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Monday, January 10, 2011

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Ji

first half of the lecture:

1. Heteroskedasticity VS Homoskedasticity
a. Heteroskedasticity: variance changes
b. Homoskedasticity: variance stay the same across X
2. How might Hete arise?
a. Learning—people do things better when they gain more experience(video game), which makes the variance decline
b. Scale variables.(income sales and wealth),low wage people variance is low, since they do not have much money to spend; wealthy people variance are bigger.
c. Better data collection techniques
d. Outliers—some big outliers bring hetero
i. Bad luck—it is very small probability that we get the tail part of the distri.
ii. From another distri. For example, some external event happen(war, tax change)
e. Model is incorrectly specified. For example, mistakenly omit one variable, that will make the error term has the same pattern of the omitted variable
f. Other reasons—incorrect functional form. Point e and point f are the most common way to get hetero.
3. Bonus: in hetero situation, OLS will pay more attention to outliers than MAD(since OLS is the square of errors and MAD is just absolute value)
4. Suppose we have hetero, what if we do OLS anyway?
a. OLS is still unbiased and consistent.
i. Unbiased means centered on true value for any give sample size.
ii. Consistent: only if sample size is approaching infinity, consistency will converge to unbiased. So unbiased is more strict than consistent
b. Β hat is not efficient, var(B) is biased.
c. Since var(B) is biased, T stat will be wrong.
5. Testing for Hetero
a. Graph u square on suspected
i. It it is horizontal, homo.
ii. If not horizontal, either increase or decline, hetero.

Ji

second half of the lecture:
LM test--Langrange Multiplier test for hetero
we like this test, cuz they are fairly robust, though not perfectly robust.
usually, there are more variables than observations, we can not estimate
we have 4 models to reduce the N+K parameters to less than N obs.
linear
Breasch-pagan-- sigma square
Glejser--sigma
park--ln of sigma
then do the chi-square test to test H0. From the functional form,we could see the alter 1 is linear(the point distri. should be linear around the fitted line); alter 2 should be the square( point distri. should be square around the fitted line, variance grows faster than the linear),alter 3 is exponetial,whether it is expand or convergent depends on the positive or negative of the exponential number
steps to regression

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