution is the problem in the 1st place
Bootstrap Approach
- special case of Monte Carlo where errors is not pre-determined
- instead of random no. generator, use random sampling of existing residuals form orig sample
